:: A List of Prime Numbers - Part I
:: by Library Committee
::
:: Received August 4, 2022
:: Copyright (c) 2022-2026 Association of Mizar Users
:: (Stowarzyszenie Uzytkownikow Mizara, Bialystok, Poland).
:: This code can be distributed under the GNU General Public Licence
:: version 3.0 or later, or the Creative Commons Attribution-ShareAlike
:: License version 3.0 or later, subject to the binding interpretation
:: detailed in file COPYING.interpretation.
:: See COPYING.GPL and COPYING.CC-BY-SA for the full text of these
:: licenses, or see http://www.gnu.org/licenses/gpl.html and
:: http://creativecommons.org/licenses/by-sa/3.0/.
environ
vocabularies NUMBERS, RELAT_1, XXREAL_0, ARYTM_3, INT_2, SUBSET_1, NAT_1,
CARD_1;
notations SUBSET_1, NUMBERS, ORDINAL1, INT_2, NAT_1, NAT_D, XXREAL_0;
constructors NAT_D, NAT_1;
registrations NAT_1, ORDINAL1, XXREAL_0, INT_1;
requirements REAL, NUMERALS, SUBSET, ARITHM;
definitions INT_2;
theorems INT_2, NAT_4, XPRIMET1;
begin
::$CT
theorem
2 is prime
proof
thus 2 > 1;
let n be Nat;
assume
A1: n divides 2;
then n <= 2 by INT_2:27;
then n = 0 or ... or n = 2;
hence thesis by A1,INT_2:3;
end;
theorem
3 is prime
proof
now
3 = 2*1 + 1; hence not 2 divides 3 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3 & n is prime
holds not n divides 3 by XPRIMET1:2;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5 is prime
proof
now
5 = 2*2 + 1; hence not 2 divides 5 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5 & n is prime
holds not n divides 5 by XPRIMET1:2;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7 is prime
proof
now
7 = 2*3 + 1; hence not 2 divides 7 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7 & n is prime
holds not n divides 7 by XPRIMET1:2;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
11 is prime
proof
now
11 = 2*5 + 1; hence not 2 divides 11 by NAT_4:9;
11 = 3*3 + 2; hence not 3 divides 11 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 11 & n is prime
holds not n divides 11 by XPRIMET1:4;
hence thesis by NAT_4:14;
end;
::$CT
theorem
13 is prime
proof
now
13 = 2*6 + 1; hence not 2 divides 13 by NAT_4:9;
13 = 3*4 + 1; hence not 3 divides 13 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 13 & n is prime
holds not n divides 13 by XPRIMET1:4;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
17 is prime
proof
now
17 = 2*8 + 1; hence not 2 divides 17 by NAT_4:9;
17 = 3*5 + 2; hence not 3 divides 17 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 17 & n is prime
holds not n divides 17 by XPRIMET1:4;
hence thesis by NAT_4:14;
end;
::$CT
theorem
19 is prime
proof
now
19 = 2*9 + 1; hence not 2 divides 19 by NAT_4:9;
19 = 3*6 + 1; hence not 3 divides 19 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 19 & n is prime
holds not n divides 19 by XPRIMET1:4;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
23 is prime
proof
now
23 = 2*11 + 1; hence not 2 divides 23 by NAT_4:9;
23 = 3*7 + 2; hence not 3 divides 23 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 23 & n is prime
holds not n divides 23 by XPRIMET1:4;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
29 is prime
proof
now
29 = 2*14 + 1; hence not 2 divides 29 by NAT_4:9;
29 = 3*9 + 2; hence not 3 divides 29 by NAT_4:9;
29 = 5*5 + 4; hence not 5 divides 29 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 29 & n is prime
holds not n divides 29 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT
theorem
31 is prime
proof
now
31 = 2*15 + 1; hence not 2 divides 31 by NAT_4:9;
31 = 3*10 + 1; hence not 3 divides 31 by NAT_4:9;
31 = 5*6 + 1; hence not 5 divides 31 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 31 & n is prime
holds not n divides 31 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
37 is prime
proof
now
37 = 2*18 + 1; hence not 2 divides 37 by NAT_4:9;
37 = 3*12 + 1; hence not 3 divides 37 by NAT_4:9;
37 = 5*7 + 2; hence not 5 divides 37 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 37 & n is prime
holds not n divides 37 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
41 is prime
proof
now
41 = 2*20 + 1; hence not 2 divides 41 by NAT_4:9;
41 = 3*13 + 2; hence not 3 divides 41 by NAT_4:9;
41 = 5*8 + 1; hence not 5 divides 41 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 41 & n is prime
holds not n divides 41 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT
theorem
43 is prime
proof
now
43 = 2*21 + 1; hence not 2 divides 43 by NAT_4:9;
43 = 3*14 + 1; hence not 3 divides 43 by NAT_4:9;
43 = 5*8 + 3; hence not 5 divides 43 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 43 & n is prime
holds not n divides 43 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
47 is prime
proof
now
47 = 2*23 + 1; hence not 2 divides 47 by NAT_4:9;
47 = 3*15 + 2; hence not 3 divides 47 by NAT_4:9;
47 = 5*9 + 2; hence not 5 divides 47 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 47 & n is prime
holds not n divides 47 by XPRIMET1:6;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
53 is prime
proof
now
53 = 2*26 + 1; hence not 2 divides 53 by NAT_4:9;
53 = 3*17 + 2; hence not 3 divides 53 by NAT_4:9;
53 = 5*10 + 3; hence not 5 divides 53 by NAT_4:9;
53 = 7*7 + 4; hence not 7 divides 53 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 53 & n is prime
holds not n divides 53 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
59 is prime
proof
now
59 = 2*29 + 1; hence not 2 divides 59 by NAT_4:9;
59 = 3*19 + 2; hence not 3 divides 59 by NAT_4:9;
59 = 5*11 + 4; hence not 5 divides 59 by NAT_4:9;
59 = 7*8 + 3; hence not 7 divides 59 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 59 & n is prime
holds not n divides 59 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT
theorem
61 is prime
proof
now
61 = 2*30 + 1; hence not 2 divides 61 by NAT_4:9;
61 = 3*20 + 1; hence not 3 divides 61 by NAT_4:9;
61 = 5*12 + 1; hence not 5 divides 61 by NAT_4:9;
61 = 7*8 + 5; hence not 7 divides 61 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 61 & n is prime
holds not n divides 61 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
67 is prime
proof
now
67 = 2*33 + 1; hence not 2 divides 67 by NAT_4:9;
67 = 3*22 + 1; hence not 3 divides 67 by NAT_4:9;
67 = 5*13 + 2; hence not 5 divides 67 by NAT_4:9;
67 = 7*9 + 4; hence not 7 divides 67 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 67 & n is prime
holds not n divides 67 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
71 is prime
proof
now
71 = 2*35 + 1; hence not 2 divides 71 by NAT_4:9;
71 = 3*23 + 2; hence not 3 divides 71 by NAT_4:9;
71 = 5*14 + 1; hence not 5 divides 71 by NAT_4:9;
71 = 7*10 + 1; hence not 7 divides 71 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 71 & n is prime
holds not n divides 71 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT
theorem
73 is prime
proof
now
73 = 2*36 + 1; hence not 2 divides 73 by NAT_4:9;
73 = 3*24 + 1; hence not 3 divides 73 by NAT_4:9;
73 = 5*14 + 3; hence not 5 divides 73 by NAT_4:9;
73 = 7*10 + 3; hence not 7 divides 73 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 73 & n is prime
holds not n divides 73 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
79 is prime
proof
now
79 = 2*39 + 1; hence not 2 divides 79 by NAT_4:9;
79 = 3*26 + 1; hence not 3 divides 79 by NAT_4:9;
79 = 5*15 + 4; hence not 5 divides 79 by NAT_4:9;
79 = 7*11 + 2; hence not 7 divides 79 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 79 & n is prime
holds not n divides 79 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
83 is prime
proof
now
83 = 2*41 + 1; hence not 2 divides 83 by NAT_4:9;
83 = 3*27 + 2; hence not 3 divides 83 by NAT_4:9;
83 = 5*16 + 3; hence not 5 divides 83 by NAT_4:9;
83 = 7*11 + 6; hence not 7 divides 83 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 83 & n is prime
holds not n divides 83 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
89 is prime
proof
now
89 = 2*44 + 1; hence not 2 divides 89 by NAT_4:9;
89 = 3*29 + 2; hence not 3 divides 89 by NAT_4:9;
89 = 5*17 + 4; hence not 5 divides 89 by NAT_4:9;
89 = 7*12 + 5; hence not 7 divides 89 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 89 & n is prime
holds not n divides 89 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
97 is prime
proof
now
97 = 2*48 + 1; hence not 2 divides 97 by NAT_4:9;
97 = 3*32 + 1; hence not 3 divides 97 by NAT_4:9;
97 = 5*19 + 2; hence not 5 divides 97 by NAT_4:9;
97 = 7*13 + 6; hence not 7 divides 97 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 97 & n is prime
holds not n divides 97 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
101 is prime
proof
now
101 = 2*50 + 1; hence not 2 divides 101 by NAT_4:9;
101 = 3*33 + 2; hence not 3 divides 101 by NAT_4:9;
101 = 5*20 + 1; hence not 5 divides 101 by NAT_4:9;
101 = 7*14 + 3; hence not 7 divides 101 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 101 & n is prime
holds not n divides 101 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT
theorem
103 is prime
proof
now
103 = 2*51 + 1; hence not 2 divides 103 by NAT_4:9;
103 = 3*34 + 1; hence not 3 divides 103 by NAT_4:9;
103 = 5*20 + 3; hence not 5 divides 103 by NAT_4:9;
103 = 7*14 + 5; hence not 7 divides 103 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 103 & n is prime
holds not n divides 103 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
107 is prime
proof
now
107 = 2*53 + 1; hence not 2 divides 107 by NAT_4:9;
107 = 3*35 + 2; hence not 3 divides 107 by NAT_4:9;
107 = 5*21 + 2; hence not 5 divides 107 by NAT_4:9;
107 = 7*15 + 2; hence not 7 divides 107 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 107 & n is prime
holds not n divides 107 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT
theorem
109 is prime
proof
now
109 = 2*54 + 1; hence not 2 divides 109 by NAT_4:9;
109 = 3*36 + 1; hence not 3 divides 109 by NAT_4:9;
109 = 5*21 + 4; hence not 5 divides 109 by NAT_4:9;
109 = 7*15 + 4; hence not 7 divides 109 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 109 & n is prime
holds not n divides 109 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
113 is prime
proof
now
113 = 2*56 + 1; hence not 2 divides 113 by NAT_4:9;
113 = 3*37 + 2; hence not 3 divides 113 by NAT_4:9;
113 = 5*22 + 3; hence not 5 divides 113 by NAT_4:9;
113 = 7*16 + 1; hence not 7 divides 113 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 113 & n is prime
holds not n divides 113 by XPRIMET1:8;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
127 is prime
proof
now
127 = 2*63 + 1; hence not 2 divides 127 by NAT_4:9;
127 = 3*42 + 1; hence not 3 divides 127 by NAT_4:9;
127 = 5*25 + 2; hence not 5 divides 127 by NAT_4:9;
127 = 7*18 + 1; hence not 7 divides 127 by NAT_4:9;
127 = 11*11 + 6; hence not 11 divides 127 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 127 & n is prime
holds not n divides 127 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
131 is prime
proof
now
131 = 2*65 + 1; hence not 2 divides 131 by NAT_4:9;
131 = 3*43 + 2; hence not 3 divides 131 by NAT_4:9;
131 = 5*26 + 1; hence not 5 divides 131 by NAT_4:9;
131 = 7*18 + 5; hence not 7 divides 131 by NAT_4:9;
131 = 11*11 + 10; hence not 11 divides 131 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 131 & n is prime
holds not n divides 131 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
137 is prime
proof
now
137 = 2*68 + 1; hence not 2 divides 137 by NAT_4:9;
137 = 3*45 + 2; hence not 3 divides 137 by NAT_4:9;
137 = 5*27 + 2; hence not 5 divides 137 by NAT_4:9;
137 = 7*19 + 4; hence not 7 divides 137 by NAT_4:9;
137 = 11*12 + 5; hence not 11 divides 137 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 137 & n is prime
holds not n divides 137 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT
theorem
139 is prime
proof
now
139 = 2*69 + 1; hence not 2 divides 139 by NAT_4:9;
139 = 3*46 + 1; hence not 3 divides 139 by NAT_4:9;
139 = 5*27 + 4; hence not 5 divides 139 by NAT_4:9;
139 = 7*19 + 6; hence not 7 divides 139 by NAT_4:9;
139 = 11*12 + 7; hence not 11 divides 139 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 139 & n is prime
holds not n divides 139 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
149 is prime
proof
now
149 = 2*74 + 1; hence not 2 divides 149 by NAT_4:9;
149 = 3*49 + 2; hence not 3 divides 149 by NAT_4:9;
149 = 5*29 + 4; hence not 5 divides 149 by NAT_4:9;
149 = 7*21 + 2; hence not 7 divides 149 by NAT_4:9;
149 = 11*13 + 6; hence not 11 divides 149 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 149 & n is prime
holds not n divides 149 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT
theorem
151 is prime
proof
now
151 = 2*75 + 1; hence not 2 divides 151 by NAT_4:9;
151 = 3*50 + 1; hence not 3 divides 151 by NAT_4:9;
151 = 5*30 + 1; hence not 5 divides 151 by NAT_4:9;
151 = 7*21 + 4; hence not 7 divides 151 by NAT_4:9;
151 = 11*13 + 8; hence not 11 divides 151 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 151 & n is prime
holds not n divides 151 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
157 is prime
proof
now
157 = 2*78 + 1; hence not 2 divides 157 by NAT_4:9;
157 = 3*52 + 1; hence not 3 divides 157 by NAT_4:9;
157 = 5*31 + 2; hence not 5 divides 157 by NAT_4:9;
157 = 7*22 + 3; hence not 7 divides 157 by NAT_4:9;
157 = 11*14 + 3; hence not 11 divides 157 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 157 & n is prime
holds not n divides 157 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
163 is prime
proof
now
163 = 2*81 + 1; hence not 2 divides 163 by NAT_4:9;
163 = 3*54 + 1; hence not 3 divides 163 by NAT_4:9;
163 = 5*32 + 3; hence not 5 divides 163 by NAT_4:9;
163 = 7*23 + 2; hence not 7 divides 163 by NAT_4:9;
163 = 11*14 + 9; hence not 11 divides 163 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 163 & n is prime
holds not n divides 163 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
167 is prime
proof
now
167 = 2*83 + 1; hence not 2 divides 167 by NAT_4:9;
167 = 3*55 + 2; hence not 3 divides 167 by NAT_4:9;
167 = 5*33 + 2; hence not 5 divides 167 by NAT_4:9;
167 = 7*23 + 6; hence not 7 divides 167 by NAT_4:9;
167 = 11*15 + 2; hence not 11 divides 167 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 167 & n is prime
holds not n divides 167 by XPRIMET1:10;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
173 is prime
proof
now
173 = 2*86 + 1; hence not 2 divides 173 by NAT_4:9;
173 = 3*57 + 2; hence not 3 divides 173 by NAT_4:9;
173 = 5*34 + 3; hence not 5 divides 173 by NAT_4:9;
173 = 7*24 + 5; hence not 7 divides 173 by NAT_4:9;
173 = 11*15 + 8; hence not 11 divides 173 by NAT_4:9;
173 = 13*13 + 4; hence not 13 divides 173 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 173 & n is prime
holds not n divides 173 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
179 is prime
proof
now
179 = 2*89 + 1; hence not 2 divides 179 by NAT_4:9;
179 = 3*59 + 2; hence not 3 divides 179 by NAT_4:9;
179 = 5*35 + 4; hence not 5 divides 179 by NAT_4:9;
179 = 7*25 + 4; hence not 7 divides 179 by NAT_4:9;
179 = 11*16 + 3; hence not 11 divides 179 by NAT_4:9;
179 = 13*13 + 10; hence not 13 divides 179 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 179 & n is prime
holds not n divides 179 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
181 is prime
proof
now
181 = 2*90 + 1; hence not 2 divides 181 by NAT_4:9;
181 = 3*60 + 1; hence not 3 divides 181 by NAT_4:9;
181 = 5*36 + 1; hence not 5 divides 181 by NAT_4:9;
181 = 7*25 + 6; hence not 7 divides 181 by NAT_4:9;
181 = 11*16 + 5; hence not 11 divides 181 by NAT_4:9;
181 = 13*13 + 12; hence not 13 divides 181 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 181 & n is prime
holds not n divides 181 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
191 is prime
proof
now
191 = 2*95 + 1; hence not 2 divides 191 by NAT_4:9;
191 = 3*63 + 2; hence not 3 divides 191 by NAT_4:9;
191 = 5*38 + 1; hence not 5 divides 191 by NAT_4:9;
191 = 7*27 + 2; hence not 7 divides 191 by NAT_4:9;
191 = 11*17 + 4; hence not 11 divides 191 by NAT_4:9;
191 = 13*14 + 9; hence not 13 divides 191 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 191 & n is prime
holds not n divides 191 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
193 is prime
proof
now
193 = 2*96 + 1; hence not 2 divides 193 by NAT_4:9;
193 = 3*64 + 1; hence not 3 divides 193 by NAT_4:9;
193 = 5*38 + 3; hence not 5 divides 193 by NAT_4:9;
193 = 7*27 + 4; hence not 7 divides 193 by NAT_4:9;
193 = 11*17 + 6; hence not 11 divides 193 by NAT_4:9;
193 = 13*14 + 11; hence not 13 divides 193 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 193 & n is prime
holds not n divides 193 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
197 is prime
proof
now
197 = 2*98 + 1; hence not 2 divides 197 by NAT_4:9;
197 = 3*65 + 2; hence not 3 divides 197 by NAT_4:9;
197 = 5*39 + 2; hence not 5 divides 197 by NAT_4:9;
197 = 7*28 + 1; hence not 7 divides 197 by NAT_4:9;
197 = 11*17 + 10; hence not 11 divides 197 by NAT_4:9;
197 = 13*15 + 2; hence not 13 divides 197 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 197 & n is prime
holds not n divides 197 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
199 is prime
proof
now
199 = 2*99 + 1; hence not 2 divides 199 by NAT_4:9;
199 = 3*66 + 1; hence not 3 divides 199 by NAT_4:9;
199 = 5*39 + 4; hence not 5 divides 199 by NAT_4:9;
199 = 7*28 + 3; hence not 7 divides 199 by NAT_4:9;
199 = 11*18 + 1; hence not 11 divides 199 by NAT_4:9;
199 = 13*15 + 4; hence not 13 divides 199 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 199 & n is prime
holds not n divides 199 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
211 is prime
proof
now
211 = 2*105 + 1; hence not 2 divides 211 by NAT_4:9;
211 = 3*70 + 1; hence not 3 divides 211 by NAT_4:9;
211 = 5*42 + 1; hence not 5 divides 211 by NAT_4:9;
211 = 7*30 + 1; hence not 7 divides 211 by NAT_4:9;
211 = 11*19 + 2; hence not 11 divides 211 by NAT_4:9;
211 = 13*16 + 3; hence not 13 divides 211 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 211 & n is prime
holds not n divides 211 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
223 is prime
proof
now
223 = 2*111 + 1; hence not 2 divides 223 by NAT_4:9;
223 = 3*74 + 1; hence not 3 divides 223 by NAT_4:9;
223 = 5*44 + 3; hence not 5 divides 223 by NAT_4:9;
223 = 7*31 + 6; hence not 7 divides 223 by NAT_4:9;
223 = 11*20 + 3; hence not 11 divides 223 by NAT_4:9;
223 = 13*17 + 2; hence not 13 divides 223 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 223 & n is prime
holds not n divides 223 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
227 is prime
proof
now
227 = 2*113 + 1; hence not 2 divides 227 by NAT_4:9;
227 = 3*75 + 2; hence not 3 divides 227 by NAT_4:9;
227 = 5*45 + 2; hence not 5 divides 227 by NAT_4:9;
227 = 7*32 + 3; hence not 7 divides 227 by NAT_4:9;
227 = 11*20 + 7; hence not 11 divides 227 by NAT_4:9;
227 = 13*17 + 6; hence not 13 divides 227 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 227 & n is prime
holds not n divides 227 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
229 is prime
proof
now
229 = 2*114 + 1; hence not 2 divides 229 by NAT_4:9;
229 = 3*76 + 1; hence not 3 divides 229 by NAT_4:9;
229 = 5*45 + 4; hence not 5 divides 229 by NAT_4:9;
229 = 7*32 + 5; hence not 7 divides 229 by NAT_4:9;
229 = 11*20 + 9; hence not 11 divides 229 by NAT_4:9;
229 = 13*17 + 8; hence not 13 divides 229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 229 & n is prime
holds not n divides 229 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
233 is prime
proof
now
233 = 2*116 + 1; hence not 2 divides 233 by NAT_4:9;
233 = 3*77 + 2; hence not 3 divides 233 by NAT_4:9;
233 = 5*46 + 3; hence not 5 divides 233 by NAT_4:9;
233 = 7*33 + 2; hence not 7 divides 233 by NAT_4:9;
233 = 11*21 + 2; hence not 11 divides 233 by NAT_4:9;
233 = 13*17 + 12; hence not 13 divides 233 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 233 & n is prime
holds not n divides 233 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
239 is prime
proof
now
239 = 2*119 + 1; hence not 2 divides 239 by NAT_4:9;
239 = 3*79 + 2; hence not 3 divides 239 by NAT_4:9;
239 = 5*47 + 4; hence not 5 divides 239 by NAT_4:9;
239 = 7*34 + 1; hence not 7 divides 239 by NAT_4:9;
239 = 11*21 + 8; hence not 11 divides 239 by NAT_4:9;
239 = 13*18 + 5; hence not 13 divides 239 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 239 & n is prime
holds not n divides 239 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
241 is prime
proof
now
241 = 2*120 + 1; hence not 2 divides 241 by NAT_4:9;
241 = 3*80 + 1; hence not 3 divides 241 by NAT_4:9;
241 = 5*48 + 1; hence not 5 divides 241 by NAT_4:9;
241 = 7*34 + 3; hence not 7 divides 241 by NAT_4:9;
241 = 11*21 + 10; hence not 11 divides 241 by NAT_4:9;
241 = 13*18 + 7; hence not 13 divides 241 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 241 & n is prime
holds not n divides 241 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
251 is prime
proof
now
251 = 2*125 + 1; hence not 2 divides 251 by NAT_4:9;
251 = 3*83 + 2; hence not 3 divides 251 by NAT_4:9;
251 = 5*50 + 1; hence not 5 divides 251 by NAT_4:9;
251 = 7*35 + 6; hence not 7 divides 251 by NAT_4:9;
251 = 11*22 + 9; hence not 11 divides 251 by NAT_4:9;
251 = 13*19 + 4; hence not 13 divides 251 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 251 & n is prime
holds not n divides 251 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
257 is prime
proof
now
257 = 2*128 + 1; hence not 2 divides 257 by NAT_4:9;
257 = 3*85 + 2; hence not 3 divides 257 by NAT_4:9;
257 = 5*51 + 2; hence not 5 divides 257 by NAT_4:9;
257 = 7*36 + 5; hence not 7 divides 257 by NAT_4:9;
257 = 11*23 + 4; hence not 11 divides 257 by NAT_4:9;
257 = 13*19 + 10; hence not 13 divides 257 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 257 & n is prime
holds not n divides 257 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
263 is prime
proof
now
263 = 2*131 + 1; hence not 2 divides 263 by NAT_4:9;
263 = 3*87 + 2; hence not 3 divides 263 by NAT_4:9;
263 = 5*52 + 3; hence not 5 divides 263 by NAT_4:9;
263 = 7*37 + 4; hence not 7 divides 263 by NAT_4:9;
263 = 11*23 + 10; hence not 11 divides 263 by NAT_4:9;
263 = 13*20 + 3; hence not 13 divides 263 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 263 & n is prime
holds not n divides 263 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
269 is prime
proof
now
269 = 2*134 + 1; hence not 2 divides 269 by NAT_4:9;
269 = 3*89 + 2; hence not 3 divides 269 by NAT_4:9;
269 = 5*53 + 4; hence not 5 divides 269 by NAT_4:9;
269 = 7*38 + 3; hence not 7 divides 269 by NAT_4:9;
269 = 11*24 + 5; hence not 11 divides 269 by NAT_4:9;
269 = 13*20 + 9; hence not 13 divides 269 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 269 & n is prime
holds not n divides 269 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
271 is prime
proof
now
271 = 2*135 + 1; hence not 2 divides 271 by NAT_4:9;
271 = 3*90 + 1; hence not 3 divides 271 by NAT_4:9;
271 = 5*54 + 1; hence not 5 divides 271 by NAT_4:9;
271 = 7*38 + 5; hence not 7 divides 271 by NAT_4:9;
271 = 11*24 + 7; hence not 11 divides 271 by NAT_4:9;
271 = 13*20 + 11; hence not 13 divides 271 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 271 & n is prime
holds not n divides 271 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
277 is prime
proof
now
277 = 2*138 + 1; hence not 2 divides 277 by NAT_4:9;
277 = 3*92 + 1; hence not 3 divides 277 by NAT_4:9;
277 = 5*55 + 2; hence not 5 divides 277 by NAT_4:9;
277 = 7*39 + 4; hence not 7 divides 277 by NAT_4:9;
277 = 11*25 + 2; hence not 11 divides 277 by NAT_4:9;
277 = 13*21 + 4; hence not 13 divides 277 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 277 & n is prime
holds not n divides 277 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
281 is prime
proof
now
281 = 2*140 + 1; hence not 2 divides 281 by NAT_4:9;
281 = 3*93 + 2; hence not 3 divides 281 by NAT_4:9;
281 = 5*56 + 1; hence not 5 divides 281 by NAT_4:9;
281 = 7*40 + 1; hence not 7 divides 281 by NAT_4:9;
281 = 11*25 + 6; hence not 11 divides 281 by NAT_4:9;
281 = 13*21 + 8; hence not 13 divides 281 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 281 & n is prime
holds not n divides 281 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT
theorem
283 is prime
proof
now
283 = 2*141 + 1; hence not 2 divides 283 by NAT_4:9;
283 = 3*94 + 1; hence not 3 divides 283 by NAT_4:9;
283 = 5*56 + 3; hence not 5 divides 283 by NAT_4:9;
283 = 7*40 + 3; hence not 7 divides 283 by NAT_4:9;
283 = 11*25 + 8; hence not 11 divides 283 by NAT_4:9;
283 = 13*21 + 10; hence not 13 divides 283 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 283 & n is prime
holds not n divides 283 by XPRIMET1:12;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
293 is prime
proof
now
293 = 2*146 + 1; hence not 2 divides 293 by NAT_4:9;
293 = 3*97 + 2; hence not 3 divides 293 by NAT_4:9;
293 = 5*58 + 3; hence not 5 divides 293 by NAT_4:9;
293 = 7*41 + 6; hence not 7 divides 293 by NAT_4:9;
293 = 11*26 + 7; hence not 11 divides 293 by NAT_4:9;
293 = 13*22 + 7; hence not 13 divides 293 by NAT_4:9;
293 = 17*17 + 4; hence not 17 divides 293 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 293 & n is prime
holds not n divides 293 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
307 is prime
proof
now
307 = 2*153 + 1; hence not 2 divides 307 by NAT_4:9;
307 = 3*102 + 1; hence not 3 divides 307 by NAT_4:9;
307 = 5*61 + 2; hence not 5 divides 307 by NAT_4:9;
307 = 7*43 + 6; hence not 7 divides 307 by NAT_4:9;
307 = 11*27 + 10; hence not 11 divides 307 by NAT_4:9;
307 = 13*23 + 8; hence not 13 divides 307 by NAT_4:9;
307 = 17*18 + 1; hence not 17 divides 307 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 307 & n is prime
holds not n divides 307 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
311 is prime
proof
now
311 = 2*155 + 1; hence not 2 divides 311 by NAT_4:9;
311 = 3*103 + 2; hence not 3 divides 311 by NAT_4:9;
311 = 5*62 + 1; hence not 5 divides 311 by NAT_4:9;
311 = 7*44 + 3; hence not 7 divides 311 by NAT_4:9;
311 = 11*28 + 3; hence not 11 divides 311 by NAT_4:9;
311 = 13*23 + 12; hence not 13 divides 311 by NAT_4:9;
311 = 17*18 + 5; hence not 17 divides 311 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 311 & n is prime
holds not n divides 311 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT
theorem
313 is prime
proof
now
313 = 2*156 + 1; hence not 2 divides 313 by NAT_4:9;
313 = 3*104 + 1; hence not 3 divides 313 by NAT_4:9;
313 = 5*62 + 3; hence not 5 divides 313 by NAT_4:9;
313 = 7*44 + 5; hence not 7 divides 313 by NAT_4:9;
313 = 11*28 + 5; hence not 11 divides 313 by NAT_4:9;
313 = 13*24 + 1; hence not 13 divides 313 by NAT_4:9;
313 = 17*18 + 7; hence not 17 divides 313 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 313 & n is prime
holds not n divides 313 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
317 is prime
proof
now
317 = 2*158 + 1; hence not 2 divides 317 by NAT_4:9;
317 = 3*105 + 2; hence not 3 divides 317 by NAT_4:9;
317 = 5*63 + 2; hence not 5 divides 317 by NAT_4:9;
317 = 7*45 + 2; hence not 7 divides 317 by NAT_4:9;
317 = 11*28 + 9; hence not 11 divides 317 by NAT_4:9;
317 = 13*24 + 5; hence not 13 divides 317 by NAT_4:9;
317 = 17*18 + 11; hence not 17 divides 317 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 317 & n is prime
holds not n divides 317 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
331 is prime
proof
now
331 = 2*165 + 1; hence not 2 divides 331 by NAT_4:9;
331 = 3*110 + 1; hence not 3 divides 331 by NAT_4:9;
331 = 5*66 + 1; hence not 5 divides 331 by NAT_4:9;
331 = 7*47 + 2; hence not 7 divides 331 by NAT_4:9;
331 = 11*30 + 1; hence not 11 divides 331 by NAT_4:9;
331 = 13*25 + 6; hence not 13 divides 331 by NAT_4:9;
331 = 17*19 + 8; hence not 17 divides 331 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 331 & n is prime
holds not n divides 331 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
337 is prime
proof
now
337 = 2*168 + 1; hence not 2 divides 337 by NAT_4:9;
337 = 3*112 + 1; hence not 3 divides 337 by NAT_4:9;
337 = 5*67 + 2; hence not 5 divides 337 by NAT_4:9;
337 = 7*48 + 1; hence not 7 divides 337 by NAT_4:9;
337 = 11*30 + 7; hence not 11 divides 337 by NAT_4:9;
337 = 13*25 + 12; hence not 13 divides 337 by NAT_4:9;
337 = 17*19 + 14; hence not 17 divides 337 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 337 & n is prime
holds not n divides 337 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
347 is prime
proof
now
347 = 2*173 + 1; hence not 2 divides 347 by NAT_4:9;
347 = 3*115 + 2; hence not 3 divides 347 by NAT_4:9;
347 = 5*69 + 2; hence not 5 divides 347 by NAT_4:9;
347 = 7*49 + 4; hence not 7 divides 347 by NAT_4:9;
347 = 11*31 + 6; hence not 11 divides 347 by NAT_4:9;
347 = 13*26 + 9; hence not 13 divides 347 by NAT_4:9;
347 = 17*20 + 7; hence not 17 divides 347 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 347 & n is prime
holds not n divides 347 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT
theorem
349 is prime
proof
now
349 = 2*174 + 1; hence not 2 divides 349 by NAT_4:9;
349 = 3*116 + 1; hence not 3 divides 349 by NAT_4:9;
349 = 5*69 + 4; hence not 5 divides 349 by NAT_4:9;
349 = 7*49 + 6; hence not 7 divides 349 by NAT_4:9;
349 = 11*31 + 8; hence not 11 divides 349 by NAT_4:9;
349 = 13*26 + 11; hence not 13 divides 349 by NAT_4:9;
349 = 17*20 + 9; hence not 17 divides 349 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 349 & n is prime
holds not n divides 349 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
353 is prime
proof
now
353 = 2*176 + 1; hence not 2 divides 353 by NAT_4:9;
353 = 3*117 + 2; hence not 3 divides 353 by NAT_4:9;
353 = 5*70 + 3; hence not 5 divides 353 by NAT_4:9;
353 = 7*50 + 3; hence not 7 divides 353 by NAT_4:9;
353 = 11*32 + 1; hence not 11 divides 353 by NAT_4:9;
353 = 13*27 + 2; hence not 13 divides 353 by NAT_4:9;
353 = 17*20 + 13; hence not 17 divides 353 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 353 & n is prime
holds not n divides 353 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
359 is prime
proof
now
359 = 2*179 + 1; hence not 2 divides 359 by NAT_4:9;
359 = 3*119 + 2; hence not 3 divides 359 by NAT_4:9;
359 = 5*71 + 4; hence not 5 divides 359 by NAT_4:9;
359 = 7*51 + 2; hence not 7 divides 359 by NAT_4:9;
359 = 11*32 + 7; hence not 11 divides 359 by NAT_4:9;
359 = 13*27 + 8; hence not 13 divides 359 by NAT_4:9;
359 = 17*21 + 2; hence not 17 divides 359 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 359 & n is prime
holds not n divides 359 by XPRIMET1:14;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
367 is prime
proof
now
367 = 2*183 + 1; hence not 2 divides 367 by NAT_4:9;
367 = 3*122 + 1; hence not 3 divides 367 by NAT_4:9;
367 = 5*73 + 2; hence not 5 divides 367 by NAT_4:9;
367 = 7*52 + 3; hence not 7 divides 367 by NAT_4:9;
367 = 11*33 + 4; hence not 11 divides 367 by NAT_4:9;
367 = 13*28 + 3; hence not 13 divides 367 by NAT_4:9;
367 = 17*21 + 10; hence not 17 divides 367 by NAT_4:9;
367 = 19*19 + 6; hence not 19 divides 367 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 367 & n is prime
holds not n divides 367 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
373 is prime
proof
now
373 = 2*186 + 1; hence not 2 divides 373 by NAT_4:9;
373 = 3*124 + 1; hence not 3 divides 373 by NAT_4:9;
373 = 5*74 + 3; hence not 5 divides 373 by NAT_4:9;
373 = 7*53 + 2; hence not 7 divides 373 by NAT_4:9;
373 = 11*33 + 10; hence not 11 divides 373 by NAT_4:9;
373 = 13*28 + 9; hence not 13 divides 373 by NAT_4:9;
373 = 17*21 + 16; hence not 17 divides 373 by NAT_4:9;
373 = 19*19 + 12; hence not 19 divides 373 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 373 & n is prime
holds not n divides 373 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
379 is prime
proof
now
379 = 2*189 + 1; hence not 2 divides 379 by NAT_4:9;
379 = 3*126 + 1; hence not 3 divides 379 by NAT_4:9;
379 = 5*75 + 4; hence not 5 divides 379 by NAT_4:9;
379 = 7*54 + 1; hence not 7 divides 379 by NAT_4:9;
379 = 11*34 + 5; hence not 11 divides 379 by NAT_4:9;
379 = 13*29 + 2; hence not 13 divides 379 by NAT_4:9;
379 = 17*22 + 5; hence not 17 divides 379 by NAT_4:9;
379 = 19*19 + 18; hence not 19 divides 379 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 379 & n is prime
holds not n divides 379 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
383 is prime
proof
now
383 = 2*191 + 1; hence not 2 divides 383 by NAT_4:9;
383 = 3*127 + 2; hence not 3 divides 383 by NAT_4:9;
383 = 5*76 + 3; hence not 5 divides 383 by NAT_4:9;
383 = 7*54 + 5; hence not 7 divides 383 by NAT_4:9;
383 = 11*34 + 9; hence not 11 divides 383 by NAT_4:9;
383 = 13*29 + 6; hence not 13 divides 383 by NAT_4:9;
383 = 17*22 + 9; hence not 17 divides 383 by NAT_4:9;
383 = 19*20 + 3; hence not 19 divides 383 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 383 & n is prime
holds not n divides 383 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
389 is prime
proof
now
389 = 2*194 + 1; hence not 2 divides 389 by NAT_4:9;
389 = 3*129 + 2; hence not 3 divides 389 by NAT_4:9;
389 = 5*77 + 4; hence not 5 divides 389 by NAT_4:9;
389 = 7*55 + 4; hence not 7 divides 389 by NAT_4:9;
389 = 11*35 + 4; hence not 11 divides 389 by NAT_4:9;
389 = 13*29 + 12; hence not 13 divides 389 by NAT_4:9;
389 = 17*22 + 15; hence not 17 divides 389 by NAT_4:9;
389 = 19*20 + 9; hence not 19 divides 389 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 389 & n is prime
holds not n divides 389 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
397 is prime
proof
now
397 = 2*198 + 1; hence not 2 divides 397 by NAT_4:9;
397 = 3*132 + 1; hence not 3 divides 397 by NAT_4:9;
397 = 5*79 + 2; hence not 5 divides 397 by NAT_4:9;
397 = 7*56 + 5; hence not 7 divides 397 by NAT_4:9;
397 = 11*36 + 1; hence not 11 divides 397 by NAT_4:9;
397 = 13*30 + 7; hence not 13 divides 397 by NAT_4:9;
397 = 17*23 + 6; hence not 17 divides 397 by NAT_4:9;
397 = 19*20 + 17; hence not 19 divides 397 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 397 & n is prime
holds not n divides 397 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
401 is prime
proof
now
401 = 2*200 + 1; hence not 2 divides 401 by NAT_4:9;
401 = 3*133 + 2; hence not 3 divides 401 by NAT_4:9;
401 = 5*80 + 1; hence not 5 divides 401 by NAT_4:9;
401 = 7*57 + 2; hence not 7 divides 401 by NAT_4:9;
401 = 11*36 + 5; hence not 11 divides 401 by NAT_4:9;
401 = 13*30 + 11; hence not 13 divides 401 by NAT_4:9;
401 = 17*23 + 10; hence not 17 divides 401 by NAT_4:9;
401 = 19*21 + 2; hence not 19 divides 401 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 401 & n is prime
holds not n divides 401 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
409 is prime
proof
now
409 = 2*204 + 1; hence not 2 divides 409 by NAT_4:9;
409 = 3*136 + 1; hence not 3 divides 409 by NAT_4:9;
409 = 5*81 + 4; hence not 5 divides 409 by NAT_4:9;
409 = 7*58 + 3; hence not 7 divides 409 by NAT_4:9;
409 = 11*37 + 2; hence not 11 divides 409 by NAT_4:9;
409 = 13*31 + 6; hence not 13 divides 409 by NAT_4:9;
409 = 17*24 + 1; hence not 17 divides 409 by NAT_4:9;
409 = 19*21 + 10; hence not 19 divides 409 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 409 & n is prime
holds not n divides 409 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
419 is prime
proof
now
419 = 2*209 + 1; hence not 2 divides 419 by NAT_4:9;
419 = 3*139 + 2; hence not 3 divides 419 by NAT_4:9;
419 = 5*83 + 4; hence not 5 divides 419 by NAT_4:9;
419 = 7*59 + 6; hence not 7 divides 419 by NAT_4:9;
419 = 11*38 + 1; hence not 11 divides 419 by NAT_4:9;
419 = 13*32 + 3; hence not 13 divides 419 by NAT_4:9;
419 = 17*24 + 11; hence not 17 divides 419 by NAT_4:9;
419 = 19*22 + 1; hence not 19 divides 419 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 419 & n is prime
holds not n divides 419 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT
theorem
421 is prime
proof
now
421 = 2*210 + 1; hence not 2 divides 421 by NAT_4:9;
421 = 3*140 + 1; hence not 3 divides 421 by NAT_4:9;
421 = 5*84 + 1; hence not 5 divides 421 by NAT_4:9;
421 = 7*60 + 1; hence not 7 divides 421 by NAT_4:9;
421 = 11*38 + 3; hence not 11 divides 421 by NAT_4:9;
421 = 13*32 + 5; hence not 13 divides 421 by NAT_4:9;
421 = 17*24 + 13; hence not 17 divides 421 by NAT_4:9;
421 = 19*22 + 3; hence not 19 divides 421 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 421 & n is prime
holds not n divides 421 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
431 is prime
proof
now
431 = 2*215 + 1; hence not 2 divides 431 by NAT_4:9;
431 = 3*143 + 2; hence not 3 divides 431 by NAT_4:9;
431 = 5*86 + 1; hence not 5 divides 431 by NAT_4:9;
431 = 7*61 + 4; hence not 7 divides 431 by NAT_4:9;
431 = 11*39 + 2; hence not 11 divides 431 by NAT_4:9;
431 = 13*33 + 2; hence not 13 divides 431 by NAT_4:9;
431 = 17*25 + 6; hence not 17 divides 431 by NAT_4:9;
431 = 19*22 + 13; hence not 19 divides 431 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 431 & n is prime
holds not n divides 431 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT
theorem
433 is prime
proof
now
433 = 2*216 + 1; hence not 2 divides 433 by NAT_4:9;
433 = 3*144 + 1; hence not 3 divides 433 by NAT_4:9;
433 = 5*86 + 3; hence not 5 divides 433 by NAT_4:9;
433 = 7*61 + 6; hence not 7 divides 433 by NAT_4:9;
433 = 11*39 + 4; hence not 11 divides 433 by NAT_4:9;
433 = 13*33 + 4; hence not 13 divides 433 by NAT_4:9;
433 = 17*25 + 8; hence not 17 divides 433 by NAT_4:9;
433 = 19*22 + 15; hence not 19 divides 433 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 433 & n is prime
holds not n divides 433 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
439 is prime
proof
now
439 = 2*219 + 1; hence not 2 divides 439 by NAT_4:9;
439 = 3*146 + 1; hence not 3 divides 439 by NAT_4:9;
439 = 5*87 + 4; hence not 5 divides 439 by NAT_4:9;
439 = 7*62 + 5; hence not 7 divides 439 by NAT_4:9;
439 = 11*39 + 10; hence not 11 divides 439 by NAT_4:9;
439 = 13*33 + 10; hence not 13 divides 439 by NAT_4:9;
439 = 17*25 + 14; hence not 17 divides 439 by NAT_4:9;
439 = 19*23 + 2; hence not 19 divides 439 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 439 & n is prime
holds not n divides 439 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
443 is prime
proof
now
443 = 2*221 + 1; hence not 2 divides 443 by NAT_4:9;
443 = 3*147 + 2; hence not 3 divides 443 by NAT_4:9;
443 = 5*88 + 3; hence not 5 divides 443 by NAT_4:9;
443 = 7*63 + 2; hence not 7 divides 443 by NAT_4:9;
443 = 11*40 + 3; hence not 11 divides 443 by NAT_4:9;
443 = 13*34 + 1; hence not 13 divides 443 by NAT_4:9;
443 = 17*26 + 1; hence not 17 divides 443 by NAT_4:9;
443 = 19*23 + 6; hence not 19 divides 443 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 443 & n is prime
holds not n divides 443 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
449 is prime
proof
now
449 = 2*224 + 1; hence not 2 divides 449 by NAT_4:9;
449 = 3*149 + 2; hence not 3 divides 449 by NAT_4:9;
449 = 5*89 + 4; hence not 5 divides 449 by NAT_4:9;
449 = 7*64 + 1; hence not 7 divides 449 by NAT_4:9;
449 = 11*40 + 9; hence not 11 divides 449 by NAT_4:9;
449 = 13*34 + 7; hence not 13 divides 449 by NAT_4:9;
449 = 17*26 + 7; hence not 17 divides 449 by NAT_4:9;
449 = 19*23 + 12; hence not 19 divides 449 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 449 & n is prime
holds not n divides 449 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
457 is prime
proof
now
457 = 2*228 + 1; hence not 2 divides 457 by NAT_4:9;
457 = 3*152 + 1; hence not 3 divides 457 by NAT_4:9;
457 = 5*91 + 2; hence not 5 divides 457 by NAT_4:9;
457 = 7*65 + 2; hence not 7 divides 457 by NAT_4:9;
457 = 11*41 + 6; hence not 11 divides 457 by NAT_4:9;
457 = 13*35 + 2; hence not 13 divides 457 by NAT_4:9;
457 = 17*26 + 15; hence not 17 divides 457 by NAT_4:9;
457 = 19*24 + 1; hence not 19 divides 457 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 457 & n is prime
holds not n divides 457 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
461 is prime
proof
now
461 = 2*230 + 1; hence not 2 divides 461 by NAT_4:9;
461 = 3*153 + 2; hence not 3 divides 461 by NAT_4:9;
461 = 5*92 + 1; hence not 5 divides 461 by NAT_4:9;
461 = 7*65 + 6; hence not 7 divides 461 by NAT_4:9;
461 = 11*41 + 10; hence not 11 divides 461 by NAT_4:9;
461 = 13*35 + 6; hence not 13 divides 461 by NAT_4:9;
461 = 17*27 + 2; hence not 17 divides 461 by NAT_4:9;
461 = 19*24 + 5; hence not 19 divides 461 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 461 & n is prime
holds not n divides 461 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT
theorem
463 is prime
proof
now
463 = 2*231 + 1; hence not 2 divides 463 by NAT_4:9;
463 = 3*154 + 1; hence not 3 divides 463 by NAT_4:9;
463 = 5*92 + 3; hence not 5 divides 463 by NAT_4:9;
463 = 7*66 + 1; hence not 7 divides 463 by NAT_4:9;
463 = 11*42 + 1; hence not 11 divides 463 by NAT_4:9;
463 = 13*35 + 8; hence not 13 divides 463 by NAT_4:9;
463 = 17*27 + 4; hence not 17 divides 463 by NAT_4:9;
463 = 19*24 + 7; hence not 19 divides 463 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 463 & n is prime
holds not n divides 463 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
467 is prime
proof
now
467 = 2*233 + 1; hence not 2 divides 467 by NAT_4:9;
467 = 3*155 + 2; hence not 3 divides 467 by NAT_4:9;
467 = 5*93 + 2; hence not 5 divides 467 by NAT_4:9;
467 = 7*66 + 5; hence not 7 divides 467 by NAT_4:9;
467 = 11*42 + 5; hence not 11 divides 467 by NAT_4:9;
467 = 13*35 + 12; hence not 13 divides 467 by NAT_4:9;
467 = 17*27 + 8; hence not 17 divides 467 by NAT_4:9;
467 = 19*24 + 11; hence not 19 divides 467 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 467 & n is prime
holds not n divides 467 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
479 is prime
proof
now
479 = 2*239 + 1; hence not 2 divides 479 by NAT_4:9;
479 = 3*159 + 2; hence not 3 divides 479 by NAT_4:9;
479 = 5*95 + 4; hence not 5 divides 479 by NAT_4:9;
479 = 7*68 + 3; hence not 7 divides 479 by NAT_4:9;
479 = 11*43 + 6; hence not 11 divides 479 by NAT_4:9;
479 = 13*36 + 11; hence not 13 divides 479 by NAT_4:9;
479 = 17*28 + 3; hence not 17 divides 479 by NAT_4:9;
479 = 19*25 + 4; hence not 19 divides 479 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 479 & n is prime
holds not n divides 479 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
487 is prime
proof
now
487 = 2*243 + 1; hence not 2 divides 487 by NAT_4:9;
487 = 3*162 + 1; hence not 3 divides 487 by NAT_4:9;
487 = 5*97 + 2; hence not 5 divides 487 by NAT_4:9;
487 = 7*69 + 4; hence not 7 divides 487 by NAT_4:9;
487 = 11*44 + 3; hence not 11 divides 487 by NAT_4:9;
487 = 13*37 + 6; hence not 13 divides 487 by NAT_4:9;
487 = 17*28 + 11; hence not 17 divides 487 by NAT_4:9;
487 = 19*25 + 12; hence not 19 divides 487 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 487 & n is prime
holds not n divides 487 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
491 is prime
proof
now
491 = 2*245 + 1; hence not 2 divides 491 by NAT_4:9;
491 = 3*163 + 2; hence not 3 divides 491 by NAT_4:9;
491 = 5*98 + 1; hence not 5 divides 491 by NAT_4:9;
491 = 7*70 + 1; hence not 7 divides 491 by NAT_4:9;
491 = 11*44 + 7; hence not 11 divides 491 by NAT_4:9;
491 = 13*37 + 10; hence not 13 divides 491 by NAT_4:9;
491 = 17*28 + 15; hence not 17 divides 491 by NAT_4:9;
491 = 19*25 + 16; hence not 19 divides 491 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 491 & n is prime
holds not n divides 491 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
499 is prime
proof
now
499 = 2*249 + 1; hence not 2 divides 499 by NAT_4:9;
499 = 3*166 + 1; hence not 3 divides 499 by NAT_4:9;
499 = 5*99 + 4; hence not 5 divides 499 by NAT_4:9;
499 = 7*71 + 2; hence not 7 divides 499 by NAT_4:9;
499 = 11*45 + 4; hence not 11 divides 499 by NAT_4:9;
499 = 13*38 + 5; hence not 13 divides 499 by NAT_4:9;
499 = 17*29 + 6; hence not 17 divides 499 by NAT_4:9;
499 = 19*26 + 5; hence not 19 divides 499 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 499 & n is prime
holds not n divides 499 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
503 is prime
proof
now
503 = 2*251 + 1; hence not 2 divides 503 by NAT_4:9;
503 = 3*167 + 2; hence not 3 divides 503 by NAT_4:9;
503 = 5*100 + 3; hence not 5 divides 503 by NAT_4:9;
503 = 7*71 + 6; hence not 7 divides 503 by NAT_4:9;
503 = 11*45 + 8; hence not 11 divides 503 by NAT_4:9;
503 = 13*38 + 9; hence not 13 divides 503 by NAT_4:9;
503 = 17*29 + 10; hence not 17 divides 503 by NAT_4:9;
503 = 19*26 + 9; hence not 19 divides 503 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 503 & n is prime
holds not n divides 503 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
509 is prime
proof
now
509 = 2*254 + 1; hence not 2 divides 509 by NAT_4:9;
509 = 3*169 + 2; hence not 3 divides 509 by NAT_4:9;
509 = 5*101 + 4; hence not 5 divides 509 by NAT_4:9;
509 = 7*72 + 5; hence not 7 divides 509 by NAT_4:9;
509 = 11*46 + 3; hence not 11 divides 509 by NAT_4:9;
509 = 13*39 + 2; hence not 13 divides 509 by NAT_4:9;
509 = 17*29 + 16; hence not 17 divides 509 by NAT_4:9;
509 = 19*26 + 15; hence not 19 divides 509 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 509 & n is prime
holds not n divides 509 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
521 is prime
proof
now
521 = 2*260 + 1; hence not 2 divides 521 by NAT_4:9;
521 = 3*173 + 2; hence not 3 divides 521 by NAT_4:9;
521 = 5*104 + 1; hence not 5 divides 521 by NAT_4:9;
521 = 7*74 + 3; hence not 7 divides 521 by NAT_4:9;
521 = 11*47 + 4; hence not 11 divides 521 by NAT_4:9;
521 = 13*40 + 1; hence not 13 divides 521 by NAT_4:9;
521 = 17*30 + 11; hence not 17 divides 521 by NAT_4:9;
521 = 19*27 + 8; hence not 19 divides 521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 521 & n is prime
holds not n divides 521 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT
theorem
523 is prime
proof
now
523 = 2*261 + 1; hence not 2 divides 523 by NAT_4:9;
523 = 3*174 + 1; hence not 3 divides 523 by NAT_4:9;
523 = 5*104 + 3; hence not 5 divides 523 by NAT_4:9;
523 = 7*74 + 5; hence not 7 divides 523 by NAT_4:9;
523 = 11*47 + 6; hence not 11 divides 523 by NAT_4:9;
523 = 13*40 + 3; hence not 13 divides 523 by NAT_4:9;
523 = 17*30 + 13; hence not 17 divides 523 by NAT_4:9;
523 = 19*27 + 10; hence not 19 divides 523 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 523 & n is prime
holds not n divides 523 by XPRIMET1:16;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
541 is prime
proof
now
541 = 2*270 + 1; hence not 2 divides 541 by NAT_4:9;
541 = 3*180 + 1; hence not 3 divides 541 by NAT_4:9;
541 = 5*108 + 1; hence not 5 divides 541 by NAT_4:9;
541 = 7*77 + 2; hence not 7 divides 541 by NAT_4:9;
541 = 11*49 + 2; hence not 11 divides 541 by NAT_4:9;
541 = 13*41 + 8; hence not 13 divides 541 by NAT_4:9;
541 = 17*31 + 14; hence not 17 divides 541 by NAT_4:9;
541 = 19*28 + 9; hence not 19 divides 541 by NAT_4:9;
541 = 23*23 + 12; hence not 23 divides 541 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 541 & n is prime
holds not n divides 541 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
547 is prime
proof
now
547 = 2*273 + 1; hence not 2 divides 547 by NAT_4:9;
547 = 3*182 + 1; hence not 3 divides 547 by NAT_4:9;
547 = 5*109 + 2; hence not 5 divides 547 by NAT_4:9;
547 = 7*78 + 1; hence not 7 divides 547 by NAT_4:9;
547 = 11*49 + 8; hence not 11 divides 547 by NAT_4:9;
547 = 13*42 + 1; hence not 13 divides 547 by NAT_4:9;
547 = 17*32 + 3; hence not 17 divides 547 by NAT_4:9;
547 = 19*28 + 15; hence not 19 divides 547 by NAT_4:9;
547 = 23*23 + 18; hence not 23 divides 547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 547 & n is prime
holds not n divides 547 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
557 is prime
proof
now
557 = 2*278 + 1; hence not 2 divides 557 by NAT_4:9;
557 = 3*185 + 2; hence not 3 divides 557 by NAT_4:9;
557 = 5*111 + 2; hence not 5 divides 557 by NAT_4:9;
557 = 7*79 + 4; hence not 7 divides 557 by NAT_4:9;
557 = 11*50 + 7; hence not 11 divides 557 by NAT_4:9;
557 = 13*42 + 11; hence not 13 divides 557 by NAT_4:9;
557 = 17*32 + 13; hence not 17 divides 557 by NAT_4:9;
557 = 19*29 + 6; hence not 19 divides 557 by NAT_4:9;
557 = 23*24 + 5; hence not 23 divides 557 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 557 & n is prime
holds not n divides 557 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
563 is prime
proof
now
563 = 2*281 + 1; hence not 2 divides 563 by NAT_4:9;
563 = 3*187 + 2; hence not 3 divides 563 by NAT_4:9;
563 = 5*112 + 3; hence not 5 divides 563 by NAT_4:9;
563 = 7*80 + 3; hence not 7 divides 563 by NAT_4:9;
563 = 11*51 + 2; hence not 11 divides 563 by NAT_4:9;
563 = 13*43 + 4; hence not 13 divides 563 by NAT_4:9;
563 = 17*33 + 2; hence not 17 divides 563 by NAT_4:9;
563 = 19*29 + 12; hence not 19 divides 563 by NAT_4:9;
563 = 23*24 + 11; hence not 23 divides 563 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 563 & n is prime
holds not n divides 563 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
569 is prime
proof
now
569 = 2*284 + 1; hence not 2 divides 569 by NAT_4:9;
569 = 3*189 + 2; hence not 3 divides 569 by NAT_4:9;
569 = 5*113 + 4; hence not 5 divides 569 by NAT_4:9;
569 = 7*81 + 2; hence not 7 divides 569 by NAT_4:9;
569 = 11*51 + 8; hence not 11 divides 569 by NAT_4:9;
569 = 13*43 + 10; hence not 13 divides 569 by NAT_4:9;
569 = 17*33 + 8; hence not 17 divides 569 by NAT_4:9;
569 = 19*29 + 18; hence not 19 divides 569 by NAT_4:9;
569 = 23*24 + 17; hence not 23 divides 569 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 569 & n is prime
holds not n divides 569 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
571 is prime
proof
now
571 = 2*285 + 1; hence not 2 divides 571 by NAT_4:9;
571 = 3*190 + 1; hence not 3 divides 571 by NAT_4:9;
571 = 5*114 + 1; hence not 5 divides 571 by NAT_4:9;
571 = 7*81 + 4; hence not 7 divides 571 by NAT_4:9;
571 = 11*51 + 10; hence not 11 divides 571 by NAT_4:9;
571 = 13*43 + 12; hence not 13 divides 571 by NAT_4:9;
571 = 17*33 + 10; hence not 17 divides 571 by NAT_4:9;
571 = 19*30 + 1; hence not 19 divides 571 by NAT_4:9;
571 = 23*24 + 19; hence not 23 divides 571 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 571 & n is prime
holds not n divides 571 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
577 is prime
proof
now
577 = 2*288 + 1; hence not 2 divides 577 by NAT_4:9;
577 = 3*192 + 1; hence not 3 divides 577 by NAT_4:9;
577 = 5*115 + 2; hence not 5 divides 577 by NAT_4:9;
577 = 7*82 + 3; hence not 7 divides 577 by NAT_4:9;
577 = 11*52 + 5; hence not 11 divides 577 by NAT_4:9;
577 = 13*44 + 5; hence not 13 divides 577 by NAT_4:9;
577 = 17*33 + 16; hence not 17 divides 577 by NAT_4:9;
577 = 19*30 + 7; hence not 19 divides 577 by NAT_4:9;
577 = 23*25 + 2; hence not 23 divides 577 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 577 & n is prime
holds not n divides 577 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
587 is prime
proof
now
587 = 2*293 + 1; hence not 2 divides 587 by NAT_4:9;
587 = 3*195 + 2; hence not 3 divides 587 by NAT_4:9;
587 = 5*117 + 2; hence not 5 divides 587 by NAT_4:9;
587 = 7*83 + 6; hence not 7 divides 587 by NAT_4:9;
587 = 11*53 + 4; hence not 11 divides 587 by NAT_4:9;
587 = 13*45 + 2; hence not 13 divides 587 by NAT_4:9;
587 = 17*34 + 9; hence not 17 divides 587 by NAT_4:9;
587 = 19*30 + 17; hence not 19 divides 587 by NAT_4:9;
587 = 23*25 + 12; hence not 23 divides 587 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 587 & n is prime
holds not n divides 587 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
593 is prime
proof
now
593 = 2*296 + 1; hence not 2 divides 593 by NAT_4:9;
593 = 3*197 + 2; hence not 3 divides 593 by NAT_4:9;
593 = 5*118 + 3; hence not 5 divides 593 by NAT_4:9;
593 = 7*84 + 5; hence not 7 divides 593 by NAT_4:9;
593 = 11*53 + 10; hence not 11 divides 593 by NAT_4:9;
593 = 13*45 + 8; hence not 13 divides 593 by NAT_4:9;
593 = 17*34 + 15; hence not 17 divides 593 by NAT_4:9;
593 = 19*31 + 4; hence not 19 divides 593 by NAT_4:9;
593 = 23*25 + 18; hence not 23 divides 593 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 593 & n is prime
holds not n divides 593 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
599 is prime
proof
now
599 = 2*299 + 1; hence not 2 divides 599 by NAT_4:9;
599 = 3*199 + 2; hence not 3 divides 599 by NAT_4:9;
599 = 5*119 + 4; hence not 5 divides 599 by NAT_4:9;
599 = 7*85 + 4; hence not 7 divides 599 by NAT_4:9;
599 = 11*54 + 5; hence not 11 divides 599 by NAT_4:9;
599 = 13*46 + 1; hence not 13 divides 599 by NAT_4:9;
599 = 17*35 + 4; hence not 17 divides 599 by NAT_4:9;
599 = 19*31 + 10; hence not 19 divides 599 by NAT_4:9;
599 = 23*26 + 1; hence not 23 divides 599 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 599 & n is prime
holds not n divides 599 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
601 is prime
proof
now
601 = 2*300 + 1; hence not 2 divides 601 by NAT_4:9;
601 = 3*200 + 1; hence not 3 divides 601 by NAT_4:9;
601 = 5*120 + 1; hence not 5 divides 601 by NAT_4:9;
601 = 7*85 + 6; hence not 7 divides 601 by NAT_4:9;
601 = 11*54 + 7; hence not 11 divides 601 by NAT_4:9;
601 = 13*46 + 3; hence not 13 divides 601 by NAT_4:9;
601 = 17*35 + 6; hence not 17 divides 601 by NAT_4:9;
601 = 19*31 + 12; hence not 19 divides 601 by NAT_4:9;
601 = 23*26 + 3; hence not 23 divides 601 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 601 & n is prime
holds not n divides 601 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
607 is prime
proof
now
607 = 2*303 + 1; hence not 2 divides 607 by NAT_4:9;
607 = 3*202 + 1; hence not 3 divides 607 by NAT_4:9;
607 = 5*121 + 2; hence not 5 divides 607 by NAT_4:9;
607 = 7*86 + 5; hence not 7 divides 607 by NAT_4:9;
607 = 11*55 + 2; hence not 11 divides 607 by NAT_4:9;
607 = 13*46 + 9; hence not 13 divides 607 by NAT_4:9;
607 = 17*35 + 12; hence not 17 divides 607 by NAT_4:9;
607 = 19*31 + 18; hence not 19 divides 607 by NAT_4:9;
607 = 23*26 + 9; hence not 23 divides 607 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 607 & n is prime
holds not n divides 607 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
613 is prime
proof
now
613 = 2*306 + 1; hence not 2 divides 613 by NAT_4:9;
613 = 3*204 + 1; hence not 3 divides 613 by NAT_4:9;
613 = 5*122 + 3; hence not 5 divides 613 by NAT_4:9;
613 = 7*87 + 4; hence not 7 divides 613 by NAT_4:9;
613 = 11*55 + 8; hence not 11 divides 613 by NAT_4:9;
613 = 13*47 + 2; hence not 13 divides 613 by NAT_4:9;
613 = 17*36 + 1; hence not 17 divides 613 by NAT_4:9;
613 = 19*32 + 5; hence not 19 divides 613 by NAT_4:9;
613 = 23*26 + 15; hence not 23 divides 613 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 613 & n is prime
holds not n divides 613 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
617 is prime
proof
now
617 = 2*308 + 1; hence not 2 divides 617 by NAT_4:9;
617 = 3*205 + 2; hence not 3 divides 617 by NAT_4:9;
617 = 5*123 + 2; hence not 5 divides 617 by NAT_4:9;
617 = 7*88 + 1; hence not 7 divides 617 by NAT_4:9;
617 = 11*56 + 1; hence not 11 divides 617 by NAT_4:9;
617 = 13*47 + 6; hence not 13 divides 617 by NAT_4:9;
617 = 17*36 + 5; hence not 17 divides 617 by NAT_4:9;
617 = 19*32 + 9; hence not 19 divides 617 by NAT_4:9;
617 = 23*26 + 19; hence not 23 divides 617 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 617 & n is prime
holds not n divides 617 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
619 is prime
proof
now
619 = 2*309 + 1; hence not 2 divides 619 by NAT_4:9;
619 = 3*206 + 1; hence not 3 divides 619 by NAT_4:9;
619 = 5*123 + 4; hence not 5 divides 619 by NAT_4:9;
619 = 7*88 + 3; hence not 7 divides 619 by NAT_4:9;
619 = 11*56 + 3; hence not 11 divides 619 by NAT_4:9;
619 = 13*47 + 8; hence not 13 divides 619 by NAT_4:9;
619 = 17*36 + 7; hence not 17 divides 619 by NAT_4:9;
619 = 19*32 + 11; hence not 19 divides 619 by NAT_4:9;
619 = 23*26 + 21; hence not 23 divides 619 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 619 & n is prime
holds not n divides 619 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
631 is prime
proof
now
631 = 2*315 + 1; hence not 2 divides 631 by NAT_4:9;
631 = 3*210 + 1; hence not 3 divides 631 by NAT_4:9;
631 = 5*126 + 1; hence not 5 divides 631 by NAT_4:9;
631 = 7*90 + 1; hence not 7 divides 631 by NAT_4:9;
631 = 11*57 + 4; hence not 11 divides 631 by NAT_4:9;
631 = 13*48 + 7; hence not 13 divides 631 by NAT_4:9;
631 = 17*37 + 2; hence not 17 divides 631 by NAT_4:9;
631 = 19*33 + 4; hence not 19 divides 631 by NAT_4:9;
631 = 23*27 + 10; hence not 23 divides 631 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 631 & n is prime
holds not n divides 631 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
641 is prime
proof
now
641 = 2*320 + 1; hence not 2 divides 641 by NAT_4:9;
641 = 3*213 + 2; hence not 3 divides 641 by NAT_4:9;
641 = 5*128 + 1; hence not 5 divides 641 by NAT_4:9;
641 = 7*91 + 4; hence not 7 divides 641 by NAT_4:9;
641 = 11*58 + 3; hence not 11 divides 641 by NAT_4:9;
641 = 13*49 + 4; hence not 13 divides 641 by NAT_4:9;
641 = 17*37 + 12; hence not 17 divides 641 by NAT_4:9;
641 = 19*33 + 14; hence not 19 divides 641 by NAT_4:9;
641 = 23*27 + 20; hence not 23 divides 641 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 641 & n is prime
holds not n divides 641 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
643 is prime
proof
now
643 = 2*321 + 1; hence not 2 divides 643 by NAT_4:9;
643 = 3*214 + 1; hence not 3 divides 643 by NAT_4:9;
643 = 5*128 + 3; hence not 5 divides 643 by NAT_4:9;
643 = 7*91 + 6; hence not 7 divides 643 by NAT_4:9;
643 = 11*58 + 5; hence not 11 divides 643 by NAT_4:9;
643 = 13*49 + 6; hence not 13 divides 643 by NAT_4:9;
643 = 17*37 + 14; hence not 17 divides 643 by NAT_4:9;
643 = 19*33 + 16; hence not 19 divides 643 by NAT_4:9;
643 = 23*27 + 22; hence not 23 divides 643 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 643 & n is prime
holds not n divides 643 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
647 is prime
proof
now
647 = 2*323 + 1; hence not 2 divides 647 by NAT_4:9;
647 = 3*215 + 2; hence not 3 divides 647 by NAT_4:9;
647 = 5*129 + 2; hence not 5 divides 647 by NAT_4:9;
647 = 7*92 + 3; hence not 7 divides 647 by NAT_4:9;
647 = 11*58 + 9; hence not 11 divides 647 by NAT_4:9;
647 = 13*49 + 10; hence not 13 divides 647 by NAT_4:9;
647 = 17*38 + 1; hence not 17 divides 647 by NAT_4:9;
647 = 19*34 + 1; hence not 19 divides 647 by NAT_4:9;
647 = 23*28 + 3; hence not 23 divides 647 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 647 & n is prime
holds not n divides 647 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
653 is prime
proof
now
653 = 2*326 + 1; hence not 2 divides 653 by NAT_4:9;
653 = 3*217 + 2; hence not 3 divides 653 by NAT_4:9;
653 = 5*130 + 3; hence not 5 divides 653 by NAT_4:9;
653 = 7*93 + 2; hence not 7 divides 653 by NAT_4:9;
653 = 11*59 + 4; hence not 11 divides 653 by NAT_4:9;
653 = 13*50 + 3; hence not 13 divides 653 by NAT_4:9;
653 = 17*38 + 7; hence not 17 divides 653 by NAT_4:9;
653 = 19*34 + 7; hence not 19 divides 653 by NAT_4:9;
653 = 23*28 + 9; hence not 23 divides 653 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 653 & n is prime
holds not n divides 653 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
659 is prime
proof
now
659 = 2*329 + 1; hence not 2 divides 659 by NAT_4:9;
659 = 3*219 + 2; hence not 3 divides 659 by NAT_4:9;
659 = 5*131 + 4; hence not 5 divides 659 by NAT_4:9;
659 = 7*94 + 1; hence not 7 divides 659 by NAT_4:9;
659 = 11*59 + 10; hence not 11 divides 659 by NAT_4:9;
659 = 13*50 + 9; hence not 13 divides 659 by NAT_4:9;
659 = 17*38 + 13; hence not 17 divides 659 by NAT_4:9;
659 = 19*34 + 13; hence not 19 divides 659 by NAT_4:9;
659 = 23*28 + 15; hence not 23 divides 659 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 659 & n is prime
holds not n divides 659 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
661 is prime
proof
now
661 = 2*330 + 1; hence not 2 divides 661 by NAT_4:9;
661 = 3*220 + 1; hence not 3 divides 661 by NAT_4:9;
661 = 5*132 + 1; hence not 5 divides 661 by NAT_4:9;
661 = 7*94 + 3; hence not 7 divides 661 by NAT_4:9;
661 = 11*60 + 1; hence not 11 divides 661 by NAT_4:9;
661 = 13*50 + 11; hence not 13 divides 661 by NAT_4:9;
661 = 17*38 + 15; hence not 17 divides 661 by NAT_4:9;
661 = 19*34 + 15; hence not 19 divides 661 by NAT_4:9;
661 = 23*28 + 17; hence not 23 divides 661 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 661 & n is prime
holds not n divides 661 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
673 is prime
proof
now
673 = 2*336 + 1; hence not 2 divides 673 by NAT_4:9;
673 = 3*224 + 1; hence not 3 divides 673 by NAT_4:9;
673 = 5*134 + 3; hence not 5 divides 673 by NAT_4:9;
673 = 7*96 + 1; hence not 7 divides 673 by NAT_4:9;
673 = 11*61 + 2; hence not 11 divides 673 by NAT_4:9;
673 = 13*51 + 10; hence not 13 divides 673 by NAT_4:9;
673 = 17*39 + 10; hence not 17 divides 673 by NAT_4:9;
673 = 19*35 + 8; hence not 19 divides 673 by NAT_4:9;
673 = 23*29 + 6; hence not 23 divides 673 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 673 & n is prime
holds not n divides 673 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
677 is prime
proof
now
677 = 2*338 + 1; hence not 2 divides 677 by NAT_4:9;
677 = 3*225 + 2; hence not 3 divides 677 by NAT_4:9;
677 = 5*135 + 2; hence not 5 divides 677 by NAT_4:9;
677 = 7*96 + 5; hence not 7 divides 677 by NAT_4:9;
677 = 11*61 + 6; hence not 11 divides 677 by NAT_4:9;
677 = 13*52 + 1; hence not 13 divides 677 by NAT_4:9;
677 = 17*39 + 14; hence not 17 divides 677 by NAT_4:9;
677 = 19*35 + 12; hence not 19 divides 677 by NAT_4:9;
677 = 23*29 + 10; hence not 23 divides 677 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 677 & n is prime
holds not n divides 677 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
683 is prime
proof
now
683 = 2*341 + 1; hence not 2 divides 683 by NAT_4:9;
683 = 3*227 + 2; hence not 3 divides 683 by NAT_4:9;
683 = 5*136 + 3; hence not 5 divides 683 by NAT_4:9;
683 = 7*97 + 4; hence not 7 divides 683 by NAT_4:9;
683 = 11*62 + 1; hence not 11 divides 683 by NAT_4:9;
683 = 13*52 + 7; hence not 13 divides 683 by NAT_4:9;
683 = 17*40 + 3; hence not 17 divides 683 by NAT_4:9;
683 = 19*35 + 18; hence not 19 divides 683 by NAT_4:9;
683 = 23*29 + 16; hence not 23 divides 683 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 683 & n is prime
holds not n divides 683 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
691 is prime
proof
now
691 = 2*345 + 1; hence not 2 divides 691 by NAT_4:9;
691 = 3*230 + 1; hence not 3 divides 691 by NAT_4:9;
691 = 5*138 + 1; hence not 5 divides 691 by NAT_4:9;
691 = 7*98 + 5; hence not 7 divides 691 by NAT_4:9;
691 = 11*62 + 9; hence not 11 divides 691 by NAT_4:9;
691 = 13*53 + 2; hence not 13 divides 691 by NAT_4:9;
691 = 17*40 + 11; hence not 17 divides 691 by NAT_4:9;
691 = 19*36 + 7; hence not 19 divides 691 by NAT_4:9;
691 = 23*30 + 1; hence not 23 divides 691 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 691 & n is prime
holds not n divides 691 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
701 is prime
proof
now
701 = 2*350 + 1; hence not 2 divides 701 by NAT_4:9;
701 = 3*233 + 2; hence not 3 divides 701 by NAT_4:9;
701 = 5*140 + 1; hence not 5 divides 701 by NAT_4:9;
701 = 7*100 + 1; hence not 7 divides 701 by NAT_4:9;
701 = 11*63 + 8; hence not 11 divides 701 by NAT_4:9;
701 = 13*53 + 12; hence not 13 divides 701 by NAT_4:9;
701 = 17*41 + 4; hence not 17 divides 701 by NAT_4:9;
701 = 19*36 + 17; hence not 19 divides 701 by NAT_4:9;
701 = 23*30 + 11; hence not 23 divides 701 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 701 & n is prime
holds not n divides 701 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
709 is prime
proof
now
709 = 2*354 + 1; hence not 2 divides 709 by NAT_4:9;
709 = 3*236 + 1; hence not 3 divides 709 by NAT_4:9;
709 = 5*141 + 4; hence not 5 divides 709 by NAT_4:9;
709 = 7*101 + 2; hence not 7 divides 709 by NAT_4:9;
709 = 11*64 + 5; hence not 11 divides 709 by NAT_4:9;
709 = 13*54 + 7; hence not 13 divides 709 by NAT_4:9;
709 = 17*41 + 12; hence not 17 divides 709 by NAT_4:9;
709 = 19*37 + 6; hence not 19 divides 709 by NAT_4:9;
709 = 23*30 + 19; hence not 23 divides 709 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 709 & n is prime
holds not n divides 709 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
719 is prime
proof
now
719 = 2*359 + 1; hence not 2 divides 719 by NAT_4:9;
719 = 3*239 + 2; hence not 3 divides 719 by NAT_4:9;
719 = 5*143 + 4; hence not 5 divides 719 by NAT_4:9;
719 = 7*102 + 5; hence not 7 divides 719 by NAT_4:9;
719 = 11*65 + 4; hence not 11 divides 719 by NAT_4:9;
719 = 13*55 + 4; hence not 13 divides 719 by NAT_4:9;
719 = 17*42 + 5; hence not 17 divides 719 by NAT_4:9;
719 = 19*37 + 16; hence not 19 divides 719 by NAT_4:9;
719 = 23*31 + 6; hence not 23 divides 719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 719 & n is prime
holds not n divides 719 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
727 is prime
proof
now
727 = 2*363 + 1; hence not 2 divides 727 by NAT_4:9;
727 = 3*242 + 1; hence not 3 divides 727 by NAT_4:9;
727 = 5*145 + 2; hence not 5 divides 727 by NAT_4:9;
727 = 7*103 + 6; hence not 7 divides 727 by NAT_4:9;
727 = 11*66 + 1; hence not 11 divides 727 by NAT_4:9;
727 = 13*55 + 12; hence not 13 divides 727 by NAT_4:9;
727 = 17*42 + 13; hence not 17 divides 727 by NAT_4:9;
727 = 19*38 + 5; hence not 19 divides 727 by NAT_4:9;
727 = 23*31 + 14; hence not 23 divides 727 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 727 & n is prime
holds not n divides 727 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
733 is prime
proof
now
733 = 2*366 + 1; hence not 2 divides 733 by NAT_4:9;
733 = 3*244 + 1; hence not 3 divides 733 by NAT_4:9;
733 = 5*146 + 3; hence not 5 divides 733 by NAT_4:9;
733 = 7*104 + 5; hence not 7 divides 733 by NAT_4:9;
733 = 11*66 + 7; hence not 11 divides 733 by NAT_4:9;
733 = 13*56 + 5; hence not 13 divides 733 by NAT_4:9;
733 = 17*43 + 2; hence not 17 divides 733 by NAT_4:9;
733 = 19*38 + 11; hence not 19 divides 733 by NAT_4:9;
733 = 23*31 + 20; hence not 23 divides 733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 733 & n is prime
holds not n divides 733 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
739 is prime
proof
now
739 = 2*369 + 1; hence not 2 divides 739 by NAT_4:9;
739 = 3*246 + 1; hence not 3 divides 739 by NAT_4:9;
739 = 5*147 + 4; hence not 5 divides 739 by NAT_4:9;
739 = 7*105 + 4; hence not 7 divides 739 by NAT_4:9;
739 = 11*67 + 2; hence not 11 divides 739 by NAT_4:9;
739 = 13*56 + 11; hence not 13 divides 739 by NAT_4:9;
739 = 17*43 + 8; hence not 17 divides 739 by NAT_4:9;
739 = 19*38 + 17; hence not 19 divides 739 by NAT_4:9;
739 = 23*32 + 3; hence not 23 divides 739 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 739 & n is prime
holds not n divides 739 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
743 is prime
proof
now
743 = 2*371 + 1; hence not 2 divides 743 by NAT_4:9;
743 = 3*247 + 2; hence not 3 divides 743 by NAT_4:9;
743 = 5*148 + 3; hence not 5 divides 743 by NAT_4:9;
743 = 7*106 + 1; hence not 7 divides 743 by NAT_4:9;
743 = 11*67 + 6; hence not 11 divides 743 by NAT_4:9;
743 = 13*57 + 2; hence not 13 divides 743 by NAT_4:9;
743 = 17*43 + 12; hence not 17 divides 743 by NAT_4:9;
743 = 19*39 + 2; hence not 19 divides 743 by NAT_4:9;
743 = 23*32 + 7; hence not 23 divides 743 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 743 & n is prime
holds not n divides 743 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
751 is prime
proof
now
751 = 2*375 + 1; hence not 2 divides 751 by NAT_4:9;
751 = 3*250 + 1; hence not 3 divides 751 by NAT_4:9;
751 = 5*150 + 1; hence not 5 divides 751 by NAT_4:9;
751 = 7*107 + 2; hence not 7 divides 751 by NAT_4:9;
751 = 11*68 + 3; hence not 11 divides 751 by NAT_4:9;
751 = 13*57 + 10; hence not 13 divides 751 by NAT_4:9;
751 = 17*44 + 3; hence not 17 divides 751 by NAT_4:9;
751 = 19*39 + 10; hence not 19 divides 751 by NAT_4:9;
751 = 23*32 + 15; hence not 23 divides 751 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 751 & n is prime
holds not n divides 751 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
757 is prime
proof
now
757 = 2*378 + 1; hence not 2 divides 757 by NAT_4:9;
757 = 3*252 + 1; hence not 3 divides 757 by NAT_4:9;
757 = 5*151 + 2; hence not 5 divides 757 by NAT_4:9;
757 = 7*108 + 1; hence not 7 divides 757 by NAT_4:9;
757 = 11*68 + 9; hence not 11 divides 757 by NAT_4:9;
757 = 13*58 + 3; hence not 13 divides 757 by NAT_4:9;
757 = 17*44 + 9; hence not 17 divides 757 by NAT_4:9;
757 = 19*39 + 16; hence not 19 divides 757 by NAT_4:9;
757 = 23*32 + 21; hence not 23 divides 757 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 757 & n is prime
holds not n divides 757 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
761 is prime
proof
now
761 = 2*380 + 1; hence not 2 divides 761 by NAT_4:9;
761 = 3*253 + 2; hence not 3 divides 761 by NAT_4:9;
761 = 5*152 + 1; hence not 5 divides 761 by NAT_4:9;
761 = 7*108 + 5; hence not 7 divides 761 by NAT_4:9;
761 = 11*69 + 2; hence not 11 divides 761 by NAT_4:9;
761 = 13*58 + 7; hence not 13 divides 761 by NAT_4:9;
761 = 17*44 + 13; hence not 17 divides 761 by NAT_4:9;
761 = 19*40 + 1; hence not 19 divides 761 by NAT_4:9;
761 = 23*33 + 2; hence not 23 divides 761 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 761 & n is prime
holds not n divides 761 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
769 is prime
proof
now
769 = 2*384 + 1; hence not 2 divides 769 by NAT_4:9;
769 = 3*256 + 1; hence not 3 divides 769 by NAT_4:9;
769 = 5*153 + 4; hence not 5 divides 769 by NAT_4:9;
769 = 7*109 + 6; hence not 7 divides 769 by NAT_4:9;
769 = 11*69 + 10; hence not 11 divides 769 by NAT_4:9;
769 = 13*59 + 2; hence not 13 divides 769 by NAT_4:9;
769 = 17*45 + 4; hence not 17 divides 769 by NAT_4:9;
769 = 19*40 + 9; hence not 19 divides 769 by NAT_4:9;
769 = 23*33 + 10; hence not 23 divides 769 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 769 & n is prime
holds not n divides 769 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
773 is prime
proof
now
773 = 2*386 + 1; hence not 2 divides 773 by NAT_4:9;
773 = 3*257 + 2; hence not 3 divides 773 by NAT_4:9;
773 = 5*154 + 3; hence not 5 divides 773 by NAT_4:9;
773 = 7*110 + 3; hence not 7 divides 773 by NAT_4:9;
773 = 11*70 + 3; hence not 11 divides 773 by NAT_4:9;
773 = 13*59 + 6; hence not 13 divides 773 by NAT_4:9;
773 = 17*45 + 8; hence not 17 divides 773 by NAT_4:9;
773 = 19*40 + 13; hence not 19 divides 773 by NAT_4:9;
773 = 23*33 + 14; hence not 23 divides 773 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 773 & n is prime
holds not n divides 773 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
787 is prime
proof
now
787 = 2*393 + 1; hence not 2 divides 787 by NAT_4:9;
787 = 3*262 + 1; hence not 3 divides 787 by NAT_4:9;
787 = 5*157 + 2; hence not 5 divides 787 by NAT_4:9;
787 = 7*112 + 3; hence not 7 divides 787 by NAT_4:9;
787 = 11*71 + 6; hence not 11 divides 787 by NAT_4:9;
787 = 13*60 + 7; hence not 13 divides 787 by NAT_4:9;
787 = 17*46 + 5; hence not 17 divides 787 by NAT_4:9;
787 = 19*41 + 8; hence not 19 divides 787 by NAT_4:9;
787 = 23*34 + 5; hence not 23 divides 787 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 787 & n is prime
holds not n divides 787 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
797 is prime
proof
now
797 = 2*398 + 1; hence not 2 divides 797 by NAT_4:9;
797 = 3*265 + 2; hence not 3 divides 797 by NAT_4:9;
797 = 5*159 + 2; hence not 5 divides 797 by NAT_4:9;
797 = 7*113 + 6; hence not 7 divides 797 by NAT_4:9;
797 = 11*72 + 5; hence not 11 divides 797 by NAT_4:9;
797 = 13*61 + 4; hence not 13 divides 797 by NAT_4:9;
797 = 17*46 + 15; hence not 17 divides 797 by NAT_4:9;
797 = 19*41 + 18; hence not 19 divides 797 by NAT_4:9;
797 = 23*34 + 15; hence not 23 divides 797 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 797 & n is prime
holds not n divides 797 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
809 is prime
proof
now
809 = 2*404 + 1; hence not 2 divides 809 by NAT_4:9;
809 = 3*269 + 2; hence not 3 divides 809 by NAT_4:9;
809 = 5*161 + 4; hence not 5 divides 809 by NAT_4:9;
809 = 7*115 + 4; hence not 7 divides 809 by NAT_4:9;
809 = 11*73 + 6; hence not 11 divides 809 by NAT_4:9;
809 = 13*62 + 3; hence not 13 divides 809 by NAT_4:9;
809 = 17*47 + 10; hence not 17 divides 809 by NAT_4:9;
809 = 19*42 + 11; hence not 19 divides 809 by NAT_4:9;
809 = 23*35 + 4; hence not 23 divides 809 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 809 & n is prime
holds not n divides 809 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
811 is prime
proof
now
811 = 2*405 + 1; hence not 2 divides 811 by NAT_4:9;
811 = 3*270 + 1; hence not 3 divides 811 by NAT_4:9;
811 = 5*162 + 1; hence not 5 divides 811 by NAT_4:9;
811 = 7*115 + 6; hence not 7 divides 811 by NAT_4:9;
811 = 11*73 + 8; hence not 11 divides 811 by NAT_4:9;
811 = 13*62 + 5; hence not 13 divides 811 by NAT_4:9;
811 = 17*47 + 12; hence not 17 divides 811 by NAT_4:9;
811 = 19*42 + 13; hence not 19 divides 811 by NAT_4:9;
811 = 23*35 + 6; hence not 23 divides 811 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 811 & n is prime
holds not n divides 811 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
821 is prime
proof
now
821 = 2*410 + 1; hence not 2 divides 821 by NAT_4:9;
821 = 3*273 + 2; hence not 3 divides 821 by NAT_4:9;
821 = 5*164 + 1; hence not 5 divides 821 by NAT_4:9;
821 = 7*117 + 2; hence not 7 divides 821 by NAT_4:9;
821 = 11*74 + 7; hence not 11 divides 821 by NAT_4:9;
821 = 13*63 + 2; hence not 13 divides 821 by NAT_4:9;
821 = 17*48 + 5; hence not 17 divides 821 by NAT_4:9;
821 = 19*43 + 4; hence not 19 divides 821 by NAT_4:9;
821 = 23*35 + 16; hence not 23 divides 821 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 821 & n is prime
holds not n divides 821 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
823 is prime
proof
now
823 = 2*411 + 1; hence not 2 divides 823 by NAT_4:9;
823 = 3*274 + 1; hence not 3 divides 823 by NAT_4:9;
823 = 5*164 + 3; hence not 5 divides 823 by NAT_4:9;
823 = 7*117 + 4; hence not 7 divides 823 by NAT_4:9;
823 = 11*74 + 9; hence not 11 divides 823 by NAT_4:9;
823 = 13*63 + 4; hence not 13 divides 823 by NAT_4:9;
823 = 17*48 + 7; hence not 17 divides 823 by NAT_4:9;
823 = 19*43 + 6; hence not 19 divides 823 by NAT_4:9;
823 = 23*35 + 18; hence not 23 divides 823 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 823 & n is prime
holds not n divides 823 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
827 is prime
proof
now
827 = 2*413 + 1; hence not 2 divides 827 by NAT_4:9;
827 = 3*275 + 2; hence not 3 divides 827 by NAT_4:9;
827 = 5*165 + 2; hence not 5 divides 827 by NAT_4:9;
827 = 7*118 + 1; hence not 7 divides 827 by NAT_4:9;
827 = 11*75 + 2; hence not 11 divides 827 by NAT_4:9;
827 = 13*63 + 8; hence not 13 divides 827 by NAT_4:9;
827 = 17*48 + 11; hence not 17 divides 827 by NAT_4:9;
827 = 19*43 + 10; hence not 19 divides 827 by NAT_4:9;
827 = 23*35 + 22; hence not 23 divides 827 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 827 & n is prime
holds not n divides 827 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT
theorem
829 is prime
proof
now
829 = 2*414 + 1; hence not 2 divides 829 by NAT_4:9;
829 = 3*276 + 1; hence not 3 divides 829 by NAT_4:9;
829 = 5*165 + 4; hence not 5 divides 829 by NAT_4:9;
829 = 7*118 + 3; hence not 7 divides 829 by NAT_4:9;
829 = 11*75 + 4; hence not 11 divides 829 by NAT_4:9;
829 = 13*63 + 10; hence not 13 divides 829 by NAT_4:9;
829 = 17*48 + 13; hence not 17 divides 829 by NAT_4:9;
829 = 19*43 + 12; hence not 19 divides 829 by NAT_4:9;
829 = 23*36 + 1; hence not 23 divides 829 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 829 & n is prime
holds not n divides 829 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
839 is prime
proof
now
839 = 2*419 + 1; hence not 2 divides 839 by NAT_4:9;
839 = 3*279 + 2; hence not 3 divides 839 by NAT_4:9;
839 = 5*167 + 4; hence not 5 divides 839 by NAT_4:9;
839 = 7*119 + 6; hence not 7 divides 839 by NAT_4:9;
839 = 11*76 + 3; hence not 11 divides 839 by NAT_4:9;
839 = 13*64 + 7; hence not 13 divides 839 by NAT_4:9;
839 = 17*49 + 6; hence not 17 divides 839 by NAT_4:9;
839 = 19*44 + 3; hence not 19 divides 839 by NAT_4:9;
839 = 23*36 + 11; hence not 23 divides 839 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 839 & n is prime
holds not n divides 839 by XPRIMET1:18;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
853 is prime
proof
now
853 = 2*426 + 1; hence not 2 divides 853 by NAT_4:9;
853 = 3*284 + 1; hence not 3 divides 853 by NAT_4:9;
853 = 5*170 + 3; hence not 5 divides 853 by NAT_4:9;
853 = 7*121 + 6; hence not 7 divides 853 by NAT_4:9;
853 = 11*77 + 6; hence not 11 divides 853 by NAT_4:9;
853 = 13*65 + 8; hence not 13 divides 853 by NAT_4:9;
853 = 17*50 + 3; hence not 17 divides 853 by NAT_4:9;
853 = 19*44 + 17; hence not 19 divides 853 by NAT_4:9;
853 = 23*37 + 2; hence not 23 divides 853 by NAT_4:9;
853 = 29*29 + 12; hence not 29 divides 853 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 853 & n is prime
holds not n divides 853 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
857 is prime
proof
now
857 = 2*428 + 1; hence not 2 divides 857 by NAT_4:9;
857 = 3*285 + 2; hence not 3 divides 857 by NAT_4:9;
857 = 5*171 + 2; hence not 5 divides 857 by NAT_4:9;
857 = 7*122 + 3; hence not 7 divides 857 by NAT_4:9;
857 = 11*77 + 10; hence not 11 divides 857 by NAT_4:9;
857 = 13*65 + 12; hence not 13 divides 857 by NAT_4:9;
857 = 17*50 + 7; hence not 17 divides 857 by NAT_4:9;
857 = 19*45 + 2; hence not 19 divides 857 by NAT_4:9;
857 = 23*37 + 6; hence not 23 divides 857 by NAT_4:9;
857 = 29*29 + 16; hence not 29 divides 857 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 857 & n is prime
holds not n divides 857 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT
theorem
859 is prime
proof
now
859 = 2*429 + 1; hence not 2 divides 859 by NAT_4:9;
859 = 3*286 + 1; hence not 3 divides 859 by NAT_4:9;
859 = 5*171 + 4; hence not 5 divides 859 by NAT_4:9;
859 = 7*122 + 5; hence not 7 divides 859 by NAT_4:9;
859 = 11*78 + 1; hence not 11 divides 859 by NAT_4:9;
859 = 13*66 + 1; hence not 13 divides 859 by NAT_4:9;
859 = 17*50 + 9; hence not 17 divides 859 by NAT_4:9;
859 = 19*45 + 4; hence not 19 divides 859 by NAT_4:9;
859 = 23*37 + 8; hence not 23 divides 859 by NAT_4:9;
859 = 29*29 + 18; hence not 29 divides 859 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 859 & n is prime
holds not n divides 859 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
863 is prime
proof
now
863 = 2*431 + 1; hence not 2 divides 863 by NAT_4:9;
863 = 3*287 + 2; hence not 3 divides 863 by NAT_4:9;
863 = 5*172 + 3; hence not 5 divides 863 by NAT_4:9;
863 = 7*123 + 2; hence not 7 divides 863 by NAT_4:9;
863 = 11*78 + 5; hence not 11 divides 863 by NAT_4:9;
863 = 13*66 + 5; hence not 13 divides 863 by NAT_4:9;
863 = 17*50 + 13; hence not 17 divides 863 by NAT_4:9;
863 = 19*45 + 8; hence not 19 divides 863 by NAT_4:9;
863 = 23*37 + 12; hence not 23 divides 863 by NAT_4:9;
863 = 29*29 + 22; hence not 29 divides 863 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 863 & n is prime
holds not n divides 863 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
877 is prime
proof
now
877 = 2*438 + 1; hence not 2 divides 877 by NAT_4:9;
877 = 3*292 + 1; hence not 3 divides 877 by NAT_4:9;
877 = 5*175 + 2; hence not 5 divides 877 by NAT_4:9;
877 = 7*125 + 2; hence not 7 divides 877 by NAT_4:9;
877 = 11*79 + 8; hence not 11 divides 877 by NAT_4:9;
877 = 13*67 + 6; hence not 13 divides 877 by NAT_4:9;
877 = 17*51 + 10; hence not 17 divides 877 by NAT_4:9;
877 = 19*46 + 3; hence not 19 divides 877 by NAT_4:9;
877 = 23*38 + 3; hence not 23 divides 877 by NAT_4:9;
877 = 29*30 + 7; hence not 29 divides 877 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 877 & n is prime
holds not n divides 877 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
881 is prime
proof
now
881 = 2*440 + 1; hence not 2 divides 881 by NAT_4:9;
881 = 3*293 + 2; hence not 3 divides 881 by NAT_4:9;
881 = 5*176 + 1; hence not 5 divides 881 by NAT_4:9;
881 = 7*125 + 6; hence not 7 divides 881 by NAT_4:9;
881 = 11*80 + 1; hence not 11 divides 881 by NAT_4:9;
881 = 13*67 + 10; hence not 13 divides 881 by NAT_4:9;
881 = 17*51 + 14; hence not 17 divides 881 by NAT_4:9;
881 = 19*46 + 7; hence not 19 divides 881 by NAT_4:9;
881 = 23*38 + 7; hence not 23 divides 881 by NAT_4:9;
881 = 29*30 + 11; hence not 29 divides 881 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 881 & n is prime
holds not n divides 881 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT
theorem
883 is prime
proof
now
883 = 2*441 + 1; hence not 2 divides 883 by NAT_4:9;
883 = 3*294 + 1; hence not 3 divides 883 by NAT_4:9;
883 = 5*176 + 3; hence not 5 divides 883 by NAT_4:9;
883 = 7*126 + 1; hence not 7 divides 883 by NAT_4:9;
883 = 11*80 + 3; hence not 11 divides 883 by NAT_4:9;
883 = 13*67 + 12; hence not 13 divides 883 by NAT_4:9;
883 = 17*51 + 16; hence not 17 divides 883 by NAT_4:9;
883 = 19*46 + 9; hence not 19 divides 883 by NAT_4:9;
883 = 23*38 + 9; hence not 23 divides 883 by NAT_4:9;
883 = 29*30 + 13; hence not 29 divides 883 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 883 & n is prime
holds not n divides 883 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
887 is prime
proof
now
887 = 2*443 + 1; hence not 2 divides 887 by NAT_4:9;
887 = 3*295 + 2; hence not 3 divides 887 by NAT_4:9;
887 = 5*177 + 2; hence not 5 divides 887 by NAT_4:9;
887 = 7*126 + 5; hence not 7 divides 887 by NAT_4:9;
887 = 11*80 + 7; hence not 11 divides 887 by NAT_4:9;
887 = 13*68 + 3; hence not 13 divides 887 by NAT_4:9;
887 = 17*52 + 3; hence not 17 divides 887 by NAT_4:9;
887 = 19*46 + 13; hence not 19 divides 887 by NAT_4:9;
887 = 23*38 + 13; hence not 23 divides 887 by NAT_4:9;
887 = 29*30 + 17; hence not 29 divides 887 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 887 & n is prime
holds not n divides 887 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
907 is prime
proof
now
907 = 2*453 + 1; hence not 2 divides 907 by NAT_4:9;
907 = 3*302 + 1; hence not 3 divides 907 by NAT_4:9;
907 = 5*181 + 2; hence not 5 divides 907 by NAT_4:9;
907 = 7*129 + 4; hence not 7 divides 907 by NAT_4:9;
907 = 11*82 + 5; hence not 11 divides 907 by NAT_4:9;
907 = 13*69 + 10; hence not 13 divides 907 by NAT_4:9;
907 = 17*53 + 6; hence not 17 divides 907 by NAT_4:9;
907 = 19*47 + 14; hence not 19 divides 907 by NAT_4:9;
907 = 23*39 + 10; hence not 23 divides 907 by NAT_4:9;
907 = 29*31 + 8; hence not 29 divides 907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 907 & n is prime
holds not n divides 907 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
911 is prime
proof
now
911 = 2*455 + 1; hence not 2 divides 911 by NAT_4:9;
911 = 3*303 + 2; hence not 3 divides 911 by NAT_4:9;
911 = 5*182 + 1; hence not 5 divides 911 by NAT_4:9;
911 = 7*130 + 1; hence not 7 divides 911 by NAT_4:9;
911 = 11*82 + 9; hence not 11 divides 911 by NAT_4:9;
911 = 13*70 + 1; hence not 13 divides 911 by NAT_4:9;
911 = 17*53 + 10; hence not 17 divides 911 by NAT_4:9;
911 = 19*47 + 18; hence not 19 divides 911 by NAT_4:9;
911 = 23*39 + 14; hence not 23 divides 911 by NAT_4:9;
911 = 29*31 + 12; hence not 29 divides 911 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 911 & n is prime
holds not n divides 911 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
919 is prime
proof
now
919 = 2*459 + 1; hence not 2 divides 919 by NAT_4:9;
919 = 3*306 + 1; hence not 3 divides 919 by NAT_4:9;
919 = 5*183 + 4; hence not 5 divides 919 by NAT_4:9;
919 = 7*131 + 2; hence not 7 divides 919 by NAT_4:9;
919 = 11*83 + 6; hence not 11 divides 919 by NAT_4:9;
919 = 13*70 + 9; hence not 13 divides 919 by NAT_4:9;
919 = 17*54 + 1; hence not 17 divides 919 by NAT_4:9;
919 = 19*48 + 7; hence not 19 divides 919 by NAT_4:9;
919 = 23*39 + 22; hence not 23 divides 919 by NAT_4:9;
919 = 29*31 + 20; hence not 29 divides 919 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 919 & n is prime
holds not n divides 919 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
929 is prime
proof
now
929 = 2*464 + 1; hence not 2 divides 929 by NAT_4:9;
929 = 3*309 + 2; hence not 3 divides 929 by NAT_4:9;
929 = 5*185 + 4; hence not 5 divides 929 by NAT_4:9;
929 = 7*132 + 5; hence not 7 divides 929 by NAT_4:9;
929 = 11*84 + 5; hence not 11 divides 929 by NAT_4:9;
929 = 13*71 + 6; hence not 13 divides 929 by NAT_4:9;
929 = 17*54 + 11; hence not 17 divides 929 by NAT_4:9;
929 = 19*48 + 17; hence not 19 divides 929 by NAT_4:9;
929 = 23*40 + 9; hence not 23 divides 929 by NAT_4:9;
929 = 29*32 + 1; hence not 29 divides 929 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 929 & n is prime
holds not n divides 929 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
937 is prime
proof
now
937 = 2*468 + 1; hence not 2 divides 937 by NAT_4:9;
937 = 3*312 + 1; hence not 3 divides 937 by NAT_4:9;
937 = 5*187 + 2; hence not 5 divides 937 by NAT_4:9;
937 = 7*133 + 6; hence not 7 divides 937 by NAT_4:9;
937 = 11*85 + 2; hence not 11 divides 937 by NAT_4:9;
937 = 13*72 + 1; hence not 13 divides 937 by NAT_4:9;
937 = 17*55 + 2; hence not 17 divides 937 by NAT_4:9;
937 = 19*49 + 6; hence not 19 divides 937 by NAT_4:9;
937 = 23*40 + 17; hence not 23 divides 937 by NAT_4:9;
937 = 29*32 + 9; hence not 29 divides 937 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 937 & n is prime
holds not n divides 937 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
941 is prime
proof
now
941 = 2*470 + 1; hence not 2 divides 941 by NAT_4:9;
941 = 3*313 + 2; hence not 3 divides 941 by NAT_4:9;
941 = 5*188 + 1; hence not 5 divides 941 by NAT_4:9;
941 = 7*134 + 3; hence not 7 divides 941 by NAT_4:9;
941 = 11*85 + 6; hence not 11 divides 941 by NAT_4:9;
941 = 13*72 + 5; hence not 13 divides 941 by NAT_4:9;
941 = 17*55 + 6; hence not 17 divides 941 by NAT_4:9;
941 = 19*49 + 10; hence not 19 divides 941 by NAT_4:9;
941 = 23*40 + 21; hence not 23 divides 941 by NAT_4:9;
941 = 29*32 + 13; hence not 29 divides 941 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 941 & n is prime
holds not n divides 941 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
947 is prime
proof
now
947 = 2*473 + 1; hence not 2 divides 947 by NAT_4:9;
947 = 3*315 + 2; hence not 3 divides 947 by NAT_4:9;
947 = 5*189 + 2; hence not 5 divides 947 by NAT_4:9;
947 = 7*135 + 2; hence not 7 divides 947 by NAT_4:9;
947 = 11*86 + 1; hence not 11 divides 947 by NAT_4:9;
947 = 13*72 + 11; hence not 13 divides 947 by NAT_4:9;
947 = 17*55 + 12; hence not 17 divides 947 by NAT_4:9;
947 = 19*49 + 16; hence not 19 divides 947 by NAT_4:9;
947 = 23*41 + 4; hence not 23 divides 947 by NAT_4:9;
947 = 29*32 + 19; hence not 29 divides 947 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 947 & n is prime
holds not n divides 947 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
953 is prime
proof
now
953 = 2*476 + 1; hence not 2 divides 953 by NAT_4:9;
953 = 3*317 + 2; hence not 3 divides 953 by NAT_4:9;
953 = 5*190 + 3; hence not 5 divides 953 by NAT_4:9;
953 = 7*136 + 1; hence not 7 divides 953 by NAT_4:9;
953 = 11*86 + 7; hence not 11 divides 953 by NAT_4:9;
953 = 13*73 + 4; hence not 13 divides 953 by NAT_4:9;
953 = 17*56 + 1; hence not 17 divides 953 by NAT_4:9;
953 = 19*50 + 3; hence not 19 divides 953 by NAT_4:9;
953 = 23*41 + 10; hence not 23 divides 953 by NAT_4:9;
953 = 29*32 + 25; hence not 29 divides 953 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 953 & n is prime
holds not n divides 953 by XPRIMET1:20;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
967 is prime
proof
now
967 = 2*483 + 1; hence not 2 divides 967 by NAT_4:9;
967 = 3*322 + 1; hence not 3 divides 967 by NAT_4:9;
967 = 5*193 + 2; hence not 5 divides 967 by NAT_4:9;
967 = 7*138 + 1; hence not 7 divides 967 by NAT_4:9;
967 = 11*87 + 10; hence not 11 divides 967 by NAT_4:9;
967 = 13*74 + 5; hence not 13 divides 967 by NAT_4:9;
967 = 17*56 + 15; hence not 17 divides 967 by NAT_4:9;
967 = 19*50 + 17; hence not 19 divides 967 by NAT_4:9;
967 = 23*42 + 1; hence not 23 divides 967 by NAT_4:9;
967 = 29*33 + 10; hence not 29 divides 967 by NAT_4:9;
967 = 31*31 + 6; hence not 31 divides 967 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 967 & n is prime
holds not n divides 967 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
971 is prime
proof
now
971 = 2*485 + 1; hence not 2 divides 971 by NAT_4:9;
971 = 3*323 + 2; hence not 3 divides 971 by NAT_4:9;
971 = 5*194 + 1; hence not 5 divides 971 by NAT_4:9;
971 = 7*138 + 5; hence not 7 divides 971 by NAT_4:9;
971 = 11*88 + 3; hence not 11 divides 971 by NAT_4:9;
971 = 13*74 + 9; hence not 13 divides 971 by NAT_4:9;
971 = 17*57 + 2; hence not 17 divides 971 by NAT_4:9;
971 = 19*51 + 2; hence not 19 divides 971 by NAT_4:9;
971 = 23*42 + 5; hence not 23 divides 971 by NAT_4:9;
971 = 29*33 + 14; hence not 29 divides 971 by NAT_4:9;
971 = 31*31 + 10; hence not 31 divides 971 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 971 & n is prime
holds not n divides 971 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
977 is prime
proof
now
977 = 2*488 + 1; hence not 2 divides 977 by NAT_4:9;
977 = 3*325 + 2; hence not 3 divides 977 by NAT_4:9;
977 = 5*195 + 2; hence not 5 divides 977 by NAT_4:9;
977 = 7*139 + 4; hence not 7 divides 977 by NAT_4:9;
977 = 11*88 + 9; hence not 11 divides 977 by NAT_4:9;
977 = 13*75 + 2; hence not 13 divides 977 by NAT_4:9;
977 = 17*57 + 8; hence not 17 divides 977 by NAT_4:9;
977 = 19*51 + 8; hence not 19 divides 977 by NAT_4:9;
977 = 23*42 + 11; hence not 23 divides 977 by NAT_4:9;
977 = 29*33 + 20; hence not 29 divides 977 by NAT_4:9;
977 = 31*31 + 16; hence not 31 divides 977 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 977 & n is prime
holds not n divides 977 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
983 is prime
proof
now
983 = 2*491 + 1; hence not 2 divides 983 by NAT_4:9;
983 = 3*327 + 2; hence not 3 divides 983 by NAT_4:9;
983 = 5*196 + 3; hence not 5 divides 983 by NAT_4:9;
983 = 7*140 + 3; hence not 7 divides 983 by NAT_4:9;
983 = 11*89 + 4; hence not 11 divides 983 by NAT_4:9;
983 = 13*75 + 8; hence not 13 divides 983 by NAT_4:9;
983 = 17*57 + 14; hence not 17 divides 983 by NAT_4:9;
983 = 19*51 + 14; hence not 19 divides 983 by NAT_4:9;
983 = 23*42 + 17; hence not 23 divides 983 by NAT_4:9;
983 = 29*33 + 26; hence not 29 divides 983 by NAT_4:9;
983 = 31*31 + 22; hence not 31 divides 983 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 983 & n is prime
holds not n divides 983 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
991 is prime
proof
now
991 = 2*495 + 1; hence not 2 divides 991 by NAT_4:9;
991 = 3*330 + 1; hence not 3 divides 991 by NAT_4:9;
991 = 5*198 + 1; hence not 5 divides 991 by NAT_4:9;
991 = 7*141 + 4; hence not 7 divides 991 by NAT_4:9;
991 = 11*90 + 1; hence not 11 divides 991 by NAT_4:9;
991 = 13*76 + 3; hence not 13 divides 991 by NAT_4:9;
991 = 17*58 + 5; hence not 17 divides 991 by NAT_4:9;
991 = 19*52 + 3; hence not 19 divides 991 by NAT_4:9;
991 = 23*43 + 2; hence not 23 divides 991 by NAT_4:9;
991 = 29*34 + 5; hence not 29 divides 991 by NAT_4:9;
991 = 31*31 + 30; hence not 31 divides 991 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 991 & n is prime
holds not n divides 991 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
997 is prime
proof
now
997 = 2*498 + 1; hence not 2 divides 997 by NAT_4:9;
997 = 3*332 + 1; hence not 3 divides 997 by NAT_4:9;
997 = 5*199 + 2; hence not 5 divides 997 by NAT_4:9;
997 = 7*142 + 3; hence not 7 divides 997 by NAT_4:9;
997 = 11*90 + 7; hence not 11 divides 997 by NAT_4:9;
997 = 13*76 + 9; hence not 13 divides 997 by NAT_4:9;
997 = 17*58 + 11; hence not 17 divides 997 by NAT_4:9;
997 = 19*52 + 9; hence not 19 divides 997 by NAT_4:9;
997 = 23*43 + 8; hence not 23 divides 997 by NAT_4:9;
997 = 29*34 + 11; hence not 29 divides 997 by NAT_4:9;
997 = 31*32 + 5; hence not 31 divides 997 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 997 & n is prime
holds not n divides 997 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1009 is prime
proof
now
1009 = 2*504 + 1; hence not 2 divides 1009 by NAT_4:9;
1009 = 3*336 + 1; hence not 3 divides 1009 by NAT_4:9;
1009 = 5*201 + 4; hence not 5 divides 1009 by NAT_4:9;
1009 = 7*144 + 1; hence not 7 divides 1009 by NAT_4:9;
1009 = 11*91 + 8; hence not 11 divides 1009 by NAT_4:9;
1009 = 13*77 + 8; hence not 13 divides 1009 by NAT_4:9;
1009 = 17*59 + 6; hence not 17 divides 1009 by NAT_4:9;
1009 = 19*53 + 2; hence not 19 divides 1009 by NAT_4:9;
1009 = 23*43 + 20; hence not 23 divides 1009 by NAT_4:9;
1009 = 29*34 + 23; hence not 29 divides 1009 by NAT_4:9;
1009 = 31*32 + 17; hence not 31 divides 1009 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1009 & n is prime
holds not n divides 1009 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1013 is prime
proof
now
1013 = 2*506 + 1; hence not 2 divides 1013 by NAT_4:9;
1013 = 3*337 + 2; hence not 3 divides 1013 by NAT_4:9;
1013 = 5*202 + 3; hence not 5 divides 1013 by NAT_4:9;
1013 = 7*144 + 5; hence not 7 divides 1013 by NAT_4:9;
1013 = 11*92 + 1; hence not 11 divides 1013 by NAT_4:9;
1013 = 13*77 + 12; hence not 13 divides 1013 by NAT_4:9;
1013 = 17*59 + 10; hence not 17 divides 1013 by NAT_4:9;
1013 = 19*53 + 6; hence not 19 divides 1013 by NAT_4:9;
1013 = 23*44 + 1; hence not 23 divides 1013 by NAT_4:9;
1013 = 29*34 + 27; hence not 29 divides 1013 by NAT_4:9;
1013 = 31*32 + 21; hence not 31 divides 1013 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1013 & n is prime
holds not n divides 1013 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1019 is prime
proof
now
1019 = 2*509 + 1; hence not 2 divides 1019 by NAT_4:9;
1019 = 3*339 + 2; hence not 3 divides 1019 by NAT_4:9;
1019 = 5*203 + 4; hence not 5 divides 1019 by NAT_4:9;
1019 = 7*145 + 4; hence not 7 divides 1019 by NAT_4:9;
1019 = 11*92 + 7; hence not 11 divides 1019 by NAT_4:9;
1019 = 13*78 + 5; hence not 13 divides 1019 by NAT_4:9;
1019 = 17*59 + 16; hence not 17 divides 1019 by NAT_4:9;
1019 = 19*53 + 12; hence not 19 divides 1019 by NAT_4:9;
1019 = 23*44 + 7; hence not 23 divides 1019 by NAT_4:9;
1019 = 29*35 + 4; hence not 29 divides 1019 by NAT_4:9;
1019 = 31*32 + 27; hence not 31 divides 1019 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1019 & n is prime
holds not n divides 1019 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1021 is prime
proof
now
1021 = 2*510 + 1; hence not 2 divides 1021 by NAT_4:9;
1021 = 3*340 + 1; hence not 3 divides 1021 by NAT_4:9;
1021 = 5*204 + 1; hence not 5 divides 1021 by NAT_4:9;
1021 = 7*145 + 6; hence not 7 divides 1021 by NAT_4:9;
1021 = 11*92 + 9; hence not 11 divides 1021 by NAT_4:9;
1021 = 13*78 + 7; hence not 13 divides 1021 by NAT_4:9;
1021 = 17*60 + 1; hence not 17 divides 1021 by NAT_4:9;
1021 = 19*53 + 14; hence not 19 divides 1021 by NAT_4:9;
1021 = 23*44 + 9; hence not 23 divides 1021 by NAT_4:9;
1021 = 29*35 + 6; hence not 29 divides 1021 by NAT_4:9;
1021 = 31*32 + 29; hence not 31 divides 1021 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1021 & n is prime
holds not n divides 1021 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1031 is prime
proof
now
1031 = 2*515 + 1; hence not 2 divides 1031 by NAT_4:9;
1031 = 3*343 + 2; hence not 3 divides 1031 by NAT_4:9;
1031 = 5*206 + 1; hence not 5 divides 1031 by NAT_4:9;
1031 = 7*147 + 2; hence not 7 divides 1031 by NAT_4:9;
1031 = 11*93 + 8; hence not 11 divides 1031 by NAT_4:9;
1031 = 13*79 + 4; hence not 13 divides 1031 by NAT_4:9;
1031 = 17*60 + 11; hence not 17 divides 1031 by NAT_4:9;
1031 = 19*54 + 5; hence not 19 divides 1031 by NAT_4:9;
1031 = 23*44 + 19; hence not 23 divides 1031 by NAT_4:9;
1031 = 29*35 + 16; hence not 29 divides 1031 by NAT_4:9;
1031 = 31*33 + 8; hence not 31 divides 1031 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1031 & n is prime
holds not n divides 1031 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1033 is prime
proof
now
1033 = 2*516 + 1; hence not 2 divides 1033 by NAT_4:9;
1033 = 3*344 + 1; hence not 3 divides 1033 by NAT_4:9;
1033 = 5*206 + 3; hence not 5 divides 1033 by NAT_4:9;
1033 = 7*147 + 4; hence not 7 divides 1033 by NAT_4:9;
1033 = 11*93 + 10; hence not 11 divides 1033 by NAT_4:9;
1033 = 13*79 + 6; hence not 13 divides 1033 by NAT_4:9;
1033 = 17*60 + 13; hence not 17 divides 1033 by NAT_4:9;
1033 = 19*54 + 7; hence not 19 divides 1033 by NAT_4:9;
1033 = 23*44 + 21; hence not 23 divides 1033 by NAT_4:9;
1033 = 29*35 + 18; hence not 29 divides 1033 by NAT_4:9;
1033 = 31*33 + 10; hence not 31 divides 1033 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1033 & n is prime
holds not n divides 1033 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1039 is prime
proof
now
1039 = 2*519 + 1; hence not 2 divides 1039 by NAT_4:9;
1039 = 3*346 + 1; hence not 3 divides 1039 by NAT_4:9;
1039 = 5*207 + 4; hence not 5 divides 1039 by NAT_4:9;
1039 = 7*148 + 3; hence not 7 divides 1039 by NAT_4:9;
1039 = 11*94 + 5; hence not 11 divides 1039 by NAT_4:9;
1039 = 13*79 + 12; hence not 13 divides 1039 by NAT_4:9;
1039 = 17*61 + 2; hence not 17 divides 1039 by NAT_4:9;
1039 = 19*54 + 13; hence not 19 divides 1039 by NAT_4:9;
1039 = 23*45 + 4; hence not 23 divides 1039 by NAT_4:9;
1039 = 29*35 + 24; hence not 29 divides 1039 by NAT_4:9;
1039 = 31*33 + 16; hence not 31 divides 1039 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1039 & n is prime
holds not n divides 1039 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1049 is prime
proof
now
1049 = 2*524 + 1; hence not 2 divides 1049 by NAT_4:9;
1049 = 3*349 + 2; hence not 3 divides 1049 by NAT_4:9;
1049 = 5*209 + 4; hence not 5 divides 1049 by NAT_4:9;
1049 = 7*149 + 6; hence not 7 divides 1049 by NAT_4:9;
1049 = 11*95 + 4; hence not 11 divides 1049 by NAT_4:9;
1049 = 13*80 + 9; hence not 13 divides 1049 by NAT_4:9;
1049 = 17*61 + 12; hence not 17 divides 1049 by NAT_4:9;
1049 = 19*55 + 4; hence not 19 divides 1049 by NAT_4:9;
1049 = 23*45 + 14; hence not 23 divides 1049 by NAT_4:9;
1049 = 29*36 + 5; hence not 29 divides 1049 by NAT_4:9;
1049 = 31*33 + 26; hence not 31 divides 1049 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1049 & n is prime
holds not n divides 1049 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1051 is prime
proof
now
1051 = 2*525 + 1; hence not 2 divides 1051 by NAT_4:9;
1051 = 3*350 + 1; hence not 3 divides 1051 by NAT_4:9;
1051 = 5*210 + 1; hence not 5 divides 1051 by NAT_4:9;
1051 = 7*150 + 1; hence not 7 divides 1051 by NAT_4:9;
1051 = 11*95 + 6; hence not 11 divides 1051 by NAT_4:9;
1051 = 13*80 + 11; hence not 13 divides 1051 by NAT_4:9;
1051 = 17*61 + 14; hence not 17 divides 1051 by NAT_4:9;
1051 = 19*55 + 6; hence not 19 divides 1051 by NAT_4:9;
1051 = 23*45 + 16; hence not 23 divides 1051 by NAT_4:9;
1051 = 29*36 + 7; hence not 29 divides 1051 by NAT_4:9;
1051 = 31*33 + 28; hence not 31 divides 1051 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1051 & n is prime
holds not n divides 1051 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1061 is prime
proof
now
1061 = 2*530 + 1; hence not 2 divides 1061 by NAT_4:9;
1061 = 3*353 + 2; hence not 3 divides 1061 by NAT_4:9;
1061 = 5*212 + 1; hence not 5 divides 1061 by NAT_4:9;
1061 = 7*151 + 4; hence not 7 divides 1061 by NAT_4:9;
1061 = 11*96 + 5; hence not 11 divides 1061 by NAT_4:9;
1061 = 13*81 + 8; hence not 13 divides 1061 by NAT_4:9;
1061 = 17*62 + 7; hence not 17 divides 1061 by NAT_4:9;
1061 = 19*55 + 16; hence not 19 divides 1061 by NAT_4:9;
1061 = 23*46 + 3; hence not 23 divides 1061 by NAT_4:9;
1061 = 29*36 + 17; hence not 29 divides 1061 by NAT_4:9;
1061 = 31*34 + 7; hence not 31 divides 1061 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1061 & n is prime
holds not n divides 1061 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1063 is prime
proof
now
1063 = 2*531 + 1; hence not 2 divides 1063 by NAT_4:9;
1063 = 3*354 + 1; hence not 3 divides 1063 by NAT_4:9;
1063 = 5*212 + 3; hence not 5 divides 1063 by NAT_4:9;
1063 = 7*151 + 6; hence not 7 divides 1063 by NAT_4:9;
1063 = 11*96 + 7; hence not 11 divides 1063 by NAT_4:9;
1063 = 13*81 + 10; hence not 13 divides 1063 by NAT_4:9;
1063 = 17*62 + 9; hence not 17 divides 1063 by NAT_4:9;
1063 = 19*55 + 18; hence not 19 divides 1063 by NAT_4:9;
1063 = 23*46 + 5; hence not 23 divides 1063 by NAT_4:9;
1063 = 29*36 + 19; hence not 29 divides 1063 by NAT_4:9;
1063 = 31*34 + 9; hence not 31 divides 1063 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1063 & n is prime
holds not n divides 1063 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1069 is prime
proof
now
1069 = 2*534 + 1; hence not 2 divides 1069 by NAT_4:9;
1069 = 3*356 + 1; hence not 3 divides 1069 by NAT_4:9;
1069 = 5*213 + 4; hence not 5 divides 1069 by NAT_4:9;
1069 = 7*152 + 5; hence not 7 divides 1069 by NAT_4:9;
1069 = 11*97 + 2; hence not 11 divides 1069 by NAT_4:9;
1069 = 13*82 + 3; hence not 13 divides 1069 by NAT_4:9;
1069 = 17*62 + 15; hence not 17 divides 1069 by NAT_4:9;
1069 = 19*56 + 5; hence not 19 divides 1069 by NAT_4:9;
1069 = 23*46 + 11; hence not 23 divides 1069 by NAT_4:9;
1069 = 29*36 + 25; hence not 29 divides 1069 by NAT_4:9;
1069 = 31*34 + 15; hence not 31 divides 1069 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1069 & n is prime
holds not n divides 1069 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
1087 is prime
proof
now
1087 = 2*543 + 1; hence not 2 divides 1087 by NAT_4:9;
1087 = 3*362 + 1; hence not 3 divides 1087 by NAT_4:9;
1087 = 5*217 + 2; hence not 5 divides 1087 by NAT_4:9;
1087 = 7*155 + 2; hence not 7 divides 1087 by NAT_4:9;
1087 = 11*98 + 9; hence not 11 divides 1087 by NAT_4:9;
1087 = 13*83 + 8; hence not 13 divides 1087 by NAT_4:9;
1087 = 17*63 + 16; hence not 17 divides 1087 by NAT_4:9;
1087 = 19*57 + 4; hence not 19 divides 1087 by NAT_4:9;
1087 = 23*47 + 6; hence not 23 divides 1087 by NAT_4:9;
1087 = 29*37 + 14; hence not 29 divides 1087 by NAT_4:9;
1087 = 31*35 + 2; hence not 31 divides 1087 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1087 & n is prime
holds not n divides 1087 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1091 is prime
proof
now
1091 = 2*545 + 1; hence not 2 divides 1091 by NAT_4:9;
1091 = 3*363 + 2; hence not 3 divides 1091 by NAT_4:9;
1091 = 5*218 + 1; hence not 5 divides 1091 by NAT_4:9;
1091 = 7*155 + 6; hence not 7 divides 1091 by NAT_4:9;
1091 = 11*99 + 2; hence not 11 divides 1091 by NAT_4:9;
1091 = 13*83 + 12; hence not 13 divides 1091 by NAT_4:9;
1091 = 17*64 + 3; hence not 17 divides 1091 by NAT_4:9;
1091 = 19*57 + 8; hence not 19 divides 1091 by NAT_4:9;
1091 = 23*47 + 10; hence not 23 divides 1091 by NAT_4:9;
1091 = 29*37 + 18; hence not 29 divides 1091 by NAT_4:9;
1091 = 31*35 + 6; hence not 31 divides 1091 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1091 & n is prime
holds not n divides 1091 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1093 is prime
proof
now
1093 = 2*546 + 1; hence not 2 divides 1093 by NAT_4:9;
1093 = 3*364 + 1; hence not 3 divides 1093 by NAT_4:9;
1093 = 5*218 + 3; hence not 5 divides 1093 by NAT_4:9;
1093 = 7*156 + 1; hence not 7 divides 1093 by NAT_4:9;
1093 = 11*99 + 4; hence not 11 divides 1093 by NAT_4:9;
1093 = 13*84 + 1; hence not 13 divides 1093 by NAT_4:9;
1093 = 17*64 + 5; hence not 17 divides 1093 by NAT_4:9;
1093 = 19*57 + 10; hence not 19 divides 1093 by NAT_4:9;
1093 = 23*47 + 12; hence not 23 divides 1093 by NAT_4:9;
1093 = 29*37 + 20; hence not 29 divides 1093 by NAT_4:9;
1093 = 31*35 + 8; hence not 31 divides 1093 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1093 & n is prime
holds not n divides 1093 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1097 is prime
proof
now
1097 = 2*548 + 1; hence not 2 divides 1097 by NAT_4:9;
1097 = 3*365 + 2; hence not 3 divides 1097 by NAT_4:9;
1097 = 5*219 + 2; hence not 5 divides 1097 by NAT_4:9;
1097 = 7*156 + 5; hence not 7 divides 1097 by NAT_4:9;
1097 = 11*99 + 8; hence not 11 divides 1097 by NAT_4:9;
1097 = 13*84 + 5; hence not 13 divides 1097 by NAT_4:9;
1097 = 17*64 + 9; hence not 17 divides 1097 by NAT_4:9;
1097 = 19*57 + 14; hence not 19 divides 1097 by NAT_4:9;
1097 = 23*47 + 16; hence not 23 divides 1097 by NAT_4:9;
1097 = 29*37 + 24; hence not 29 divides 1097 by NAT_4:9;
1097 = 31*35 + 12; hence not 31 divides 1097 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1097 & n is prime
holds not n divides 1097 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1103 is prime
proof
now
1103 = 2*551 + 1; hence not 2 divides 1103 by NAT_4:9;
1103 = 3*367 + 2; hence not 3 divides 1103 by NAT_4:9;
1103 = 5*220 + 3; hence not 5 divides 1103 by NAT_4:9;
1103 = 7*157 + 4; hence not 7 divides 1103 by NAT_4:9;
1103 = 11*100 + 3; hence not 11 divides 1103 by NAT_4:9;
1103 = 13*84 + 11; hence not 13 divides 1103 by NAT_4:9;
1103 = 17*64 + 15; hence not 17 divides 1103 by NAT_4:9;
1103 = 19*58 + 1; hence not 19 divides 1103 by NAT_4:9;
1103 = 23*47 + 22; hence not 23 divides 1103 by NAT_4:9;
1103 = 29*38 + 1; hence not 29 divides 1103 by NAT_4:9;
1103 = 31*35 + 18; hence not 31 divides 1103 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1103 & n is prime
holds not n divides 1103 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1109 is prime
proof
now
1109 = 2*554 + 1; hence not 2 divides 1109 by NAT_4:9;
1109 = 3*369 + 2; hence not 3 divides 1109 by NAT_4:9;
1109 = 5*221 + 4; hence not 5 divides 1109 by NAT_4:9;
1109 = 7*158 + 3; hence not 7 divides 1109 by NAT_4:9;
1109 = 11*100 + 9; hence not 11 divides 1109 by NAT_4:9;
1109 = 13*85 + 4; hence not 13 divides 1109 by NAT_4:9;
1109 = 17*65 + 4; hence not 17 divides 1109 by NAT_4:9;
1109 = 19*58 + 7; hence not 19 divides 1109 by NAT_4:9;
1109 = 23*48 + 5; hence not 23 divides 1109 by NAT_4:9;
1109 = 29*38 + 7; hence not 29 divides 1109 by NAT_4:9;
1109 = 31*35 + 24; hence not 31 divides 1109 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1109 & n is prime
holds not n divides 1109 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1117 is prime
proof
now
1117 = 2*558 + 1; hence not 2 divides 1117 by NAT_4:9;
1117 = 3*372 + 1; hence not 3 divides 1117 by NAT_4:9;
1117 = 5*223 + 2; hence not 5 divides 1117 by NAT_4:9;
1117 = 7*159 + 4; hence not 7 divides 1117 by NAT_4:9;
1117 = 11*101 + 6; hence not 11 divides 1117 by NAT_4:9;
1117 = 13*85 + 12; hence not 13 divides 1117 by NAT_4:9;
1117 = 17*65 + 12; hence not 17 divides 1117 by NAT_4:9;
1117 = 19*58 + 15; hence not 19 divides 1117 by NAT_4:9;
1117 = 23*48 + 13; hence not 23 divides 1117 by NAT_4:9;
1117 = 29*38 + 15; hence not 29 divides 1117 by NAT_4:9;
1117 = 31*36 + 1; hence not 31 divides 1117 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1117 & n is prime
holds not n divides 1117 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1123 is prime
proof
now
1123 = 2*561 + 1; hence not 2 divides 1123 by NAT_4:9;
1123 = 3*374 + 1; hence not 3 divides 1123 by NAT_4:9;
1123 = 5*224 + 3; hence not 5 divides 1123 by NAT_4:9;
1123 = 7*160 + 3; hence not 7 divides 1123 by NAT_4:9;
1123 = 11*102 + 1; hence not 11 divides 1123 by NAT_4:9;
1123 = 13*86 + 5; hence not 13 divides 1123 by NAT_4:9;
1123 = 17*66 + 1; hence not 17 divides 1123 by NAT_4:9;
1123 = 19*59 + 2; hence not 19 divides 1123 by NAT_4:9;
1123 = 23*48 + 19; hence not 23 divides 1123 by NAT_4:9;
1123 = 29*38 + 21; hence not 29 divides 1123 by NAT_4:9;
1123 = 31*36 + 7; hence not 31 divides 1123 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1123 & n is prime
holds not n divides 1123 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1129 is prime
proof
now
1129 = 2*564 + 1; hence not 2 divides 1129 by NAT_4:9;
1129 = 3*376 + 1; hence not 3 divides 1129 by NAT_4:9;
1129 = 5*225 + 4; hence not 5 divides 1129 by NAT_4:9;
1129 = 7*161 + 2; hence not 7 divides 1129 by NAT_4:9;
1129 = 11*102 + 7; hence not 11 divides 1129 by NAT_4:9;
1129 = 13*86 + 11; hence not 13 divides 1129 by NAT_4:9;
1129 = 17*66 + 7; hence not 17 divides 1129 by NAT_4:9;
1129 = 19*59 + 8; hence not 19 divides 1129 by NAT_4:9;
1129 = 23*49 + 2; hence not 23 divides 1129 by NAT_4:9;
1129 = 29*38 + 27; hence not 29 divides 1129 by NAT_4:9;
1129 = 31*36 + 13; hence not 31 divides 1129 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1129 & n is prime
holds not n divides 1129 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
1151 is prime
proof
now
1151 = 2*575 + 1; hence not 2 divides 1151 by NAT_4:9;
1151 = 3*383 + 2; hence not 3 divides 1151 by NAT_4:9;
1151 = 5*230 + 1; hence not 5 divides 1151 by NAT_4:9;
1151 = 7*164 + 3; hence not 7 divides 1151 by NAT_4:9;
1151 = 11*104 + 7; hence not 11 divides 1151 by NAT_4:9;
1151 = 13*88 + 7; hence not 13 divides 1151 by NAT_4:9;
1151 = 17*67 + 12; hence not 17 divides 1151 by NAT_4:9;
1151 = 19*60 + 11; hence not 19 divides 1151 by NAT_4:9;
1151 = 23*50 + 1; hence not 23 divides 1151 by NAT_4:9;
1151 = 29*39 + 20; hence not 29 divides 1151 by NAT_4:9;
1151 = 31*37 + 4; hence not 31 divides 1151 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1151 & n is prime
holds not n divides 1151 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1153 is prime
proof
now
1153 = 2*576 + 1; hence not 2 divides 1153 by NAT_4:9;
1153 = 3*384 + 1; hence not 3 divides 1153 by NAT_4:9;
1153 = 5*230 + 3; hence not 5 divides 1153 by NAT_4:9;
1153 = 7*164 + 5; hence not 7 divides 1153 by NAT_4:9;
1153 = 11*104 + 9; hence not 11 divides 1153 by NAT_4:9;
1153 = 13*88 + 9; hence not 13 divides 1153 by NAT_4:9;
1153 = 17*67 + 14; hence not 17 divides 1153 by NAT_4:9;
1153 = 19*60 + 13; hence not 19 divides 1153 by NAT_4:9;
1153 = 23*50 + 3; hence not 23 divides 1153 by NAT_4:9;
1153 = 29*39 + 22; hence not 29 divides 1153 by NAT_4:9;
1153 = 31*37 + 6; hence not 31 divides 1153 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1153 & n is prime
holds not n divides 1153 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1163 is prime
proof
now
1163 = 2*581 + 1; hence not 2 divides 1163 by NAT_4:9;
1163 = 3*387 + 2; hence not 3 divides 1163 by NAT_4:9;
1163 = 5*232 + 3; hence not 5 divides 1163 by NAT_4:9;
1163 = 7*166 + 1; hence not 7 divides 1163 by NAT_4:9;
1163 = 11*105 + 8; hence not 11 divides 1163 by NAT_4:9;
1163 = 13*89 + 6; hence not 13 divides 1163 by NAT_4:9;
1163 = 17*68 + 7; hence not 17 divides 1163 by NAT_4:9;
1163 = 19*61 + 4; hence not 19 divides 1163 by NAT_4:9;
1163 = 23*50 + 13; hence not 23 divides 1163 by NAT_4:9;
1163 = 29*40 + 3; hence not 29 divides 1163 by NAT_4:9;
1163 = 31*37 + 16; hence not 31 divides 1163 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1163 & n is prime
holds not n divides 1163 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1171 is prime
proof
now
1171 = 2*585 + 1; hence not 2 divides 1171 by NAT_4:9;
1171 = 3*390 + 1; hence not 3 divides 1171 by NAT_4:9;
1171 = 5*234 + 1; hence not 5 divides 1171 by NAT_4:9;
1171 = 7*167 + 2; hence not 7 divides 1171 by NAT_4:9;
1171 = 11*106 + 5; hence not 11 divides 1171 by NAT_4:9;
1171 = 13*90 + 1; hence not 13 divides 1171 by NAT_4:9;
1171 = 17*68 + 15; hence not 17 divides 1171 by NAT_4:9;
1171 = 19*61 + 12; hence not 19 divides 1171 by NAT_4:9;
1171 = 23*50 + 21; hence not 23 divides 1171 by NAT_4:9;
1171 = 29*40 + 11; hence not 29 divides 1171 by NAT_4:9;
1171 = 31*37 + 24; hence not 31 divides 1171 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1171 & n is prime
holds not n divides 1171 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1181 is prime
proof
now
1181 = 2*590 + 1; hence not 2 divides 1181 by NAT_4:9;
1181 = 3*393 + 2; hence not 3 divides 1181 by NAT_4:9;
1181 = 5*236 + 1; hence not 5 divides 1181 by NAT_4:9;
1181 = 7*168 + 5; hence not 7 divides 1181 by NAT_4:9;
1181 = 11*107 + 4; hence not 11 divides 1181 by NAT_4:9;
1181 = 13*90 + 11; hence not 13 divides 1181 by NAT_4:9;
1181 = 17*69 + 8; hence not 17 divides 1181 by NAT_4:9;
1181 = 19*62 + 3; hence not 19 divides 1181 by NAT_4:9;
1181 = 23*51 + 8; hence not 23 divides 1181 by NAT_4:9;
1181 = 29*40 + 21; hence not 29 divides 1181 by NAT_4:9;
1181 = 31*38 + 3; hence not 31 divides 1181 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1181 & n is prime
holds not n divides 1181 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1187 is prime
proof
now
1187 = 2*593 + 1; hence not 2 divides 1187 by NAT_4:9;
1187 = 3*395 + 2; hence not 3 divides 1187 by NAT_4:9;
1187 = 5*237 + 2; hence not 5 divides 1187 by NAT_4:9;
1187 = 7*169 + 4; hence not 7 divides 1187 by NAT_4:9;
1187 = 11*107 + 10; hence not 11 divides 1187 by NAT_4:9;
1187 = 13*91 + 4; hence not 13 divides 1187 by NAT_4:9;
1187 = 17*69 + 14; hence not 17 divides 1187 by NAT_4:9;
1187 = 19*62 + 9; hence not 19 divides 1187 by NAT_4:9;
1187 = 23*51 + 14; hence not 23 divides 1187 by NAT_4:9;
1187 = 29*40 + 27; hence not 29 divides 1187 by NAT_4:9;
1187 = 31*38 + 9; hence not 31 divides 1187 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1187 & n is prime
holds not n divides 1187 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1193 is prime
proof
now
1193 = 2*596 + 1; hence not 2 divides 1193 by NAT_4:9;
1193 = 3*397 + 2; hence not 3 divides 1193 by NAT_4:9;
1193 = 5*238 + 3; hence not 5 divides 1193 by NAT_4:9;
1193 = 7*170 + 3; hence not 7 divides 1193 by NAT_4:9;
1193 = 11*108 + 5; hence not 11 divides 1193 by NAT_4:9;
1193 = 13*91 + 10; hence not 13 divides 1193 by NAT_4:9;
1193 = 17*70 + 3; hence not 17 divides 1193 by NAT_4:9;
1193 = 19*62 + 15; hence not 19 divides 1193 by NAT_4:9;
1193 = 23*51 + 20; hence not 23 divides 1193 by NAT_4:9;
1193 = 29*41 + 4; hence not 29 divides 1193 by NAT_4:9;
1193 = 31*38 + 15; hence not 31 divides 1193 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1193 & n is prime
holds not n divides 1193 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1201 is prime
proof
now
1201 = 2*600 + 1; hence not 2 divides 1201 by NAT_4:9;
1201 = 3*400 + 1; hence not 3 divides 1201 by NAT_4:9;
1201 = 5*240 + 1; hence not 5 divides 1201 by NAT_4:9;
1201 = 7*171 + 4; hence not 7 divides 1201 by NAT_4:9;
1201 = 11*109 + 2; hence not 11 divides 1201 by NAT_4:9;
1201 = 13*92 + 5; hence not 13 divides 1201 by NAT_4:9;
1201 = 17*70 + 11; hence not 17 divides 1201 by NAT_4:9;
1201 = 19*63 + 4; hence not 19 divides 1201 by NAT_4:9;
1201 = 23*52 + 5; hence not 23 divides 1201 by NAT_4:9;
1201 = 29*41 + 12; hence not 29 divides 1201 by NAT_4:9;
1201 = 31*38 + 23; hence not 31 divides 1201 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1201 & n is prime
holds not n divides 1201 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1213 is prime
proof
now
1213 = 2*606 + 1; hence not 2 divides 1213 by NAT_4:9;
1213 = 3*404 + 1; hence not 3 divides 1213 by NAT_4:9;
1213 = 5*242 + 3; hence not 5 divides 1213 by NAT_4:9;
1213 = 7*173 + 2; hence not 7 divides 1213 by NAT_4:9;
1213 = 11*110 + 3; hence not 11 divides 1213 by NAT_4:9;
1213 = 13*93 + 4; hence not 13 divides 1213 by NAT_4:9;
1213 = 17*71 + 6; hence not 17 divides 1213 by NAT_4:9;
1213 = 19*63 + 16; hence not 19 divides 1213 by NAT_4:9;
1213 = 23*52 + 17; hence not 23 divides 1213 by NAT_4:9;
1213 = 29*41 + 24; hence not 29 divides 1213 by NAT_4:9;
1213 = 31*39 + 4; hence not 31 divides 1213 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1213 & n is prime
holds not n divides 1213 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1217 is prime
proof
now
1217 = 2*608 + 1; hence not 2 divides 1217 by NAT_4:9;
1217 = 3*405 + 2; hence not 3 divides 1217 by NAT_4:9;
1217 = 5*243 + 2; hence not 5 divides 1217 by NAT_4:9;
1217 = 7*173 + 6; hence not 7 divides 1217 by NAT_4:9;
1217 = 11*110 + 7; hence not 11 divides 1217 by NAT_4:9;
1217 = 13*93 + 8; hence not 13 divides 1217 by NAT_4:9;
1217 = 17*71 + 10; hence not 17 divides 1217 by NAT_4:9;
1217 = 19*64 + 1; hence not 19 divides 1217 by NAT_4:9;
1217 = 23*52 + 21; hence not 23 divides 1217 by NAT_4:9;
1217 = 29*41 + 28; hence not 29 divides 1217 by NAT_4:9;
1217 = 31*39 + 8; hence not 31 divides 1217 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1217 & n is prime
holds not n divides 1217 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1223 is prime
proof
now
1223 = 2*611 + 1; hence not 2 divides 1223 by NAT_4:9;
1223 = 3*407 + 2; hence not 3 divides 1223 by NAT_4:9;
1223 = 5*244 + 3; hence not 5 divides 1223 by NAT_4:9;
1223 = 7*174 + 5; hence not 7 divides 1223 by NAT_4:9;
1223 = 11*111 + 2; hence not 11 divides 1223 by NAT_4:9;
1223 = 13*94 + 1; hence not 13 divides 1223 by NAT_4:9;
1223 = 17*71 + 16; hence not 17 divides 1223 by NAT_4:9;
1223 = 19*64 + 7; hence not 19 divides 1223 by NAT_4:9;
1223 = 23*53 + 4; hence not 23 divides 1223 by NAT_4:9;
1223 = 29*42 + 5; hence not 29 divides 1223 by NAT_4:9;
1223 = 31*39 + 14; hence not 31 divides 1223 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1223 & n is prime
holds not n divides 1223 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1229 is prime
proof
now
1229 = 2*614 + 1; hence not 2 divides 1229 by NAT_4:9;
1229 = 3*409 + 2; hence not 3 divides 1229 by NAT_4:9;
1229 = 5*245 + 4; hence not 5 divides 1229 by NAT_4:9;
1229 = 7*175 + 4; hence not 7 divides 1229 by NAT_4:9;
1229 = 11*111 + 8; hence not 11 divides 1229 by NAT_4:9;
1229 = 13*94 + 7; hence not 13 divides 1229 by NAT_4:9;
1229 = 17*72 + 5; hence not 17 divides 1229 by NAT_4:9;
1229 = 19*64 + 13; hence not 19 divides 1229 by NAT_4:9;
1229 = 23*53 + 10; hence not 23 divides 1229 by NAT_4:9;
1229 = 29*42 + 11; hence not 29 divides 1229 by NAT_4:9;
1229 = 31*39 + 20; hence not 31 divides 1229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1229 & n is prime
holds not n divides 1229 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1231 is prime
proof
now
1231 = 2*615 + 1; hence not 2 divides 1231 by NAT_4:9;
1231 = 3*410 + 1; hence not 3 divides 1231 by NAT_4:9;
1231 = 5*246 + 1; hence not 5 divides 1231 by NAT_4:9;
1231 = 7*175 + 6; hence not 7 divides 1231 by NAT_4:9;
1231 = 11*111 + 10; hence not 11 divides 1231 by NAT_4:9;
1231 = 13*94 + 9; hence not 13 divides 1231 by NAT_4:9;
1231 = 17*72 + 7; hence not 17 divides 1231 by NAT_4:9;
1231 = 19*64 + 15; hence not 19 divides 1231 by NAT_4:9;
1231 = 23*53 + 12; hence not 23 divides 1231 by NAT_4:9;
1231 = 29*42 + 13; hence not 29 divides 1231 by NAT_4:9;
1231 = 31*39 + 22; hence not 31 divides 1231 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1231 & n is prime
holds not n divides 1231 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1237 is prime
proof
now
1237 = 2*618 + 1; hence not 2 divides 1237 by NAT_4:9;
1237 = 3*412 + 1; hence not 3 divides 1237 by NAT_4:9;
1237 = 5*247 + 2; hence not 5 divides 1237 by NAT_4:9;
1237 = 7*176 + 5; hence not 7 divides 1237 by NAT_4:9;
1237 = 11*112 + 5; hence not 11 divides 1237 by NAT_4:9;
1237 = 13*95 + 2; hence not 13 divides 1237 by NAT_4:9;
1237 = 17*72 + 13; hence not 17 divides 1237 by NAT_4:9;
1237 = 19*65 + 2; hence not 19 divides 1237 by NAT_4:9;
1237 = 23*53 + 18; hence not 23 divides 1237 by NAT_4:9;
1237 = 29*42 + 19; hence not 29 divides 1237 by NAT_4:9;
1237 = 31*39 + 28; hence not 31 divides 1237 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1237 & n is prime
holds not n divides 1237 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1249 is prime
proof
now
1249 = 2*624 + 1; hence not 2 divides 1249 by NAT_4:9;
1249 = 3*416 + 1; hence not 3 divides 1249 by NAT_4:9;
1249 = 5*249 + 4; hence not 5 divides 1249 by NAT_4:9;
1249 = 7*178 + 3; hence not 7 divides 1249 by NAT_4:9;
1249 = 11*113 + 6; hence not 11 divides 1249 by NAT_4:9;
1249 = 13*96 + 1; hence not 13 divides 1249 by NAT_4:9;
1249 = 17*73 + 8; hence not 17 divides 1249 by NAT_4:9;
1249 = 19*65 + 14; hence not 19 divides 1249 by NAT_4:9;
1249 = 23*54 + 7; hence not 23 divides 1249 by NAT_4:9;
1249 = 29*43 + 2; hence not 29 divides 1249 by NAT_4:9;
1249 = 31*40 + 9; hence not 31 divides 1249 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1249 & n is prime
holds not n divides 1249 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1259 is prime
proof
now
1259 = 2*629 + 1; hence not 2 divides 1259 by NAT_4:9;
1259 = 3*419 + 2; hence not 3 divides 1259 by NAT_4:9;
1259 = 5*251 + 4; hence not 5 divides 1259 by NAT_4:9;
1259 = 7*179 + 6; hence not 7 divides 1259 by NAT_4:9;
1259 = 11*114 + 5; hence not 11 divides 1259 by NAT_4:9;
1259 = 13*96 + 11; hence not 13 divides 1259 by NAT_4:9;
1259 = 17*74 + 1; hence not 17 divides 1259 by NAT_4:9;
1259 = 19*66 + 5; hence not 19 divides 1259 by NAT_4:9;
1259 = 23*54 + 17; hence not 23 divides 1259 by NAT_4:9;
1259 = 29*43 + 12; hence not 29 divides 1259 by NAT_4:9;
1259 = 31*40 + 19; hence not 31 divides 1259 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1259 & n is prime
holds not n divides 1259 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
1277 is prime
proof
now
1277 = 2*638 + 1; hence not 2 divides 1277 by NAT_4:9;
1277 = 3*425 + 2; hence not 3 divides 1277 by NAT_4:9;
1277 = 5*255 + 2; hence not 5 divides 1277 by NAT_4:9;
1277 = 7*182 + 3; hence not 7 divides 1277 by NAT_4:9;
1277 = 11*116 + 1; hence not 11 divides 1277 by NAT_4:9;
1277 = 13*98 + 3; hence not 13 divides 1277 by NAT_4:9;
1277 = 17*75 + 2; hence not 17 divides 1277 by NAT_4:9;
1277 = 19*67 + 4; hence not 19 divides 1277 by NAT_4:9;
1277 = 23*55 + 12; hence not 23 divides 1277 by NAT_4:9;
1277 = 29*44 + 1; hence not 29 divides 1277 by NAT_4:9;
1277 = 31*41 + 6; hence not 31 divides 1277 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1277 & n is prime
holds not n divides 1277 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1279 is prime
proof
now
1279 = 2*639 + 1; hence not 2 divides 1279 by NAT_4:9;
1279 = 3*426 + 1; hence not 3 divides 1279 by NAT_4:9;
1279 = 5*255 + 4; hence not 5 divides 1279 by NAT_4:9;
1279 = 7*182 + 5; hence not 7 divides 1279 by NAT_4:9;
1279 = 11*116 + 3; hence not 11 divides 1279 by NAT_4:9;
1279 = 13*98 + 5; hence not 13 divides 1279 by NAT_4:9;
1279 = 17*75 + 4; hence not 17 divides 1279 by NAT_4:9;
1279 = 19*67 + 6; hence not 19 divides 1279 by NAT_4:9;
1279 = 23*55 + 14; hence not 23 divides 1279 by NAT_4:9;
1279 = 29*44 + 3; hence not 29 divides 1279 by NAT_4:9;
1279 = 31*41 + 8; hence not 31 divides 1279 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1279 & n is prime
holds not n divides 1279 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1283 is prime
proof
now
1283 = 2*641 + 1; hence not 2 divides 1283 by NAT_4:9;
1283 = 3*427 + 2; hence not 3 divides 1283 by NAT_4:9;
1283 = 5*256 + 3; hence not 5 divides 1283 by NAT_4:9;
1283 = 7*183 + 2; hence not 7 divides 1283 by NAT_4:9;
1283 = 11*116 + 7; hence not 11 divides 1283 by NAT_4:9;
1283 = 13*98 + 9; hence not 13 divides 1283 by NAT_4:9;
1283 = 17*75 + 8; hence not 17 divides 1283 by NAT_4:9;
1283 = 19*67 + 10; hence not 19 divides 1283 by NAT_4:9;
1283 = 23*55 + 18; hence not 23 divides 1283 by NAT_4:9;
1283 = 29*44 + 7; hence not 29 divides 1283 by NAT_4:9;
1283 = 31*41 + 12; hence not 31 divides 1283 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1283 & n is prime
holds not n divides 1283 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1289 is prime
proof
now
1289 = 2*644 + 1; hence not 2 divides 1289 by NAT_4:9;
1289 = 3*429 + 2; hence not 3 divides 1289 by NAT_4:9;
1289 = 5*257 + 4; hence not 5 divides 1289 by NAT_4:9;
1289 = 7*184 + 1; hence not 7 divides 1289 by NAT_4:9;
1289 = 11*117 + 2; hence not 11 divides 1289 by NAT_4:9;
1289 = 13*99 + 2; hence not 13 divides 1289 by NAT_4:9;
1289 = 17*75 + 14; hence not 17 divides 1289 by NAT_4:9;
1289 = 19*67 + 16; hence not 19 divides 1289 by NAT_4:9;
1289 = 23*56 + 1; hence not 23 divides 1289 by NAT_4:9;
1289 = 29*44 + 13; hence not 29 divides 1289 by NAT_4:9;
1289 = 31*41 + 18; hence not 31 divides 1289 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1289 & n is prime
holds not n divides 1289 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1291 is prime
proof
now
1291 = 2*645 + 1; hence not 2 divides 1291 by NAT_4:9;
1291 = 3*430 + 1; hence not 3 divides 1291 by NAT_4:9;
1291 = 5*258 + 1; hence not 5 divides 1291 by NAT_4:9;
1291 = 7*184 + 3; hence not 7 divides 1291 by NAT_4:9;
1291 = 11*117 + 4; hence not 11 divides 1291 by NAT_4:9;
1291 = 13*99 + 4; hence not 13 divides 1291 by NAT_4:9;
1291 = 17*75 + 16; hence not 17 divides 1291 by NAT_4:9;
1291 = 19*67 + 18; hence not 19 divides 1291 by NAT_4:9;
1291 = 23*56 + 3; hence not 23 divides 1291 by NAT_4:9;
1291 = 29*44 + 15; hence not 29 divides 1291 by NAT_4:9;
1291 = 31*41 + 20; hence not 31 divides 1291 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1291 & n is prime
holds not n divides 1291 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1297 is prime
proof
now
1297 = 2*648 + 1; hence not 2 divides 1297 by NAT_4:9;
1297 = 3*432 + 1; hence not 3 divides 1297 by NAT_4:9;
1297 = 5*259 + 2; hence not 5 divides 1297 by NAT_4:9;
1297 = 7*185 + 2; hence not 7 divides 1297 by NAT_4:9;
1297 = 11*117 + 10; hence not 11 divides 1297 by NAT_4:9;
1297 = 13*99 + 10; hence not 13 divides 1297 by NAT_4:9;
1297 = 17*76 + 5; hence not 17 divides 1297 by NAT_4:9;
1297 = 19*68 + 5; hence not 19 divides 1297 by NAT_4:9;
1297 = 23*56 + 9; hence not 23 divides 1297 by NAT_4:9;
1297 = 29*44 + 21; hence not 29 divides 1297 by NAT_4:9;
1297 = 31*41 + 26; hence not 31 divides 1297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1297 & n is prime
holds not n divides 1297 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1301 is prime
proof
now
1301 = 2*650 + 1; hence not 2 divides 1301 by NAT_4:9;
1301 = 3*433 + 2; hence not 3 divides 1301 by NAT_4:9;
1301 = 5*260 + 1; hence not 5 divides 1301 by NAT_4:9;
1301 = 7*185 + 6; hence not 7 divides 1301 by NAT_4:9;
1301 = 11*118 + 3; hence not 11 divides 1301 by NAT_4:9;
1301 = 13*100 + 1; hence not 13 divides 1301 by NAT_4:9;
1301 = 17*76 + 9; hence not 17 divides 1301 by NAT_4:9;
1301 = 19*68 + 9; hence not 19 divides 1301 by NAT_4:9;
1301 = 23*56 + 13; hence not 23 divides 1301 by NAT_4:9;
1301 = 29*44 + 25; hence not 29 divides 1301 by NAT_4:9;
1301 = 31*41 + 30; hence not 31 divides 1301 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1301 & n is prime
holds not n divides 1301 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1303 is prime
proof
now
1303 = 2*651 + 1; hence not 2 divides 1303 by NAT_4:9;
1303 = 3*434 + 1; hence not 3 divides 1303 by NAT_4:9;
1303 = 5*260 + 3; hence not 5 divides 1303 by NAT_4:9;
1303 = 7*186 + 1; hence not 7 divides 1303 by NAT_4:9;
1303 = 11*118 + 5; hence not 11 divides 1303 by NAT_4:9;
1303 = 13*100 + 3; hence not 13 divides 1303 by NAT_4:9;
1303 = 17*76 + 11; hence not 17 divides 1303 by NAT_4:9;
1303 = 19*68 + 11; hence not 19 divides 1303 by NAT_4:9;
1303 = 23*56 + 15; hence not 23 divides 1303 by NAT_4:9;
1303 = 29*44 + 27; hence not 29 divides 1303 by NAT_4:9;
1303 = 31*42 + 1; hence not 31 divides 1303 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1303 & n is prime
holds not n divides 1303 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1307 is prime
proof
now
1307 = 2*653 + 1; hence not 2 divides 1307 by NAT_4:9;
1307 = 3*435 + 2; hence not 3 divides 1307 by NAT_4:9;
1307 = 5*261 + 2; hence not 5 divides 1307 by NAT_4:9;
1307 = 7*186 + 5; hence not 7 divides 1307 by NAT_4:9;
1307 = 11*118 + 9; hence not 11 divides 1307 by NAT_4:9;
1307 = 13*100 + 7; hence not 13 divides 1307 by NAT_4:9;
1307 = 17*76 + 15; hence not 17 divides 1307 by NAT_4:9;
1307 = 19*68 + 15; hence not 19 divides 1307 by NAT_4:9;
1307 = 23*56 + 19; hence not 23 divides 1307 by NAT_4:9;
1307 = 29*45 + 2; hence not 29 divides 1307 by NAT_4:9;
1307 = 31*42 + 5; hence not 31 divides 1307 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1307 & n is prime
holds not n divides 1307 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1319 is prime
proof
now
1319 = 2*659 + 1; hence not 2 divides 1319 by NAT_4:9;
1319 = 3*439 + 2; hence not 3 divides 1319 by NAT_4:9;
1319 = 5*263 + 4; hence not 5 divides 1319 by NAT_4:9;
1319 = 7*188 + 3; hence not 7 divides 1319 by NAT_4:9;
1319 = 11*119 + 10; hence not 11 divides 1319 by NAT_4:9;
1319 = 13*101 + 6; hence not 13 divides 1319 by NAT_4:9;
1319 = 17*77 + 10; hence not 17 divides 1319 by NAT_4:9;
1319 = 19*69 + 8; hence not 19 divides 1319 by NAT_4:9;
1319 = 23*57 + 8; hence not 23 divides 1319 by NAT_4:9;
1319 = 29*45 + 14; hence not 29 divides 1319 by NAT_4:9;
1319 = 31*42 + 17; hence not 31 divides 1319 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1319 & n is prime
holds not n divides 1319 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1321 is prime
proof
now
1321 = 2*660 + 1; hence not 2 divides 1321 by NAT_4:9;
1321 = 3*440 + 1; hence not 3 divides 1321 by NAT_4:9;
1321 = 5*264 + 1; hence not 5 divides 1321 by NAT_4:9;
1321 = 7*188 + 5; hence not 7 divides 1321 by NAT_4:9;
1321 = 11*120 + 1; hence not 11 divides 1321 by NAT_4:9;
1321 = 13*101 + 8; hence not 13 divides 1321 by NAT_4:9;
1321 = 17*77 + 12; hence not 17 divides 1321 by NAT_4:9;
1321 = 19*69 + 10; hence not 19 divides 1321 by NAT_4:9;
1321 = 23*57 + 10; hence not 23 divides 1321 by NAT_4:9;
1321 = 29*45 + 16; hence not 29 divides 1321 by NAT_4:9;
1321 = 31*42 + 19; hence not 31 divides 1321 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1321 & n is prime
holds not n divides 1321 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1327 is prime
proof
now
1327 = 2*663 + 1; hence not 2 divides 1327 by NAT_4:9;
1327 = 3*442 + 1; hence not 3 divides 1327 by NAT_4:9;
1327 = 5*265 + 2; hence not 5 divides 1327 by NAT_4:9;
1327 = 7*189 + 4; hence not 7 divides 1327 by NAT_4:9;
1327 = 11*120 + 7; hence not 11 divides 1327 by NAT_4:9;
1327 = 13*102 + 1; hence not 13 divides 1327 by NAT_4:9;
1327 = 17*78 + 1; hence not 17 divides 1327 by NAT_4:9;
1327 = 19*69 + 16; hence not 19 divides 1327 by NAT_4:9;
1327 = 23*57 + 16; hence not 23 divides 1327 by NAT_4:9;
1327 = 29*45 + 22; hence not 29 divides 1327 by NAT_4:9;
1327 = 31*42 + 25; hence not 31 divides 1327 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1327 & n is prime
holds not n divides 1327 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 33
theorem
1361 is prime
proof
now
1361 = 2*680 + 1; hence not 2 divides 1361 by NAT_4:9;
1361 = 3*453 + 2; hence not 3 divides 1361 by NAT_4:9;
1361 = 5*272 + 1; hence not 5 divides 1361 by NAT_4:9;
1361 = 7*194 + 3; hence not 7 divides 1361 by NAT_4:9;
1361 = 11*123 + 8; hence not 11 divides 1361 by NAT_4:9;
1361 = 13*104 + 9; hence not 13 divides 1361 by NAT_4:9;
1361 = 17*80 + 1; hence not 17 divides 1361 by NAT_4:9;
1361 = 19*71 + 12; hence not 19 divides 1361 by NAT_4:9;
1361 = 23*59 + 4; hence not 23 divides 1361 by NAT_4:9;
1361 = 29*46 + 27; hence not 29 divides 1361 by NAT_4:9;
1361 = 31*43 + 28; hence not 31 divides 1361 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1361 & n is prime
holds not n divides 1361 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1367 is prime
proof
now
1367 = 2*683 + 1; hence not 2 divides 1367 by NAT_4:9;
1367 = 3*455 + 2; hence not 3 divides 1367 by NAT_4:9;
1367 = 5*273 + 2; hence not 5 divides 1367 by NAT_4:9;
1367 = 7*195 + 2; hence not 7 divides 1367 by NAT_4:9;
1367 = 11*124 + 3; hence not 11 divides 1367 by NAT_4:9;
1367 = 13*105 + 2; hence not 13 divides 1367 by NAT_4:9;
1367 = 17*80 + 7; hence not 17 divides 1367 by NAT_4:9;
1367 = 19*71 + 18; hence not 19 divides 1367 by NAT_4:9;
1367 = 23*59 + 10; hence not 23 divides 1367 by NAT_4:9;
1367 = 29*47 + 4; hence not 29 divides 1367 by NAT_4:9;
1367 = 31*44 + 3; hence not 31 divides 1367 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1367 & n is prime
holds not n divides 1367 by XPRIMET1:22;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1373 is prime
proof
now
1373 = 2*686 + 1; hence not 2 divides 1373 by NAT_4:9;
1373 = 3*457 + 2; hence not 3 divides 1373 by NAT_4:9;
1373 = 5*274 + 3; hence not 5 divides 1373 by NAT_4:9;
1373 = 7*196 + 1; hence not 7 divides 1373 by NAT_4:9;
1373 = 11*124 + 9; hence not 11 divides 1373 by NAT_4:9;
1373 = 13*105 + 8; hence not 13 divides 1373 by NAT_4:9;
1373 = 17*80 + 13; hence not 17 divides 1373 by NAT_4:9;
1373 = 19*72 + 5; hence not 19 divides 1373 by NAT_4:9;
1373 = 23*59 + 16; hence not 23 divides 1373 by NAT_4:9;
1373 = 29*47 + 10; hence not 29 divides 1373 by NAT_4:9;
1373 = 31*44 + 9; hence not 31 divides 1373 by NAT_4:9;
1373 = 37*37 + 4; hence not 37 divides 1373 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1373 & n is prime
holds not n divides 1373 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1381 is prime
proof
now
1381 = 2*690 + 1; hence not 2 divides 1381 by NAT_4:9;
1381 = 3*460 + 1; hence not 3 divides 1381 by NAT_4:9;
1381 = 5*276 + 1; hence not 5 divides 1381 by NAT_4:9;
1381 = 7*197 + 2; hence not 7 divides 1381 by NAT_4:9;
1381 = 11*125 + 6; hence not 11 divides 1381 by NAT_4:9;
1381 = 13*106 + 3; hence not 13 divides 1381 by NAT_4:9;
1381 = 17*81 + 4; hence not 17 divides 1381 by NAT_4:9;
1381 = 19*72 + 13; hence not 19 divides 1381 by NAT_4:9;
1381 = 23*60 + 1; hence not 23 divides 1381 by NAT_4:9;
1381 = 29*47 + 18; hence not 29 divides 1381 by NAT_4:9;
1381 = 31*44 + 17; hence not 31 divides 1381 by NAT_4:9;
1381 = 37*37 + 12; hence not 37 divides 1381 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1381 & n is prime
holds not n divides 1381 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
1399 is prime
proof
now
1399 = 2*699 + 1; hence not 2 divides 1399 by NAT_4:9;
1399 = 3*466 + 1; hence not 3 divides 1399 by NAT_4:9;
1399 = 5*279 + 4; hence not 5 divides 1399 by NAT_4:9;
1399 = 7*199 + 6; hence not 7 divides 1399 by NAT_4:9;
1399 = 11*127 + 2; hence not 11 divides 1399 by NAT_4:9;
1399 = 13*107 + 8; hence not 13 divides 1399 by NAT_4:9;
1399 = 17*82 + 5; hence not 17 divides 1399 by NAT_4:9;
1399 = 19*73 + 12; hence not 19 divides 1399 by NAT_4:9;
1399 = 23*60 + 19; hence not 23 divides 1399 by NAT_4:9;
1399 = 29*48 + 7; hence not 29 divides 1399 by NAT_4:9;
1399 = 31*45 + 4; hence not 31 divides 1399 by NAT_4:9;
1399 = 37*37 + 30; hence not 37 divides 1399 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1399 & n is prime
holds not n divides 1399 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1409 is prime
proof
now
1409 = 2*704 + 1; hence not 2 divides 1409 by NAT_4:9;
1409 = 3*469 + 2; hence not 3 divides 1409 by NAT_4:9;
1409 = 5*281 + 4; hence not 5 divides 1409 by NAT_4:9;
1409 = 7*201 + 2; hence not 7 divides 1409 by NAT_4:9;
1409 = 11*128 + 1; hence not 11 divides 1409 by NAT_4:9;
1409 = 13*108 + 5; hence not 13 divides 1409 by NAT_4:9;
1409 = 17*82 + 15; hence not 17 divides 1409 by NAT_4:9;
1409 = 19*74 + 3; hence not 19 divides 1409 by NAT_4:9;
1409 = 23*61 + 6; hence not 23 divides 1409 by NAT_4:9;
1409 = 29*48 + 17; hence not 29 divides 1409 by NAT_4:9;
1409 = 31*45 + 14; hence not 31 divides 1409 by NAT_4:9;
1409 = 37*38 + 3; hence not 37 divides 1409 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1409 & n is prime
holds not n divides 1409 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
1423 is prime
proof
now
1423 = 2*711 + 1; hence not 2 divides 1423 by NAT_4:9;
1423 = 3*474 + 1; hence not 3 divides 1423 by NAT_4:9;
1423 = 5*284 + 3; hence not 5 divides 1423 by NAT_4:9;
1423 = 7*203 + 2; hence not 7 divides 1423 by NAT_4:9;
1423 = 11*129 + 4; hence not 11 divides 1423 by NAT_4:9;
1423 = 13*109 + 6; hence not 13 divides 1423 by NAT_4:9;
1423 = 17*83 + 12; hence not 17 divides 1423 by NAT_4:9;
1423 = 19*74 + 17; hence not 19 divides 1423 by NAT_4:9;
1423 = 23*61 + 20; hence not 23 divides 1423 by NAT_4:9;
1423 = 29*49 + 2; hence not 29 divides 1423 by NAT_4:9;
1423 = 31*45 + 28; hence not 31 divides 1423 by NAT_4:9;
1423 = 37*38 + 17; hence not 37 divides 1423 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1423 & n is prime
holds not n divides 1423 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1427 is prime
proof
now
1427 = 2*713 + 1; hence not 2 divides 1427 by NAT_4:9;
1427 = 3*475 + 2; hence not 3 divides 1427 by NAT_4:9;
1427 = 5*285 + 2; hence not 5 divides 1427 by NAT_4:9;
1427 = 7*203 + 6; hence not 7 divides 1427 by NAT_4:9;
1427 = 11*129 + 8; hence not 11 divides 1427 by NAT_4:9;
1427 = 13*109 + 10; hence not 13 divides 1427 by NAT_4:9;
1427 = 17*83 + 16; hence not 17 divides 1427 by NAT_4:9;
1427 = 19*75 + 2; hence not 19 divides 1427 by NAT_4:9;
1427 = 23*62 + 1; hence not 23 divides 1427 by NAT_4:9;
1427 = 29*49 + 6; hence not 29 divides 1427 by NAT_4:9;
1427 = 31*46 + 1; hence not 31 divides 1427 by NAT_4:9;
1427 = 37*38 + 21; hence not 37 divides 1427 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1427 & n is prime
holds not n divides 1427 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1429 is prime
proof
now
1429 = 2*714 + 1; hence not 2 divides 1429 by NAT_4:9;
1429 = 3*476 + 1; hence not 3 divides 1429 by NAT_4:9;
1429 = 5*285 + 4; hence not 5 divides 1429 by NAT_4:9;
1429 = 7*204 + 1; hence not 7 divides 1429 by NAT_4:9;
1429 = 11*129 + 10; hence not 11 divides 1429 by NAT_4:9;
1429 = 13*109 + 12; hence not 13 divides 1429 by NAT_4:9;
1429 = 17*84 + 1; hence not 17 divides 1429 by NAT_4:9;
1429 = 19*75 + 4; hence not 19 divides 1429 by NAT_4:9;
1429 = 23*62 + 3; hence not 23 divides 1429 by NAT_4:9;
1429 = 29*49 + 8; hence not 29 divides 1429 by NAT_4:9;
1429 = 31*46 + 3; hence not 31 divides 1429 by NAT_4:9;
1429 = 37*38 + 23; hence not 37 divides 1429 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1429 & n is prime
holds not n divides 1429 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1433 is prime
proof
now
1433 = 2*716 + 1; hence not 2 divides 1433 by NAT_4:9;
1433 = 3*477 + 2; hence not 3 divides 1433 by NAT_4:9;
1433 = 5*286 + 3; hence not 5 divides 1433 by NAT_4:9;
1433 = 7*204 + 5; hence not 7 divides 1433 by NAT_4:9;
1433 = 11*130 + 3; hence not 11 divides 1433 by NAT_4:9;
1433 = 13*110 + 3; hence not 13 divides 1433 by NAT_4:9;
1433 = 17*84 + 5; hence not 17 divides 1433 by NAT_4:9;
1433 = 19*75 + 8; hence not 19 divides 1433 by NAT_4:9;
1433 = 23*62 + 7; hence not 23 divides 1433 by NAT_4:9;
1433 = 29*49 + 12; hence not 29 divides 1433 by NAT_4:9;
1433 = 31*46 + 7; hence not 31 divides 1433 by NAT_4:9;
1433 = 37*38 + 27; hence not 37 divides 1433 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1433 & n is prime
holds not n divides 1433 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1439 is prime
proof
now
1439 = 2*719 + 1; hence not 2 divides 1439 by NAT_4:9;
1439 = 3*479 + 2; hence not 3 divides 1439 by NAT_4:9;
1439 = 5*287 + 4; hence not 5 divides 1439 by NAT_4:9;
1439 = 7*205 + 4; hence not 7 divides 1439 by NAT_4:9;
1439 = 11*130 + 9; hence not 11 divides 1439 by NAT_4:9;
1439 = 13*110 + 9; hence not 13 divides 1439 by NAT_4:9;
1439 = 17*84 + 11; hence not 17 divides 1439 by NAT_4:9;
1439 = 19*75 + 14; hence not 19 divides 1439 by NAT_4:9;
1439 = 23*62 + 13; hence not 23 divides 1439 by NAT_4:9;
1439 = 29*49 + 18; hence not 29 divides 1439 by NAT_4:9;
1439 = 31*46 + 13; hence not 31 divides 1439 by NAT_4:9;
1439 = 37*38 + 33; hence not 37 divides 1439 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1439 & n is prime
holds not n divides 1439 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1447 is prime
proof
now
1447 = 2*723 + 1; hence not 2 divides 1447 by NAT_4:9;
1447 = 3*482 + 1; hence not 3 divides 1447 by NAT_4:9;
1447 = 5*289 + 2; hence not 5 divides 1447 by NAT_4:9;
1447 = 7*206 + 5; hence not 7 divides 1447 by NAT_4:9;
1447 = 11*131 + 6; hence not 11 divides 1447 by NAT_4:9;
1447 = 13*111 + 4; hence not 13 divides 1447 by NAT_4:9;
1447 = 17*85 + 2; hence not 17 divides 1447 by NAT_4:9;
1447 = 19*76 + 3; hence not 19 divides 1447 by NAT_4:9;
1447 = 23*62 + 21; hence not 23 divides 1447 by NAT_4:9;
1447 = 29*49 + 26; hence not 29 divides 1447 by NAT_4:9;
1447 = 31*46 + 21; hence not 31 divides 1447 by NAT_4:9;
1447 = 37*39 + 4; hence not 37 divides 1447 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1447 & n is prime
holds not n divides 1447 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1451 is prime
proof
now
1451 = 2*725 + 1; hence not 2 divides 1451 by NAT_4:9;
1451 = 3*483 + 2; hence not 3 divides 1451 by NAT_4:9;
1451 = 5*290 + 1; hence not 5 divides 1451 by NAT_4:9;
1451 = 7*207 + 2; hence not 7 divides 1451 by NAT_4:9;
1451 = 11*131 + 10; hence not 11 divides 1451 by NAT_4:9;
1451 = 13*111 + 8; hence not 13 divides 1451 by NAT_4:9;
1451 = 17*85 + 6; hence not 17 divides 1451 by NAT_4:9;
1451 = 19*76 + 7; hence not 19 divides 1451 by NAT_4:9;
1451 = 23*63 + 2; hence not 23 divides 1451 by NAT_4:9;
1451 = 29*50 + 1; hence not 29 divides 1451 by NAT_4:9;
1451 = 31*46 + 25; hence not 31 divides 1451 by NAT_4:9;
1451 = 37*39 + 8; hence not 37 divides 1451 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1451 & n is prime
holds not n divides 1451 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1453 is prime
proof
now
1453 = 2*726 + 1; hence not 2 divides 1453 by NAT_4:9;
1453 = 3*484 + 1; hence not 3 divides 1453 by NAT_4:9;
1453 = 5*290 + 3; hence not 5 divides 1453 by NAT_4:9;
1453 = 7*207 + 4; hence not 7 divides 1453 by NAT_4:9;
1453 = 11*132 + 1; hence not 11 divides 1453 by NAT_4:9;
1453 = 13*111 + 10; hence not 13 divides 1453 by NAT_4:9;
1453 = 17*85 + 8; hence not 17 divides 1453 by NAT_4:9;
1453 = 19*76 + 9; hence not 19 divides 1453 by NAT_4:9;
1453 = 23*63 + 4; hence not 23 divides 1453 by NAT_4:9;
1453 = 29*50 + 3; hence not 29 divides 1453 by NAT_4:9;
1453 = 31*46 + 27; hence not 31 divides 1453 by NAT_4:9;
1453 = 37*39 + 10; hence not 37 divides 1453 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1453 & n is prime
holds not n divides 1453 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1459 is prime
proof
now
1459 = 2*729 + 1; hence not 2 divides 1459 by NAT_4:9;
1459 = 3*486 + 1; hence not 3 divides 1459 by NAT_4:9;
1459 = 5*291 + 4; hence not 5 divides 1459 by NAT_4:9;
1459 = 7*208 + 3; hence not 7 divides 1459 by NAT_4:9;
1459 = 11*132 + 7; hence not 11 divides 1459 by NAT_4:9;
1459 = 13*112 + 3; hence not 13 divides 1459 by NAT_4:9;
1459 = 17*85 + 14; hence not 17 divides 1459 by NAT_4:9;
1459 = 19*76 + 15; hence not 19 divides 1459 by NAT_4:9;
1459 = 23*63 + 10; hence not 23 divides 1459 by NAT_4:9;
1459 = 29*50 + 9; hence not 29 divides 1459 by NAT_4:9;
1459 = 31*47 + 2; hence not 31 divides 1459 by NAT_4:9;
1459 = 37*39 + 16; hence not 37 divides 1459 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1459 & n is prime
holds not n divides 1459 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1471 is prime
proof
now
1471 = 2*735 + 1; hence not 2 divides 1471 by NAT_4:9;
1471 = 3*490 + 1; hence not 3 divides 1471 by NAT_4:9;
1471 = 5*294 + 1; hence not 5 divides 1471 by NAT_4:9;
1471 = 7*210 + 1; hence not 7 divides 1471 by NAT_4:9;
1471 = 11*133 + 8; hence not 11 divides 1471 by NAT_4:9;
1471 = 13*113 + 2; hence not 13 divides 1471 by NAT_4:9;
1471 = 17*86 + 9; hence not 17 divides 1471 by NAT_4:9;
1471 = 19*77 + 8; hence not 19 divides 1471 by NAT_4:9;
1471 = 23*63 + 22; hence not 23 divides 1471 by NAT_4:9;
1471 = 29*50 + 21; hence not 29 divides 1471 by NAT_4:9;
1471 = 31*47 + 14; hence not 31 divides 1471 by NAT_4:9;
1471 = 37*39 + 28; hence not 37 divides 1471 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1471 & n is prime
holds not n divides 1471 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1481 is prime
proof
now
1481 = 2*740 + 1; hence not 2 divides 1481 by NAT_4:9;
1481 = 3*493 + 2; hence not 3 divides 1481 by NAT_4:9;
1481 = 5*296 + 1; hence not 5 divides 1481 by NAT_4:9;
1481 = 7*211 + 4; hence not 7 divides 1481 by NAT_4:9;
1481 = 11*134 + 7; hence not 11 divides 1481 by NAT_4:9;
1481 = 13*113 + 12; hence not 13 divides 1481 by NAT_4:9;
1481 = 17*87 + 2; hence not 17 divides 1481 by NAT_4:9;
1481 = 19*77 + 18; hence not 19 divides 1481 by NAT_4:9;
1481 = 23*64 + 9; hence not 23 divides 1481 by NAT_4:9;
1481 = 29*51 + 2; hence not 29 divides 1481 by NAT_4:9;
1481 = 31*47 + 24; hence not 31 divides 1481 by NAT_4:9;
1481 = 37*40 + 1; hence not 37 divides 1481 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1481 & n is prime
holds not n divides 1481 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1483 is prime
proof
now
1483 = 2*741 + 1; hence not 2 divides 1483 by NAT_4:9;
1483 = 3*494 + 1; hence not 3 divides 1483 by NAT_4:9;
1483 = 5*296 + 3; hence not 5 divides 1483 by NAT_4:9;
1483 = 7*211 + 6; hence not 7 divides 1483 by NAT_4:9;
1483 = 11*134 + 9; hence not 11 divides 1483 by NAT_4:9;
1483 = 13*114 + 1; hence not 13 divides 1483 by NAT_4:9;
1483 = 17*87 + 4; hence not 17 divides 1483 by NAT_4:9;
1483 = 19*78 + 1; hence not 19 divides 1483 by NAT_4:9;
1483 = 23*64 + 11; hence not 23 divides 1483 by NAT_4:9;
1483 = 29*51 + 4; hence not 29 divides 1483 by NAT_4:9;
1483 = 31*47 + 26; hence not 31 divides 1483 by NAT_4:9;
1483 = 37*40 + 3; hence not 37 divides 1483 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1483 & n is prime
holds not n divides 1483 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1487 is prime
proof
now
1487 = 2*743 + 1; hence not 2 divides 1487 by NAT_4:9;
1487 = 3*495 + 2; hence not 3 divides 1487 by NAT_4:9;
1487 = 5*297 + 2; hence not 5 divides 1487 by NAT_4:9;
1487 = 7*212 + 3; hence not 7 divides 1487 by NAT_4:9;
1487 = 11*135 + 2; hence not 11 divides 1487 by NAT_4:9;
1487 = 13*114 + 5; hence not 13 divides 1487 by NAT_4:9;
1487 = 17*87 + 8; hence not 17 divides 1487 by NAT_4:9;
1487 = 19*78 + 5; hence not 19 divides 1487 by NAT_4:9;
1487 = 23*64 + 15; hence not 23 divides 1487 by NAT_4:9;
1487 = 29*51 + 8; hence not 29 divides 1487 by NAT_4:9;
1487 = 31*47 + 30; hence not 31 divides 1487 by NAT_4:9;
1487 = 37*40 + 7; hence not 37 divides 1487 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1487 & n is prime
holds not n divides 1487 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1489 is prime
proof
now
1489 = 2*744 + 1; hence not 2 divides 1489 by NAT_4:9;
1489 = 3*496 + 1; hence not 3 divides 1489 by NAT_4:9;
1489 = 5*297 + 4; hence not 5 divides 1489 by NAT_4:9;
1489 = 7*212 + 5; hence not 7 divides 1489 by NAT_4:9;
1489 = 11*135 + 4; hence not 11 divides 1489 by NAT_4:9;
1489 = 13*114 + 7; hence not 13 divides 1489 by NAT_4:9;
1489 = 17*87 + 10; hence not 17 divides 1489 by NAT_4:9;
1489 = 19*78 + 7; hence not 19 divides 1489 by NAT_4:9;
1489 = 23*64 + 17; hence not 23 divides 1489 by NAT_4:9;
1489 = 29*51 + 10; hence not 29 divides 1489 by NAT_4:9;
1489 = 31*48 + 1; hence not 31 divides 1489 by NAT_4:9;
1489 = 37*40 + 9; hence not 37 divides 1489 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1489 & n is prime
holds not n divides 1489 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1493 is prime
proof
now
1493 = 2*746 + 1; hence not 2 divides 1493 by NAT_4:9;
1493 = 3*497 + 2; hence not 3 divides 1493 by NAT_4:9;
1493 = 5*298 + 3; hence not 5 divides 1493 by NAT_4:9;
1493 = 7*213 + 2; hence not 7 divides 1493 by NAT_4:9;
1493 = 11*135 + 8; hence not 11 divides 1493 by NAT_4:9;
1493 = 13*114 + 11; hence not 13 divides 1493 by NAT_4:9;
1493 = 17*87 + 14; hence not 17 divides 1493 by NAT_4:9;
1493 = 19*78 + 11; hence not 19 divides 1493 by NAT_4:9;
1493 = 23*64 + 21; hence not 23 divides 1493 by NAT_4:9;
1493 = 29*51 + 14; hence not 29 divides 1493 by NAT_4:9;
1493 = 31*48 + 5; hence not 31 divides 1493 by NAT_4:9;
1493 = 37*40 + 13; hence not 37 divides 1493 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1493 & n is prime
holds not n divides 1493 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1499 is prime
proof
now
1499 = 2*749 + 1; hence not 2 divides 1499 by NAT_4:9;
1499 = 3*499 + 2; hence not 3 divides 1499 by NAT_4:9;
1499 = 5*299 + 4; hence not 5 divides 1499 by NAT_4:9;
1499 = 7*214 + 1; hence not 7 divides 1499 by NAT_4:9;
1499 = 11*136 + 3; hence not 11 divides 1499 by NAT_4:9;
1499 = 13*115 + 4; hence not 13 divides 1499 by NAT_4:9;
1499 = 17*88 + 3; hence not 17 divides 1499 by NAT_4:9;
1499 = 19*78 + 17; hence not 19 divides 1499 by NAT_4:9;
1499 = 23*65 + 4; hence not 23 divides 1499 by NAT_4:9;
1499 = 29*51 + 20; hence not 29 divides 1499 by NAT_4:9;
1499 = 31*48 + 11; hence not 31 divides 1499 by NAT_4:9;
1499 = 37*40 + 19; hence not 37 divides 1499 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1499 & n is prime
holds not n divides 1499 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1511 is prime
proof
now
1511 = 2*755 + 1; hence not 2 divides 1511 by NAT_4:9;
1511 = 3*503 + 2; hence not 3 divides 1511 by NAT_4:9;
1511 = 5*302 + 1; hence not 5 divides 1511 by NAT_4:9;
1511 = 7*215 + 6; hence not 7 divides 1511 by NAT_4:9;
1511 = 11*137 + 4; hence not 11 divides 1511 by NAT_4:9;
1511 = 13*116 + 3; hence not 13 divides 1511 by NAT_4:9;
1511 = 17*88 + 15; hence not 17 divides 1511 by NAT_4:9;
1511 = 19*79 + 10; hence not 19 divides 1511 by NAT_4:9;
1511 = 23*65 + 16; hence not 23 divides 1511 by NAT_4:9;
1511 = 29*52 + 3; hence not 29 divides 1511 by NAT_4:9;
1511 = 31*48 + 23; hence not 31 divides 1511 by NAT_4:9;
1511 = 37*40 + 31; hence not 37 divides 1511 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1511 & n is prime
holds not n divides 1511 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1523 is prime
proof
now
1523 = 2*761 + 1; hence not 2 divides 1523 by NAT_4:9;
1523 = 3*507 + 2; hence not 3 divides 1523 by NAT_4:9;
1523 = 5*304 + 3; hence not 5 divides 1523 by NAT_4:9;
1523 = 7*217 + 4; hence not 7 divides 1523 by NAT_4:9;
1523 = 11*138 + 5; hence not 11 divides 1523 by NAT_4:9;
1523 = 13*117 + 2; hence not 13 divides 1523 by NAT_4:9;
1523 = 17*89 + 10; hence not 17 divides 1523 by NAT_4:9;
1523 = 19*80 + 3; hence not 19 divides 1523 by NAT_4:9;
1523 = 23*66 + 5; hence not 23 divides 1523 by NAT_4:9;
1523 = 29*52 + 15; hence not 29 divides 1523 by NAT_4:9;
1523 = 31*49 + 4; hence not 31 divides 1523 by NAT_4:9;
1523 = 37*41 + 6; hence not 37 divides 1523 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1523 & n is prime
holds not n divides 1523 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1531 is prime
proof
now
1531 = 2*765 + 1; hence not 2 divides 1531 by NAT_4:9;
1531 = 3*510 + 1; hence not 3 divides 1531 by NAT_4:9;
1531 = 5*306 + 1; hence not 5 divides 1531 by NAT_4:9;
1531 = 7*218 + 5; hence not 7 divides 1531 by NAT_4:9;
1531 = 11*139 + 2; hence not 11 divides 1531 by NAT_4:9;
1531 = 13*117 + 10; hence not 13 divides 1531 by NAT_4:9;
1531 = 17*90 + 1; hence not 17 divides 1531 by NAT_4:9;
1531 = 19*80 + 11; hence not 19 divides 1531 by NAT_4:9;
1531 = 23*66 + 13; hence not 23 divides 1531 by NAT_4:9;
1531 = 29*52 + 23; hence not 29 divides 1531 by NAT_4:9;
1531 = 31*49 + 12; hence not 31 divides 1531 by NAT_4:9;
1531 = 37*41 + 14; hence not 37 divides 1531 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1531 & n is prime
holds not n divides 1531 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1543 is prime
proof
now
1543 = 2*771 + 1; hence not 2 divides 1543 by NAT_4:9;
1543 = 3*514 + 1; hence not 3 divides 1543 by NAT_4:9;
1543 = 5*308 + 3; hence not 5 divides 1543 by NAT_4:9;
1543 = 7*220 + 3; hence not 7 divides 1543 by NAT_4:9;
1543 = 11*140 + 3; hence not 11 divides 1543 by NAT_4:9;
1543 = 13*118 + 9; hence not 13 divides 1543 by NAT_4:9;
1543 = 17*90 + 13; hence not 17 divides 1543 by NAT_4:9;
1543 = 19*81 + 4; hence not 19 divides 1543 by NAT_4:9;
1543 = 23*67 + 2; hence not 23 divides 1543 by NAT_4:9;
1543 = 29*53 + 6; hence not 29 divides 1543 by NAT_4:9;
1543 = 31*49 + 24; hence not 31 divides 1543 by NAT_4:9;
1543 = 37*41 + 26; hence not 37 divides 1543 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1543 & n is prime
holds not n divides 1543 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1549 is prime
proof
now
1549 = 2*774 + 1; hence not 2 divides 1549 by NAT_4:9;
1549 = 3*516 + 1; hence not 3 divides 1549 by NAT_4:9;
1549 = 5*309 + 4; hence not 5 divides 1549 by NAT_4:9;
1549 = 7*221 + 2; hence not 7 divides 1549 by NAT_4:9;
1549 = 11*140 + 9; hence not 11 divides 1549 by NAT_4:9;
1549 = 13*119 + 2; hence not 13 divides 1549 by NAT_4:9;
1549 = 17*91 + 2; hence not 17 divides 1549 by NAT_4:9;
1549 = 19*81 + 10; hence not 19 divides 1549 by NAT_4:9;
1549 = 23*67 + 8; hence not 23 divides 1549 by NAT_4:9;
1549 = 29*53 + 12; hence not 29 divides 1549 by NAT_4:9;
1549 = 31*49 + 30; hence not 31 divides 1549 by NAT_4:9;
1549 = 37*41 + 32; hence not 37 divides 1549 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1549 & n is prime
holds not n divides 1549 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1553 is prime
proof
now
1553 = 2*776 + 1; hence not 2 divides 1553 by NAT_4:9;
1553 = 3*517 + 2; hence not 3 divides 1553 by NAT_4:9;
1553 = 5*310 + 3; hence not 5 divides 1553 by NAT_4:9;
1553 = 7*221 + 6; hence not 7 divides 1553 by NAT_4:9;
1553 = 11*141 + 2; hence not 11 divides 1553 by NAT_4:9;
1553 = 13*119 + 6; hence not 13 divides 1553 by NAT_4:9;
1553 = 17*91 + 6; hence not 17 divides 1553 by NAT_4:9;
1553 = 19*81 + 14; hence not 19 divides 1553 by NAT_4:9;
1553 = 23*67 + 12; hence not 23 divides 1553 by NAT_4:9;
1553 = 29*53 + 16; hence not 29 divides 1553 by NAT_4:9;
1553 = 31*50 + 3; hence not 31 divides 1553 by NAT_4:9;
1553 = 37*41 + 36; hence not 37 divides 1553 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1553 & n is prime
holds not n divides 1553 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1559 is prime
proof
now
1559 = 2*779 + 1; hence not 2 divides 1559 by NAT_4:9;
1559 = 3*519 + 2; hence not 3 divides 1559 by NAT_4:9;
1559 = 5*311 + 4; hence not 5 divides 1559 by NAT_4:9;
1559 = 7*222 + 5; hence not 7 divides 1559 by NAT_4:9;
1559 = 11*141 + 8; hence not 11 divides 1559 by NAT_4:9;
1559 = 13*119 + 12; hence not 13 divides 1559 by NAT_4:9;
1559 = 17*91 + 12; hence not 17 divides 1559 by NAT_4:9;
1559 = 19*82 + 1; hence not 19 divides 1559 by NAT_4:9;
1559 = 23*67 + 18; hence not 23 divides 1559 by NAT_4:9;
1559 = 29*53 + 22; hence not 29 divides 1559 by NAT_4:9;
1559 = 31*50 + 9; hence not 31 divides 1559 by NAT_4:9;
1559 = 37*42 + 5; hence not 37 divides 1559 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1559 & n is prime
holds not n divides 1559 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1567 is prime
proof
now
1567 = 2*783 + 1; hence not 2 divides 1567 by NAT_4:9;
1567 = 3*522 + 1; hence not 3 divides 1567 by NAT_4:9;
1567 = 5*313 + 2; hence not 5 divides 1567 by NAT_4:9;
1567 = 7*223 + 6; hence not 7 divides 1567 by NAT_4:9;
1567 = 11*142 + 5; hence not 11 divides 1567 by NAT_4:9;
1567 = 13*120 + 7; hence not 13 divides 1567 by NAT_4:9;
1567 = 17*92 + 3; hence not 17 divides 1567 by NAT_4:9;
1567 = 19*82 + 9; hence not 19 divides 1567 by NAT_4:9;
1567 = 23*68 + 3; hence not 23 divides 1567 by NAT_4:9;
1567 = 29*54 + 1; hence not 29 divides 1567 by NAT_4:9;
1567 = 31*50 + 17; hence not 31 divides 1567 by NAT_4:9;
1567 = 37*42 + 13; hence not 37 divides 1567 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1567 & n is prime
holds not n divides 1567 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1571 is prime
proof
now
1571 = 2*785 + 1; hence not 2 divides 1571 by NAT_4:9;
1571 = 3*523 + 2; hence not 3 divides 1571 by NAT_4:9;
1571 = 5*314 + 1; hence not 5 divides 1571 by NAT_4:9;
1571 = 7*224 + 3; hence not 7 divides 1571 by NAT_4:9;
1571 = 11*142 + 9; hence not 11 divides 1571 by NAT_4:9;
1571 = 13*120 + 11; hence not 13 divides 1571 by NAT_4:9;
1571 = 17*92 + 7; hence not 17 divides 1571 by NAT_4:9;
1571 = 19*82 + 13; hence not 19 divides 1571 by NAT_4:9;
1571 = 23*68 + 7; hence not 23 divides 1571 by NAT_4:9;
1571 = 29*54 + 5; hence not 29 divides 1571 by NAT_4:9;
1571 = 31*50 + 21; hence not 31 divides 1571 by NAT_4:9;
1571 = 37*42 + 17; hence not 37 divides 1571 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1571 & n is prime
holds not n divides 1571 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1579 is prime
proof
now
1579 = 2*789 + 1; hence not 2 divides 1579 by NAT_4:9;
1579 = 3*526 + 1; hence not 3 divides 1579 by NAT_4:9;
1579 = 5*315 + 4; hence not 5 divides 1579 by NAT_4:9;
1579 = 7*225 + 4; hence not 7 divides 1579 by NAT_4:9;
1579 = 11*143 + 6; hence not 11 divides 1579 by NAT_4:9;
1579 = 13*121 + 6; hence not 13 divides 1579 by NAT_4:9;
1579 = 17*92 + 15; hence not 17 divides 1579 by NAT_4:9;
1579 = 19*83 + 2; hence not 19 divides 1579 by NAT_4:9;
1579 = 23*68 + 15; hence not 23 divides 1579 by NAT_4:9;
1579 = 29*54 + 13; hence not 29 divides 1579 by NAT_4:9;
1579 = 31*50 + 29; hence not 31 divides 1579 by NAT_4:9;
1579 = 37*42 + 25; hence not 37 divides 1579 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1579 & n is prime
holds not n divides 1579 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1583 is prime
proof
now
1583 = 2*791 + 1; hence not 2 divides 1583 by NAT_4:9;
1583 = 3*527 + 2; hence not 3 divides 1583 by NAT_4:9;
1583 = 5*316 + 3; hence not 5 divides 1583 by NAT_4:9;
1583 = 7*226 + 1; hence not 7 divides 1583 by NAT_4:9;
1583 = 11*143 + 10; hence not 11 divides 1583 by NAT_4:9;
1583 = 13*121 + 10; hence not 13 divides 1583 by NAT_4:9;
1583 = 17*93 + 2; hence not 17 divides 1583 by NAT_4:9;
1583 = 19*83 + 6; hence not 19 divides 1583 by NAT_4:9;
1583 = 23*68 + 19; hence not 23 divides 1583 by NAT_4:9;
1583 = 29*54 + 17; hence not 29 divides 1583 by NAT_4:9;
1583 = 31*51 + 2; hence not 31 divides 1583 by NAT_4:9;
1583 = 37*42 + 29; hence not 37 divides 1583 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1583 & n is prime
holds not n divides 1583 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
1597 is prime
proof
now
1597 = 2*798 + 1; hence not 2 divides 1597 by NAT_4:9;
1597 = 3*532 + 1; hence not 3 divides 1597 by NAT_4:9;
1597 = 5*319 + 2; hence not 5 divides 1597 by NAT_4:9;
1597 = 7*228 + 1; hence not 7 divides 1597 by NAT_4:9;
1597 = 11*145 + 2; hence not 11 divides 1597 by NAT_4:9;
1597 = 13*122 + 11; hence not 13 divides 1597 by NAT_4:9;
1597 = 17*93 + 16; hence not 17 divides 1597 by NAT_4:9;
1597 = 19*84 + 1; hence not 19 divides 1597 by NAT_4:9;
1597 = 23*69 + 10; hence not 23 divides 1597 by NAT_4:9;
1597 = 29*55 + 2; hence not 29 divides 1597 by NAT_4:9;
1597 = 31*51 + 16; hence not 31 divides 1597 by NAT_4:9;
1597 = 37*43 + 6; hence not 37 divides 1597 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1597 & n is prime
holds not n divides 1597 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1601 is prime
proof
now
1601 = 2*800 + 1; hence not 2 divides 1601 by NAT_4:9;
1601 = 3*533 + 2; hence not 3 divides 1601 by NAT_4:9;
1601 = 5*320 + 1; hence not 5 divides 1601 by NAT_4:9;
1601 = 7*228 + 5; hence not 7 divides 1601 by NAT_4:9;
1601 = 11*145 + 6; hence not 11 divides 1601 by NAT_4:9;
1601 = 13*123 + 2; hence not 13 divides 1601 by NAT_4:9;
1601 = 17*94 + 3; hence not 17 divides 1601 by NAT_4:9;
1601 = 19*84 + 5; hence not 19 divides 1601 by NAT_4:9;
1601 = 23*69 + 14; hence not 23 divides 1601 by NAT_4:9;
1601 = 29*55 + 6; hence not 29 divides 1601 by NAT_4:9;
1601 = 31*51 + 20; hence not 31 divides 1601 by NAT_4:9;
1601 = 37*43 + 10; hence not 37 divides 1601 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1601 & n is prime
holds not n divides 1601 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1607 is prime
proof
now
1607 = 2*803 + 1; hence not 2 divides 1607 by NAT_4:9;
1607 = 3*535 + 2; hence not 3 divides 1607 by NAT_4:9;
1607 = 5*321 + 2; hence not 5 divides 1607 by NAT_4:9;
1607 = 7*229 + 4; hence not 7 divides 1607 by NAT_4:9;
1607 = 11*146 + 1; hence not 11 divides 1607 by NAT_4:9;
1607 = 13*123 + 8; hence not 13 divides 1607 by NAT_4:9;
1607 = 17*94 + 9; hence not 17 divides 1607 by NAT_4:9;
1607 = 19*84 + 11; hence not 19 divides 1607 by NAT_4:9;
1607 = 23*69 + 20; hence not 23 divides 1607 by NAT_4:9;
1607 = 29*55 + 12; hence not 29 divides 1607 by NAT_4:9;
1607 = 31*51 + 26; hence not 31 divides 1607 by NAT_4:9;
1607 = 37*43 + 16; hence not 37 divides 1607 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1607 & n is prime
holds not n divides 1607 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1609 is prime
proof
now
1609 = 2*804 + 1; hence not 2 divides 1609 by NAT_4:9;
1609 = 3*536 + 1; hence not 3 divides 1609 by NAT_4:9;
1609 = 5*321 + 4; hence not 5 divides 1609 by NAT_4:9;
1609 = 7*229 + 6; hence not 7 divides 1609 by NAT_4:9;
1609 = 11*146 + 3; hence not 11 divides 1609 by NAT_4:9;
1609 = 13*123 + 10; hence not 13 divides 1609 by NAT_4:9;
1609 = 17*94 + 11; hence not 17 divides 1609 by NAT_4:9;
1609 = 19*84 + 13; hence not 19 divides 1609 by NAT_4:9;
1609 = 23*69 + 22; hence not 23 divides 1609 by NAT_4:9;
1609 = 29*55 + 14; hence not 29 divides 1609 by NAT_4:9;
1609 = 31*51 + 28; hence not 31 divides 1609 by NAT_4:9;
1609 = 37*43 + 18; hence not 37 divides 1609 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1609 & n is prime
holds not n divides 1609 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1613 is prime
proof
now
1613 = 2*806 + 1; hence not 2 divides 1613 by NAT_4:9;
1613 = 3*537 + 2; hence not 3 divides 1613 by NAT_4:9;
1613 = 5*322 + 3; hence not 5 divides 1613 by NAT_4:9;
1613 = 7*230 + 3; hence not 7 divides 1613 by NAT_4:9;
1613 = 11*146 + 7; hence not 11 divides 1613 by NAT_4:9;
1613 = 13*124 + 1; hence not 13 divides 1613 by NAT_4:9;
1613 = 17*94 + 15; hence not 17 divides 1613 by NAT_4:9;
1613 = 19*84 + 17; hence not 19 divides 1613 by NAT_4:9;
1613 = 23*70 + 3; hence not 23 divides 1613 by NAT_4:9;
1613 = 29*55 + 18; hence not 29 divides 1613 by NAT_4:9;
1613 = 31*52 + 1; hence not 31 divides 1613 by NAT_4:9;
1613 = 37*43 + 22; hence not 37 divides 1613 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1613 & n is prime
holds not n divides 1613 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1619 is prime
proof
now
1619 = 2*809 + 1; hence not 2 divides 1619 by NAT_4:9;
1619 = 3*539 + 2; hence not 3 divides 1619 by NAT_4:9;
1619 = 5*323 + 4; hence not 5 divides 1619 by NAT_4:9;
1619 = 7*231 + 2; hence not 7 divides 1619 by NAT_4:9;
1619 = 11*147 + 2; hence not 11 divides 1619 by NAT_4:9;
1619 = 13*124 + 7; hence not 13 divides 1619 by NAT_4:9;
1619 = 17*95 + 4; hence not 17 divides 1619 by NAT_4:9;
1619 = 19*85 + 4; hence not 19 divides 1619 by NAT_4:9;
1619 = 23*70 + 9; hence not 23 divides 1619 by NAT_4:9;
1619 = 29*55 + 24; hence not 29 divides 1619 by NAT_4:9;
1619 = 31*52 + 7; hence not 31 divides 1619 by NAT_4:9;
1619 = 37*43 + 28; hence not 37 divides 1619 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1619 & n is prime
holds not n divides 1619 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1621 is prime
proof
now
1621 = 2*810 + 1; hence not 2 divides 1621 by NAT_4:9;
1621 = 3*540 + 1; hence not 3 divides 1621 by NAT_4:9;
1621 = 5*324 + 1; hence not 5 divides 1621 by NAT_4:9;
1621 = 7*231 + 4; hence not 7 divides 1621 by NAT_4:9;
1621 = 11*147 + 4; hence not 11 divides 1621 by NAT_4:9;
1621 = 13*124 + 9; hence not 13 divides 1621 by NAT_4:9;
1621 = 17*95 + 6; hence not 17 divides 1621 by NAT_4:9;
1621 = 19*85 + 6; hence not 19 divides 1621 by NAT_4:9;
1621 = 23*70 + 11; hence not 23 divides 1621 by NAT_4:9;
1621 = 29*55 + 26; hence not 29 divides 1621 by NAT_4:9;
1621 = 31*52 + 9; hence not 31 divides 1621 by NAT_4:9;
1621 = 37*43 + 30; hence not 37 divides 1621 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1621 & n is prime
holds not n divides 1621 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1627 is prime
proof
now
1627 = 2*813 + 1; hence not 2 divides 1627 by NAT_4:9;
1627 = 3*542 + 1; hence not 3 divides 1627 by NAT_4:9;
1627 = 5*325 + 2; hence not 5 divides 1627 by NAT_4:9;
1627 = 7*232 + 3; hence not 7 divides 1627 by NAT_4:9;
1627 = 11*147 + 10; hence not 11 divides 1627 by NAT_4:9;
1627 = 13*125 + 2; hence not 13 divides 1627 by NAT_4:9;
1627 = 17*95 + 12; hence not 17 divides 1627 by NAT_4:9;
1627 = 19*85 + 12; hence not 19 divides 1627 by NAT_4:9;
1627 = 23*70 + 17; hence not 23 divides 1627 by NAT_4:9;
1627 = 29*56 + 3; hence not 29 divides 1627 by NAT_4:9;
1627 = 31*52 + 15; hence not 31 divides 1627 by NAT_4:9;
1627 = 37*43 + 36; hence not 37 divides 1627 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1627 & n is prime
holds not n divides 1627 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1637 is prime
proof
now
1637 = 2*818 + 1; hence not 2 divides 1637 by NAT_4:9;
1637 = 3*545 + 2; hence not 3 divides 1637 by NAT_4:9;
1637 = 5*327 + 2; hence not 5 divides 1637 by NAT_4:9;
1637 = 7*233 + 6; hence not 7 divides 1637 by NAT_4:9;
1637 = 11*148 + 9; hence not 11 divides 1637 by NAT_4:9;
1637 = 13*125 + 12; hence not 13 divides 1637 by NAT_4:9;
1637 = 17*96 + 5; hence not 17 divides 1637 by NAT_4:9;
1637 = 19*86 + 3; hence not 19 divides 1637 by NAT_4:9;
1637 = 23*71 + 4; hence not 23 divides 1637 by NAT_4:9;
1637 = 29*56 + 13; hence not 29 divides 1637 by NAT_4:9;
1637 = 31*52 + 25; hence not 31 divides 1637 by NAT_4:9;
1637 = 37*44 + 9; hence not 37 divides 1637 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1637 & n is prime
holds not n divides 1637 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
1657 is prime
proof
now
1657 = 2*828 + 1; hence not 2 divides 1657 by NAT_4:9;
1657 = 3*552 + 1; hence not 3 divides 1657 by NAT_4:9;
1657 = 5*331 + 2; hence not 5 divides 1657 by NAT_4:9;
1657 = 7*236 + 5; hence not 7 divides 1657 by NAT_4:9;
1657 = 11*150 + 7; hence not 11 divides 1657 by NAT_4:9;
1657 = 13*127 + 6; hence not 13 divides 1657 by NAT_4:9;
1657 = 17*97 + 8; hence not 17 divides 1657 by NAT_4:9;
1657 = 19*87 + 4; hence not 19 divides 1657 by NAT_4:9;
1657 = 23*72 + 1; hence not 23 divides 1657 by NAT_4:9;
1657 = 29*57 + 4; hence not 29 divides 1657 by NAT_4:9;
1657 = 31*53 + 14; hence not 31 divides 1657 by NAT_4:9;
1657 = 37*44 + 29; hence not 37 divides 1657 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1657 & n is prime
holds not n divides 1657 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1663 is prime
proof
now
1663 = 2*831 + 1; hence not 2 divides 1663 by NAT_4:9;
1663 = 3*554 + 1; hence not 3 divides 1663 by NAT_4:9;
1663 = 5*332 + 3; hence not 5 divides 1663 by NAT_4:9;
1663 = 7*237 + 4; hence not 7 divides 1663 by NAT_4:9;
1663 = 11*151 + 2; hence not 11 divides 1663 by NAT_4:9;
1663 = 13*127 + 12; hence not 13 divides 1663 by NAT_4:9;
1663 = 17*97 + 14; hence not 17 divides 1663 by NAT_4:9;
1663 = 19*87 + 10; hence not 19 divides 1663 by NAT_4:9;
1663 = 23*72 + 7; hence not 23 divides 1663 by NAT_4:9;
1663 = 29*57 + 10; hence not 29 divides 1663 by NAT_4:9;
1663 = 31*53 + 20; hence not 31 divides 1663 by NAT_4:9;
1663 = 37*44 + 35; hence not 37 divides 1663 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1663 & n is prime
holds not n divides 1663 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1667 is prime
proof
now
1667 = 2*833 + 1; hence not 2 divides 1667 by NAT_4:9;
1667 = 3*555 + 2; hence not 3 divides 1667 by NAT_4:9;
1667 = 5*333 + 2; hence not 5 divides 1667 by NAT_4:9;
1667 = 7*238 + 1; hence not 7 divides 1667 by NAT_4:9;
1667 = 11*151 + 6; hence not 11 divides 1667 by NAT_4:9;
1667 = 13*128 + 3; hence not 13 divides 1667 by NAT_4:9;
1667 = 17*98 + 1; hence not 17 divides 1667 by NAT_4:9;
1667 = 19*87 + 14; hence not 19 divides 1667 by NAT_4:9;
1667 = 23*72 + 11; hence not 23 divides 1667 by NAT_4:9;
1667 = 29*57 + 14; hence not 29 divides 1667 by NAT_4:9;
1667 = 31*53 + 24; hence not 31 divides 1667 by NAT_4:9;
1667 = 37*45 + 2; hence not 37 divides 1667 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1667 & n is prime
holds not n divides 1667 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1669 is prime
proof
now
1669 = 2*834 + 1; hence not 2 divides 1669 by NAT_4:9;
1669 = 3*556 + 1; hence not 3 divides 1669 by NAT_4:9;
1669 = 5*333 + 4; hence not 5 divides 1669 by NAT_4:9;
1669 = 7*238 + 3; hence not 7 divides 1669 by NAT_4:9;
1669 = 11*151 + 8; hence not 11 divides 1669 by NAT_4:9;
1669 = 13*128 + 5; hence not 13 divides 1669 by NAT_4:9;
1669 = 17*98 + 3; hence not 17 divides 1669 by NAT_4:9;
1669 = 19*87 + 16; hence not 19 divides 1669 by NAT_4:9;
1669 = 23*72 + 13; hence not 23 divides 1669 by NAT_4:9;
1669 = 29*57 + 16; hence not 29 divides 1669 by NAT_4:9;
1669 = 31*53 + 26; hence not 31 divides 1669 by NAT_4:9;
1669 = 37*45 + 4; hence not 37 divides 1669 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1669 & n is prime
holds not n divides 1669 by XPRIMET1:24;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
1693 is prime
proof
now
1693 = 2*846 + 1; hence not 2 divides 1693 by NAT_4:9;
1693 = 3*564 + 1; hence not 3 divides 1693 by NAT_4:9;
1693 = 5*338 + 3; hence not 5 divides 1693 by NAT_4:9;
1693 = 7*241 + 6; hence not 7 divides 1693 by NAT_4:9;
1693 = 11*153 + 10; hence not 11 divides 1693 by NAT_4:9;
1693 = 13*130 + 3; hence not 13 divides 1693 by NAT_4:9;
1693 = 17*99 + 10; hence not 17 divides 1693 by NAT_4:9;
1693 = 19*89 + 2; hence not 19 divides 1693 by NAT_4:9;
1693 = 23*73 + 14; hence not 23 divides 1693 by NAT_4:9;
1693 = 29*58 + 11; hence not 29 divides 1693 by NAT_4:9;
1693 = 31*54 + 19; hence not 31 divides 1693 by NAT_4:9;
1693 = 37*45 + 28; hence not 37 divides 1693 by NAT_4:9;
1693 = 41*41 + 12; hence not 41 divides 1693 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1693 & n is prime
holds not n divides 1693 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1697 is prime
proof
now
1697 = 2*848 + 1; hence not 2 divides 1697 by NAT_4:9;
1697 = 3*565 + 2; hence not 3 divides 1697 by NAT_4:9;
1697 = 5*339 + 2; hence not 5 divides 1697 by NAT_4:9;
1697 = 7*242 + 3; hence not 7 divides 1697 by NAT_4:9;
1697 = 11*154 + 3; hence not 11 divides 1697 by NAT_4:9;
1697 = 13*130 + 7; hence not 13 divides 1697 by NAT_4:9;
1697 = 17*99 + 14; hence not 17 divides 1697 by NAT_4:9;
1697 = 19*89 + 6; hence not 19 divides 1697 by NAT_4:9;
1697 = 23*73 + 18; hence not 23 divides 1697 by NAT_4:9;
1697 = 29*58 + 15; hence not 29 divides 1697 by NAT_4:9;
1697 = 31*54 + 23; hence not 31 divides 1697 by NAT_4:9;
1697 = 37*45 + 32; hence not 37 divides 1697 by NAT_4:9;
1697 = 41*41 + 16; hence not 41 divides 1697 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1697 & n is prime
holds not n divides 1697 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1699 is prime
proof
now
1699 = 2*849 + 1; hence not 2 divides 1699 by NAT_4:9;
1699 = 3*566 + 1; hence not 3 divides 1699 by NAT_4:9;
1699 = 5*339 + 4; hence not 5 divides 1699 by NAT_4:9;
1699 = 7*242 + 5; hence not 7 divides 1699 by NAT_4:9;
1699 = 11*154 + 5; hence not 11 divides 1699 by NAT_4:9;
1699 = 13*130 + 9; hence not 13 divides 1699 by NAT_4:9;
1699 = 17*99 + 16; hence not 17 divides 1699 by NAT_4:9;
1699 = 19*89 + 8; hence not 19 divides 1699 by NAT_4:9;
1699 = 23*73 + 20; hence not 23 divides 1699 by NAT_4:9;
1699 = 29*58 + 17; hence not 29 divides 1699 by NAT_4:9;
1699 = 31*54 + 25; hence not 31 divides 1699 by NAT_4:9;
1699 = 37*45 + 34; hence not 37 divides 1699 by NAT_4:9;
1699 = 41*41 + 18; hence not 41 divides 1699 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1699 & n is prime
holds not n divides 1699 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1709 is prime
proof
now
1709 = 2*854 + 1; hence not 2 divides 1709 by NAT_4:9;
1709 = 3*569 + 2; hence not 3 divides 1709 by NAT_4:9;
1709 = 5*341 + 4; hence not 5 divides 1709 by NAT_4:9;
1709 = 7*244 + 1; hence not 7 divides 1709 by NAT_4:9;
1709 = 11*155 + 4; hence not 11 divides 1709 by NAT_4:9;
1709 = 13*131 + 6; hence not 13 divides 1709 by NAT_4:9;
1709 = 17*100 + 9; hence not 17 divides 1709 by NAT_4:9;
1709 = 19*89 + 18; hence not 19 divides 1709 by NAT_4:9;
1709 = 23*74 + 7; hence not 23 divides 1709 by NAT_4:9;
1709 = 29*58 + 27; hence not 29 divides 1709 by NAT_4:9;
1709 = 31*55 + 4; hence not 31 divides 1709 by NAT_4:9;
1709 = 37*46 + 7; hence not 37 divides 1709 by NAT_4:9;
1709 = 41*41 + 28; hence not 41 divides 1709 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1709 & n is prime
holds not n divides 1709 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1721 is prime
proof
now
1721 = 2*860 + 1; hence not 2 divides 1721 by NAT_4:9;
1721 = 3*573 + 2; hence not 3 divides 1721 by NAT_4:9;
1721 = 5*344 + 1; hence not 5 divides 1721 by NAT_4:9;
1721 = 7*245 + 6; hence not 7 divides 1721 by NAT_4:9;
1721 = 11*156 + 5; hence not 11 divides 1721 by NAT_4:9;
1721 = 13*132 + 5; hence not 13 divides 1721 by NAT_4:9;
1721 = 17*101 + 4; hence not 17 divides 1721 by NAT_4:9;
1721 = 19*90 + 11; hence not 19 divides 1721 by NAT_4:9;
1721 = 23*74 + 19; hence not 23 divides 1721 by NAT_4:9;
1721 = 29*59 + 10; hence not 29 divides 1721 by NAT_4:9;
1721 = 31*55 + 16; hence not 31 divides 1721 by NAT_4:9;
1721 = 37*46 + 19; hence not 37 divides 1721 by NAT_4:9;
1721 = 41*41 + 40; hence not 41 divides 1721 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1721 & n is prime
holds not n divides 1721 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1723 is prime
proof
now
1723 = 2*861 + 1; hence not 2 divides 1723 by NAT_4:9;
1723 = 3*574 + 1; hence not 3 divides 1723 by NAT_4:9;
1723 = 5*344 + 3; hence not 5 divides 1723 by NAT_4:9;
1723 = 7*246 + 1; hence not 7 divides 1723 by NAT_4:9;
1723 = 11*156 + 7; hence not 11 divides 1723 by NAT_4:9;
1723 = 13*132 + 7; hence not 13 divides 1723 by NAT_4:9;
1723 = 17*101 + 6; hence not 17 divides 1723 by NAT_4:9;
1723 = 19*90 + 13; hence not 19 divides 1723 by NAT_4:9;
1723 = 23*74 + 21; hence not 23 divides 1723 by NAT_4:9;
1723 = 29*59 + 12; hence not 29 divides 1723 by NAT_4:9;
1723 = 31*55 + 18; hence not 31 divides 1723 by NAT_4:9;
1723 = 37*46 + 21; hence not 37 divides 1723 by NAT_4:9;
1723 = 41*42 + 1; hence not 41 divides 1723 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1723 & n is prime
holds not n divides 1723 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1733 is prime
proof
now
1733 = 2*866 + 1; hence not 2 divides 1733 by NAT_4:9;
1733 = 3*577 + 2; hence not 3 divides 1733 by NAT_4:9;
1733 = 5*346 + 3; hence not 5 divides 1733 by NAT_4:9;
1733 = 7*247 + 4; hence not 7 divides 1733 by NAT_4:9;
1733 = 11*157 + 6; hence not 11 divides 1733 by NAT_4:9;
1733 = 13*133 + 4; hence not 13 divides 1733 by NAT_4:9;
1733 = 17*101 + 16; hence not 17 divides 1733 by NAT_4:9;
1733 = 19*91 + 4; hence not 19 divides 1733 by NAT_4:9;
1733 = 23*75 + 8; hence not 23 divides 1733 by NAT_4:9;
1733 = 29*59 + 22; hence not 29 divides 1733 by NAT_4:9;
1733 = 31*55 + 28; hence not 31 divides 1733 by NAT_4:9;
1733 = 37*46 + 31; hence not 37 divides 1733 by NAT_4:9;
1733 = 41*42 + 11; hence not 41 divides 1733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1733 & n is prime
holds not n divides 1733 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1741 is prime
proof
now
1741 = 2*870 + 1; hence not 2 divides 1741 by NAT_4:9;
1741 = 3*580 + 1; hence not 3 divides 1741 by NAT_4:9;
1741 = 5*348 + 1; hence not 5 divides 1741 by NAT_4:9;
1741 = 7*248 + 5; hence not 7 divides 1741 by NAT_4:9;
1741 = 11*158 + 3; hence not 11 divides 1741 by NAT_4:9;
1741 = 13*133 + 12; hence not 13 divides 1741 by NAT_4:9;
1741 = 17*102 + 7; hence not 17 divides 1741 by NAT_4:9;
1741 = 19*91 + 12; hence not 19 divides 1741 by NAT_4:9;
1741 = 23*75 + 16; hence not 23 divides 1741 by NAT_4:9;
1741 = 29*60 + 1; hence not 29 divides 1741 by NAT_4:9;
1741 = 31*56 + 5; hence not 31 divides 1741 by NAT_4:9;
1741 = 37*47 + 2; hence not 37 divides 1741 by NAT_4:9;
1741 = 41*42 + 19; hence not 41 divides 1741 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1741 & n is prime
holds not n divides 1741 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1747 is prime
proof
now
1747 = 2*873 + 1; hence not 2 divides 1747 by NAT_4:9;
1747 = 3*582 + 1; hence not 3 divides 1747 by NAT_4:9;
1747 = 5*349 + 2; hence not 5 divides 1747 by NAT_4:9;
1747 = 7*249 + 4; hence not 7 divides 1747 by NAT_4:9;
1747 = 11*158 + 9; hence not 11 divides 1747 by NAT_4:9;
1747 = 13*134 + 5; hence not 13 divides 1747 by NAT_4:9;
1747 = 17*102 + 13; hence not 17 divides 1747 by NAT_4:9;
1747 = 19*91 + 18; hence not 19 divides 1747 by NAT_4:9;
1747 = 23*75 + 22; hence not 23 divides 1747 by NAT_4:9;
1747 = 29*60 + 7; hence not 29 divides 1747 by NAT_4:9;
1747 = 31*56 + 11; hence not 31 divides 1747 by NAT_4:9;
1747 = 37*47 + 8; hence not 37 divides 1747 by NAT_4:9;
1747 = 41*42 + 25; hence not 41 divides 1747 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1747 & n is prime
holds not n divides 1747 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1753 is prime
proof
now
1753 = 2*876 + 1; hence not 2 divides 1753 by NAT_4:9;
1753 = 3*584 + 1; hence not 3 divides 1753 by NAT_4:9;
1753 = 5*350 + 3; hence not 5 divides 1753 by NAT_4:9;
1753 = 7*250 + 3; hence not 7 divides 1753 by NAT_4:9;
1753 = 11*159 + 4; hence not 11 divides 1753 by NAT_4:9;
1753 = 13*134 + 11; hence not 13 divides 1753 by NAT_4:9;
1753 = 17*103 + 2; hence not 17 divides 1753 by NAT_4:9;
1753 = 19*92 + 5; hence not 19 divides 1753 by NAT_4:9;
1753 = 23*76 + 5; hence not 23 divides 1753 by NAT_4:9;
1753 = 29*60 + 13; hence not 29 divides 1753 by NAT_4:9;
1753 = 31*56 + 17; hence not 31 divides 1753 by NAT_4:9;
1753 = 37*47 + 14; hence not 37 divides 1753 by NAT_4:9;
1753 = 41*42 + 31; hence not 41 divides 1753 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1753 & n is prime
holds not n divides 1753 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1759 is prime
proof
now
1759 = 2*879 + 1; hence not 2 divides 1759 by NAT_4:9;
1759 = 3*586 + 1; hence not 3 divides 1759 by NAT_4:9;
1759 = 5*351 + 4; hence not 5 divides 1759 by NAT_4:9;
1759 = 7*251 + 2; hence not 7 divides 1759 by NAT_4:9;
1759 = 11*159 + 10; hence not 11 divides 1759 by NAT_4:9;
1759 = 13*135 + 4; hence not 13 divides 1759 by NAT_4:9;
1759 = 17*103 + 8; hence not 17 divides 1759 by NAT_4:9;
1759 = 19*92 + 11; hence not 19 divides 1759 by NAT_4:9;
1759 = 23*76 + 11; hence not 23 divides 1759 by NAT_4:9;
1759 = 29*60 + 19; hence not 29 divides 1759 by NAT_4:9;
1759 = 31*56 + 23; hence not 31 divides 1759 by NAT_4:9;
1759 = 37*47 + 20; hence not 37 divides 1759 by NAT_4:9;
1759 = 41*42 + 37; hence not 41 divides 1759 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1759 & n is prime
holds not n divides 1759 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
1777 is prime
proof
now
1777 = 2*888 + 1; hence not 2 divides 1777 by NAT_4:9;
1777 = 3*592 + 1; hence not 3 divides 1777 by NAT_4:9;
1777 = 5*355 + 2; hence not 5 divides 1777 by NAT_4:9;
1777 = 7*253 + 6; hence not 7 divides 1777 by NAT_4:9;
1777 = 11*161 + 6; hence not 11 divides 1777 by NAT_4:9;
1777 = 13*136 + 9; hence not 13 divides 1777 by NAT_4:9;
1777 = 17*104 + 9; hence not 17 divides 1777 by NAT_4:9;
1777 = 19*93 + 10; hence not 19 divides 1777 by NAT_4:9;
1777 = 23*77 + 6; hence not 23 divides 1777 by NAT_4:9;
1777 = 29*61 + 8; hence not 29 divides 1777 by NAT_4:9;
1777 = 31*57 + 10; hence not 31 divides 1777 by NAT_4:9;
1777 = 37*48 + 1; hence not 37 divides 1777 by NAT_4:9;
1777 = 41*43 + 14; hence not 41 divides 1777 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1777 & n is prime
holds not n divides 1777 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1783 is prime
proof
now
1783 = 2*891 + 1; hence not 2 divides 1783 by NAT_4:9;
1783 = 3*594 + 1; hence not 3 divides 1783 by NAT_4:9;
1783 = 5*356 + 3; hence not 5 divides 1783 by NAT_4:9;
1783 = 7*254 + 5; hence not 7 divides 1783 by NAT_4:9;
1783 = 11*162 + 1; hence not 11 divides 1783 by NAT_4:9;
1783 = 13*137 + 2; hence not 13 divides 1783 by NAT_4:9;
1783 = 17*104 + 15; hence not 17 divides 1783 by NAT_4:9;
1783 = 19*93 + 16; hence not 19 divides 1783 by NAT_4:9;
1783 = 23*77 + 12; hence not 23 divides 1783 by NAT_4:9;
1783 = 29*61 + 14; hence not 29 divides 1783 by NAT_4:9;
1783 = 31*57 + 16; hence not 31 divides 1783 by NAT_4:9;
1783 = 37*48 + 7; hence not 37 divides 1783 by NAT_4:9;
1783 = 41*43 + 20; hence not 41 divides 1783 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1783 & n is prime
holds not n divides 1783 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1787 is prime
proof
now
1787 = 2*893 + 1; hence not 2 divides 1787 by NAT_4:9;
1787 = 3*595 + 2; hence not 3 divides 1787 by NAT_4:9;
1787 = 5*357 + 2; hence not 5 divides 1787 by NAT_4:9;
1787 = 7*255 + 2; hence not 7 divides 1787 by NAT_4:9;
1787 = 11*162 + 5; hence not 11 divides 1787 by NAT_4:9;
1787 = 13*137 + 6; hence not 13 divides 1787 by NAT_4:9;
1787 = 17*105 + 2; hence not 17 divides 1787 by NAT_4:9;
1787 = 19*94 + 1; hence not 19 divides 1787 by NAT_4:9;
1787 = 23*77 + 16; hence not 23 divides 1787 by NAT_4:9;
1787 = 29*61 + 18; hence not 29 divides 1787 by NAT_4:9;
1787 = 31*57 + 20; hence not 31 divides 1787 by NAT_4:9;
1787 = 37*48 + 11; hence not 37 divides 1787 by NAT_4:9;
1787 = 41*43 + 24; hence not 41 divides 1787 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1787 & n is prime
holds not n divides 1787 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1789 is prime
proof
now
1789 = 2*894 + 1; hence not 2 divides 1789 by NAT_4:9;
1789 = 3*596 + 1; hence not 3 divides 1789 by NAT_4:9;
1789 = 5*357 + 4; hence not 5 divides 1789 by NAT_4:9;
1789 = 7*255 + 4; hence not 7 divides 1789 by NAT_4:9;
1789 = 11*162 + 7; hence not 11 divides 1789 by NAT_4:9;
1789 = 13*137 + 8; hence not 13 divides 1789 by NAT_4:9;
1789 = 17*105 + 4; hence not 17 divides 1789 by NAT_4:9;
1789 = 19*94 + 3; hence not 19 divides 1789 by NAT_4:9;
1789 = 23*77 + 18; hence not 23 divides 1789 by NAT_4:9;
1789 = 29*61 + 20; hence not 29 divides 1789 by NAT_4:9;
1789 = 31*57 + 22; hence not 31 divides 1789 by NAT_4:9;
1789 = 37*48 + 13; hence not 37 divides 1789 by NAT_4:9;
1789 = 41*43 + 26; hence not 41 divides 1789 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1789 & n is prime
holds not n divides 1789 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1801 is prime
proof
now
1801 = 2*900 + 1; hence not 2 divides 1801 by NAT_4:9;
1801 = 3*600 + 1; hence not 3 divides 1801 by NAT_4:9;
1801 = 5*360 + 1; hence not 5 divides 1801 by NAT_4:9;
1801 = 7*257 + 2; hence not 7 divides 1801 by NAT_4:9;
1801 = 11*163 + 8; hence not 11 divides 1801 by NAT_4:9;
1801 = 13*138 + 7; hence not 13 divides 1801 by NAT_4:9;
1801 = 17*105 + 16; hence not 17 divides 1801 by NAT_4:9;
1801 = 19*94 + 15; hence not 19 divides 1801 by NAT_4:9;
1801 = 23*78 + 7; hence not 23 divides 1801 by NAT_4:9;
1801 = 29*62 + 3; hence not 29 divides 1801 by NAT_4:9;
1801 = 31*58 + 3; hence not 31 divides 1801 by NAT_4:9;
1801 = 37*48 + 25; hence not 37 divides 1801 by NAT_4:9;
1801 = 41*43 + 38; hence not 41 divides 1801 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1801 & n is prime
holds not n divides 1801 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1811 is prime
proof
now
1811 = 2*905 + 1; hence not 2 divides 1811 by NAT_4:9;
1811 = 3*603 + 2; hence not 3 divides 1811 by NAT_4:9;
1811 = 5*362 + 1; hence not 5 divides 1811 by NAT_4:9;
1811 = 7*258 + 5; hence not 7 divides 1811 by NAT_4:9;
1811 = 11*164 + 7; hence not 11 divides 1811 by NAT_4:9;
1811 = 13*139 + 4; hence not 13 divides 1811 by NAT_4:9;
1811 = 17*106 + 9; hence not 17 divides 1811 by NAT_4:9;
1811 = 19*95 + 6; hence not 19 divides 1811 by NAT_4:9;
1811 = 23*78 + 17; hence not 23 divides 1811 by NAT_4:9;
1811 = 29*62 + 13; hence not 29 divides 1811 by NAT_4:9;
1811 = 31*58 + 13; hence not 31 divides 1811 by NAT_4:9;
1811 = 37*48 + 35; hence not 37 divides 1811 by NAT_4:9;
1811 = 41*44 + 7; hence not 41 divides 1811 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1811 & n is prime
holds not n divides 1811 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1823 is prime
proof
now
1823 = 2*911 + 1; hence not 2 divides 1823 by NAT_4:9;
1823 = 3*607 + 2; hence not 3 divides 1823 by NAT_4:9;
1823 = 5*364 + 3; hence not 5 divides 1823 by NAT_4:9;
1823 = 7*260 + 3; hence not 7 divides 1823 by NAT_4:9;
1823 = 11*165 + 8; hence not 11 divides 1823 by NAT_4:9;
1823 = 13*140 + 3; hence not 13 divides 1823 by NAT_4:9;
1823 = 17*107 + 4; hence not 17 divides 1823 by NAT_4:9;
1823 = 19*95 + 18; hence not 19 divides 1823 by NAT_4:9;
1823 = 23*79 + 6; hence not 23 divides 1823 by NAT_4:9;
1823 = 29*62 + 25; hence not 29 divides 1823 by NAT_4:9;
1823 = 31*58 + 25; hence not 31 divides 1823 by NAT_4:9;
1823 = 37*49 + 10; hence not 37 divides 1823 by NAT_4:9;
1823 = 41*44 + 19; hence not 41 divides 1823 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1823 & n is prime
holds not n divides 1823 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1831 is prime
proof
now
1831 = 2*915 + 1; hence not 2 divides 1831 by NAT_4:9;
1831 = 3*610 + 1; hence not 3 divides 1831 by NAT_4:9;
1831 = 5*366 + 1; hence not 5 divides 1831 by NAT_4:9;
1831 = 7*261 + 4; hence not 7 divides 1831 by NAT_4:9;
1831 = 11*166 + 5; hence not 11 divides 1831 by NAT_4:9;
1831 = 13*140 + 11; hence not 13 divides 1831 by NAT_4:9;
1831 = 17*107 + 12; hence not 17 divides 1831 by NAT_4:9;
1831 = 19*96 + 7; hence not 19 divides 1831 by NAT_4:9;
1831 = 23*79 + 14; hence not 23 divides 1831 by NAT_4:9;
1831 = 29*63 + 4; hence not 29 divides 1831 by NAT_4:9;
1831 = 31*59 + 2; hence not 31 divides 1831 by NAT_4:9;
1831 = 37*49 + 18; hence not 37 divides 1831 by NAT_4:9;
1831 = 41*44 + 27; hence not 41 divides 1831 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1831 & n is prime
holds not n divides 1831 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
1847 is prime
proof
now
1847 = 2*923 + 1; hence not 2 divides 1847 by NAT_4:9;
1847 = 3*615 + 2; hence not 3 divides 1847 by NAT_4:9;
1847 = 5*369 + 2; hence not 5 divides 1847 by NAT_4:9;
1847 = 7*263 + 6; hence not 7 divides 1847 by NAT_4:9;
1847 = 11*167 + 10; hence not 11 divides 1847 by NAT_4:9;
1847 = 13*142 + 1; hence not 13 divides 1847 by NAT_4:9;
1847 = 17*108 + 11; hence not 17 divides 1847 by NAT_4:9;
1847 = 19*97 + 4; hence not 19 divides 1847 by NAT_4:9;
1847 = 23*80 + 7; hence not 23 divides 1847 by NAT_4:9;
1847 = 29*63 + 20; hence not 29 divides 1847 by NAT_4:9;
1847 = 31*59 + 18; hence not 31 divides 1847 by NAT_4:9;
1847 = 37*49 + 34; hence not 37 divides 1847 by NAT_4:9;
1847 = 41*45 + 2; hence not 41 divides 1847 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1847 & n is prime
holds not n divides 1847 by XPRIMET1:26;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
1861 is prime
proof
now
1861 = 2*930 + 1; hence not 2 divides 1861 by NAT_4:9;
1861 = 3*620 + 1; hence not 3 divides 1861 by NAT_4:9;
1861 = 5*372 + 1; hence not 5 divides 1861 by NAT_4:9;
1861 = 7*265 + 6; hence not 7 divides 1861 by NAT_4:9;
1861 = 11*169 + 2; hence not 11 divides 1861 by NAT_4:9;
1861 = 13*143 + 2; hence not 13 divides 1861 by NAT_4:9;
1861 = 17*109 + 8; hence not 17 divides 1861 by NAT_4:9;
1861 = 19*97 + 18; hence not 19 divides 1861 by NAT_4:9;
1861 = 23*80 + 21; hence not 23 divides 1861 by NAT_4:9;
1861 = 29*64 + 5; hence not 29 divides 1861 by NAT_4:9;
1861 = 31*60 + 1; hence not 31 divides 1861 by NAT_4:9;
1861 = 37*50 + 11; hence not 37 divides 1861 by NAT_4:9;
1861 = 41*45 + 16; hence not 41 divides 1861 by NAT_4:9;
1861 = 43*43 + 12; hence not 43 divides 1861 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1861 & n is prime
holds not n divides 1861 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1867 is prime
proof
now
1867 = 2*933 + 1; hence not 2 divides 1867 by NAT_4:9;
1867 = 3*622 + 1; hence not 3 divides 1867 by NAT_4:9;
1867 = 5*373 + 2; hence not 5 divides 1867 by NAT_4:9;
1867 = 7*266 + 5; hence not 7 divides 1867 by NAT_4:9;
1867 = 11*169 + 8; hence not 11 divides 1867 by NAT_4:9;
1867 = 13*143 + 8; hence not 13 divides 1867 by NAT_4:9;
1867 = 17*109 + 14; hence not 17 divides 1867 by NAT_4:9;
1867 = 19*98 + 5; hence not 19 divides 1867 by NAT_4:9;
1867 = 23*81 + 4; hence not 23 divides 1867 by NAT_4:9;
1867 = 29*64 + 11; hence not 29 divides 1867 by NAT_4:9;
1867 = 31*60 + 7; hence not 31 divides 1867 by NAT_4:9;
1867 = 37*50 + 17; hence not 37 divides 1867 by NAT_4:9;
1867 = 41*45 + 22; hence not 41 divides 1867 by NAT_4:9;
1867 = 43*43 + 18; hence not 43 divides 1867 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1867 & n is prime
holds not n divides 1867 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1871 is prime
proof
now
1871 = 2*935 + 1; hence not 2 divides 1871 by NAT_4:9;
1871 = 3*623 + 2; hence not 3 divides 1871 by NAT_4:9;
1871 = 5*374 + 1; hence not 5 divides 1871 by NAT_4:9;
1871 = 7*267 + 2; hence not 7 divides 1871 by NAT_4:9;
1871 = 11*170 + 1; hence not 11 divides 1871 by NAT_4:9;
1871 = 13*143 + 12; hence not 13 divides 1871 by NAT_4:9;
1871 = 17*110 + 1; hence not 17 divides 1871 by NAT_4:9;
1871 = 19*98 + 9; hence not 19 divides 1871 by NAT_4:9;
1871 = 23*81 + 8; hence not 23 divides 1871 by NAT_4:9;
1871 = 29*64 + 15; hence not 29 divides 1871 by NAT_4:9;
1871 = 31*60 + 11; hence not 31 divides 1871 by NAT_4:9;
1871 = 37*50 + 21; hence not 37 divides 1871 by NAT_4:9;
1871 = 41*45 + 26; hence not 41 divides 1871 by NAT_4:9;
1871 = 43*43 + 22; hence not 43 divides 1871 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1871 & n is prime
holds not n divides 1871 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1873 is prime
proof
now
1873 = 2*936 + 1; hence not 2 divides 1873 by NAT_4:9;
1873 = 3*624 + 1; hence not 3 divides 1873 by NAT_4:9;
1873 = 5*374 + 3; hence not 5 divides 1873 by NAT_4:9;
1873 = 7*267 + 4; hence not 7 divides 1873 by NAT_4:9;
1873 = 11*170 + 3; hence not 11 divides 1873 by NAT_4:9;
1873 = 13*144 + 1; hence not 13 divides 1873 by NAT_4:9;
1873 = 17*110 + 3; hence not 17 divides 1873 by NAT_4:9;
1873 = 19*98 + 11; hence not 19 divides 1873 by NAT_4:9;
1873 = 23*81 + 10; hence not 23 divides 1873 by NAT_4:9;
1873 = 29*64 + 17; hence not 29 divides 1873 by NAT_4:9;
1873 = 31*60 + 13; hence not 31 divides 1873 by NAT_4:9;
1873 = 37*50 + 23; hence not 37 divides 1873 by NAT_4:9;
1873 = 41*45 + 28; hence not 41 divides 1873 by NAT_4:9;
1873 = 43*43 + 24; hence not 43 divides 1873 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1873 & n is prime
holds not n divides 1873 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1877 is prime
proof
now
1877 = 2*938 + 1; hence not 2 divides 1877 by NAT_4:9;
1877 = 3*625 + 2; hence not 3 divides 1877 by NAT_4:9;
1877 = 5*375 + 2; hence not 5 divides 1877 by NAT_4:9;
1877 = 7*268 + 1; hence not 7 divides 1877 by NAT_4:9;
1877 = 11*170 + 7; hence not 11 divides 1877 by NAT_4:9;
1877 = 13*144 + 5; hence not 13 divides 1877 by NAT_4:9;
1877 = 17*110 + 7; hence not 17 divides 1877 by NAT_4:9;
1877 = 19*98 + 15; hence not 19 divides 1877 by NAT_4:9;
1877 = 23*81 + 14; hence not 23 divides 1877 by NAT_4:9;
1877 = 29*64 + 21; hence not 29 divides 1877 by NAT_4:9;
1877 = 31*60 + 17; hence not 31 divides 1877 by NAT_4:9;
1877 = 37*50 + 27; hence not 37 divides 1877 by NAT_4:9;
1877 = 41*45 + 32; hence not 41 divides 1877 by NAT_4:9;
1877 = 43*43 + 28; hence not 43 divides 1877 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1877 & n is prime
holds not n divides 1877 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1879 is prime
proof
now
1879 = 2*939 + 1; hence not 2 divides 1879 by NAT_4:9;
1879 = 3*626 + 1; hence not 3 divides 1879 by NAT_4:9;
1879 = 5*375 + 4; hence not 5 divides 1879 by NAT_4:9;
1879 = 7*268 + 3; hence not 7 divides 1879 by NAT_4:9;
1879 = 11*170 + 9; hence not 11 divides 1879 by NAT_4:9;
1879 = 13*144 + 7; hence not 13 divides 1879 by NAT_4:9;
1879 = 17*110 + 9; hence not 17 divides 1879 by NAT_4:9;
1879 = 19*98 + 17; hence not 19 divides 1879 by NAT_4:9;
1879 = 23*81 + 16; hence not 23 divides 1879 by NAT_4:9;
1879 = 29*64 + 23; hence not 29 divides 1879 by NAT_4:9;
1879 = 31*60 + 19; hence not 31 divides 1879 by NAT_4:9;
1879 = 37*50 + 29; hence not 37 divides 1879 by NAT_4:9;
1879 = 41*45 + 34; hence not 41 divides 1879 by NAT_4:9;
1879 = 43*43 + 30; hence not 43 divides 1879 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1879 & n is prime
holds not n divides 1879 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
1889 is prime
proof
now
1889 = 2*944 + 1; hence not 2 divides 1889 by NAT_4:9;
1889 = 3*629 + 2; hence not 3 divides 1889 by NAT_4:9;
1889 = 5*377 + 4; hence not 5 divides 1889 by NAT_4:9;
1889 = 7*269 + 6; hence not 7 divides 1889 by NAT_4:9;
1889 = 11*171 + 8; hence not 11 divides 1889 by NAT_4:9;
1889 = 13*145 + 4; hence not 13 divides 1889 by NAT_4:9;
1889 = 17*111 + 2; hence not 17 divides 1889 by NAT_4:9;
1889 = 19*99 + 8; hence not 19 divides 1889 by NAT_4:9;
1889 = 23*82 + 3; hence not 23 divides 1889 by NAT_4:9;
1889 = 29*65 + 4; hence not 29 divides 1889 by NAT_4:9;
1889 = 31*60 + 29; hence not 31 divides 1889 by NAT_4:9;
1889 = 37*51 + 2; hence not 37 divides 1889 by NAT_4:9;
1889 = 41*46 + 3; hence not 41 divides 1889 by NAT_4:9;
1889 = 43*43 + 40; hence not 43 divides 1889 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1889 & n is prime
holds not n divides 1889 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
1901 is prime
proof
now
1901 = 2*950 + 1; hence not 2 divides 1901 by NAT_4:9;
1901 = 3*633 + 2; hence not 3 divides 1901 by NAT_4:9;
1901 = 5*380 + 1; hence not 5 divides 1901 by NAT_4:9;
1901 = 7*271 + 4; hence not 7 divides 1901 by NAT_4:9;
1901 = 11*172 + 9; hence not 11 divides 1901 by NAT_4:9;
1901 = 13*146 + 3; hence not 13 divides 1901 by NAT_4:9;
1901 = 17*111 + 14; hence not 17 divides 1901 by NAT_4:9;
1901 = 19*100 + 1; hence not 19 divides 1901 by NAT_4:9;
1901 = 23*82 + 15; hence not 23 divides 1901 by NAT_4:9;
1901 = 29*65 + 16; hence not 29 divides 1901 by NAT_4:9;
1901 = 31*61 + 10; hence not 31 divides 1901 by NAT_4:9;
1901 = 37*51 + 14; hence not 37 divides 1901 by NAT_4:9;
1901 = 41*46 + 15; hence not 41 divides 1901 by NAT_4:9;
1901 = 43*44 + 9; hence not 43 divides 1901 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1901 & n is prime
holds not n divides 1901 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1907 is prime
proof
now
1907 = 2*953 + 1; hence not 2 divides 1907 by NAT_4:9;
1907 = 3*635 + 2; hence not 3 divides 1907 by NAT_4:9;
1907 = 5*381 + 2; hence not 5 divides 1907 by NAT_4:9;
1907 = 7*272 + 3; hence not 7 divides 1907 by NAT_4:9;
1907 = 11*173 + 4; hence not 11 divides 1907 by NAT_4:9;
1907 = 13*146 + 9; hence not 13 divides 1907 by NAT_4:9;
1907 = 17*112 + 3; hence not 17 divides 1907 by NAT_4:9;
1907 = 19*100 + 7; hence not 19 divides 1907 by NAT_4:9;
1907 = 23*82 + 21; hence not 23 divides 1907 by NAT_4:9;
1907 = 29*65 + 22; hence not 29 divides 1907 by NAT_4:9;
1907 = 31*61 + 16; hence not 31 divides 1907 by NAT_4:9;
1907 = 37*51 + 20; hence not 37 divides 1907 by NAT_4:9;
1907 = 41*46 + 21; hence not 41 divides 1907 by NAT_4:9;
1907 = 43*44 + 15; hence not 43 divides 1907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1907 & n is prime
holds not n divides 1907 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1913 is prime
proof
now
1913 = 2*956 + 1; hence not 2 divides 1913 by NAT_4:9;
1913 = 3*637 + 2; hence not 3 divides 1913 by NAT_4:9;
1913 = 5*382 + 3; hence not 5 divides 1913 by NAT_4:9;
1913 = 7*273 + 2; hence not 7 divides 1913 by NAT_4:9;
1913 = 11*173 + 10; hence not 11 divides 1913 by NAT_4:9;
1913 = 13*147 + 2; hence not 13 divides 1913 by NAT_4:9;
1913 = 17*112 + 9; hence not 17 divides 1913 by NAT_4:9;
1913 = 19*100 + 13; hence not 19 divides 1913 by NAT_4:9;
1913 = 23*83 + 4; hence not 23 divides 1913 by NAT_4:9;
1913 = 29*65 + 28; hence not 29 divides 1913 by NAT_4:9;
1913 = 31*61 + 22; hence not 31 divides 1913 by NAT_4:9;
1913 = 37*51 + 26; hence not 37 divides 1913 by NAT_4:9;
1913 = 41*46 + 27; hence not 41 divides 1913 by NAT_4:9;
1913 = 43*44 + 21; hence not 43 divides 1913 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1913 & n is prime
holds not n divides 1913 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
1931 is prime
proof
now
1931 = 2*965 + 1; hence not 2 divides 1931 by NAT_4:9;
1931 = 3*643 + 2; hence not 3 divides 1931 by NAT_4:9;
1931 = 5*386 + 1; hence not 5 divides 1931 by NAT_4:9;
1931 = 7*275 + 6; hence not 7 divides 1931 by NAT_4:9;
1931 = 11*175 + 6; hence not 11 divides 1931 by NAT_4:9;
1931 = 13*148 + 7; hence not 13 divides 1931 by NAT_4:9;
1931 = 17*113 + 10; hence not 17 divides 1931 by NAT_4:9;
1931 = 19*101 + 12; hence not 19 divides 1931 by NAT_4:9;
1931 = 23*83 + 22; hence not 23 divides 1931 by NAT_4:9;
1931 = 29*66 + 17; hence not 29 divides 1931 by NAT_4:9;
1931 = 31*62 + 9; hence not 31 divides 1931 by NAT_4:9;
1931 = 37*52 + 7; hence not 37 divides 1931 by NAT_4:9;
1931 = 41*47 + 4; hence not 41 divides 1931 by NAT_4:9;
1931 = 43*44 + 39; hence not 43 divides 1931 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1931 & n is prime
holds not n divides 1931 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1933 is prime
proof
now
1933 = 2*966 + 1; hence not 2 divides 1933 by NAT_4:9;
1933 = 3*644 + 1; hence not 3 divides 1933 by NAT_4:9;
1933 = 5*386 + 3; hence not 5 divides 1933 by NAT_4:9;
1933 = 7*276 + 1; hence not 7 divides 1933 by NAT_4:9;
1933 = 11*175 + 8; hence not 11 divides 1933 by NAT_4:9;
1933 = 13*148 + 9; hence not 13 divides 1933 by NAT_4:9;
1933 = 17*113 + 12; hence not 17 divides 1933 by NAT_4:9;
1933 = 19*101 + 14; hence not 19 divides 1933 by NAT_4:9;
1933 = 23*84 + 1; hence not 23 divides 1933 by NAT_4:9;
1933 = 29*66 + 19; hence not 29 divides 1933 by NAT_4:9;
1933 = 31*62 + 11; hence not 31 divides 1933 by NAT_4:9;
1933 = 37*52 + 9; hence not 37 divides 1933 by NAT_4:9;
1933 = 41*47 + 6; hence not 41 divides 1933 by NAT_4:9;
1933 = 43*44 + 41; hence not 43 divides 1933 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1933 & n is prime
holds not n divides 1933 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
1949 is prime
proof
now
1949 = 2*974 + 1; hence not 2 divides 1949 by NAT_4:9;
1949 = 3*649 + 2; hence not 3 divides 1949 by NAT_4:9;
1949 = 5*389 + 4; hence not 5 divides 1949 by NAT_4:9;
1949 = 7*278 + 3; hence not 7 divides 1949 by NAT_4:9;
1949 = 11*177 + 2; hence not 11 divides 1949 by NAT_4:9;
1949 = 13*149 + 12; hence not 13 divides 1949 by NAT_4:9;
1949 = 17*114 + 11; hence not 17 divides 1949 by NAT_4:9;
1949 = 19*102 + 11; hence not 19 divides 1949 by NAT_4:9;
1949 = 23*84 + 17; hence not 23 divides 1949 by NAT_4:9;
1949 = 29*67 + 6; hence not 29 divides 1949 by NAT_4:9;
1949 = 31*62 + 27; hence not 31 divides 1949 by NAT_4:9;
1949 = 37*52 + 25; hence not 37 divides 1949 by NAT_4:9;
1949 = 41*47 + 22; hence not 41 divides 1949 by NAT_4:9;
1949 = 43*45 + 14; hence not 43 divides 1949 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1949 & n is prime
holds not n divides 1949 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1951 is prime
proof
now
1951 = 2*975 + 1; hence not 2 divides 1951 by NAT_4:9;
1951 = 3*650 + 1; hence not 3 divides 1951 by NAT_4:9;
1951 = 5*390 + 1; hence not 5 divides 1951 by NAT_4:9;
1951 = 7*278 + 5; hence not 7 divides 1951 by NAT_4:9;
1951 = 11*177 + 4; hence not 11 divides 1951 by NAT_4:9;
1951 = 13*150 + 1; hence not 13 divides 1951 by NAT_4:9;
1951 = 17*114 + 13; hence not 17 divides 1951 by NAT_4:9;
1951 = 19*102 + 13; hence not 19 divides 1951 by NAT_4:9;
1951 = 23*84 + 19; hence not 23 divides 1951 by NAT_4:9;
1951 = 29*67 + 8; hence not 29 divides 1951 by NAT_4:9;
1951 = 31*62 + 29; hence not 31 divides 1951 by NAT_4:9;
1951 = 37*52 + 27; hence not 37 divides 1951 by NAT_4:9;
1951 = 41*47 + 24; hence not 41 divides 1951 by NAT_4:9;
1951 = 43*45 + 16; hence not 43 divides 1951 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1951 & n is prime
holds not n divides 1951 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
1973 is prime
proof
now
1973 = 2*986 + 1; hence not 2 divides 1973 by NAT_4:9;
1973 = 3*657 + 2; hence not 3 divides 1973 by NAT_4:9;
1973 = 5*394 + 3; hence not 5 divides 1973 by NAT_4:9;
1973 = 7*281 + 6; hence not 7 divides 1973 by NAT_4:9;
1973 = 11*179 + 4; hence not 11 divides 1973 by NAT_4:9;
1973 = 13*151 + 10; hence not 13 divides 1973 by NAT_4:9;
1973 = 17*116 + 1; hence not 17 divides 1973 by NAT_4:9;
1973 = 19*103 + 16; hence not 19 divides 1973 by NAT_4:9;
1973 = 23*85 + 18; hence not 23 divides 1973 by NAT_4:9;
1973 = 29*68 + 1; hence not 29 divides 1973 by NAT_4:9;
1973 = 31*63 + 20; hence not 31 divides 1973 by NAT_4:9;
1973 = 37*53 + 12; hence not 37 divides 1973 by NAT_4:9;
1973 = 41*48 + 5; hence not 41 divides 1973 by NAT_4:9;
1973 = 43*45 + 38; hence not 43 divides 1973 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1973 & n is prime
holds not n divides 1973 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1979 is prime
proof
now
1979 = 2*989 + 1; hence not 2 divides 1979 by NAT_4:9;
1979 = 3*659 + 2; hence not 3 divides 1979 by NAT_4:9;
1979 = 5*395 + 4; hence not 5 divides 1979 by NAT_4:9;
1979 = 7*282 + 5; hence not 7 divides 1979 by NAT_4:9;
1979 = 11*179 + 10; hence not 11 divides 1979 by NAT_4:9;
1979 = 13*152 + 3; hence not 13 divides 1979 by NAT_4:9;
1979 = 17*116 + 7; hence not 17 divides 1979 by NAT_4:9;
1979 = 19*104 + 3; hence not 19 divides 1979 by NAT_4:9;
1979 = 23*86 + 1; hence not 23 divides 1979 by NAT_4:9;
1979 = 29*68 + 7; hence not 29 divides 1979 by NAT_4:9;
1979 = 31*63 + 26; hence not 31 divides 1979 by NAT_4:9;
1979 = 37*53 + 18; hence not 37 divides 1979 by NAT_4:9;
1979 = 41*48 + 11; hence not 41 divides 1979 by NAT_4:9;
1979 = 43*46 + 1; hence not 43 divides 1979 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1979 & n is prime
holds not n divides 1979 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
1987 is prime
proof
now
1987 = 2*993 + 1; hence not 2 divides 1987 by NAT_4:9;
1987 = 3*662 + 1; hence not 3 divides 1987 by NAT_4:9;
1987 = 5*397 + 2; hence not 5 divides 1987 by NAT_4:9;
1987 = 7*283 + 6; hence not 7 divides 1987 by NAT_4:9;
1987 = 11*180 + 7; hence not 11 divides 1987 by NAT_4:9;
1987 = 13*152 + 11; hence not 13 divides 1987 by NAT_4:9;
1987 = 17*116 + 15; hence not 17 divides 1987 by NAT_4:9;
1987 = 19*104 + 11; hence not 19 divides 1987 by NAT_4:9;
1987 = 23*86 + 9; hence not 23 divides 1987 by NAT_4:9;
1987 = 29*68 + 15; hence not 29 divides 1987 by NAT_4:9;
1987 = 31*64 + 3; hence not 31 divides 1987 by NAT_4:9;
1987 = 37*53 + 26; hence not 37 divides 1987 by NAT_4:9;
1987 = 41*48 + 19; hence not 41 divides 1987 by NAT_4:9;
1987 = 43*46 + 9; hence not 43 divides 1987 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1987 & n is prime
holds not n divides 1987 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
1993 is prime
proof
now
1993 = 2*996 + 1; hence not 2 divides 1993 by NAT_4:9;
1993 = 3*664 + 1; hence not 3 divides 1993 by NAT_4:9;
1993 = 5*398 + 3; hence not 5 divides 1993 by NAT_4:9;
1993 = 7*284 + 5; hence not 7 divides 1993 by NAT_4:9;
1993 = 11*181 + 2; hence not 11 divides 1993 by NAT_4:9;
1993 = 13*153 + 4; hence not 13 divides 1993 by NAT_4:9;
1993 = 17*117 + 4; hence not 17 divides 1993 by NAT_4:9;
1993 = 19*104 + 17; hence not 19 divides 1993 by NAT_4:9;
1993 = 23*86 + 15; hence not 23 divides 1993 by NAT_4:9;
1993 = 29*68 + 21; hence not 29 divides 1993 by NAT_4:9;
1993 = 31*64 + 9; hence not 31 divides 1993 by NAT_4:9;
1993 = 37*53 + 32; hence not 37 divides 1993 by NAT_4:9;
1993 = 41*48 + 25; hence not 41 divides 1993 by NAT_4:9;
1993 = 43*46 + 15; hence not 43 divides 1993 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1993 & n is prime
holds not n divides 1993 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
1997 is prime
proof
now
1997 = 2*998 + 1; hence not 2 divides 1997 by NAT_4:9;
1997 = 3*665 + 2; hence not 3 divides 1997 by NAT_4:9;
1997 = 5*399 + 2; hence not 5 divides 1997 by NAT_4:9;
1997 = 7*285 + 2; hence not 7 divides 1997 by NAT_4:9;
1997 = 11*181 + 6; hence not 11 divides 1997 by NAT_4:9;
1997 = 13*153 + 8; hence not 13 divides 1997 by NAT_4:9;
1997 = 17*117 + 8; hence not 17 divides 1997 by NAT_4:9;
1997 = 19*105 + 2; hence not 19 divides 1997 by NAT_4:9;
1997 = 23*86 + 19; hence not 23 divides 1997 by NAT_4:9;
1997 = 29*68 + 25; hence not 29 divides 1997 by NAT_4:9;
1997 = 31*64 + 13; hence not 31 divides 1997 by NAT_4:9;
1997 = 37*53 + 36; hence not 37 divides 1997 by NAT_4:9;
1997 = 41*48 + 29; hence not 41 divides 1997 by NAT_4:9;
1997 = 43*46 + 19; hence not 43 divides 1997 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1997 & n is prime
holds not n divides 1997 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
1999 is prime
proof
now
1999 = 2*999 + 1; hence not 2 divides 1999 by NAT_4:9;
1999 = 3*666 + 1; hence not 3 divides 1999 by NAT_4:9;
1999 = 5*399 + 4; hence not 5 divides 1999 by NAT_4:9;
1999 = 7*285 + 4; hence not 7 divides 1999 by NAT_4:9;
1999 = 11*181 + 8; hence not 11 divides 1999 by NAT_4:9;
1999 = 13*153 + 10; hence not 13 divides 1999 by NAT_4:9;
1999 = 17*117 + 10; hence not 17 divides 1999 by NAT_4:9;
1999 = 19*105 + 4; hence not 19 divides 1999 by NAT_4:9;
1999 = 23*86 + 21; hence not 23 divides 1999 by NAT_4:9;
1999 = 29*68 + 27; hence not 29 divides 1999 by NAT_4:9;
1999 = 31*64 + 15; hence not 31 divides 1999 by NAT_4:9;
1999 = 37*54 + 1; hence not 37 divides 1999 by NAT_4:9;
1999 = 41*48 + 31; hence not 41 divides 1999 by NAT_4:9;
1999 = 43*46 + 21; hence not 43 divides 1999 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 1999 & n is prime
holds not n divides 1999 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2003 is prime
proof
now
2003 = 2*1001 + 1; hence not 2 divides 2003 by NAT_4:9;
2003 = 3*667 + 2; hence not 3 divides 2003 by NAT_4:9;
2003 = 5*400 + 3; hence not 5 divides 2003 by NAT_4:9;
2003 = 7*286 + 1; hence not 7 divides 2003 by NAT_4:9;
2003 = 11*182 + 1; hence not 11 divides 2003 by NAT_4:9;
2003 = 13*154 + 1; hence not 13 divides 2003 by NAT_4:9;
2003 = 17*117 + 14; hence not 17 divides 2003 by NAT_4:9;
2003 = 19*105 + 8; hence not 19 divides 2003 by NAT_4:9;
2003 = 23*87 + 2; hence not 23 divides 2003 by NAT_4:9;
2003 = 29*69 + 2; hence not 29 divides 2003 by NAT_4:9;
2003 = 31*64 + 19; hence not 31 divides 2003 by NAT_4:9;
2003 = 37*54 + 5; hence not 37 divides 2003 by NAT_4:9;
2003 = 41*48 + 35; hence not 41 divides 2003 by NAT_4:9;
2003 = 43*46 + 25; hence not 43 divides 2003 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2003 & n is prime
holds not n divides 2003 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2011 is prime
proof
now
2011 = 2*1005 + 1; hence not 2 divides 2011 by NAT_4:9;
2011 = 3*670 + 1; hence not 3 divides 2011 by NAT_4:9;
2011 = 5*402 + 1; hence not 5 divides 2011 by NAT_4:9;
2011 = 7*287 + 2; hence not 7 divides 2011 by NAT_4:9;
2011 = 11*182 + 9; hence not 11 divides 2011 by NAT_4:9;
2011 = 13*154 + 9; hence not 13 divides 2011 by NAT_4:9;
2011 = 17*118 + 5; hence not 17 divides 2011 by NAT_4:9;
2011 = 19*105 + 16; hence not 19 divides 2011 by NAT_4:9;
2011 = 23*87 + 10; hence not 23 divides 2011 by NAT_4:9;
2011 = 29*69 + 10; hence not 29 divides 2011 by NAT_4:9;
2011 = 31*64 + 27; hence not 31 divides 2011 by NAT_4:9;
2011 = 37*54 + 13; hence not 37 divides 2011 by NAT_4:9;
2011 = 41*49 + 2; hence not 41 divides 2011 by NAT_4:9;
2011 = 43*46 + 33; hence not 43 divides 2011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2011 & n is prime
holds not n divides 2011 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2017 is prime
proof
now
2017 = 2*1008 + 1; hence not 2 divides 2017 by NAT_4:9;
2017 = 3*672 + 1; hence not 3 divides 2017 by NAT_4:9;
2017 = 5*403 + 2; hence not 5 divides 2017 by NAT_4:9;
2017 = 7*288 + 1; hence not 7 divides 2017 by NAT_4:9;
2017 = 11*183 + 4; hence not 11 divides 2017 by NAT_4:9;
2017 = 13*155 + 2; hence not 13 divides 2017 by NAT_4:9;
2017 = 17*118 + 11; hence not 17 divides 2017 by NAT_4:9;
2017 = 19*106 + 3; hence not 19 divides 2017 by NAT_4:9;
2017 = 23*87 + 16; hence not 23 divides 2017 by NAT_4:9;
2017 = 29*69 + 16; hence not 29 divides 2017 by NAT_4:9;
2017 = 31*65 + 2; hence not 31 divides 2017 by NAT_4:9;
2017 = 37*54 + 19; hence not 37 divides 2017 by NAT_4:9;
2017 = 41*49 + 8; hence not 41 divides 2017 by NAT_4:9;
2017 = 43*46 + 39; hence not 43 divides 2017 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2017 & n is prime
holds not n divides 2017 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2027 is prime
proof
now
2027 = 2*1013 + 1; hence not 2 divides 2027 by NAT_4:9;
2027 = 3*675 + 2; hence not 3 divides 2027 by NAT_4:9;
2027 = 5*405 + 2; hence not 5 divides 2027 by NAT_4:9;
2027 = 7*289 + 4; hence not 7 divides 2027 by NAT_4:9;
2027 = 11*184 + 3; hence not 11 divides 2027 by NAT_4:9;
2027 = 13*155 + 12; hence not 13 divides 2027 by NAT_4:9;
2027 = 17*119 + 4; hence not 17 divides 2027 by NAT_4:9;
2027 = 19*106 + 13; hence not 19 divides 2027 by NAT_4:9;
2027 = 23*88 + 3; hence not 23 divides 2027 by NAT_4:9;
2027 = 29*69 + 26; hence not 29 divides 2027 by NAT_4:9;
2027 = 31*65 + 12; hence not 31 divides 2027 by NAT_4:9;
2027 = 37*54 + 29; hence not 37 divides 2027 by NAT_4:9;
2027 = 41*49 + 18; hence not 41 divides 2027 by NAT_4:9;
2027 = 43*47 + 6; hence not 43 divides 2027 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2027 & n is prime
holds not n divides 2027 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2029 is prime
proof
now
2029 = 2*1014 + 1; hence not 2 divides 2029 by NAT_4:9;
2029 = 3*676 + 1; hence not 3 divides 2029 by NAT_4:9;
2029 = 5*405 + 4; hence not 5 divides 2029 by NAT_4:9;
2029 = 7*289 + 6; hence not 7 divides 2029 by NAT_4:9;
2029 = 11*184 + 5; hence not 11 divides 2029 by NAT_4:9;
2029 = 13*156 + 1; hence not 13 divides 2029 by NAT_4:9;
2029 = 17*119 + 6; hence not 17 divides 2029 by NAT_4:9;
2029 = 19*106 + 15; hence not 19 divides 2029 by NAT_4:9;
2029 = 23*88 + 5; hence not 23 divides 2029 by NAT_4:9;
2029 = 29*69 + 28; hence not 29 divides 2029 by NAT_4:9;
2029 = 31*65 + 14; hence not 31 divides 2029 by NAT_4:9;
2029 = 37*54 + 31; hence not 37 divides 2029 by NAT_4:9;
2029 = 41*49 + 20; hence not 41 divides 2029 by NAT_4:9;
2029 = 43*47 + 8; hence not 43 divides 2029 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2029 & n is prime
holds not n divides 2029 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2039 is prime
proof
now
2039 = 2*1019 + 1; hence not 2 divides 2039 by NAT_4:9;
2039 = 3*679 + 2; hence not 3 divides 2039 by NAT_4:9;
2039 = 5*407 + 4; hence not 5 divides 2039 by NAT_4:9;
2039 = 7*291 + 2; hence not 7 divides 2039 by NAT_4:9;
2039 = 11*185 + 4; hence not 11 divides 2039 by NAT_4:9;
2039 = 13*156 + 11; hence not 13 divides 2039 by NAT_4:9;
2039 = 17*119 + 16; hence not 17 divides 2039 by NAT_4:9;
2039 = 19*107 + 6; hence not 19 divides 2039 by NAT_4:9;
2039 = 23*88 + 15; hence not 23 divides 2039 by NAT_4:9;
2039 = 29*70 + 9; hence not 29 divides 2039 by NAT_4:9;
2039 = 31*65 + 24; hence not 31 divides 2039 by NAT_4:9;
2039 = 37*55 + 4; hence not 37 divides 2039 by NAT_4:9;
2039 = 41*49 + 30; hence not 41 divides 2039 by NAT_4:9;
2039 = 43*47 + 18; hence not 43 divides 2039 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2039 & n is prime
holds not n divides 2039 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2053 is prime
proof
now
2053 = 2*1026 + 1; hence not 2 divides 2053 by NAT_4:9;
2053 = 3*684 + 1; hence not 3 divides 2053 by NAT_4:9;
2053 = 5*410 + 3; hence not 5 divides 2053 by NAT_4:9;
2053 = 7*293 + 2; hence not 7 divides 2053 by NAT_4:9;
2053 = 11*186 + 7; hence not 11 divides 2053 by NAT_4:9;
2053 = 13*157 + 12; hence not 13 divides 2053 by NAT_4:9;
2053 = 17*120 + 13; hence not 17 divides 2053 by NAT_4:9;
2053 = 19*108 + 1; hence not 19 divides 2053 by NAT_4:9;
2053 = 23*89 + 6; hence not 23 divides 2053 by NAT_4:9;
2053 = 29*70 + 23; hence not 29 divides 2053 by NAT_4:9;
2053 = 31*66 + 7; hence not 31 divides 2053 by NAT_4:9;
2053 = 37*55 + 18; hence not 37 divides 2053 by NAT_4:9;
2053 = 41*50 + 3; hence not 41 divides 2053 by NAT_4:9;
2053 = 43*47 + 32; hence not 43 divides 2053 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2053 & n is prime
holds not n divides 2053 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2063 is prime
proof
now
2063 = 2*1031 + 1; hence not 2 divides 2063 by NAT_4:9;
2063 = 3*687 + 2; hence not 3 divides 2063 by NAT_4:9;
2063 = 5*412 + 3; hence not 5 divides 2063 by NAT_4:9;
2063 = 7*294 + 5; hence not 7 divides 2063 by NAT_4:9;
2063 = 11*187 + 6; hence not 11 divides 2063 by NAT_4:9;
2063 = 13*158 + 9; hence not 13 divides 2063 by NAT_4:9;
2063 = 17*121 + 6; hence not 17 divides 2063 by NAT_4:9;
2063 = 19*108 + 11; hence not 19 divides 2063 by NAT_4:9;
2063 = 23*89 + 16; hence not 23 divides 2063 by NAT_4:9;
2063 = 29*71 + 4; hence not 29 divides 2063 by NAT_4:9;
2063 = 31*66 + 17; hence not 31 divides 2063 by NAT_4:9;
2063 = 37*55 + 28; hence not 37 divides 2063 by NAT_4:9;
2063 = 41*50 + 13; hence not 41 divides 2063 by NAT_4:9;
2063 = 43*47 + 42; hence not 43 divides 2063 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2063 & n is prime
holds not n divides 2063 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2069 is prime
proof
now
2069 = 2*1034 + 1; hence not 2 divides 2069 by NAT_4:9;
2069 = 3*689 + 2; hence not 3 divides 2069 by NAT_4:9;
2069 = 5*413 + 4; hence not 5 divides 2069 by NAT_4:9;
2069 = 7*295 + 4; hence not 7 divides 2069 by NAT_4:9;
2069 = 11*188 + 1; hence not 11 divides 2069 by NAT_4:9;
2069 = 13*159 + 2; hence not 13 divides 2069 by NAT_4:9;
2069 = 17*121 + 12; hence not 17 divides 2069 by NAT_4:9;
2069 = 19*108 + 17; hence not 19 divides 2069 by NAT_4:9;
2069 = 23*89 + 22; hence not 23 divides 2069 by NAT_4:9;
2069 = 29*71 + 10; hence not 29 divides 2069 by NAT_4:9;
2069 = 31*66 + 23; hence not 31 divides 2069 by NAT_4:9;
2069 = 37*55 + 34; hence not 37 divides 2069 by NAT_4:9;
2069 = 41*50 + 19; hence not 41 divides 2069 by NAT_4:9;
2069 = 43*48 + 5; hence not 43 divides 2069 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2069 & n is prime
holds not n divides 2069 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2081 is prime
proof
now
2081 = 2*1040 + 1; hence not 2 divides 2081 by NAT_4:9;
2081 = 3*693 + 2; hence not 3 divides 2081 by NAT_4:9;
2081 = 5*416 + 1; hence not 5 divides 2081 by NAT_4:9;
2081 = 7*297 + 2; hence not 7 divides 2081 by NAT_4:9;
2081 = 11*189 + 2; hence not 11 divides 2081 by NAT_4:9;
2081 = 13*160 + 1; hence not 13 divides 2081 by NAT_4:9;
2081 = 17*122 + 7; hence not 17 divides 2081 by NAT_4:9;
2081 = 19*109 + 10; hence not 19 divides 2081 by NAT_4:9;
2081 = 23*90 + 11; hence not 23 divides 2081 by NAT_4:9;
2081 = 29*71 + 22; hence not 29 divides 2081 by NAT_4:9;
2081 = 31*67 + 4; hence not 31 divides 2081 by NAT_4:9;
2081 = 37*56 + 9; hence not 37 divides 2081 by NAT_4:9;
2081 = 41*50 + 31; hence not 41 divides 2081 by NAT_4:9;
2081 = 43*48 + 17; hence not 43 divides 2081 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2081 & n is prime
holds not n divides 2081 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2083 is prime
proof
now
2083 = 2*1041 + 1; hence not 2 divides 2083 by NAT_4:9;
2083 = 3*694 + 1; hence not 3 divides 2083 by NAT_4:9;
2083 = 5*416 + 3; hence not 5 divides 2083 by NAT_4:9;
2083 = 7*297 + 4; hence not 7 divides 2083 by NAT_4:9;
2083 = 11*189 + 4; hence not 11 divides 2083 by NAT_4:9;
2083 = 13*160 + 3; hence not 13 divides 2083 by NAT_4:9;
2083 = 17*122 + 9; hence not 17 divides 2083 by NAT_4:9;
2083 = 19*109 + 12; hence not 19 divides 2083 by NAT_4:9;
2083 = 23*90 + 13; hence not 23 divides 2083 by NAT_4:9;
2083 = 29*71 + 24; hence not 29 divides 2083 by NAT_4:9;
2083 = 31*67 + 6; hence not 31 divides 2083 by NAT_4:9;
2083 = 37*56 + 11; hence not 37 divides 2083 by NAT_4:9;
2083 = 41*50 + 33; hence not 41 divides 2083 by NAT_4:9;
2083 = 43*48 + 19; hence not 43 divides 2083 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2083 & n is prime
holds not n divides 2083 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2087 is prime
proof
now
2087 = 2*1043 + 1; hence not 2 divides 2087 by NAT_4:9;
2087 = 3*695 + 2; hence not 3 divides 2087 by NAT_4:9;
2087 = 5*417 + 2; hence not 5 divides 2087 by NAT_4:9;
2087 = 7*298 + 1; hence not 7 divides 2087 by NAT_4:9;
2087 = 11*189 + 8; hence not 11 divides 2087 by NAT_4:9;
2087 = 13*160 + 7; hence not 13 divides 2087 by NAT_4:9;
2087 = 17*122 + 13; hence not 17 divides 2087 by NAT_4:9;
2087 = 19*109 + 16; hence not 19 divides 2087 by NAT_4:9;
2087 = 23*90 + 17; hence not 23 divides 2087 by NAT_4:9;
2087 = 29*71 + 28; hence not 29 divides 2087 by NAT_4:9;
2087 = 31*67 + 10; hence not 31 divides 2087 by NAT_4:9;
2087 = 37*56 + 15; hence not 37 divides 2087 by NAT_4:9;
2087 = 41*50 + 37; hence not 41 divides 2087 by NAT_4:9;
2087 = 43*48 + 23; hence not 43 divides 2087 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2087 & n is prime
holds not n divides 2087 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2089 is prime
proof
now
2089 = 2*1044 + 1; hence not 2 divides 2089 by NAT_4:9;
2089 = 3*696 + 1; hence not 3 divides 2089 by NAT_4:9;
2089 = 5*417 + 4; hence not 5 divides 2089 by NAT_4:9;
2089 = 7*298 + 3; hence not 7 divides 2089 by NAT_4:9;
2089 = 11*189 + 10; hence not 11 divides 2089 by NAT_4:9;
2089 = 13*160 + 9; hence not 13 divides 2089 by NAT_4:9;
2089 = 17*122 + 15; hence not 17 divides 2089 by NAT_4:9;
2089 = 19*109 + 18; hence not 19 divides 2089 by NAT_4:9;
2089 = 23*90 + 19; hence not 23 divides 2089 by NAT_4:9;
2089 = 29*72 + 1; hence not 29 divides 2089 by NAT_4:9;
2089 = 31*67 + 12; hence not 31 divides 2089 by NAT_4:9;
2089 = 37*56 + 17; hence not 37 divides 2089 by NAT_4:9;
2089 = 41*50 + 39; hence not 41 divides 2089 by NAT_4:9;
2089 = 43*48 + 25; hence not 43 divides 2089 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2089 & n is prime
holds not n divides 2089 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2099 is prime
proof
now
2099 = 2*1049 + 1; hence not 2 divides 2099 by NAT_4:9;
2099 = 3*699 + 2; hence not 3 divides 2099 by NAT_4:9;
2099 = 5*419 + 4; hence not 5 divides 2099 by NAT_4:9;
2099 = 7*299 + 6; hence not 7 divides 2099 by NAT_4:9;
2099 = 11*190 + 9; hence not 11 divides 2099 by NAT_4:9;
2099 = 13*161 + 6; hence not 13 divides 2099 by NAT_4:9;
2099 = 17*123 + 8; hence not 17 divides 2099 by NAT_4:9;
2099 = 19*110 + 9; hence not 19 divides 2099 by NAT_4:9;
2099 = 23*91 + 6; hence not 23 divides 2099 by NAT_4:9;
2099 = 29*72 + 11; hence not 29 divides 2099 by NAT_4:9;
2099 = 31*67 + 22; hence not 31 divides 2099 by NAT_4:9;
2099 = 37*56 + 27; hence not 37 divides 2099 by NAT_4:9;
2099 = 41*51 + 8; hence not 41 divides 2099 by NAT_4:9;
2099 = 43*48 + 35; hence not 43 divides 2099 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2099 & n is prime
holds not n divides 2099 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2111 is prime
proof
now
2111 = 2*1055 + 1; hence not 2 divides 2111 by NAT_4:9;
2111 = 3*703 + 2; hence not 3 divides 2111 by NAT_4:9;
2111 = 5*422 + 1; hence not 5 divides 2111 by NAT_4:9;
2111 = 7*301 + 4; hence not 7 divides 2111 by NAT_4:9;
2111 = 11*191 + 10; hence not 11 divides 2111 by NAT_4:9;
2111 = 13*162 + 5; hence not 13 divides 2111 by NAT_4:9;
2111 = 17*124 + 3; hence not 17 divides 2111 by NAT_4:9;
2111 = 19*111 + 2; hence not 19 divides 2111 by NAT_4:9;
2111 = 23*91 + 18; hence not 23 divides 2111 by NAT_4:9;
2111 = 29*72 + 23; hence not 29 divides 2111 by NAT_4:9;
2111 = 31*68 + 3; hence not 31 divides 2111 by NAT_4:9;
2111 = 37*57 + 2; hence not 37 divides 2111 by NAT_4:9;
2111 = 41*51 + 20; hence not 41 divides 2111 by NAT_4:9;
2111 = 43*49 + 4; hence not 43 divides 2111 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2111 & n is prime
holds not n divides 2111 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2113 is prime
proof
now
2113 = 2*1056 + 1; hence not 2 divides 2113 by NAT_4:9;
2113 = 3*704 + 1; hence not 3 divides 2113 by NAT_4:9;
2113 = 5*422 + 3; hence not 5 divides 2113 by NAT_4:9;
2113 = 7*301 + 6; hence not 7 divides 2113 by NAT_4:9;
2113 = 11*192 + 1; hence not 11 divides 2113 by NAT_4:9;
2113 = 13*162 + 7; hence not 13 divides 2113 by NAT_4:9;
2113 = 17*124 + 5; hence not 17 divides 2113 by NAT_4:9;
2113 = 19*111 + 4; hence not 19 divides 2113 by NAT_4:9;
2113 = 23*91 + 20; hence not 23 divides 2113 by NAT_4:9;
2113 = 29*72 + 25; hence not 29 divides 2113 by NAT_4:9;
2113 = 31*68 + 5; hence not 31 divides 2113 by NAT_4:9;
2113 = 37*57 + 4; hence not 37 divides 2113 by NAT_4:9;
2113 = 41*51 + 22; hence not 41 divides 2113 by NAT_4:9;
2113 = 43*49 + 6; hence not 43 divides 2113 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2113 & n is prime
holds not n divides 2113 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
2129 is prime
proof
now
2129 = 2*1064 + 1; hence not 2 divides 2129 by NAT_4:9;
2129 = 3*709 + 2; hence not 3 divides 2129 by NAT_4:9;
2129 = 5*425 + 4; hence not 5 divides 2129 by NAT_4:9;
2129 = 7*304 + 1; hence not 7 divides 2129 by NAT_4:9;
2129 = 11*193 + 6; hence not 11 divides 2129 by NAT_4:9;
2129 = 13*163 + 10; hence not 13 divides 2129 by NAT_4:9;
2129 = 17*125 + 4; hence not 17 divides 2129 by NAT_4:9;
2129 = 19*112 + 1; hence not 19 divides 2129 by NAT_4:9;
2129 = 23*92 + 13; hence not 23 divides 2129 by NAT_4:9;
2129 = 29*73 + 12; hence not 29 divides 2129 by NAT_4:9;
2129 = 31*68 + 21; hence not 31 divides 2129 by NAT_4:9;
2129 = 37*57 + 20; hence not 37 divides 2129 by NAT_4:9;
2129 = 41*51 + 38; hence not 41 divides 2129 by NAT_4:9;
2129 = 43*49 + 22; hence not 43 divides 2129 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2129 & n is prime
holds not n divides 2129 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2131 is prime
proof
now
2131 = 2*1065 + 1; hence not 2 divides 2131 by NAT_4:9;
2131 = 3*710 + 1; hence not 3 divides 2131 by NAT_4:9;
2131 = 5*426 + 1; hence not 5 divides 2131 by NAT_4:9;
2131 = 7*304 + 3; hence not 7 divides 2131 by NAT_4:9;
2131 = 11*193 + 8; hence not 11 divides 2131 by NAT_4:9;
2131 = 13*163 + 12; hence not 13 divides 2131 by NAT_4:9;
2131 = 17*125 + 6; hence not 17 divides 2131 by NAT_4:9;
2131 = 19*112 + 3; hence not 19 divides 2131 by NAT_4:9;
2131 = 23*92 + 15; hence not 23 divides 2131 by NAT_4:9;
2131 = 29*73 + 14; hence not 29 divides 2131 by NAT_4:9;
2131 = 31*68 + 23; hence not 31 divides 2131 by NAT_4:9;
2131 = 37*57 + 22; hence not 37 divides 2131 by NAT_4:9;
2131 = 41*51 + 40; hence not 41 divides 2131 by NAT_4:9;
2131 = 43*49 + 24; hence not 43 divides 2131 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2131 & n is prime
holds not n divides 2131 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2137 is prime
proof
now
2137 = 2*1068 + 1; hence not 2 divides 2137 by NAT_4:9;
2137 = 3*712 + 1; hence not 3 divides 2137 by NAT_4:9;
2137 = 5*427 + 2; hence not 5 divides 2137 by NAT_4:9;
2137 = 7*305 + 2; hence not 7 divides 2137 by NAT_4:9;
2137 = 11*194 + 3; hence not 11 divides 2137 by NAT_4:9;
2137 = 13*164 + 5; hence not 13 divides 2137 by NAT_4:9;
2137 = 17*125 + 12; hence not 17 divides 2137 by NAT_4:9;
2137 = 19*112 + 9; hence not 19 divides 2137 by NAT_4:9;
2137 = 23*92 + 21; hence not 23 divides 2137 by NAT_4:9;
2137 = 29*73 + 20; hence not 29 divides 2137 by NAT_4:9;
2137 = 31*68 + 29; hence not 31 divides 2137 by NAT_4:9;
2137 = 37*57 + 28; hence not 37 divides 2137 by NAT_4:9;
2137 = 41*52 + 5; hence not 41 divides 2137 by NAT_4:9;
2137 = 43*49 + 30; hence not 43 divides 2137 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2137 & n is prime
holds not n divides 2137 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2141 is prime
proof
now
2141 = 2*1070 + 1; hence not 2 divides 2141 by NAT_4:9;
2141 = 3*713 + 2; hence not 3 divides 2141 by NAT_4:9;
2141 = 5*428 + 1; hence not 5 divides 2141 by NAT_4:9;
2141 = 7*305 + 6; hence not 7 divides 2141 by NAT_4:9;
2141 = 11*194 + 7; hence not 11 divides 2141 by NAT_4:9;
2141 = 13*164 + 9; hence not 13 divides 2141 by NAT_4:9;
2141 = 17*125 + 16; hence not 17 divides 2141 by NAT_4:9;
2141 = 19*112 + 13; hence not 19 divides 2141 by NAT_4:9;
2141 = 23*93 + 2; hence not 23 divides 2141 by NAT_4:9;
2141 = 29*73 + 24; hence not 29 divides 2141 by NAT_4:9;
2141 = 31*69 + 2; hence not 31 divides 2141 by NAT_4:9;
2141 = 37*57 + 32; hence not 37 divides 2141 by NAT_4:9;
2141 = 41*52 + 9; hence not 41 divides 2141 by NAT_4:9;
2141 = 43*49 + 34; hence not 43 divides 2141 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2141 & n is prime
holds not n divides 2141 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2143 is prime
proof
now
2143 = 2*1071 + 1; hence not 2 divides 2143 by NAT_4:9;
2143 = 3*714 + 1; hence not 3 divides 2143 by NAT_4:9;
2143 = 5*428 + 3; hence not 5 divides 2143 by NAT_4:9;
2143 = 7*306 + 1; hence not 7 divides 2143 by NAT_4:9;
2143 = 11*194 + 9; hence not 11 divides 2143 by NAT_4:9;
2143 = 13*164 + 11; hence not 13 divides 2143 by NAT_4:9;
2143 = 17*126 + 1; hence not 17 divides 2143 by NAT_4:9;
2143 = 19*112 + 15; hence not 19 divides 2143 by NAT_4:9;
2143 = 23*93 + 4; hence not 23 divides 2143 by NAT_4:9;
2143 = 29*73 + 26; hence not 29 divides 2143 by NAT_4:9;
2143 = 31*69 + 4; hence not 31 divides 2143 by NAT_4:9;
2143 = 37*57 + 34; hence not 37 divides 2143 by NAT_4:9;
2143 = 41*52 + 11; hence not 41 divides 2143 by NAT_4:9;
2143 = 43*49 + 36; hence not 43 divides 2143 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2143 & n is prime
holds not n divides 2143 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2153 is prime
proof
now
2153 = 2*1076 + 1; hence not 2 divides 2153 by NAT_4:9;
2153 = 3*717 + 2; hence not 3 divides 2153 by NAT_4:9;
2153 = 5*430 + 3; hence not 5 divides 2153 by NAT_4:9;
2153 = 7*307 + 4; hence not 7 divides 2153 by NAT_4:9;
2153 = 11*195 + 8; hence not 11 divides 2153 by NAT_4:9;
2153 = 13*165 + 8; hence not 13 divides 2153 by NAT_4:9;
2153 = 17*126 + 11; hence not 17 divides 2153 by NAT_4:9;
2153 = 19*113 + 6; hence not 19 divides 2153 by NAT_4:9;
2153 = 23*93 + 14; hence not 23 divides 2153 by NAT_4:9;
2153 = 29*74 + 7; hence not 29 divides 2153 by NAT_4:9;
2153 = 31*69 + 14; hence not 31 divides 2153 by NAT_4:9;
2153 = 37*58 + 7; hence not 37 divides 2153 by NAT_4:9;
2153 = 41*52 + 21; hence not 41 divides 2153 by NAT_4:9;
2153 = 43*50 + 3; hence not 43 divides 2153 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2153 & n is prime
holds not n divides 2153 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2161 is prime
proof
now
2161 = 2*1080 + 1; hence not 2 divides 2161 by NAT_4:9;
2161 = 3*720 + 1; hence not 3 divides 2161 by NAT_4:9;
2161 = 5*432 + 1; hence not 5 divides 2161 by NAT_4:9;
2161 = 7*308 + 5; hence not 7 divides 2161 by NAT_4:9;
2161 = 11*196 + 5; hence not 11 divides 2161 by NAT_4:9;
2161 = 13*166 + 3; hence not 13 divides 2161 by NAT_4:9;
2161 = 17*127 + 2; hence not 17 divides 2161 by NAT_4:9;
2161 = 19*113 + 14; hence not 19 divides 2161 by NAT_4:9;
2161 = 23*93 + 22; hence not 23 divides 2161 by NAT_4:9;
2161 = 29*74 + 15; hence not 29 divides 2161 by NAT_4:9;
2161 = 31*69 + 22; hence not 31 divides 2161 by NAT_4:9;
2161 = 37*58 + 15; hence not 37 divides 2161 by NAT_4:9;
2161 = 41*52 + 29; hence not 41 divides 2161 by NAT_4:9;
2161 = 43*50 + 11; hence not 43 divides 2161 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2161 & n is prime
holds not n divides 2161 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
2179 is prime
proof
now
2179 = 2*1089 + 1; hence not 2 divides 2179 by NAT_4:9;
2179 = 3*726 + 1; hence not 3 divides 2179 by NAT_4:9;
2179 = 5*435 + 4; hence not 5 divides 2179 by NAT_4:9;
2179 = 7*311 + 2; hence not 7 divides 2179 by NAT_4:9;
2179 = 11*198 + 1; hence not 11 divides 2179 by NAT_4:9;
2179 = 13*167 + 8; hence not 13 divides 2179 by NAT_4:9;
2179 = 17*128 + 3; hence not 17 divides 2179 by NAT_4:9;
2179 = 19*114 + 13; hence not 19 divides 2179 by NAT_4:9;
2179 = 23*94 + 17; hence not 23 divides 2179 by NAT_4:9;
2179 = 29*75 + 4; hence not 29 divides 2179 by NAT_4:9;
2179 = 31*70 + 9; hence not 31 divides 2179 by NAT_4:9;
2179 = 37*58 + 33; hence not 37 divides 2179 by NAT_4:9;
2179 = 41*53 + 6; hence not 41 divides 2179 by NAT_4:9;
2179 = 43*50 + 29; hence not 43 divides 2179 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2179 & n is prime
holds not n divides 2179 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
2203 is prime
proof
now
2203 = 2*1101 + 1; hence not 2 divides 2203 by NAT_4:9;
2203 = 3*734 + 1; hence not 3 divides 2203 by NAT_4:9;
2203 = 5*440 + 3; hence not 5 divides 2203 by NAT_4:9;
2203 = 7*314 + 5; hence not 7 divides 2203 by NAT_4:9;
2203 = 11*200 + 3; hence not 11 divides 2203 by NAT_4:9;
2203 = 13*169 + 6; hence not 13 divides 2203 by NAT_4:9;
2203 = 17*129 + 10; hence not 17 divides 2203 by NAT_4:9;
2203 = 19*115 + 18; hence not 19 divides 2203 by NAT_4:9;
2203 = 23*95 + 18; hence not 23 divides 2203 by NAT_4:9;
2203 = 29*75 + 28; hence not 29 divides 2203 by NAT_4:9;
2203 = 31*71 + 2; hence not 31 divides 2203 by NAT_4:9;
2203 = 37*59 + 20; hence not 37 divides 2203 by NAT_4:9;
2203 = 41*53 + 30; hence not 41 divides 2203 by NAT_4:9;
2203 = 43*51 + 10; hence not 43 divides 2203 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2203 & n is prime
holds not n divides 2203 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2207 is prime
proof
now
2207 = 2*1103 + 1; hence not 2 divides 2207 by NAT_4:9;
2207 = 3*735 + 2; hence not 3 divides 2207 by NAT_4:9;
2207 = 5*441 + 2; hence not 5 divides 2207 by NAT_4:9;
2207 = 7*315 + 2; hence not 7 divides 2207 by NAT_4:9;
2207 = 11*200 + 7; hence not 11 divides 2207 by NAT_4:9;
2207 = 13*169 + 10; hence not 13 divides 2207 by NAT_4:9;
2207 = 17*129 + 14; hence not 17 divides 2207 by NAT_4:9;
2207 = 19*116 + 3; hence not 19 divides 2207 by NAT_4:9;
2207 = 23*95 + 22; hence not 23 divides 2207 by NAT_4:9;
2207 = 29*76 + 3; hence not 29 divides 2207 by NAT_4:9;
2207 = 31*71 + 6; hence not 31 divides 2207 by NAT_4:9;
2207 = 37*59 + 24; hence not 37 divides 2207 by NAT_4:9;
2207 = 41*53 + 34; hence not 41 divides 2207 by NAT_4:9;
2207 = 43*51 + 14; hence not 43 divides 2207 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2207 & n is prime
holds not n divides 2207 by XPRIMET1:28;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2213 is prime
proof
now
2213 = 2*1106 + 1; hence not 2 divides 2213 by NAT_4:9;
2213 = 3*737 + 2; hence not 3 divides 2213 by NAT_4:9;
2213 = 5*442 + 3; hence not 5 divides 2213 by NAT_4:9;
2213 = 7*316 + 1; hence not 7 divides 2213 by NAT_4:9;
2213 = 11*201 + 2; hence not 11 divides 2213 by NAT_4:9;
2213 = 13*170 + 3; hence not 13 divides 2213 by NAT_4:9;
2213 = 17*130 + 3; hence not 17 divides 2213 by NAT_4:9;
2213 = 19*116 + 9; hence not 19 divides 2213 by NAT_4:9;
2213 = 23*96 + 5; hence not 23 divides 2213 by NAT_4:9;
2213 = 29*76 + 9; hence not 29 divides 2213 by NAT_4:9;
2213 = 31*71 + 12; hence not 31 divides 2213 by NAT_4:9;
2213 = 37*59 + 30; hence not 37 divides 2213 by NAT_4:9;
2213 = 41*53 + 40; hence not 41 divides 2213 by NAT_4:9;
2213 = 43*51 + 20; hence not 43 divides 2213 by NAT_4:9;
2213 = 47*47 + 4; hence not 47 divides 2213 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2213 & n is prime
holds not n divides 2213 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2221 is prime
proof
now
2221 = 2*1110 + 1; hence not 2 divides 2221 by NAT_4:9;
2221 = 3*740 + 1; hence not 3 divides 2221 by NAT_4:9;
2221 = 5*444 + 1; hence not 5 divides 2221 by NAT_4:9;
2221 = 7*317 + 2; hence not 7 divides 2221 by NAT_4:9;
2221 = 11*201 + 10; hence not 11 divides 2221 by NAT_4:9;
2221 = 13*170 + 11; hence not 13 divides 2221 by NAT_4:9;
2221 = 17*130 + 11; hence not 17 divides 2221 by NAT_4:9;
2221 = 19*116 + 17; hence not 19 divides 2221 by NAT_4:9;
2221 = 23*96 + 13; hence not 23 divides 2221 by NAT_4:9;
2221 = 29*76 + 17; hence not 29 divides 2221 by NAT_4:9;
2221 = 31*71 + 20; hence not 31 divides 2221 by NAT_4:9;
2221 = 37*60 + 1; hence not 37 divides 2221 by NAT_4:9;
2221 = 41*54 + 7; hence not 41 divides 2221 by NAT_4:9;
2221 = 43*51 + 28; hence not 43 divides 2221 by NAT_4:9;
2221 = 47*47 + 12; hence not 47 divides 2221 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2221 & n is prime
holds not n divides 2221 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
2237 is prime
proof
now
2237 = 2*1118 + 1; hence not 2 divides 2237 by NAT_4:9;
2237 = 3*745 + 2; hence not 3 divides 2237 by NAT_4:9;
2237 = 5*447 + 2; hence not 5 divides 2237 by NAT_4:9;
2237 = 7*319 + 4; hence not 7 divides 2237 by NAT_4:9;
2237 = 11*203 + 4; hence not 11 divides 2237 by NAT_4:9;
2237 = 13*172 + 1; hence not 13 divides 2237 by NAT_4:9;
2237 = 17*131 + 10; hence not 17 divides 2237 by NAT_4:9;
2237 = 19*117 + 14; hence not 19 divides 2237 by NAT_4:9;
2237 = 23*97 + 6; hence not 23 divides 2237 by NAT_4:9;
2237 = 29*77 + 4; hence not 29 divides 2237 by NAT_4:9;
2237 = 31*72 + 5; hence not 31 divides 2237 by NAT_4:9;
2237 = 37*60 + 17; hence not 37 divides 2237 by NAT_4:9;
2237 = 41*54 + 23; hence not 41 divides 2237 by NAT_4:9;
2237 = 43*52 + 1; hence not 43 divides 2237 by NAT_4:9;
2237 = 47*47 + 28; hence not 47 divides 2237 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2237 & n is prime
holds not n divides 2237 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2239 is prime
proof
now
2239 = 2*1119 + 1; hence not 2 divides 2239 by NAT_4:9;
2239 = 3*746 + 1; hence not 3 divides 2239 by NAT_4:9;
2239 = 5*447 + 4; hence not 5 divides 2239 by NAT_4:9;
2239 = 7*319 + 6; hence not 7 divides 2239 by NAT_4:9;
2239 = 11*203 + 6; hence not 11 divides 2239 by NAT_4:9;
2239 = 13*172 + 3; hence not 13 divides 2239 by NAT_4:9;
2239 = 17*131 + 12; hence not 17 divides 2239 by NAT_4:9;
2239 = 19*117 + 16; hence not 19 divides 2239 by NAT_4:9;
2239 = 23*97 + 8; hence not 23 divides 2239 by NAT_4:9;
2239 = 29*77 + 6; hence not 29 divides 2239 by NAT_4:9;
2239 = 31*72 + 7; hence not 31 divides 2239 by NAT_4:9;
2239 = 37*60 + 19; hence not 37 divides 2239 by NAT_4:9;
2239 = 41*54 + 25; hence not 41 divides 2239 by NAT_4:9;
2239 = 43*52 + 3; hence not 43 divides 2239 by NAT_4:9;
2239 = 47*47 + 30; hence not 47 divides 2239 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2239 & n is prime
holds not n divides 2239 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2243 is prime
proof
now
2243 = 2*1121 + 1; hence not 2 divides 2243 by NAT_4:9;
2243 = 3*747 + 2; hence not 3 divides 2243 by NAT_4:9;
2243 = 5*448 + 3; hence not 5 divides 2243 by NAT_4:9;
2243 = 7*320 + 3; hence not 7 divides 2243 by NAT_4:9;
2243 = 11*203 + 10; hence not 11 divides 2243 by NAT_4:9;
2243 = 13*172 + 7; hence not 13 divides 2243 by NAT_4:9;
2243 = 17*131 + 16; hence not 17 divides 2243 by NAT_4:9;
2243 = 19*118 + 1; hence not 19 divides 2243 by NAT_4:9;
2243 = 23*97 + 12; hence not 23 divides 2243 by NAT_4:9;
2243 = 29*77 + 10; hence not 29 divides 2243 by NAT_4:9;
2243 = 31*72 + 11; hence not 31 divides 2243 by NAT_4:9;
2243 = 37*60 + 23; hence not 37 divides 2243 by NAT_4:9;
2243 = 41*54 + 29; hence not 41 divides 2243 by NAT_4:9;
2243 = 43*52 + 7; hence not 43 divides 2243 by NAT_4:9;
2243 = 47*47 + 34; hence not 47 divides 2243 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2243 & n is prime
holds not n divides 2243 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2251 is prime
proof
now
2251 = 2*1125 + 1; hence not 2 divides 2251 by NAT_4:9;
2251 = 3*750 + 1; hence not 3 divides 2251 by NAT_4:9;
2251 = 5*450 + 1; hence not 5 divides 2251 by NAT_4:9;
2251 = 7*321 + 4; hence not 7 divides 2251 by NAT_4:9;
2251 = 11*204 + 7; hence not 11 divides 2251 by NAT_4:9;
2251 = 13*173 + 2; hence not 13 divides 2251 by NAT_4:9;
2251 = 17*132 + 7; hence not 17 divides 2251 by NAT_4:9;
2251 = 19*118 + 9; hence not 19 divides 2251 by NAT_4:9;
2251 = 23*97 + 20; hence not 23 divides 2251 by NAT_4:9;
2251 = 29*77 + 18; hence not 29 divides 2251 by NAT_4:9;
2251 = 31*72 + 19; hence not 31 divides 2251 by NAT_4:9;
2251 = 37*60 + 31; hence not 37 divides 2251 by NAT_4:9;
2251 = 41*54 + 37; hence not 41 divides 2251 by NAT_4:9;
2251 = 43*52 + 15; hence not 43 divides 2251 by NAT_4:9;
2251 = 47*47 + 42; hence not 47 divides 2251 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2251 & n is prime
holds not n divides 2251 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
2267 is prime
proof
now
2267 = 2*1133 + 1; hence not 2 divides 2267 by NAT_4:9;
2267 = 3*755 + 2; hence not 3 divides 2267 by NAT_4:9;
2267 = 5*453 + 2; hence not 5 divides 2267 by NAT_4:9;
2267 = 7*323 + 6; hence not 7 divides 2267 by NAT_4:9;
2267 = 11*206 + 1; hence not 11 divides 2267 by NAT_4:9;
2267 = 13*174 + 5; hence not 13 divides 2267 by NAT_4:9;
2267 = 17*133 + 6; hence not 17 divides 2267 by NAT_4:9;
2267 = 19*119 + 6; hence not 19 divides 2267 by NAT_4:9;
2267 = 23*98 + 13; hence not 23 divides 2267 by NAT_4:9;
2267 = 29*78 + 5; hence not 29 divides 2267 by NAT_4:9;
2267 = 31*73 + 4; hence not 31 divides 2267 by NAT_4:9;
2267 = 37*61 + 10; hence not 37 divides 2267 by NAT_4:9;
2267 = 41*55 + 12; hence not 41 divides 2267 by NAT_4:9;
2267 = 43*52 + 31; hence not 43 divides 2267 by NAT_4:9;
2267 = 47*48 + 11; hence not 47 divides 2267 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2267 & n is prime
holds not n divides 2267 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2269 is prime
proof
now
2269 = 2*1134 + 1; hence not 2 divides 2269 by NAT_4:9;
2269 = 3*756 + 1; hence not 3 divides 2269 by NAT_4:9;
2269 = 5*453 + 4; hence not 5 divides 2269 by NAT_4:9;
2269 = 7*324 + 1; hence not 7 divides 2269 by NAT_4:9;
2269 = 11*206 + 3; hence not 11 divides 2269 by NAT_4:9;
2269 = 13*174 + 7; hence not 13 divides 2269 by NAT_4:9;
2269 = 17*133 + 8; hence not 17 divides 2269 by NAT_4:9;
2269 = 19*119 + 8; hence not 19 divides 2269 by NAT_4:9;
2269 = 23*98 + 15; hence not 23 divides 2269 by NAT_4:9;
2269 = 29*78 + 7; hence not 29 divides 2269 by NAT_4:9;
2269 = 31*73 + 6; hence not 31 divides 2269 by NAT_4:9;
2269 = 37*61 + 12; hence not 37 divides 2269 by NAT_4:9;
2269 = 41*55 + 14; hence not 41 divides 2269 by NAT_4:9;
2269 = 43*52 + 33; hence not 43 divides 2269 by NAT_4:9;
2269 = 47*48 + 13; hence not 47 divides 2269 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2269 & n is prime
holds not n divides 2269 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2273 is prime
proof
now
2273 = 2*1136 + 1; hence not 2 divides 2273 by NAT_4:9;
2273 = 3*757 + 2; hence not 3 divides 2273 by NAT_4:9;
2273 = 5*454 + 3; hence not 5 divides 2273 by NAT_4:9;
2273 = 7*324 + 5; hence not 7 divides 2273 by NAT_4:9;
2273 = 11*206 + 7; hence not 11 divides 2273 by NAT_4:9;
2273 = 13*174 + 11; hence not 13 divides 2273 by NAT_4:9;
2273 = 17*133 + 12; hence not 17 divides 2273 by NAT_4:9;
2273 = 19*119 + 12; hence not 19 divides 2273 by NAT_4:9;
2273 = 23*98 + 19; hence not 23 divides 2273 by NAT_4:9;
2273 = 29*78 + 11; hence not 29 divides 2273 by NAT_4:9;
2273 = 31*73 + 10; hence not 31 divides 2273 by NAT_4:9;
2273 = 37*61 + 16; hence not 37 divides 2273 by NAT_4:9;
2273 = 41*55 + 18; hence not 41 divides 2273 by NAT_4:9;
2273 = 43*52 + 37; hence not 43 divides 2273 by NAT_4:9;
2273 = 47*48 + 17; hence not 47 divides 2273 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2273 & n is prime
holds not n divides 2273 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2281 is prime
proof
now
2281 = 2*1140 + 1; hence not 2 divides 2281 by NAT_4:9;
2281 = 3*760 + 1; hence not 3 divides 2281 by NAT_4:9;
2281 = 5*456 + 1; hence not 5 divides 2281 by NAT_4:9;
2281 = 7*325 + 6; hence not 7 divides 2281 by NAT_4:9;
2281 = 11*207 + 4; hence not 11 divides 2281 by NAT_4:9;
2281 = 13*175 + 6; hence not 13 divides 2281 by NAT_4:9;
2281 = 17*134 + 3; hence not 17 divides 2281 by NAT_4:9;
2281 = 19*120 + 1; hence not 19 divides 2281 by NAT_4:9;
2281 = 23*99 + 4; hence not 23 divides 2281 by NAT_4:9;
2281 = 29*78 + 19; hence not 29 divides 2281 by NAT_4:9;
2281 = 31*73 + 18; hence not 31 divides 2281 by NAT_4:9;
2281 = 37*61 + 24; hence not 37 divides 2281 by NAT_4:9;
2281 = 41*55 + 26; hence not 41 divides 2281 by NAT_4:9;
2281 = 43*53 + 2; hence not 43 divides 2281 by NAT_4:9;
2281 = 47*48 + 25; hence not 47 divides 2281 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2281 & n is prime
holds not n divides 2281 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2287 is prime
proof
now
2287 = 2*1143 + 1; hence not 2 divides 2287 by NAT_4:9;
2287 = 3*762 + 1; hence not 3 divides 2287 by NAT_4:9;
2287 = 5*457 + 2; hence not 5 divides 2287 by NAT_4:9;
2287 = 7*326 + 5; hence not 7 divides 2287 by NAT_4:9;
2287 = 11*207 + 10; hence not 11 divides 2287 by NAT_4:9;
2287 = 13*175 + 12; hence not 13 divides 2287 by NAT_4:9;
2287 = 17*134 + 9; hence not 17 divides 2287 by NAT_4:9;
2287 = 19*120 + 7; hence not 19 divides 2287 by NAT_4:9;
2287 = 23*99 + 10; hence not 23 divides 2287 by NAT_4:9;
2287 = 29*78 + 25; hence not 29 divides 2287 by NAT_4:9;
2287 = 31*73 + 24; hence not 31 divides 2287 by NAT_4:9;
2287 = 37*61 + 30; hence not 37 divides 2287 by NAT_4:9;
2287 = 41*55 + 32; hence not 41 divides 2287 by NAT_4:9;
2287 = 43*53 + 8; hence not 43 divides 2287 by NAT_4:9;
2287 = 47*48 + 31; hence not 47 divides 2287 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2287 & n is prime
holds not n divides 2287 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2293 is prime
proof
now
2293 = 2*1146 + 1; hence not 2 divides 2293 by NAT_4:9;
2293 = 3*764 + 1; hence not 3 divides 2293 by NAT_4:9;
2293 = 5*458 + 3; hence not 5 divides 2293 by NAT_4:9;
2293 = 7*327 + 4; hence not 7 divides 2293 by NAT_4:9;
2293 = 11*208 + 5; hence not 11 divides 2293 by NAT_4:9;
2293 = 13*176 + 5; hence not 13 divides 2293 by NAT_4:9;
2293 = 17*134 + 15; hence not 17 divides 2293 by NAT_4:9;
2293 = 19*120 + 13; hence not 19 divides 2293 by NAT_4:9;
2293 = 23*99 + 16; hence not 23 divides 2293 by NAT_4:9;
2293 = 29*79 + 2; hence not 29 divides 2293 by NAT_4:9;
2293 = 31*73 + 30; hence not 31 divides 2293 by NAT_4:9;
2293 = 37*61 + 36; hence not 37 divides 2293 by NAT_4:9;
2293 = 41*55 + 38; hence not 41 divides 2293 by NAT_4:9;
2293 = 43*53 + 14; hence not 43 divides 2293 by NAT_4:9;
2293 = 47*48 + 37; hence not 47 divides 2293 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2293 & n is prime
holds not n divides 2293 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2297 is prime
proof
now
2297 = 2*1148 + 1; hence not 2 divides 2297 by NAT_4:9;
2297 = 3*765 + 2; hence not 3 divides 2297 by NAT_4:9;
2297 = 5*459 + 2; hence not 5 divides 2297 by NAT_4:9;
2297 = 7*328 + 1; hence not 7 divides 2297 by NAT_4:9;
2297 = 11*208 + 9; hence not 11 divides 2297 by NAT_4:9;
2297 = 13*176 + 9; hence not 13 divides 2297 by NAT_4:9;
2297 = 17*135 + 2; hence not 17 divides 2297 by NAT_4:9;
2297 = 19*120 + 17; hence not 19 divides 2297 by NAT_4:9;
2297 = 23*99 + 20; hence not 23 divides 2297 by NAT_4:9;
2297 = 29*79 + 6; hence not 29 divides 2297 by NAT_4:9;
2297 = 31*74 + 3; hence not 31 divides 2297 by NAT_4:9;
2297 = 37*62 + 3; hence not 37 divides 2297 by NAT_4:9;
2297 = 41*56 + 1; hence not 41 divides 2297 by NAT_4:9;
2297 = 43*53 + 18; hence not 43 divides 2297 by NAT_4:9;
2297 = 47*48 + 41; hence not 47 divides 2297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2297 & n is prime
holds not n divides 2297 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2309 is prime
proof
now
2309 = 2*1154 + 1; hence not 2 divides 2309 by NAT_4:9;
2309 = 3*769 + 2; hence not 3 divides 2309 by NAT_4:9;
2309 = 5*461 + 4; hence not 5 divides 2309 by NAT_4:9;
2309 = 7*329 + 6; hence not 7 divides 2309 by NAT_4:9;
2309 = 11*209 + 10; hence not 11 divides 2309 by NAT_4:9;
2309 = 13*177 + 8; hence not 13 divides 2309 by NAT_4:9;
2309 = 17*135 + 14; hence not 17 divides 2309 by NAT_4:9;
2309 = 19*121 + 10; hence not 19 divides 2309 by NAT_4:9;
2309 = 23*100 + 9; hence not 23 divides 2309 by NAT_4:9;
2309 = 29*79 + 18; hence not 29 divides 2309 by NAT_4:9;
2309 = 31*74 + 15; hence not 31 divides 2309 by NAT_4:9;
2309 = 37*62 + 15; hence not 37 divides 2309 by NAT_4:9;
2309 = 41*56 + 13; hence not 41 divides 2309 by NAT_4:9;
2309 = 43*53 + 30; hence not 43 divides 2309 by NAT_4:9;
2309 = 47*49 + 6; hence not 47 divides 2309 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2309 & n is prime
holds not n divides 2309 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2311 is prime
proof
now
2311 = 2*1155 + 1; hence not 2 divides 2311 by NAT_4:9;
2311 = 3*770 + 1; hence not 3 divides 2311 by NAT_4:9;
2311 = 5*462 + 1; hence not 5 divides 2311 by NAT_4:9;
2311 = 7*330 + 1; hence not 7 divides 2311 by NAT_4:9;
2311 = 11*210 + 1; hence not 11 divides 2311 by NAT_4:9;
2311 = 13*177 + 10; hence not 13 divides 2311 by NAT_4:9;
2311 = 17*135 + 16; hence not 17 divides 2311 by NAT_4:9;
2311 = 19*121 + 12; hence not 19 divides 2311 by NAT_4:9;
2311 = 23*100 + 11; hence not 23 divides 2311 by NAT_4:9;
2311 = 29*79 + 20; hence not 29 divides 2311 by NAT_4:9;
2311 = 31*74 + 17; hence not 31 divides 2311 by NAT_4:9;
2311 = 37*62 + 17; hence not 37 divides 2311 by NAT_4:9;
2311 = 41*56 + 15; hence not 41 divides 2311 by NAT_4:9;
2311 = 43*53 + 32; hence not 43 divides 2311 by NAT_4:9;
2311 = 47*49 + 8; hence not 47 divides 2311 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2311 & n is prime
holds not n divides 2311 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
2333 is prime
proof
now
2333 = 2*1166 + 1; hence not 2 divides 2333 by NAT_4:9;
2333 = 3*777 + 2; hence not 3 divides 2333 by NAT_4:9;
2333 = 5*466 + 3; hence not 5 divides 2333 by NAT_4:9;
2333 = 7*333 + 2; hence not 7 divides 2333 by NAT_4:9;
2333 = 11*212 + 1; hence not 11 divides 2333 by NAT_4:9;
2333 = 13*179 + 6; hence not 13 divides 2333 by NAT_4:9;
2333 = 17*137 + 4; hence not 17 divides 2333 by NAT_4:9;
2333 = 19*122 + 15; hence not 19 divides 2333 by NAT_4:9;
2333 = 23*101 + 10; hence not 23 divides 2333 by NAT_4:9;
2333 = 29*80 + 13; hence not 29 divides 2333 by NAT_4:9;
2333 = 31*75 + 8; hence not 31 divides 2333 by NAT_4:9;
2333 = 37*63 + 2; hence not 37 divides 2333 by NAT_4:9;
2333 = 41*56 + 37; hence not 41 divides 2333 by NAT_4:9;
2333 = 43*54 + 11; hence not 43 divides 2333 by NAT_4:9;
2333 = 47*49 + 30; hence not 47 divides 2333 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2333 & n is prime
holds not n divides 2333 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2339 is prime
proof
now
2339 = 2*1169 + 1; hence not 2 divides 2339 by NAT_4:9;
2339 = 3*779 + 2; hence not 3 divides 2339 by NAT_4:9;
2339 = 5*467 + 4; hence not 5 divides 2339 by NAT_4:9;
2339 = 7*334 + 1; hence not 7 divides 2339 by NAT_4:9;
2339 = 11*212 + 7; hence not 11 divides 2339 by NAT_4:9;
2339 = 13*179 + 12; hence not 13 divides 2339 by NAT_4:9;
2339 = 17*137 + 10; hence not 17 divides 2339 by NAT_4:9;
2339 = 19*123 + 2; hence not 19 divides 2339 by NAT_4:9;
2339 = 23*101 + 16; hence not 23 divides 2339 by NAT_4:9;
2339 = 29*80 + 19; hence not 29 divides 2339 by NAT_4:9;
2339 = 31*75 + 14; hence not 31 divides 2339 by NAT_4:9;
2339 = 37*63 + 8; hence not 37 divides 2339 by NAT_4:9;
2339 = 41*57 + 2; hence not 41 divides 2339 by NAT_4:9;
2339 = 43*54 + 17; hence not 43 divides 2339 by NAT_4:9;
2339 = 47*49 + 36; hence not 47 divides 2339 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2339 & n is prime
holds not n divides 2339 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2341 is prime
proof
now
2341 = 2*1170 + 1; hence not 2 divides 2341 by NAT_4:9;
2341 = 3*780 + 1; hence not 3 divides 2341 by NAT_4:9;
2341 = 5*468 + 1; hence not 5 divides 2341 by NAT_4:9;
2341 = 7*334 + 3; hence not 7 divides 2341 by NAT_4:9;
2341 = 11*212 + 9; hence not 11 divides 2341 by NAT_4:9;
2341 = 13*180 + 1; hence not 13 divides 2341 by NAT_4:9;
2341 = 17*137 + 12; hence not 17 divides 2341 by NAT_4:9;
2341 = 19*123 + 4; hence not 19 divides 2341 by NAT_4:9;
2341 = 23*101 + 18; hence not 23 divides 2341 by NAT_4:9;
2341 = 29*80 + 21; hence not 29 divides 2341 by NAT_4:9;
2341 = 31*75 + 16; hence not 31 divides 2341 by NAT_4:9;
2341 = 37*63 + 10; hence not 37 divides 2341 by NAT_4:9;
2341 = 41*57 + 4; hence not 41 divides 2341 by NAT_4:9;
2341 = 43*54 + 19; hence not 43 divides 2341 by NAT_4:9;
2341 = 47*49 + 38; hence not 47 divides 2341 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2341 & n is prime
holds not n divides 2341 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2347 is prime
proof
now
2347 = 2*1173 + 1; hence not 2 divides 2347 by NAT_4:9;
2347 = 3*782 + 1; hence not 3 divides 2347 by NAT_4:9;
2347 = 5*469 + 2; hence not 5 divides 2347 by NAT_4:9;
2347 = 7*335 + 2; hence not 7 divides 2347 by NAT_4:9;
2347 = 11*213 + 4; hence not 11 divides 2347 by NAT_4:9;
2347 = 13*180 + 7; hence not 13 divides 2347 by NAT_4:9;
2347 = 17*138 + 1; hence not 17 divides 2347 by NAT_4:9;
2347 = 19*123 + 10; hence not 19 divides 2347 by NAT_4:9;
2347 = 23*102 + 1; hence not 23 divides 2347 by NAT_4:9;
2347 = 29*80 + 27; hence not 29 divides 2347 by NAT_4:9;
2347 = 31*75 + 22; hence not 31 divides 2347 by NAT_4:9;
2347 = 37*63 + 16; hence not 37 divides 2347 by NAT_4:9;
2347 = 41*57 + 10; hence not 41 divides 2347 by NAT_4:9;
2347 = 43*54 + 25; hence not 43 divides 2347 by NAT_4:9;
2347 = 47*49 + 44; hence not 47 divides 2347 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2347 & n is prime
holds not n divides 2347 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2351 is prime
proof
now
2351 = 2*1175 + 1; hence not 2 divides 2351 by NAT_4:9;
2351 = 3*783 + 2; hence not 3 divides 2351 by NAT_4:9;
2351 = 5*470 + 1; hence not 5 divides 2351 by NAT_4:9;
2351 = 7*335 + 6; hence not 7 divides 2351 by NAT_4:9;
2351 = 11*213 + 8; hence not 11 divides 2351 by NAT_4:9;
2351 = 13*180 + 11; hence not 13 divides 2351 by NAT_4:9;
2351 = 17*138 + 5; hence not 17 divides 2351 by NAT_4:9;
2351 = 19*123 + 14; hence not 19 divides 2351 by NAT_4:9;
2351 = 23*102 + 5; hence not 23 divides 2351 by NAT_4:9;
2351 = 29*81 + 2; hence not 29 divides 2351 by NAT_4:9;
2351 = 31*75 + 26; hence not 31 divides 2351 by NAT_4:9;
2351 = 37*63 + 20; hence not 37 divides 2351 by NAT_4:9;
2351 = 41*57 + 14; hence not 41 divides 2351 by NAT_4:9;
2351 = 43*54 + 29; hence not 43 divides 2351 by NAT_4:9;
2351 = 47*50 + 1; hence not 47 divides 2351 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2351 & n is prime
holds not n divides 2351 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2357 is prime
proof
now
2357 = 2*1178 + 1; hence not 2 divides 2357 by NAT_4:9;
2357 = 3*785 + 2; hence not 3 divides 2357 by NAT_4:9;
2357 = 5*471 + 2; hence not 5 divides 2357 by NAT_4:9;
2357 = 7*336 + 5; hence not 7 divides 2357 by NAT_4:9;
2357 = 11*214 + 3; hence not 11 divides 2357 by NAT_4:9;
2357 = 13*181 + 4; hence not 13 divides 2357 by NAT_4:9;
2357 = 17*138 + 11; hence not 17 divides 2357 by NAT_4:9;
2357 = 19*124 + 1; hence not 19 divides 2357 by NAT_4:9;
2357 = 23*102 + 11; hence not 23 divides 2357 by NAT_4:9;
2357 = 29*81 + 8; hence not 29 divides 2357 by NAT_4:9;
2357 = 31*76 + 1; hence not 31 divides 2357 by NAT_4:9;
2357 = 37*63 + 26; hence not 37 divides 2357 by NAT_4:9;
2357 = 41*57 + 20; hence not 41 divides 2357 by NAT_4:9;
2357 = 43*54 + 35; hence not 43 divides 2357 by NAT_4:9;
2357 = 47*50 + 7; hence not 47 divides 2357 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2357 & n is prime
holds not n divides 2357 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2371 is prime
proof
now
2371 = 2*1185 + 1; hence not 2 divides 2371 by NAT_4:9;
2371 = 3*790 + 1; hence not 3 divides 2371 by NAT_4:9;
2371 = 5*474 + 1; hence not 5 divides 2371 by NAT_4:9;
2371 = 7*338 + 5; hence not 7 divides 2371 by NAT_4:9;
2371 = 11*215 + 6; hence not 11 divides 2371 by NAT_4:9;
2371 = 13*182 + 5; hence not 13 divides 2371 by NAT_4:9;
2371 = 17*139 + 8; hence not 17 divides 2371 by NAT_4:9;
2371 = 19*124 + 15; hence not 19 divides 2371 by NAT_4:9;
2371 = 23*103 + 2; hence not 23 divides 2371 by NAT_4:9;
2371 = 29*81 + 22; hence not 29 divides 2371 by NAT_4:9;
2371 = 31*76 + 15; hence not 31 divides 2371 by NAT_4:9;
2371 = 37*64 + 3; hence not 37 divides 2371 by NAT_4:9;
2371 = 41*57 + 34; hence not 41 divides 2371 by NAT_4:9;
2371 = 43*55 + 6; hence not 43 divides 2371 by NAT_4:9;
2371 = 47*50 + 21; hence not 47 divides 2371 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2371 & n is prime
holds not n divides 2371 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2377 is prime
proof
now
2377 = 2*1188 + 1; hence not 2 divides 2377 by NAT_4:9;
2377 = 3*792 + 1; hence not 3 divides 2377 by NAT_4:9;
2377 = 5*475 + 2; hence not 5 divides 2377 by NAT_4:9;
2377 = 7*339 + 4; hence not 7 divides 2377 by NAT_4:9;
2377 = 11*216 + 1; hence not 11 divides 2377 by NAT_4:9;
2377 = 13*182 + 11; hence not 13 divides 2377 by NAT_4:9;
2377 = 17*139 + 14; hence not 17 divides 2377 by NAT_4:9;
2377 = 19*125 + 2; hence not 19 divides 2377 by NAT_4:9;
2377 = 23*103 + 8; hence not 23 divides 2377 by NAT_4:9;
2377 = 29*81 + 28; hence not 29 divides 2377 by NAT_4:9;
2377 = 31*76 + 21; hence not 31 divides 2377 by NAT_4:9;
2377 = 37*64 + 9; hence not 37 divides 2377 by NAT_4:9;
2377 = 41*57 + 40; hence not 41 divides 2377 by NAT_4:9;
2377 = 43*55 + 12; hence not 43 divides 2377 by NAT_4:9;
2377 = 47*50 + 27; hence not 47 divides 2377 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2377 & n is prime
holds not n divides 2377 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2381 is prime
proof
now
2381 = 2*1190 + 1; hence not 2 divides 2381 by NAT_4:9;
2381 = 3*793 + 2; hence not 3 divides 2381 by NAT_4:9;
2381 = 5*476 + 1; hence not 5 divides 2381 by NAT_4:9;
2381 = 7*340 + 1; hence not 7 divides 2381 by NAT_4:9;
2381 = 11*216 + 5; hence not 11 divides 2381 by NAT_4:9;
2381 = 13*183 + 2; hence not 13 divides 2381 by NAT_4:9;
2381 = 17*140 + 1; hence not 17 divides 2381 by NAT_4:9;
2381 = 19*125 + 6; hence not 19 divides 2381 by NAT_4:9;
2381 = 23*103 + 12; hence not 23 divides 2381 by NAT_4:9;
2381 = 29*82 + 3; hence not 29 divides 2381 by NAT_4:9;
2381 = 31*76 + 25; hence not 31 divides 2381 by NAT_4:9;
2381 = 37*64 + 13; hence not 37 divides 2381 by NAT_4:9;
2381 = 41*58 + 3; hence not 41 divides 2381 by NAT_4:9;
2381 = 43*55 + 16; hence not 43 divides 2381 by NAT_4:9;
2381 = 47*50 + 31; hence not 47 divides 2381 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2381 & n is prime
holds not n divides 2381 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2383 is prime
proof
now
2383 = 2*1191 + 1; hence not 2 divides 2383 by NAT_4:9;
2383 = 3*794 + 1; hence not 3 divides 2383 by NAT_4:9;
2383 = 5*476 + 3; hence not 5 divides 2383 by NAT_4:9;
2383 = 7*340 + 3; hence not 7 divides 2383 by NAT_4:9;
2383 = 11*216 + 7; hence not 11 divides 2383 by NAT_4:9;
2383 = 13*183 + 4; hence not 13 divides 2383 by NAT_4:9;
2383 = 17*140 + 3; hence not 17 divides 2383 by NAT_4:9;
2383 = 19*125 + 8; hence not 19 divides 2383 by NAT_4:9;
2383 = 23*103 + 14; hence not 23 divides 2383 by NAT_4:9;
2383 = 29*82 + 5; hence not 29 divides 2383 by NAT_4:9;
2383 = 31*76 + 27; hence not 31 divides 2383 by NAT_4:9;
2383 = 37*64 + 15; hence not 37 divides 2383 by NAT_4:9;
2383 = 41*58 + 5; hence not 41 divides 2383 by NAT_4:9;
2383 = 43*55 + 18; hence not 43 divides 2383 by NAT_4:9;
2383 = 47*50 + 33; hence not 47 divides 2383 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2383 & n is prime
holds not n divides 2383 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2389 is prime
proof
now
2389 = 2*1194 + 1; hence not 2 divides 2389 by NAT_4:9;
2389 = 3*796 + 1; hence not 3 divides 2389 by NAT_4:9;
2389 = 5*477 + 4; hence not 5 divides 2389 by NAT_4:9;
2389 = 7*341 + 2; hence not 7 divides 2389 by NAT_4:9;
2389 = 11*217 + 2; hence not 11 divides 2389 by NAT_4:9;
2389 = 13*183 + 10; hence not 13 divides 2389 by NAT_4:9;
2389 = 17*140 + 9; hence not 17 divides 2389 by NAT_4:9;
2389 = 19*125 + 14; hence not 19 divides 2389 by NAT_4:9;
2389 = 23*103 + 20; hence not 23 divides 2389 by NAT_4:9;
2389 = 29*82 + 11; hence not 29 divides 2389 by NAT_4:9;
2389 = 31*77 + 2; hence not 31 divides 2389 by NAT_4:9;
2389 = 37*64 + 21; hence not 37 divides 2389 by NAT_4:9;
2389 = 41*58 + 11; hence not 41 divides 2389 by NAT_4:9;
2389 = 43*55 + 24; hence not 43 divides 2389 by NAT_4:9;
2389 = 47*50 + 39; hence not 47 divides 2389 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2389 & n is prime
holds not n divides 2389 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2393 is prime
proof
now
2393 = 2*1196 + 1; hence not 2 divides 2393 by NAT_4:9;
2393 = 3*797 + 2; hence not 3 divides 2393 by NAT_4:9;
2393 = 5*478 + 3; hence not 5 divides 2393 by NAT_4:9;
2393 = 7*341 + 6; hence not 7 divides 2393 by NAT_4:9;
2393 = 11*217 + 6; hence not 11 divides 2393 by NAT_4:9;
2393 = 13*184 + 1; hence not 13 divides 2393 by NAT_4:9;
2393 = 17*140 + 13; hence not 17 divides 2393 by NAT_4:9;
2393 = 19*125 + 18; hence not 19 divides 2393 by NAT_4:9;
2393 = 23*104 + 1; hence not 23 divides 2393 by NAT_4:9;
2393 = 29*82 + 15; hence not 29 divides 2393 by NAT_4:9;
2393 = 31*77 + 6; hence not 31 divides 2393 by NAT_4:9;
2393 = 37*64 + 25; hence not 37 divides 2393 by NAT_4:9;
2393 = 41*58 + 15; hence not 41 divides 2393 by NAT_4:9;
2393 = 43*55 + 28; hence not 43 divides 2393 by NAT_4:9;
2393 = 47*50 + 43; hence not 47 divides 2393 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2393 & n is prime
holds not n divides 2393 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2399 is prime
proof
now
2399 = 2*1199 + 1; hence not 2 divides 2399 by NAT_4:9;
2399 = 3*799 + 2; hence not 3 divides 2399 by NAT_4:9;
2399 = 5*479 + 4; hence not 5 divides 2399 by NAT_4:9;
2399 = 7*342 + 5; hence not 7 divides 2399 by NAT_4:9;
2399 = 11*218 + 1; hence not 11 divides 2399 by NAT_4:9;
2399 = 13*184 + 7; hence not 13 divides 2399 by NAT_4:9;
2399 = 17*141 + 2; hence not 17 divides 2399 by NAT_4:9;
2399 = 19*126 + 5; hence not 19 divides 2399 by NAT_4:9;
2399 = 23*104 + 7; hence not 23 divides 2399 by NAT_4:9;
2399 = 29*82 + 21; hence not 29 divides 2399 by NAT_4:9;
2399 = 31*77 + 12; hence not 31 divides 2399 by NAT_4:9;
2399 = 37*64 + 31; hence not 37 divides 2399 by NAT_4:9;
2399 = 41*58 + 21; hence not 41 divides 2399 by NAT_4:9;
2399 = 43*55 + 34; hence not 43 divides 2399 by NAT_4:9;
2399 = 47*51 + 2; hence not 47 divides 2399 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2399 & n is prime
holds not n divides 2399 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2411 is prime
proof
now
2411 = 2*1205 + 1; hence not 2 divides 2411 by NAT_4:9;
2411 = 3*803 + 2; hence not 3 divides 2411 by NAT_4:9;
2411 = 5*482 + 1; hence not 5 divides 2411 by NAT_4:9;
2411 = 7*344 + 3; hence not 7 divides 2411 by NAT_4:9;
2411 = 11*219 + 2; hence not 11 divides 2411 by NAT_4:9;
2411 = 13*185 + 6; hence not 13 divides 2411 by NAT_4:9;
2411 = 17*141 + 14; hence not 17 divides 2411 by NAT_4:9;
2411 = 19*126 + 17; hence not 19 divides 2411 by NAT_4:9;
2411 = 23*104 + 19; hence not 23 divides 2411 by NAT_4:9;
2411 = 29*83 + 4; hence not 29 divides 2411 by NAT_4:9;
2411 = 31*77 + 24; hence not 31 divides 2411 by NAT_4:9;
2411 = 37*65 + 6; hence not 37 divides 2411 by NAT_4:9;
2411 = 41*58 + 33; hence not 41 divides 2411 by NAT_4:9;
2411 = 43*56 + 3; hence not 43 divides 2411 by NAT_4:9;
2411 = 47*51 + 14; hence not 47 divides 2411 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2411 & n is prime
holds not n divides 2411 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2417 is prime
proof
now
2417 = 2*1208 + 1; hence not 2 divides 2417 by NAT_4:9;
2417 = 3*805 + 2; hence not 3 divides 2417 by NAT_4:9;
2417 = 5*483 + 2; hence not 5 divides 2417 by NAT_4:9;
2417 = 7*345 + 2; hence not 7 divides 2417 by NAT_4:9;
2417 = 11*219 + 8; hence not 11 divides 2417 by NAT_4:9;
2417 = 13*185 + 12; hence not 13 divides 2417 by NAT_4:9;
2417 = 17*142 + 3; hence not 17 divides 2417 by NAT_4:9;
2417 = 19*127 + 4; hence not 19 divides 2417 by NAT_4:9;
2417 = 23*105 + 2; hence not 23 divides 2417 by NAT_4:9;
2417 = 29*83 + 10; hence not 29 divides 2417 by NAT_4:9;
2417 = 31*77 + 30; hence not 31 divides 2417 by NAT_4:9;
2417 = 37*65 + 12; hence not 37 divides 2417 by NAT_4:9;
2417 = 41*58 + 39; hence not 41 divides 2417 by NAT_4:9;
2417 = 43*56 + 9; hence not 43 divides 2417 by NAT_4:9;
2417 = 47*51 + 20; hence not 47 divides 2417 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2417 & n is prime
holds not n divides 2417 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2423 is prime
proof
now
2423 = 2*1211 + 1; hence not 2 divides 2423 by NAT_4:9;
2423 = 3*807 + 2; hence not 3 divides 2423 by NAT_4:9;
2423 = 5*484 + 3; hence not 5 divides 2423 by NAT_4:9;
2423 = 7*346 + 1; hence not 7 divides 2423 by NAT_4:9;
2423 = 11*220 + 3; hence not 11 divides 2423 by NAT_4:9;
2423 = 13*186 + 5; hence not 13 divides 2423 by NAT_4:9;
2423 = 17*142 + 9; hence not 17 divides 2423 by NAT_4:9;
2423 = 19*127 + 10; hence not 19 divides 2423 by NAT_4:9;
2423 = 23*105 + 8; hence not 23 divides 2423 by NAT_4:9;
2423 = 29*83 + 16; hence not 29 divides 2423 by NAT_4:9;
2423 = 31*78 + 5; hence not 31 divides 2423 by NAT_4:9;
2423 = 37*65 + 18; hence not 37 divides 2423 by NAT_4:9;
2423 = 41*59 + 4; hence not 41 divides 2423 by NAT_4:9;
2423 = 43*56 + 15; hence not 43 divides 2423 by NAT_4:9;
2423 = 47*51 + 26; hence not 47 divides 2423 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2423 & n is prime
holds not n divides 2423 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2437 is prime
proof
now
2437 = 2*1218 + 1; hence not 2 divides 2437 by NAT_4:9;
2437 = 3*812 + 1; hence not 3 divides 2437 by NAT_4:9;
2437 = 5*487 + 2; hence not 5 divides 2437 by NAT_4:9;
2437 = 7*348 + 1; hence not 7 divides 2437 by NAT_4:9;
2437 = 11*221 + 6; hence not 11 divides 2437 by NAT_4:9;
2437 = 13*187 + 6; hence not 13 divides 2437 by NAT_4:9;
2437 = 17*143 + 6; hence not 17 divides 2437 by NAT_4:9;
2437 = 19*128 + 5; hence not 19 divides 2437 by NAT_4:9;
2437 = 23*105 + 22; hence not 23 divides 2437 by NAT_4:9;
2437 = 29*84 + 1; hence not 29 divides 2437 by NAT_4:9;
2437 = 31*78 + 19; hence not 31 divides 2437 by NAT_4:9;
2437 = 37*65 + 32; hence not 37 divides 2437 by NAT_4:9;
2437 = 41*59 + 18; hence not 41 divides 2437 by NAT_4:9;
2437 = 43*56 + 29; hence not 43 divides 2437 by NAT_4:9;
2437 = 47*51 + 40; hence not 47 divides 2437 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2437 & n is prime
holds not n divides 2437 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2441 is prime
proof
now
2441 = 2*1220 + 1; hence not 2 divides 2441 by NAT_4:9;
2441 = 3*813 + 2; hence not 3 divides 2441 by NAT_4:9;
2441 = 5*488 + 1; hence not 5 divides 2441 by NAT_4:9;
2441 = 7*348 + 5; hence not 7 divides 2441 by NAT_4:9;
2441 = 11*221 + 10; hence not 11 divides 2441 by NAT_4:9;
2441 = 13*187 + 10; hence not 13 divides 2441 by NAT_4:9;
2441 = 17*143 + 10; hence not 17 divides 2441 by NAT_4:9;
2441 = 19*128 + 9; hence not 19 divides 2441 by NAT_4:9;
2441 = 23*106 + 3; hence not 23 divides 2441 by NAT_4:9;
2441 = 29*84 + 5; hence not 29 divides 2441 by NAT_4:9;
2441 = 31*78 + 23; hence not 31 divides 2441 by NAT_4:9;
2441 = 37*65 + 36; hence not 37 divides 2441 by NAT_4:9;
2441 = 41*59 + 22; hence not 41 divides 2441 by NAT_4:9;
2441 = 43*56 + 33; hence not 43 divides 2441 by NAT_4:9;
2441 = 47*51 + 44; hence not 47 divides 2441 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2441 & n is prime
holds not n divides 2441 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2447 is prime
proof
now
2447 = 2*1223 + 1; hence not 2 divides 2447 by NAT_4:9;
2447 = 3*815 + 2; hence not 3 divides 2447 by NAT_4:9;
2447 = 5*489 + 2; hence not 5 divides 2447 by NAT_4:9;
2447 = 7*349 + 4; hence not 7 divides 2447 by NAT_4:9;
2447 = 11*222 + 5; hence not 11 divides 2447 by NAT_4:9;
2447 = 13*188 + 3; hence not 13 divides 2447 by NAT_4:9;
2447 = 17*143 + 16; hence not 17 divides 2447 by NAT_4:9;
2447 = 19*128 + 15; hence not 19 divides 2447 by NAT_4:9;
2447 = 23*106 + 9; hence not 23 divides 2447 by NAT_4:9;
2447 = 29*84 + 11; hence not 29 divides 2447 by NAT_4:9;
2447 = 31*78 + 29; hence not 31 divides 2447 by NAT_4:9;
2447 = 37*66 + 5; hence not 37 divides 2447 by NAT_4:9;
2447 = 41*59 + 28; hence not 41 divides 2447 by NAT_4:9;
2447 = 43*56 + 39; hence not 43 divides 2447 by NAT_4:9;
2447 = 47*52 + 3; hence not 47 divides 2447 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2447 & n is prime
holds not n divides 2447 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2459 is prime
proof
now
2459 = 2*1229 + 1; hence not 2 divides 2459 by NAT_4:9;
2459 = 3*819 + 2; hence not 3 divides 2459 by NAT_4:9;
2459 = 5*491 + 4; hence not 5 divides 2459 by NAT_4:9;
2459 = 7*351 + 2; hence not 7 divides 2459 by NAT_4:9;
2459 = 11*223 + 6; hence not 11 divides 2459 by NAT_4:9;
2459 = 13*189 + 2; hence not 13 divides 2459 by NAT_4:9;
2459 = 17*144 + 11; hence not 17 divides 2459 by NAT_4:9;
2459 = 19*129 + 8; hence not 19 divides 2459 by NAT_4:9;
2459 = 23*106 + 21; hence not 23 divides 2459 by NAT_4:9;
2459 = 29*84 + 23; hence not 29 divides 2459 by NAT_4:9;
2459 = 31*79 + 10; hence not 31 divides 2459 by NAT_4:9;
2459 = 37*66 + 17; hence not 37 divides 2459 by NAT_4:9;
2459 = 41*59 + 40; hence not 41 divides 2459 by NAT_4:9;
2459 = 43*57 + 8; hence not 43 divides 2459 by NAT_4:9;
2459 = 47*52 + 15; hence not 47 divides 2459 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2459 & n is prime
holds not n divides 2459 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2467 is prime
proof
now
2467 = 2*1233 + 1; hence not 2 divides 2467 by NAT_4:9;
2467 = 3*822 + 1; hence not 3 divides 2467 by NAT_4:9;
2467 = 5*493 + 2; hence not 5 divides 2467 by NAT_4:9;
2467 = 7*352 + 3; hence not 7 divides 2467 by NAT_4:9;
2467 = 11*224 + 3; hence not 11 divides 2467 by NAT_4:9;
2467 = 13*189 + 10; hence not 13 divides 2467 by NAT_4:9;
2467 = 17*145 + 2; hence not 17 divides 2467 by NAT_4:9;
2467 = 19*129 + 16; hence not 19 divides 2467 by NAT_4:9;
2467 = 23*107 + 6; hence not 23 divides 2467 by NAT_4:9;
2467 = 29*85 + 2; hence not 29 divides 2467 by NAT_4:9;
2467 = 31*79 + 18; hence not 31 divides 2467 by NAT_4:9;
2467 = 37*66 + 25; hence not 37 divides 2467 by NAT_4:9;
2467 = 41*60 + 7; hence not 41 divides 2467 by NAT_4:9;
2467 = 43*57 + 16; hence not 43 divides 2467 by NAT_4:9;
2467 = 47*52 + 23; hence not 47 divides 2467 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2467 & n is prime
holds not n divides 2467 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2473 is prime
proof
now
2473 = 2*1236 + 1; hence not 2 divides 2473 by NAT_4:9;
2473 = 3*824 + 1; hence not 3 divides 2473 by NAT_4:9;
2473 = 5*494 + 3; hence not 5 divides 2473 by NAT_4:9;
2473 = 7*353 + 2; hence not 7 divides 2473 by NAT_4:9;
2473 = 11*224 + 9; hence not 11 divides 2473 by NAT_4:9;
2473 = 13*190 + 3; hence not 13 divides 2473 by NAT_4:9;
2473 = 17*145 + 8; hence not 17 divides 2473 by NAT_4:9;
2473 = 19*130 + 3; hence not 19 divides 2473 by NAT_4:9;
2473 = 23*107 + 12; hence not 23 divides 2473 by NAT_4:9;
2473 = 29*85 + 8; hence not 29 divides 2473 by NAT_4:9;
2473 = 31*79 + 24; hence not 31 divides 2473 by NAT_4:9;
2473 = 37*66 + 31; hence not 37 divides 2473 by NAT_4:9;
2473 = 41*60 + 13; hence not 41 divides 2473 by NAT_4:9;
2473 = 43*57 + 22; hence not 43 divides 2473 by NAT_4:9;
2473 = 47*52 + 29; hence not 47 divides 2473 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2473 & n is prime
holds not n divides 2473 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2477 is prime
proof
now
2477 = 2*1238 + 1; hence not 2 divides 2477 by NAT_4:9;
2477 = 3*825 + 2; hence not 3 divides 2477 by NAT_4:9;
2477 = 5*495 + 2; hence not 5 divides 2477 by NAT_4:9;
2477 = 7*353 + 6; hence not 7 divides 2477 by NAT_4:9;
2477 = 11*225 + 2; hence not 11 divides 2477 by NAT_4:9;
2477 = 13*190 + 7; hence not 13 divides 2477 by NAT_4:9;
2477 = 17*145 + 12; hence not 17 divides 2477 by NAT_4:9;
2477 = 19*130 + 7; hence not 19 divides 2477 by NAT_4:9;
2477 = 23*107 + 16; hence not 23 divides 2477 by NAT_4:9;
2477 = 29*85 + 12; hence not 29 divides 2477 by NAT_4:9;
2477 = 31*79 + 28; hence not 31 divides 2477 by NAT_4:9;
2477 = 37*66 + 35; hence not 37 divides 2477 by NAT_4:9;
2477 = 41*60 + 17; hence not 41 divides 2477 by NAT_4:9;
2477 = 43*57 + 26; hence not 43 divides 2477 by NAT_4:9;
2477 = 47*52 + 33; hence not 47 divides 2477 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2477 & n is prime
holds not n divides 2477 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 25
theorem
2503 is prime
proof
now
2503 = 2*1251 + 1; hence not 2 divides 2503 by NAT_4:9;
2503 = 3*834 + 1; hence not 3 divides 2503 by NAT_4:9;
2503 = 5*500 + 3; hence not 5 divides 2503 by NAT_4:9;
2503 = 7*357 + 4; hence not 7 divides 2503 by NAT_4:9;
2503 = 11*227 + 6; hence not 11 divides 2503 by NAT_4:9;
2503 = 13*192 + 7; hence not 13 divides 2503 by NAT_4:9;
2503 = 17*147 + 4; hence not 17 divides 2503 by NAT_4:9;
2503 = 19*131 + 14; hence not 19 divides 2503 by NAT_4:9;
2503 = 23*108 + 19; hence not 23 divides 2503 by NAT_4:9;
2503 = 29*86 + 9; hence not 29 divides 2503 by NAT_4:9;
2503 = 31*80 + 23; hence not 31 divides 2503 by NAT_4:9;
2503 = 37*67 + 24; hence not 37 divides 2503 by NAT_4:9;
2503 = 41*61 + 2; hence not 41 divides 2503 by NAT_4:9;
2503 = 43*58 + 9; hence not 43 divides 2503 by NAT_4:9;
2503 = 47*53 + 12; hence not 47 divides 2503 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2503 & n is prime
holds not n divides 2503 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
2521 is prime
proof
now
2521 = 2*1260 + 1; hence not 2 divides 2521 by NAT_4:9;
2521 = 3*840 + 1; hence not 3 divides 2521 by NAT_4:9;
2521 = 5*504 + 1; hence not 5 divides 2521 by NAT_4:9;
2521 = 7*360 + 1; hence not 7 divides 2521 by NAT_4:9;
2521 = 11*229 + 2; hence not 11 divides 2521 by NAT_4:9;
2521 = 13*193 + 12; hence not 13 divides 2521 by NAT_4:9;
2521 = 17*148 + 5; hence not 17 divides 2521 by NAT_4:9;
2521 = 19*132 + 13; hence not 19 divides 2521 by NAT_4:9;
2521 = 23*109 + 14; hence not 23 divides 2521 by NAT_4:9;
2521 = 29*86 + 27; hence not 29 divides 2521 by NAT_4:9;
2521 = 31*81 + 10; hence not 31 divides 2521 by NAT_4:9;
2521 = 37*68 + 5; hence not 37 divides 2521 by NAT_4:9;
2521 = 41*61 + 20; hence not 41 divides 2521 by NAT_4:9;
2521 = 43*58 + 27; hence not 43 divides 2521 by NAT_4:9;
2521 = 47*53 + 30; hence not 47 divides 2521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2521 & n is prime
holds not n divides 2521 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2531 is prime
proof
now
2531 = 2*1265 + 1; hence not 2 divides 2531 by NAT_4:9;
2531 = 3*843 + 2; hence not 3 divides 2531 by NAT_4:9;
2531 = 5*506 + 1; hence not 5 divides 2531 by NAT_4:9;
2531 = 7*361 + 4; hence not 7 divides 2531 by NAT_4:9;
2531 = 11*230 + 1; hence not 11 divides 2531 by NAT_4:9;
2531 = 13*194 + 9; hence not 13 divides 2531 by NAT_4:9;
2531 = 17*148 + 15; hence not 17 divides 2531 by NAT_4:9;
2531 = 19*133 + 4; hence not 19 divides 2531 by NAT_4:9;
2531 = 23*110 + 1; hence not 23 divides 2531 by NAT_4:9;
2531 = 29*87 + 8; hence not 29 divides 2531 by NAT_4:9;
2531 = 31*81 + 20; hence not 31 divides 2531 by NAT_4:9;
2531 = 37*68 + 15; hence not 37 divides 2531 by NAT_4:9;
2531 = 41*61 + 30; hence not 41 divides 2531 by NAT_4:9;
2531 = 43*58 + 37; hence not 43 divides 2531 by NAT_4:9;
2531 = 47*53 + 40; hence not 47 divides 2531 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2531 & n is prime
holds not n divides 2531 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2539 is prime
proof
now
2539 = 2*1269 + 1; hence not 2 divides 2539 by NAT_4:9;
2539 = 3*846 + 1; hence not 3 divides 2539 by NAT_4:9;
2539 = 5*507 + 4; hence not 5 divides 2539 by NAT_4:9;
2539 = 7*362 + 5; hence not 7 divides 2539 by NAT_4:9;
2539 = 11*230 + 9; hence not 11 divides 2539 by NAT_4:9;
2539 = 13*195 + 4; hence not 13 divides 2539 by NAT_4:9;
2539 = 17*149 + 6; hence not 17 divides 2539 by NAT_4:9;
2539 = 19*133 + 12; hence not 19 divides 2539 by NAT_4:9;
2539 = 23*110 + 9; hence not 23 divides 2539 by NAT_4:9;
2539 = 29*87 + 16; hence not 29 divides 2539 by NAT_4:9;
2539 = 31*81 + 28; hence not 31 divides 2539 by NAT_4:9;
2539 = 37*68 + 23; hence not 37 divides 2539 by NAT_4:9;
2539 = 41*61 + 38; hence not 41 divides 2539 by NAT_4:9;
2539 = 43*59 + 2; hence not 43 divides 2539 by NAT_4:9;
2539 = 47*54 + 1; hence not 47 divides 2539 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2539 & n is prime
holds not n divides 2539 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2543 is prime
proof
now
2543 = 2*1271 + 1; hence not 2 divides 2543 by NAT_4:9;
2543 = 3*847 + 2; hence not 3 divides 2543 by NAT_4:9;
2543 = 5*508 + 3; hence not 5 divides 2543 by NAT_4:9;
2543 = 7*363 + 2; hence not 7 divides 2543 by NAT_4:9;
2543 = 11*231 + 2; hence not 11 divides 2543 by NAT_4:9;
2543 = 13*195 + 8; hence not 13 divides 2543 by NAT_4:9;
2543 = 17*149 + 10; hence not 17 divides 2543 by NAT_4:9;
2543 = 19*133 + 16; hence not 19 divides 2543 by NAT_4:9;
2543 = 23*110 + 13; hence not 23 divides 2543 by NAT_4:9;
2543 = 29*87 + 20; hence not 29 divides 2543 by NAT_4:9;
2543 = 31*82 + 1; hence not 31 divides 2543 by NAT_4:9;
2543 = 37*68 + 27; hence not 37 divides 2543 by NAT_4:9;
2543 = 41*62 + 1; hence not 41 divides 2543 by NAT_4:9;
2543 = 43*59 + 6; hence not 43 divides 2543 by NAT_4:9;
2543 = 47*54 + 5; hence not 47 divides 2543 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2543 & n is prime
holds not n divides 2543 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2549 is prime
proof
now
2549 = 2*1274 + 1; hence not 2 divides 2549 by NAT_4:9;
2549 = 3*849 + 2; hence not 3 divides 2549 by NAT_4:9;
2549 = 5*509 + 4; hence not 5 divides 2549 by NAT_4:9;
2549 = 7*364 + 1; hence not 7 divides 2549 by NAT_4:9;
2549 = 11*231 + 8; hence not 11 divides 2549 by NAT_4:9;
2549 = 13*196 + 1; hence not 13 divides 2549 by NAT_4:9;
2549 = 17*149 + 16; hence not 17 divides 2549 by NAT_4:9;
2549 = 19*134 + 3; hence not 19 divides 2549 by NAT_4:9;
2549 = 23*110 + 19; hence not 23 divides 2549 by NAT_4:9;
2549 = 29*87 + 26; hence not 29 divides 2549 by NAT_4:9;
2549 = 31*82 + 7; hence not 31 divides 2549 by NAT_4:9;
2549 = 37*68 + 33; hence not 37 divides 2549 by NAT_4:9;
2549 = 41*62 + 7; hence not 41 divides 2549 by NAT_4:9;
2549 = 43*59 + 12; hence not 43 divides 2549 by NAT_4:9;
2549 = 47*54 + 11; hence not 47 divides 2549 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2549 & n is prime
holds not n divides 2549 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2551 is prime
proof
now
2551 = 2*1275 + 1; hence not 2 divides 2551 by NAT_4:9;
2551 = 3*850 + 1; hence not 3 divides 2551 by NAT_4:9;
2551 = 5*510 + 1; hence not 5 divides 2551 by NAT_4:9;
2551 = 7*364 + 3; hence not 7 divides 2551 by NAT_4:9;
2551 = 11*231 + 10; hence not 11 divides 2551 by NAT_4:9;
2551 = 13*196 + 3; hence not 13 divides 2551 by NAT_4:9;
2551 = 17*150 + 1; hence not 17 divides 2551 by NAT_4:9;
2551 = 19*134 + 5; hence not 19 divides 2551 by NAT_4:9;
2551 = 23*110 + 21; hence not 23 divides 2551 by NAT_4:9;
2551 = 29*87 + 28; hence not 29 divides 2551 by NAT_4:9;
2551 = 31*82 + 9; hence not 31 divides 2551 by NAT_4:9;
2551 = 37*68 + 35; hence not 37 divides 2551 by NAT_4:9;
2551 = 41*62 + 9; hence not 41 divides 2551 by NAT_4:9;
2551 = 43*59 + 14; hence not 43 divides 2551 by NAT_4:9;
2551 = 47*54 + 13; hence not 47 divides 2551 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2551 & n is prime
holds not n divides 2551 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2557 is prime
proof
now
2557 = 2*1278 + 1; hence not 2 divides 2557 by NAT_4:9;
2557 = 3*852 + 1; hence not 3 divides 2557 by NAT_4:9;
2557 = 5*511 + 2; hence not 5 divides 2557 by NAT_4:9;
2557 = 7*365 + 2; hence not 7 divides 2557 by NAT_4:9;
2557 = 11*232 + 5; hence not 11 divides 2557 by NAT_4:9;
2557 = 13*196 + 9; hence not 13 divides 2557 by NAT_4:9;
2557 = 17*150 + 7; hence not 17 divides 2557 by NAT_4:9;
2557 = 19*134 + 11; hence not 19 divides 2557 by NAT_4:9;
2557 = 23*111 + 4; hence not 23 divides 2557 by NAT_4:9;
2557 = 29*88 + 5; hence not 29 divides 2557 by NAT_4:9;
2557 = 31*82 + 15; hence not 31 divides 2557 by NAT_4:9;
2557 = 37*69 + 4; hence not 37 divides 2557 by NAT_4:9;
2557 = 41*62 + 15; hence not 41 divides 2557 by NAT_4:9;
2557 = 43*59 + 20; hence not 43 divides 2557 by NAT_4:9;
2557 = 47*54 + 19; hence not 47 divides 2557 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2557 & n is prime
holds not n divides 2557 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
2579 is prime
proof
now
2579 = 2*1289 + 1; hence not 2 divides 2579 by NAT_4:9;
2579 = 3*859 + 2; hence not 3 divides 2579 by NAT_4:9;
2579 = 5*515 + 4; hence not 5 divides 2579 by NAT_4:9;
2579 = 7*368 + 3; hence not 7 divides 2579 by NAT_4:9;
2579 = 11*234 + 5; hence not 11 divides 2579 by NAT_4:9;
2579 = 13*198 + 5; hence not 13 divides 2579 by NAT_4:9;
2579 = 17*151 + 12; hence not 17 divides 2579 by NAT_4:9;
2579 = 19*135 + 14; hence not 19 divides 2579 by NAT_4:9;
2579 = 23*112 + 3; hence not 23 divides 2579 by NAT_4:9;
2579 = 29*88 + 27; hence not 29 divides 2579 by NAT_4:9;
2579 = 31*83 + 6; hence not 31 divides 2579 by NAT_4:9;
2579 = 37*69 + 26; hence not 37 divides 2579 by NAT_4:9;
2579 = 41*62 + 37; hence not 41 divides 2579 by NAT_4:9;
2579 = 43*59 + 42; hence not 43 divides 2579 by NAT_4:9;
2579 = 47*54 + 41; hence not 47 divides 2579 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2579 & n is prime
holds not n divides 2579 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2591 is prime
proof
now
2591 = 2*1295 + 1; hence not 2 divides 2591 by NAT_4:9;
2591 = 3*863 + 2; hence not 3 divides 2591 by NAT_4:9;
2591 = 5*518 + 1; hence not 5 divides 2591 by NAT_4:9;
2591 = 7*370 + 1; hence not 7 divides 2591 by NAT_4:9;
2591 = 11*235 + 6; hence not 11 divides 2591 by NAT_4:9;
2591 = 13*199 + 4; hence not 13 divides 2591 by NAT_4:9;
2591 = 17*152 + 7; hence not 17 divides 2591 by NAT_4:9;
2591 = 19*136 + 7; hence not 19 divides 2591 by NAT_4:9;
2591 = 23*112 + 15; hence not 23 divides 2591 by NAT_4:9;
2591 = 29*89 + 10; hence not 29 divides 2591 by NAT_4:9;
2591 = 31*83 + 18; hence not 31 divides 2591 by NAT_4:9;
2591 = 37*70 + 1; hence not 37 divides 2591 by NAT_4:9;
2591 = 41*63 + 8; hence not 41 divides 2591 by NAT_4:9;
2591 = 43*60 + 11; hence not 43 divides 2591 by NAT_4:9;
2591 = 47*55 + 6; hence not 47 divides 2591 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2591 & n is prime
holds not n divides 2591 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2593 is prime
proof
now
2593 = 2*1296 + 1; hence not 2 divides 2593 by NAT_4:9;
2593 = 3*864 + 1; hence not 3 divides 2593 by NAT_4:9;
2593 = 5*518 + 3; hence not 5 divides 2593 by NAT_4:9;
2593 = 7*370 + 3; hence not 7 divides 2593 by NAT_4:9;
2593 = 11*235 + 8; hence not 11 divides 2593 by NAT_4:9;
2593 = 13*199 + 6; hence not 13 divides 2593 by NAT_4:9;
2593 = 17*152 + 9; hence not 17 divides 2593 by NAT_4:9;
2593 = 19*136 + 9; hence not 19 divides 2593 by NAT_4:9;
2593 = 23*112 + 17; hence not 23 divides 2593 by NAT_4:9;
2593 = 29*89 + 12; hence not 29 divides 2593 by NAT_4:9;
2593 = 31*83 + 20; hence not 31 divides 2593 by NAT_4:9;
2593 = 37*70 + 3; hence not 37 divides 2593 by NAT_4:9;
2593 = 41*63 + 10; hence not 41 divides 2593 by NAT_4:9;
2593 = 43*60 + 13; hence not 43 divides 2593 by NAT_4:9;
2593 = 47*55 + 8; hence not 47 divides 2593 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2593 & n is prime
holds not n divides 2593 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
2609 is prime
proof
now
2609 = 2*1304 + 1; hence not 2 divides 2609 by NAT_4:9;
2609 = 3*869 + 2; hence not 3 divides 2609 by NAT_4:9;
2609 = 5*521 + 4; hence not 5 divides 2609 by NAT_4:9;
2609 = 7*372 + 5; hence not 7 divides 2609 by NAT_4:9;
2609 = 11*237 + 2; hence not 11 divides 2609 by NAT_4:9;
2609 = 13*200 + 9; hence not 13 divides 2609 by NAT_4:9;
2609 = 17*153 + 8; hence not 17 divides 2609 by NAT_4:9;
2609 = 19*137 + 6; hence not 19 divides 2609 by NAT_4:9;
2609 = 23*113 + 10; hence not 23 divides 2609 by NAT_4:9;
2609 = 29*89 + 28; hence not 29 divides 2609 by NAT_4:9;
2609 = 31*84 + 5; hence not 31 divides 2609 by NAT_4:9;
2609 = 37*70 + 19; hence not 37 divides 2609 by NAT_4:9;
2609 = 41*63 + 26; hence not 41 divides 2609 by NAT_4:9;
2609 = 43*60 + 29; hence not 43 divides 2609 by NAT_4:9;
2609 = 47*55 + 24; hence not 47 divides 2609 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2609 & n is prime
holds not n divides 2609 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2617 is prime
proof
now
2617 = 2*1308 + 1; hence not 2 divides 2617 by NAT_4:9;
2617 = 3*872 + 1; hence not 3 divides 2617 by NAT_4:9;
2617 = 5*523 + 2; hence not 5 divides 2617 by NAT_4:9;
2617 = 7*373 + 6; hence not 7 divides 2617 by NAT_4:9;
2617 = 11*237 + 10; hence not 11 divides 2617 by NAT_4:9;
2617 = 13*201 + 4; hence not 13 divides 2617 by NAT_4:9;
2617 = 17*153 + 16; hence not 17 divides 2617 by NAT_4:9;
2617 = 19*137 + 14; hence not 19 divides 2617 by NAT_4:9;
2617 = 23*113 + 18; hence not 23 divides 2617 by NAT_4:9;
2617 = 29*90 + 7; hence not 29 divides 2617 by NAT_4:9;
2617 = 31*84 + 13; hence not 31 divides 2617 by NAT_4:9;
2617 = 37*70 + 27; hence not 37 divides 2617 by NAT_4:9;
2617 = 41*63 + 34; hence not 41 divides 2617 by NAT_4:9;
2617 = 43*60 + 37; hence not 43 divides 2617 by NAT_4:9;
2617 = 47*55 + 32; hence not 47 divides 2617 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2617 & n is prime
holds not n divides 2617 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2621 is prime
proof
now
2621 = 2*1310 + 1; hence not 2 divides 2621 by NAT_4:9;
2621 = 3*873 + 2; hence not 3 divides 2621 by NAT_4:9;
2621 = 5*524 + 1; hence not 5 divides 2621 by NAT_4:9;
2621 = 7*374 + 3; hence not 7 divides 2621 by NAT_4:9;
2621 = 11*238 + 3; hence not 11 divides 2621 by NAT_4:9;
2621 = 13*201 + 8; hence not 13 divides 2621 by NAT_4:9;
2621 = 17*154 + 3; hence not 17 divides 2621 by NAT_4:9;
2621 = 19*137 + 18; hence not 19 divides 2621 by NAT_4:9;
2621 = 23*113 + 22; hence not 23 divides 2621 by NAT_4:9;
2621 = 29*90 + 11; hence not 29 divides 2621 by NAT_4:9;
2621 = 31*84 + 17; hence not 31 divides 2621 by NAT_4:9;
2621 = 37*70 + 31; hence not 37 divides 2621 by NAT_4:9;
2621 = 41*63 + 38; hence not 41 divides 2621 by NAT_4:9;
2621 = 43*60 + 41; hence not 43 divides 2621 by NAT_4:9;
2621 = 47*55 + 36; hence not 47 divides 2621 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2621 & n is prime
holds not n divides 2621 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2633 is prime
proof
now
2633 = 2*1316 + 1; hence not 2 divides 2633 by NAT_4:9;
2633 = 3*877 + 2; hence not 3 divides 2633 by NAT_4:9;
2633 = 5*526 + 3; hence not 5 divides 2633 by NAT_4:9;
2633 = 7*376 + 1; hence not 7 divides 2633 by NAT_4:9;
2633 = 11*239 + 4; hence not 11 divides 2633 by NAT_4:9;
2633 = 13*202 + 7; hence not 13 divides 2633 by NAT_4:9;
2633 = 17*154 + 15; hence not 17 divides 2633 by NAT_4:9;
2633 = 19*138 + 11; hence not 19 divides 2633 by NAT_4:9;
2633 = 23*114 + 11; hence not 23 divides 2633 by NAT_4:9;
2633 = 29*90 + 23; hence not 29 divides 2633 by NAT_4:9;
2633 = 31*84 + 29; hence not 31 divides 2633 by NAT_4:9;
2633 = 37*71 + 6; hence not 37 divides 2633 by NAT_4:9;
2633 = 41*64 + 9; hence not 41 divides 2633 by NAT_4:9;
2633 = 43*61 + 10; hence not 43 divides 2633 by NAT_4:9;
2633 = 47*56 + 1; hence not 47 divides 2633 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2633 & n is prime
holds not n divides 2633 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2647 is prime
proof
now
2647 = 2*1323 + 1; hence not 2 divides 2647 by NAT_4:9;
2647 = 3*882 + 1; hence not 3 divides 2647 by NAT_4:9;
2647 = 5*529 + 2; hence not 5 divides 2647 by NAT_4:9;
2647 = 7*378 + 1; hence not 7 divides 2647 by NAT_4:9;
2647 = 11*240 + 7; hence not 11 divides 2647 by NAT_4:9;
2647 = 13*203 + 8; hence not 13 divides 2647 by NAT_4:9;
2647 = 17*155 + 12; hence not 17 divides 2647 by NAT_4:9;
2647 = 19*139 + 6; hence not 19 divides 2647 by NAT_4:9;
2647 = 23*115 + 2; hence not 23 divides 2647 by NAT_4:9;
2647 = 29*91 + 8; hence not 29 divides 2647 by NAT_4:9;
2647 = 31*85 + 12; hence not 31 divides 2647 by NAT_4:9;
2647 = 37*71 + 20; hence not 37 divides 2647 by NAT_4:9;
2647 = 41*64 + 23; hence not 41 divides 2647 by NAT_4:9;
2647 = 43*61 + 24; hence not 43 divides 2647 by NAT_4:9;
2647 = 47*56 + 15; hence not 47 divides 2647 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2647 & n is prime
holds not n divides 2647 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2657 is prime
proof
now
2657 = 2*1328 + 1; hence not 2 divides 2657 by NAT_4:9;
2657 = 3*885 + 2; hence not 3 divides 2657 by NAT_4:9;
2657 = 5*531 + 2; hence not 5 divides 2657 by NAT_4:9;
2657 = 7*379 + 4; hence not 7 divides 2657 by NAT_4:9;
2657 = 11*241 + 6; hence not 11 divides 2657 by NAT_4:9;
2657 = 13*204 + 5; hence not 13 divides 2657 by NAT_4:9;
2657 = 17*156 + 5; hence not 17 divides 2657 by NAT_4:9;
2657 = 19*139 + 16; hence not 19 divides 2657 by NAT_4:9;
2657 = 23*115 + 12; hence not 23 divides 2657 by NAT_4:9;
2657 = 29*91 + 18; hence not 29 divides 2657 by NAT_4:9;
2657 = 31*85 + 22; hence not 31 divides 2657 by NAT_4:9;
2657 = 37*71 + 30; hence not 37 divides 2657 by NAT_4:9;
2657 = 41*64 + 33; hence not 41 divides 2657 by NAT_4:9;
2657 = 43*61 + 34; hence not 43 divides 2657 by NAT_4:9;
2657 = 47*56 + 25; hence not 47 divides 2657 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2657 & n is prime
holds not n divides 2657 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2659 is prime
proof
now
2659 = 2*1329 + 1; hence not 2 divides 2659 by NAT_4:9;
2659 = 3*886 + 1; hence not 3 divides 2659 by NAT_4:9;
2659 = 5*531 + 4; hence not 5 divides 2659 by NAT_4:9;
2659 = 7*379 + 6; hence not 7 divides 2659 by NAT_4:9;
2659 = 11*241 + 8; hence not 11 divides 2659 by NAT_4:9;
2659 = 13*204 + 7; hence not 13 divides 2659 by NAT_4:9;
2659 = 17*156 + 7; hence not 17 divides 2659 by NAT_4:9;
2659 = 19*139 + 18; hence not 19 divides 2659 by NAT_4:9;
2659 = 23*115 + 14; hence not 23 divides 2659 by NAT_4:9;
2659 = 29*91 + 20; hence not 29 divides 2659 by NAT_4:9;
2659 = 31*85 + 24; hence not 31 divides 2659 by NAT_4:9;
2659 = 37*71 + 32; hence not 37 divides 2659 by NAT_4:9;
2659 = 41*64 + 35; hence not 41 divides 2659 by NAT_4:9;
2659 = 43*61 + 36; hence not 43 divides 2659 by NAT_4:9;
2659 = 47*56 + 27; hence not 47 divides 2659 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2659 & n is prime
holds not n divides 2659 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2663 is prime
proof
now
2663 = 2*1331 + 1; hence not 2 divides 2663 by NAT_4:9;
2663 = 3*887 + 2; hence not 3 divides 2663 by NAT_4:9;
2663 = 5*532 + 3; hence not 5 divides 2663 by NAT_4:9;
2663 = 7*380 + 3; hence not 7 divides 2663 by NAT_4:9;
2663 = 11*242 + 1; hence not 11 divides 2663 by NAT_4:9;
2663 = 13*204 + 11; hence not 13 divides 2663 by NAT_4:9;
2663 = 17*156 + 11; hence not 17 divides 2663 by NAT_4:9;
2663 = 19*140 + 3; hence not 19 divides 2663 by NAT_4:9;
2663 = 23*115 + 18; hence not 23 divides 2663 by NAT_4:9;
2663 = 29*91 + 24; hence not 29 divides 2663 by NAT_4:9;
2663 = 31*85 + 28; hence not 31 divides 2663 by NAT_4:9;
2663 = 37*71 + 36; hence not 37 divides 2663 by NAT_4:9;
2663 = 41*64 + 39; hence not 41 divides 2663 by NAT_4:9;
2663 = 43*61 + 40; hence not 43 divides 2663 by NAT_4:9;
2663 = 47*56 + 31; hence not 47 divides 2663 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2663 & n is prime
holds not n divides 2663 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2671 is prime
proof
now
2671 = 2*1335 + 1; hence not 2 divides 2671 by NAT_4:9;
2671 = 3*890 + 1; hence not 3 divides 2671 by NAT_4:9;
2671 = 5*534 + 1; hence not 5 divides 2671 by NAT_4:9;
2671 = 7*381 + 4; hence not 7 divides 2671 by NAT_4:9;
2671 = 11*242 + 9; hence not 11 divides 2671 by NAT_4:9;
2671 = 13*205 + 6; hence not 13 divides 2671 by NAT_4:9;
2671 = 17*157 + 2; hence not 17 divides 2671 by NAT_4:9;
2671 = 19*140 + 11; hence not 19 divides 2671 by NAT_4:9;
2671 = 23*116 + 3; hence not 23 divides 2671 by NAT_4:9;
2671 = 29*92 + 3; hence not 29 divides 2671 by NAT_4:9;
2671 = 31*86 + 5; hence not 31 divides 2671 by NAT_4:9;
2671 = 37*72 + 7; hence not 37 divides 2671 by NAT_4:9;
2671 = 41*65 + 6; hence not 41 divides 2671 by NAT_4:9;
2671 = 43*62 + 5; hence not 43 divides 2671 by NAT_4:9;
2671 = 47*56 + 39; hence not 47 divides 2671 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2671 & n is prime
holds not n divides 2671 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2677 is prime
proof
now
2677 = 2*1338 + 1; hence not 2 divides 2677 by NAT_4:9;
2677 = 3*892 + 1; hence not 3 divides 2677 by NAT_4:9;
2677 = 5*535 + 2; hence not 5 divides 2677 by NAT_4:9;
2677 = 7*382 + 3; hence not 7 divides 2677 by NAT_4:9;
2677 = 11*243 + 4; hence not 11 divides 2677 by NAT_4:9;
2677 = 13*205 + 12; hence not 13 divides 2677 by NAT_4:9;
2677 = 17*157 + 8; hence not 17 divides 2677 by NAT_4:9;
2677 = 19*140 + 17; hence not 19 divides 2677 by NAT_4:9;
2677 = 23*116 + 9; hence not 23 divides 2677 by NAT_4:9;
2677 = 29*92 + 9; hence not 29 divides 2677 by NAT_4:9;
2677 = 31*86 + 11; hence not 31 divides 2677 by NAT_4:9;
2677 = 37*72 + 13; hence not 37 divides 2677 by NAT_4:9;
2677 = 41*65 + 12; hence not 41 divides 2677 by NAT_4:9;
2677 = 43*62 + 11; hence not 43 divides 2677 by NAT_4:9;
2677 = 47*56 + 45; hence not 47 divides 2677 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2677 & n is prime
holds not n divides 2677 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2683 is prime
proof
now
2683 = 2*1341 + 1; hence not 2 divides 2683 by NAT_4:9;
2683 = 3*894 + 1; hence not 3 divides 2683 by NAT_4:9;
2683 = 5*536 + 3; hence not 5 divides 2683 by NAT_4:9;
2683 = 7*383 + 2; hence not 7 divides 2683 by NAT_4:9;
2683 = 11*243 + 10; hence not 11 divides 2683 by NAT_4:9;
2683 = 13*206 + 5; hence not 13 divides 2683 by NAT_4:9;
2683 = 17*157 + 14; hence not 17 divides 2683 by NAT_4:9;
2683 = 19*141 + 4; hence not 19 divides 2683 by NAT_4:9;
2683 = 23*116 + 15; hence not 23 divides 2683 by NAT_4:9;
2683 = 29*92 + 15; hence not 29 divides 2683 by NAT_4:9;
2683 = 31*86 + 17; hence not 31 divides 2683 by NAT_4:9;
2683 = 37*72 + 19; hence not 37 divides 2683 by NAT_4:9;
2683 = 41*65 + 18; hence not 41 divides 2683 by NAT_4:9;
2683 = 43*62 + 17; hence not 43 divides 2683 by NAT_4:9;
2683 = 47*57 + 4; hence not 47 divides 2683 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2683 & n is prime
holds not n divides 2683 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2687 is prime
proof
now
2687 = 2*1343 + 1; hence not 2 divides 2687 by NAT_4:9;
2687 = 3*895 + 2; hence not 3 divides 2687 by NAT_4:9;
2687 = 5*537 + 2; hence not 5 divides 2687 by NAT_4:9;
2687 = 7*383 + 6; hence not 7 divides 2687 by NAT_4:9;
2687 = 11*244 + 3; hence not 11 divides 2687 by NAT_4:9;
2687 = 13*206 + 9; hence not 13 divides 2687 by NAT_4:9;
2687 = 17*158 + 1; hence not 17 divides 2687 by NAT_4:9;
2687 = 19*141 + 8; hence not 19 divides 2687 by NAT_4:9;
2687 = 23*116 + 19; hence not 23 divides 2687 by NAT_4:9;
2687 = 29*92 + 19; hence not 29 divides 2687 by NAT_4:9;
2687 = 31*86 + 21; hence not 31 divides 2687 by NAT_4:9;
2687 = 37*72 + 23; hence not 37 divides 2687 by NAT_4:9;
2687 = 41*65 + 22; hence not 41 divides 2687 by NAT_4:9;
2687 = 43*62 + 21; hence not 43 divides 2687 by NAT_4:9;
2687 = 47*57 + 8; hence not 47 divides 2687 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2687 & n is prime
holds not n divides 2687 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2689 is prime
proof
now
2689 = 2*1344 + 1; hence not 2 divides 2689 by NAT_4:9;
2689 = 3*896 + 1; hence not 3 divides 2689 by NAT_4:9;
2689 = 5*537 + 4; hence not 5 divides 2689 by NAT_4:9;
2689 = 7*384 + 1; hence not 7 divides 2689 by NAT_4:9;
2689 = 11*244 + 5; hence not 11 divides 2689 by NAT_4:9;
2689 = 13*206 + 11; hence not 13 divides 2689 by NAT_4:9;
2689 = 17*158 + 3; hence not 17 divides 2689 by NAT_4:9;
2689 = 19*141 + 10; hence not 19 divides 2689 by NAT_4:9;
2689 = 23*116 + 21; hence not 23 divides 2689 by NAT_4:9;
2689 = 29*92 + 21; hence not 29 divides 2689 by NAT_4:9;
2689 = 31*86 + 23; hence not 31 divides 2689 by NAT_4:9;
2689 = 37*72 + 25; hence not 37 divides 2689 by NAT_4:9;
2689 = 41*65 + 24; hence not 41 divides 2689 by NAT_4:9;
2689 = 43*62 + 23; hence not 43 divides 2689 by NAT_4:9;
2689 = 47*57 + 10; hence not 47 divides 2689 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2689 & n is prime
holds not n divides 2689 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2693 is prime
proof
now
2693 = 2*1346 + 1; hence not 2 divides 2693 by NAT_4:9;
2693 = 3*897 + 2; hence not 3 divides 2693 by NAT_4:9;
2693 = 5*538 + 3; hence not 5 divides 2693 by NAT_4:9;
2693 = 7*384 + 5; hence not 7 divides 2693 by NAT_4:9;
2693 = 11*244 + 9; hence not 11 divides 2693 by NAT_4:9;
2693 = 13*207 + 2; hence not 13 divides 2693 by NAT_4:9;
2693 = 17*158 + 7; hence not 17 divides 2693 by NAT_4:9;
2693 = 19*141 + 14; hence not 19 divides 2693 by NAT_4:9;
2693 = 23*117 + 2; hence not 23 divides 2693 by NAT_4:9;
2693 = 29*92 + 25; hence not 29 divides 2693 by NAT_4:9;
2693 = 31*86 + 27; hence not 31 divides 2693 by NAT_4:9;
2693 = 37*72 + 29; hence not 37 divides 2693 by NAT_4:9;
2693 = 41*65 + 28; hence not 41 divides 2693 by NAT_4:9;
2693 = 43*62 + 27; hence not 43 divides 2693 by NAT_4:9;
2693 = 47*57 + 14; hence not 47 divides 2693 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2693 & n is prime
holds not n divides 2693 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2699 is prime
proof
now
2699 = 2*1349 + 1; hence not 2 divides 2699 by NAT_4:9;
2699 = 3*899 + 2; hence not 3 divides 2699 by NAT_4:9;
2699 = 5*539 + 4; hence not 5 divides 2699 by NAT_4:9;
2699 = 7*385 + 4; hence not 7 divides 2699 by NAT_4:9;
2699 = 11*245 + 4; hence not 11 divides 2699 by NAT_4:9;
2699 = 13*207 + 8; hence not 13 divides 2699 by NAT_4:9;
2699 = 17*158 + 13; hence not 17 divides 2699 by NAT_4:9;
2699 = 19*142 + 1; hence not 19 divides 2699 by NAT_4:9;
2699 = 23*117 + 8; hence not 23 divides 2699 by NAT_4:9;
2699 = 29*93 + 2; hence not 29 divides 2699 by NAT_4:9;
2699 = 31*87 + 2; hence not 31 divides 2699 by NAT_4:9;
2699 = 37*72 + 35; hence not 37 divides 2699 by NAT_4:9;
2699 = 41*65 + 34; hence not 41 divides 2699 by NAT_4:9;
2699 = 43*62 + 33; hence not 43 divides 2699 by NAT_4:9;
2699 = 47*57 + 20; hence not 47 divides 2699 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2699 & n is prime
holds not n divides 2699 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2707 is prime
proof
now
2707 = 2*1353 + 1; hence not 2 divides 2707 by NAT_4:9;
2707 = 3*902 + 1; hence not 3 divides 2707 by NAT_4:9;
2707 = 5*541 + 2; hence not 5 divides 2707 by NAT_4:9;
2707 = 7*386 + 5; hence not 7 divides 2707 by NAT_4:9;
2707 = 11*246 + 1; hence not 11 divides 2707 by NAT_4:9;
2707 = 13*208 + 3; hence not 13 divides 2707 by NAT_4:9;
2707 = 17*159 + 4; hence not 17 divides 2707 by NAT_4:9;
2707 = 19*142 + 9; hence not 19 divides 2707 by NAT_4:9;
2707 = 23*117 + 16; hence not 23 divides 2707 by NAT_4:9;
2707 = 29*93 + 10; hence not 29 divides 2707 by NAT_4:9;
2707 = 31*87 + 10; hence not 31 divides 2707 by NAT_4:9;
2707 = 37*73 + 6; hence not 37 divides 2707 by NAT_4:9;
2707 = 41*66 + 1; hence not 41 divides 2707 by NAT_4:9;
2707 = 43*62 + 41; hence not 43 divides 2707 by NAT_4:9;
2707 = 47*57 + 28; hence not 47 divides 2707 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2707 & n is prime
holds not n divides 2707 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2711 is prime
proof
now
2711 = 2*1355 + 1; hence not 2 divides 2711 by NAT_4:9;
2711 = 3*903 + 2; hence not 3 divides 2711 by NAT_4:9;
2711 = 5*542 + 1; hence not 5 divides 2711 by NAT_4:9;
2711 = 7*387 + 2; hence not 7 divides 2711 by NAT_4:9;
2711 = 11*246 + 5; hence not 11 divides 2711 by NAT_4:9;
2711 = 13*208 + 7; hence not 13 divides 2711 by NAT_4:9;
2711 = 17*159 + 8; hence not 17 divides 2711 by NAT_4:9;
2711 = 19*142 + 13; hence not 19 divides 2711 by NAT_4:9;
2711 = 23*117 + 20; hence not 23 divides 2711 by NAT_4:9;
2711 = 29*93 + 14; hence not 29 divides 2711 by NAT_4:9;
2711 = 31*87 + 14; hence not 31 divides 2711 by NAT_4:9;
2711 = 37*73 + 10; hence not 37 divides 2711 by NAT_4:9;
2711 = 41*66 + 5; hence not 41 divides 2711 by NAT_4:9;
2711 = 43*63 + 2; hence not 43 divides 2711 by NAT_4:9;
2711 = 47*57 + 32; hence not 47 divides 2711 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2711 & n is prime
holds not n divides 2711 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2713 is prime
proof
now
2713 = 2*1356 + 1; hence not 2 divides 2713 by NAT_4:9;
2713 = 3*904 + 1; hence not 3 divides 2713 by NAT_4:9;
2713 = 5*542 + 3; hence not 5 divides 2713 by NAT_4:9;
2713 = 7*387 + 4; hence not 7 divides 2713 by NAT_4:9;
2713 = 11*246 + 7; hence not 11 divides 2713 by NAT_4:9;
2713 = 13*208 + 9; hence not 13 divides 2713 by NAT_4:9;
2713 = 17*159 + 10; hence not 17 divides 2713 by NAT_4:9;
2713 = 19*142 + 15; hence not 19 divides 2713 by NAT_4:9;
2713 = 23*117 + 22; hence not 23 divides 2713 by NAT_4:9;
2713 = 29*93 + 16; hence not 29 divides 2713 by NAT_4:9;
2713 = 31*87 + 16; hence not 31 divides 2713 by NAT_4:9;
2713 = 37*73 + 12; hence not 37 divides 2713 by NAT_4:9;
2713 = 41*66 + 7; hence not 41 divides 2713 by NAT_4:9;
2713 = 43*63 + 4; hence not 43 divides 2713 by NAT_4:9;
2713 = 47*57 + 34; hence not 47 divides 2713 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2713 & n is prime
holds not n divides 2713 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2719 is prime
proof
now
2719 = 2*1359 + 1; hence not 2 divides 2719 by NAT_4:9;
2719 = 3*906 + 1; hence not 3 divides 2719 by NAT_4:9;
2719 = 5*543 + 4; hence not 5 divides 2719 by NAT_4:9;
2719 = 7*388 + 3; hence not 7 divides 2719 by NAT_4:9;
2719 = 11*247 + 2; hence not 11 divides 2719 by NAT_4:9;
2719 = 13*209 + 2; hence not 13 divides 2719 by NAT_4:9;
2719 = 17*159 + 16; hence not 17 divides 2719 by NAT_4:9;
2719 = 19*143 + 2; hence not 19 divides 2719 by NAT_4:9;
2719 = 23*118 + 5; hence not 23 divides 2719 by NAT_4:9;
2719 = 29*93 + 22; hence not 29 divides 2719 by NAT_4:9;
2719 = 31*87 + 22; hence not 31 divides 2719 by NAT_4:9;
2719 = 37*73 + 18; hence not 37 divides 2719 by NAT_4:9;
2719 = 41*66 + 13; hence not 41 divides 2719 by NAT_4:9;
2719 = 43*63 + 10; hence not 43 divides 2719 by NAT_4:9;
2719 = 47*57 + 40; hence not 47 divides 2719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2719 & n is prime
holds not n divides 2719 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2729 is prime
proof
now
2729 = 2*1364 + 1; hence not 2 divides 2729 by NAT_4:9;
2729 = 3*909 + 2; hence not 3 divides 2729 by NAT_4:9;
2729 = 5*545 + 4; hence not 5 divides 2729 by NAT_4:9;
2729 = 7*389 + 6; hence not 7 divides 2729 by NAT_4:9;
2729 = 11*248 + 1; hence not 11 divides 2729 by NAT_4:9;
2729 = 13*209 + 12; hence not 13 divides 2729 by NAT_4:9;
2729 = 17*160 + 9; hence not 17 divides 2729 by NAT_4:9;
2729 = 19*143 + 12; hence not 19 divides 2729 by NAT_4:9;
2729 = 23*118 + 15; hence not 23 divides 2729 by NAT_4:9;
2729 = 29*94 + 3; hence not 29 divides 2729 by NAT_4:9;
2729 = 31*88 + 1; hence not 31 divides 2729 by NAT_4:9;
2729 = 37*73 + 28; hence not 37 divides 2729 by NAT_4:9;
2729 = 41*66 + 23; hence not 41 divides 2729 by NAT_4:9;
2729 = 43*63 + 20; hence not 43 divides 2729 by NAT_4:9;
2729 = 47*58 + 3; hence not 47 divides 2729 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2729 & n is prime
holds not n divides 2729 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2731 is prime
proof
now
2731 = 2*1365 + 1; hence not 2 divides 2731 by NAT_4:9;
2731 = 3*910 + 1; hence not 3 divides 2731 by NAT_4:9;
2731 = 5*546 + 1; hence not 5 divides 2731 by NAT_4:9;
2731 = 7*390 + 1; hence not 7 divides 2731 by NAT_4:9;
2731 = 11*248 + 3; hence not 11 divides 2731 by NAT_4:9;
2731 = 13*210 + 1; hence not 13 divides 2731 by NAT_4:9;
2731 = 17*160 + 11; hence not 17 divides 2731 by NAT_4:9;
2731 = 19*143 + 14; hence not 19 divides 2731 by NAT_4:9;
2731 = 23*118 + 17; hence not 23 divides 2731 by NAT_4:9;
2731 = 29*94 + 5; hence not 29 divides 2731 by NAT_4:9;
2731 = 31*88 + 3; hence not 31 divides 2731 by NAT_4:9;
2731 = 37*73 + 30; hence not 37 divides 2731 by NAT_4:9;
2731 = 41*66 + 25; hence not 41 divides 2731 by NAT_4:9;
2731 = 43*63 + 22; hence not 43 divides 2731 by NAT_4:9;
2731 = 47*58 + 5; hence not 47 divides 2731 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2731 & n is prime
holds not n divides 2731 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2741 is prime
proof
now
2741 = 2*1370 + 1; hence not 2 divides 2741 by NAT_4:9;
2741 = 3*913 + 2; hence not 3 divides 2741 by NAT_4:9;
2741 = 5*548 + 1; hence not 5 divides 2741 by NAT_4:9;
2741 = 7*391 + 4; hence not 7 divides 2741 by NAT_4:9;
2741 = 11*249 + 2; hence not 11 divides 2741 by NAT_4:9;
2741 = 13*210 + 11; hence not 13 divides 2741 by NAT_4:9;
2741 = 17*161 + 4; hence not 17 divides 2741 by NAT_4:9;
2741 = 19*144 + 5; hence not 19 divides 2741 by NAT_4:9;
2741 = 23*119 + 4; hence not 23 divides 2741 by NAT_4:9;
2741 = 29*94 + 15; hence not 29 divides 2741 by NAT_4:9;
2741 = 31*88 + 13; hence not 31 divides 2741 by NAT_4:9;
2741 = 37*74 + 3; hence not 37 divides 2741 by NAT_4:9;
2741 = 41*66 + 35; hence not 41 divides 2741 by NAT_4:9;
2741 = 43*63 + 32; hence not 43 divides 2741 by NAT_4:9;
2741 = 47*58 + 15; hence not 47 divides 2741 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2741 & n is prime
holds not n divides 2741 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2749 is prime
proof
now
2749 = 2*1374 + 1; hence not 2 divides 2749 by NAT_4:9;
2749 = 3*916 + 1; hence not 3 divides 2749 by NAT_4:9;
2749 = 5*549 + 4; hence not 5 divides 2749 by NAT_4:9;
2749 = 7*392 + 5; hence not 7 divides 2749 by NAT_4:9;
2749 = 11*249 + 10; hence not 11 divides 2749 by NAT_4:9;
2749 = 13*211 + 6; hence not 13 divides 2749 by NAT_4:9;
2749 = 17*161 + 12; hence not 17 divides 2749 by NAT_4:9;
2749 = 19*144 + 13; hence not 19 divides 2749 by NAT_4:9;
2749 = 23*119 + 12; hence not 23 divides 2749 by NAT_4:9;
2749 = 29*94 + 23; hence not 29 divides 2749 by NAT_4:9;
2749 = 31*88 + 21; hence not 31 divides 2749 by NAT_4:9;
2749 = 37*74 + 11; hence not 37 divides 2749 by NAT_4:9;
2749 = 41*67 + 2; hence not 41 divides 2749 by NAT_4:9;
2749 = 43*63 + 40; hence not 43 divides 2749 by NAT_4:9;
2749 = 47*58 + 23; hence not 47 divides 2749 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2749 & n is prime
holds not n divides 2749 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2753 is prime
proof
now
2753 = 2*1376 + 1; hence not 2 divides 2753 by NAT_4:9;
2753 = 3*917 + 2; hence not 3 divides 2753 by NAT_4:9;
2753 = 5*550 + 3; hence not 5 divides 2753 by NAT_4:9;
2753 = 7*393 + 2; hence not 7 divides 2753 by NAT_4:9;
2753 = 11*250 + 3; hence not 11 divides 2753 by NAT_4:9;
2753 = 13*211 + 10; hence not 13 divides 2753 by NAT_4:9;
2753 = 17*161 + 16; hence not 17 divides 2753 by NAT_4:9;
2753 = 19*144 + 17; hence not 19 divides 2753 by NAT_4:9;
2753 = 23*119 + 16; hence not 23 divides 2753 by NAT_4:9;
2753 = 29*94 + 27; hence not 29 divides 2753 by NAT_4:9;
2753 = 31*88 + 25; hence not 31 divides 2753 by NAT_4:9;
2753 = 37*74 + 15; hence not 37 divides 2753 by NAT_4:9;
2753 = 41*67 + 6; hence not 41 divides 2753 by NAT_4:9;
2753 = 43*64 + 1; hence not 43 divides 2753 by NAT_4:9;
2753 = 47*58 + 27; hence not 47 divides 2753 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2753 & n is prime
holds not n divides 2753 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2767 is prime
proof
now
2767 = 2*1383 + 1; hence not 2 divides 2767 by NAT_4:9;
2767 = 3*922 + 1; hence not 3 divides 2767 by NAT_4:9;
2767 = 5*553 + 2; hence not 5 divides 2767 by NAT_4:9;
2767 = 7*395 + 2; hence not 7 divides 2767 by NAT_4:9;
2767 = 11*251 + 6; hence not 11 divides 2767 by NAT_4:9;
2767 = 13*212 + 11; hence not 13 divides 2767 by NAT_4:9;
2767 = 17*162 + 13; hence not 17 divides 2767 by NAT_4:9;
2767 = 19*145 + 12; hence not 19 divides 2767 by NAT_4:9;
2767 = 23*120 + 7; hence not 23 divides 2767 by NAT_4:9;
2767 = 29*95 + 12; hence not 29 divides 2767 by NAT_4:9;
2767 = 31*89 + 8; hence not 31 divides 2767 by NAT_4:9;
2767 = 37*74 + 29; hence not 37 divides 2767 by NAT_4:9;
2767 = 41*67 + 20; hence not 41 divides 2767 by NAT_4:9;
2767 = 43*64 + 15; hence not 43 divides 2767 by NAT_4:9;
2767 = 47*58 + 41; hence not 47 divides 2767 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2767 & n is prime
holds not n divides 2767 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2777 is prime
proof
now
2777 = 2*1388 + 1; hence not 2 divides 2777 by NAT_4:9;
2777 = 3*925 + 2; hence not 3 divides 2777 by NAT_4:9;
2777 = 5*555 + 2; hence not 5 divides 2777 by NAT_4:9;
2777 = 7*396 + 5; hence not 7 divides 2777 by NAT_4:9;
2777 = 11*252 + 5; hence not 11 divides 2777 by NAT_4:9;
2777 = 13*213 + 8; hence not 13 divides 2777 by NAT_4:9;
2777 = 17*163 + 6; hence not 17 divides 2777 by NAT_4:9;
2777 = 19*146 + 3; hence not 19 divides 2777 by NAT_4:9;
2777 = 23*120 + 17; hence not 23 divides 2777 by NAT_4:9;
2777 = 29*95 + 22; hence not 29 divides 2777 by NAT_4:9;
2777 = 31*89 + 18; hence not 31 divides 2777 by NAT_4:9;
2777 = 37*75 + 2; hence not 37 divides 2777 by NAT_4:9;
2777 = 41*67 + 30; hence not 41 divides 2777 by NAT_4:9;
2777 = 43*64 + 25; hence not 43 divides 2777 by NAT_4:9;
2777 = 47*59 + 4; hence not 47 divides 2777 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2777 & n is prime
holds not n divides 2777 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2789 is prime
proof
now
2789 = 2*1394 + 1; hence not 2 divides 2789 by NAT_4:9;
2789 = 3*929 + 2; hence not 3 divides 2789 by NAT_4:9;
2789 = 5*557 + 4; hence not 5 divides 2789 by NAT_4:9;
2789 = 7*398 + 3; hence not 7 divides 2789 by NAT_4:9;
2789 = 11*253 + 6; hence not 11 divides 2789 by NAT_4:9;
2789 = 13*214 + 7; hence not 13 divides 2789 by NAT_4:9;
2789 = 17*164 + 1; hence not 17 divides 2789 by NAT_4:9;
2789 = 19*146 + 15; hence not 19 divides 2789 by NAT_4:9;
2789 = 23*121 + 6; hence not 23 divides 2789 by NAT_4:9;
2789 = 29*96 + 5; hence not 29 divides 2789 by NAT_4:9;
2789 = 31*89 + 30; hence not 31 divides 2789 by NAT_4:9;
2789 = 37*75 + 14; hence not 37 divides 2789 by NAT_4:9;
2789 = 41*68 + 1; hence not 41 divides 2789 by NAT_4:9;
2789 = 43*64 + 37; hence not 43 divides 2789 by NAT_4:9;
2789 = 47*59 + 16; hence not 47 divides 2789 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2789 & n is prime
holds not n divides 2789 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2791 is prime
proof
now
2791 = 2*1395 + 1; hence not 2 divides 2791 by NAT_4:9;
2791 = 3*930 + 1; hence not 3 divides 2791 by NAT_4:9;
2791 = 5*558 + 1; hence not 5 divides 2791 by NAT_4:9;
2791 = 7*398 + 5; hence not 7 divides 2791 by NAT_4:9;
2791 = 11*253 + 8; hence not 11 divides 2791 by NAT_4:9;
2791 = 13*214 + 9; hence not 13 divides 2791 by NAT_4:9;
2791 = 17*164 + 3; hence not 17 divides 2791 by NAT_4:9;
2791 = 19*146 + 17; hence not 19 divides 2791 by NAT_4:9;
2791 = 23*121 + 8; hence not 23 divides 2791 by NAT_4:9;
2791 = 29*96 + 7; hence not 29 divides 2791 by NAT_4:9;
2791 = 31*90 + 1; hence not 31 divides 2791 by NAT_4:9;
2791 = 37*75 + 16; hence not 37 divides 2791 by NAT_4:9;
2791 = 41*68 + 3; hence not 41 divides 2791 by NAT_4:9;
2791 = 43*64 + 39; hence not 43 divides 2791 by NAT_4:9;
2791 = 47*59 + 18; hence not 47 divides 2791 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2791 & n is prime
holds not n divides 2791 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2797 is prime
proof
now
2797 = 2*1398 + 1; hence not 2 divides 2797 by NAT_4:9;
2797 = 3*932 + 1; hence not 3 divides 2797 by NAT_4:9;
2797 = 5*559 + 2; hence not 5 divides 2797 by NAT_4:9;
2797 = 7*399 + 4; hence not 7 divides 2797 by NAT_4:9;
2797 = 11*254 + 3; hence not 11 divides 2797 by NAT_4:9;
2797 = 13*215 + 2; hence not 13 divides 2797 by NAT_4:9;
2797 = 17*164 + 9; hence not 17 divides 2797 by NAT_4:9;
2797 = 19*147 + 4; hence not 19 divides 2797 by NAT_4:9;
2797 = 23*121 + 14; hence not 23 divides 2797 by NAT_4:9;
2797 = 29*96 + 13; hence not 29 divides 2797 by NAT_4:9;
2797 = 31*90 + 7; hence not 31 divides 2797 by NAT_4:9;
2797 = 37*75 + 22; hence not 37 divides 2797 by NAT_4:9;
2797 = 41*68 + 9; hence not 41 divides 2797 by NAT_4:9;
2797 = 43*65 + 2; hence not 43 divides 2797 by NAT_4:9;
2797 = 47*59 + 24; hence not 47 divides 2797 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2797 & n is prime
holds not n divides 2797 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2801 is prime
proof
now
2801 = 2*1400 + 1; hence not 2 divides 2801 by NAT_4:9;
2801 = 3*933 + 2; hence not 3 divides 2801 by NAT_4:9;
2801 = 5*560 + 1; hence not 5 divides 2801 by NAT_4:9;
2801 = 7*400 + 1; hence not 7 divides 2801 by NAT_4:9;
2801 = 11*254 + 7; hence not 11 divides 2801 by NAT_4:9;
2801 = 13*215 + 6; hence not 13 divides 2801 by NAT_4:9;
2801 = 17*164 + 13; hence not 17 divides 2801 by NAT_4:9;
2801 = 19*147 + 8; hence not 19 divides 2801 by NAT_4:9;
2801 = 23*121 + 18; hence not 23 divides 2801 by NAT_4:9;
2801 = 29*96 + 17; hence not 29 divides 2801 by NAT_4:9;
2801 = 31*90 + 11; hence not 31 divides 2801 by NAT_4:9;
2801 = 37*75 + 26; hence not 37 divides 2801 by NAT_4:9;
2801 = 41*68 + 13; hence not 41 divides 2801 by NAT_4:9;
2801 = 43*65 + 6; hence not 43 divides 2801 by NAT_4:9;
2801 = 47*59 + 28; hence not 47 divides 2801 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2801 & n is prime
holds not n divides 2801 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2803 is prime
proof
now
2803 = 2*1401 + 1; hence not 2 divides 2803 by NAT_4:9;
2803 = 3*934 + 1; hence not 3 divides 2803 by NAT_4:9;
2803 = 5*560 + 3; hence not 5 divides 2803 by NAT_4:9;
2803 = 7*400 + 3; hence not 7 divides 2803 by NAT_4:9;
2803 = 11*254 + 9; hence not 11 divides 2803 by NAT_4:9;
2803 = 13*215 + 8; hence not 13 divides 2803 by NAT_4:9;
2803 = 17*164 + 15; hence not 17 divides 2803 by NAT_4:9;
2803 = 19*147 + 10; hence not 19 divides 2803 by NAT_4:9;
2803 = 23*121 + 20; hence not 23 divides 2803 by NAT_4:9;
2803 = 29*96 + 19; hence not 29 divides 2803 by NAT_4:9;
2803 = 31*90 + 13; hence not 31 divides 2803 by NAT_4:9;
2803 = 37*75 + 28; hence not 37 divides 2803 by NAT_4:9;
2803 = 41*68 + 15; hence not 41 divides 2803 by NAT_4:9;
2803 = 43*65 + 8; hence not 43 divides 2803 by NAT_4:9;
2803 = 47*59 + 30; hence not 47 divides 2803 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2803 & n is prime
holds not n divides 2803 by XPRIMET1:30;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
2819 is prime
proof
now
2819 = 2*1409 + 1; hence not 2 divides 2819 by NAT_4:9;
2819 = 3*939 + 2; hence not 3 divides 2819 by NAT_4:9;
2819 = 5*563 + 4; hence not 5 divides 2819 by NAT_4:9;
2819 = 7*402 + 5; hence not 7 divides 2819 by NAT_4:9;
2819 = 11*256 + 3; hence not 11 divides 2819 by NAT_4:9;
2819 = 13*216 + 11; hence not 13 divides 2819 by NAT_4:9;
2819 = 17*165 + 14; hence not 17 divides 2819 by NAT_4:9;
2819 = 19*148 + 7; hence not 19 divides 2819 by NAT_4:9;
2819 = 23*122 + 13; hence not 23 divides 2819 by NAT_4:9;
2819 = 29*97 + 6; hence not 29 divides 2819 by NAT_4:9;
2819 = 31*90 + 29; hence not 31 divides 2819 by NAT_4:9;
2819 = 37*76 + 7; hence not 37 divides 2819 by NAT_4:9;
2819 = 41*68 + 31; hence not 41 divides 2819 by NAT_4:9;
2819 = 43*65 + 24; hence not 43 divides 2819 by NAT_4:9;
2819 = 47*59 + 46; hence not 47 divides 2819 by NAT_4:9;
2819 = 53*53 + 10; hence not 53 divides 2819 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2819 & n is prime
holds not n divides 2819 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2833 is prime
proof
now
2833 = 2*1416 + 1; hence not 2 divides 2833 by NAT_4:9;
2833 = 3*944 + 1; hence not 3 divides 2833 by NAT_4:9;
2833 = 5*566 + 3; hence not 5 divides 2833 by NAT_4:9;
2833 = 7*404 + 5; hence not 7 divides 2833 by NAT_4:9;
2833 = 11*257 + 6; hence not 11 divides 2833 by NAT_4:9;
2833 = 13*217 + 12; hence not 13 divides 2833 by NAT_4:9;
2833 = 17*166 + 11; hence not 17 divides 2833 by NAT_4:9;
2833 = 19*149 + 2; hence not 19 divides 2833 by NAT_4:9;
2833 = 23*123 + 4; hence not 23 divides 2833 by NAT_4:9;
2833 = 29*97 + 20; hence not 29 divides 2833 by NAT_4:9;
2833 = 31*91 + 12; hence not 31 divides 2833 by NAT_4:9;
2833 = 37*76 + 21; hence not 37 divides 2833 by NAT_4:9;
2833 = 41*69 + 4; hence not 41 divides 2833 by NAT_4:9;
2833 = 43*65 + 38; hence not 43 divides 2833 by NAT_4:9;
2833 = 47*60 + 13; hence not 47 divides 2833 by NAT_4:9;
2833 = 53*53 + 24; hence not 53 divides 2833 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2833 & n is prime
holds not n divides 2833 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2837 is prime
proof
now
2837 = 2*1418 + 1; hence not 2 divides 2837 by NAT_4:9;
2837 = 3*945 + 2; hence not 3 divides 2837 by NAT_4:9;
2837 = 5*567 + 2; hence not 5 divides 2837 by NAT_4:9;
2837 = 7*405 + 2; hence not 7 divides 2837 by NAT_4:9;
2837 = 11*257 + 10; hence not 11 divides 2837 by NAT_4:9;
2837 = 13*218 + 3; hence not 13 divides 2837 by NAT_4:9;
2837 = 17*166 + 15; hence not 17 divides 2837 by NAT_4:9;
2837 = 19*149 + 6; hence not 19 divides 2837 by NAT_4:9;
2837 = 23*123 + 8; hence not 23 divides 2837 by NAT_4:9;
2837 = 29*97 + 24; hence not 29 divides 2837 by NAT_4:9;
2837 = 31*91 + 16; hence not 31 divides 2837 by NAT_4:9;
2837 = 37*76 + 25; hence not 37 divides 2837 by NAT_4:9;
2837 = 41*69 + 8; hence not 41 divides 2837 by NAT_4:9;
2837 = 43*65 + 42; hence not 43 divides 2837 by NAT_4:9;
2837 = 47*60 + 17; hence not 47 divides 2837 by NAT_4:9;
2837 = 53*53 + 28; hence not 53 divides 2837 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2837 & n is prime
holds not n divides 2837 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2843 is prime
proof
now
2843 = 2*1421 + 1; hence not 2 divides 2843 by NAT_4:9;
2843 = 3*947 + 2; hence not 3 divides 2843 by NAT_4:9;
2843 = 5*568 + 3; hence not 5 divides 2843 by NAT_4:9;
2843 = 7*406 + 1; hence not 7 divides 2843 by NAT_4:9;
2843 = 11*258 + 5; hence not 11 divides 2843 by NAT_4:9;
2843 = 13*218 + 9; hence not 13 divides 2843 by NAT_4:9;
2843 = 17*167 + 4; hence not 17 divides 2843 by NAT_4:9;
2843 = 19*149 + 12; hence not 19 divides 2843 by NAT_4:9;
2843 = 23*123 + 14; hence not 23 divides 2843 by NAT_4:9;
2843 = 29*98 + 1; hence not 29 divides 2843 by NAT_4:9;
2843 = 31*91 + 22; hence not 31 divides 2843 by NAT_4:9;
2843 = 37*76 + 31; hence not 37 divides 2843 by NAT_4:9;
2843 = 41*69 + 14; hence not 41 divides 2843 by NAT_4:9;
2843 = 43*66 + 5; hence not 43 divides 2843 by NAT_4:9;
2843 = 47*60 + 23; hence not 47 divides 2843 by NAT_4:9;
2843 = 53*53 + 34; hence not 53 divides 2843 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2843 & n is prime
holds not n divides 2843 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2851 is prime
proof
now
2851 = 2*1425 + 1; hence not 2 divides 2851 by NAT_4:9;
2851 = 3*950 + 1; hence not 3 divides 2851 by NAT_4:9;
2851 = 5*570 + 1; hence not 5 divides 2851 by NAT_4:9;
2851 = 7*407 + 2; hence not 7 divides 2851 by NAT_4:9;
2851 = 11*259 + 2; hence not 11 divides 2851 by NAT_4:9;
2851 = 13*219 + 4; hence not 13 divides 2851 by NAT_4:9;
2851 = 17*167 + 12; hence not 17 divides 2851 by NAT_4:9;
2851 = 19*150 + 1; hence not 19 divides 2851 by NAT_4:9;
2851 = 23*123 + 22; hence not 23 divides 2851 by NAT_4:9;
2851 = 29*98 + 9; hence not 29 divides 2851 by NAT_4:9;
2851 = 31*91 + 30; hence not 31 divides 2851 by NAT_4:9;
2851 = 37*77 + 2; hence not 37 divides 2851 by NAT_4:9;
2851 = 41*69 + 22; hence not 41 divides 2851 by NAT_4:9;
2851 = 43*66 + 13; hence not 43 divides 2851 by NAT_4:9;
2851 = 47*60 + 31; hence not 47 divides 2851 by NAT_4:9;
2851 = 53*53 + 42; hence not 53 divides 2851 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2851 & n is prime
holds not n divides 2851 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2857 is prime
proof
now
2857 = 2*1428 + 1; hence not 2 divides 2857 by NAT_4:9;
2857 = 3*952 + 1; hence not 3 divides 2857 by NAT_4:9;
2857 = 5*571 + 2; hence not 5 divides 2857 by NAT_4:9;
2857 = 7*408 + 1; hence not 7 divides 2857 by NAT_4:9;
2857 = 11*259 + 8; hence not 11 divides 2857 by NAT_4:9;
2857 = 13*219 + 10; hence not 13 divides 2857 by NAT_4:9;
2857 = 17*168 + 1; hence not 17 divides 2857 by NAT_4:9;
2857 = 19*150 + 7; hence not 19 divides 2857 by NAT_4:9;
2857 = 23*124 + 5; hence not 23 divides 2857 by NAT_4:9;
2857 = 29*98 + 15; hence not 29 divides 2857 by NAT_4:9;
2857 = 31*92 + 5; hence not 31 divides 2857 by NAT_4:9;
2857 = 37*77 + 8; hence not 37 divides 2857 by NAT_4:9;
2857 = 41*69 + 28; hence not 41 divides 2857 by NAT_4:9;
2857 = 43*66 + 19; hence not 43 divides 2857 by NAT_4:9;
2857 = 47*60 + 37; hence not 47 divides 2857 by NAT_4:9;
2857 = 53*53 + 48; hence not 53 divides 2857 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2857 & n is prime
holds not n divides 2857 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2861 is prime
proof
now
2861 = 2*1430 + 1; hence not 2 divides 2861 by NAT_4:9;
2861 = 3*953 + 2; hence not 3 divides 2861 by NAT_4:9;
2861 = 5*572 + 1; hence not 5 divides 2861 by NAT_4:9;
2861 = 7*408 + 5; hence not 7 divides 2861 by NAT_4:9;
2861 = 11*260 + 1; hence not 11 divides 2861 by NAT_4:9;
2861 = 13*220 + 1; hence not 13 divides 2861 by NAT_4:9;
2861 = 17*168 + 5; hence not 17 divides 2861 by NAT_4:9;
2861 = 19*150 + 11; hence not 19 divides 2861 by NAT_4:9;
2861 = 23*124 + 9; hence not 23 divides 2861 by NAT_4:9;
2861 = 29*98 + 19; hence not 29 divides 2861 by NAT_4:9;
2861 = 31*92 + 9; hence not 31 divides 2861 by NAT_4:9;
2861 = 37*77 + 12; hence not 37 divides 2861 by NAT_4:9;
2861 = 41*69 + 32; hence not 41 divides 2861 by NAT_4:9;
2861 = 43*66 + 23; hence not 43 divides 2861 by NAT_4:9;
2861 = 47*60 + 41; hence not 47 divides 2861 by NAT_4:9;
2861 = 53*53 + 52; hence not 53 divides 2861 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2861 & n is prime
holds not n divides 2861 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
2879 is prime
proof
now
2879 = 2*1439 + 1; hence not 2 divides 2879 by NAT_4:9;
2879 = 3*959 + 2; hence not 3 divides 2879 by NAT_4:9;
2879 = 5*575 + 4; hence not 5 divides 2879 by NAT_4:9;
2879 = 7*411 + 2; hence not 7 divides 2879 by NAT_4:9;
2879 = 11*261 + 8; hence not 11 divides 2879 by NAT_4:9;
2879 = 13*221 + 6; hence not 13 divides 2879 by NAT_4:9;
2879 = 17*169 + 6; hence not 17 divides 2879 by NAT_4:9;
2879 = 19*151 + 10; hence not 19 divides 2879 by NAT_4:9;
2879 = 23*125 + 4; hence not 23 divides 2879 by NAT_4:9;
2879 = 29*99 + 8; hence not 29 divides 2879 by NAT_4:9;
2879 = 31*92 + 27; hence not 31 divides 2879 by NAT_4:9;
2879 = 37*77 + 30; hence not 37 divides 2879 by NAT_4:9;
2879 = 41*70 + 9; hence not 41 divides 2879 by NAT_4:9;
2879 = 43*66 + 41; hence not 43 divides 2879 by NAT_4:9;
2879 = 47*61 + 12; hence not 47 divides 2879 by NAT_4:9;
2879 = 53*54 + 17; hence not 53 divides 2879 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2879 & n is prime
holds not n divides 2879 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2887 is prime
proof
now
2887 = 2*1443 + 1; hence not 2 divides 2887 by NAT_4:9;
2887 = 3*962 + 1; hence not 3 divides 2887 by NAT_4:9;
2887 = 5*577 + 2; hence not 5 divides 2887 by NAT_4:9;
2887 = 7*412 + 3; hence not 7 divides 2887 by NAT_4:9;
2887 = 11*262 + 5; hence not 11 divides 2887 by NAT_4:9;
2887 = 13*222 + 1; hence not 13 divides 2887 by NAT_4:9;
2887 = 17*169 + 14; hence not 17 divides 2887 by NAT_4:9;
2887 = 19*151 + 18; hence not 19 divides 2887 by NAT_4:9;
2887 = 23*125 + 12; hence not 23 divides 2887 by NAT_4:9;
2887 = 29*99 + 16; hence not 29 divides 2887 by NAT_4:9;
2887 = 31*93 + 4; hence not 31 divides 2887 by NAT_4:9;
2887 = 37*78 + 1; hence not 37 divides 2887 by NAT_4:9;
2887 = 41*70 + 17; hence not 41 divides 2887 by NAT_4:9;
2887 = 43*67 + 6; hence not 43 divides 2887 by NAT_4:9;
2887 = 47*61 + 20; hence not 47 divides 2887 by NAT_4:9;
2887 = 53*54 + 25; hence not 53 divides 2887 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2887 & n is prime
holds not n divides 2887 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2897 is prime
proof
now
2897 = 2*1448 + 1; hence not 2 divides 2897 by NAT_4:9;
2897 = 3*965 + 2; hence not 3 divides 2897 by NAT_4:9;
2897 = 5*579 + 2; hence not 5 divides 2897 by NAT_4:9;
2897 = 7*413 + 6; hence not 7 divides 2897 by NAT_4:9;
2897 = 11*263 + 4; hence not 11 divides 2897 by NAT_4:9;
2897 = 13*222 + 11; hence not 13 divides 2897 by NAT_4:9;
2897 = 17*170 + 7; hence not 17 divides 2897 by NAT_4:9;
2897 = 19*152 + 9; hence not 19 divides 2897 by NAT_4:9;
2897 = 23*125 + 22; hence not 23 divides 2897 by NAT_4:9;
2897 = 29*99 + 26; hence not 29 divides 2897 by NAT_4:9;
2897 = 31*93 + 14; hence not 31 divides 2897 by NAT_4:9;
2897 = 37*78 + 11; hence not 37 divides 2897 by NAT_4:9;
2897 = 41*70 + 27; hence not 41 divides 2897 by NAT_4:9;
2897 = 43*67 + 16; hence not 43 divides 2897 by NAT_4:9;
2897 = 47*61 + 30; hence not 47 divides 2897 by NAT_4:9;
2897 = 53*54 + 35; hence not 53 divides 2897 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2897 & n is prime
holds not n divides 2897 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2903 is prime
proof
now
2903 = 2*1451 + 1; hence not 2 divides 2903 by NAT_4:9;
2903 = 3*967 + 2; hence not 3 divides 2903 by NAT_4:9;
2903 = 5*580 + 3; hence not 5 divides 2903 by NAT_4:9;
2903 = 7*414 + 5; hence not 7 divides 2903 by NAT_4:9;
2903 = 11*263 + 10; hence not 11 divides 2903 by NAT_4:9;
2903 = 13*223 + 4; hence not 13 divides 2903 by NAT_4:9;
2903 = 17*170 + 13; hence not 17 divides 2903 by NAT_4:9;
2903 = 19*152 + 15; hence not 19 divides 2903 by NAT_4:9;
2903 = 23*126 + 5; hence not 23 divides 2903 by NAT_4:9;
2903 = 29*100 + 3; hence not 29 divides 2903 by NAT_4:9;
2903 = 31*93 + 20; hence not 31 divides 2903 by NAT_4:9;
2903 = 37*78 + 17; hence not 37 divides 2903 by NAT_4:9;
2903 = 41*70 + 33; hence not 41 divides 2903 by NAT_4:9;
2903 = 43*67 + 22; hence not 43 divides 2903 by NAT_4:9;
2903 = 47*61 + 36; hence not 47 divides 2903 by NAT_4:9;
2903 = 53*54 + 41; hence not 53 divides 2903 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2903 & n is prime
holds not n divides 2903 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2909 is prime
proof
now
2909 = 2*1454 + 1; hence not 2 divides 2909 by NAT_4:9;
2909 = 3*969 + 2; hence not 3 divides 2909 by NAT_4:9;
2909 = 5*581 + 4; hence not 5 divides 2909 by NAT_4:9;
2909 = 7*415 + 4; hence not 7 divides 2909 by NAT_4:9;
2909 = 11*264 + 5; hence not 11 divides 2909 by NAT_4:9;
2909 = 13*223 + 10; hence not 13 divides 2909 by NAT_4:9;
2909 = 17*171 + 2; hence not 17 divides 2909 by NAT_4:9;
2909 = 19*153 + 2; hence not 19 divides 2909 by NAT_4:9;
2909 = 23*126 + 11; hence not 23 divides 2909 by NAT_4:9;
2909 = 29*100 + 9; hence not 29 divides 2909 by NAT_4:9;
2909 = 31*93 + 26; hence not 31 divides 2909 by NAT_4:9;
2909 = 37*78 + 23; hence not 37 divides 2909 by NAT_4:9;
2909 = 41*70 + 39; hence not 41 divides 2909 by NAT_4:9;
2909 = 43*67 + 28; hence not 43 divides 2909 by NAT_4:9;
2909 = 47*61 + 42; hence not 47 divides 2909 by NAT_4:9;
2909 = 53*54 + 47; hence not 53 divides 2909 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2909 & n is prime
holds not n divides 2909 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
2917 is prime
proof
now
2917 = 2*1458 + 1; hence not 2 divides 2917 by NAT_4:9;
2917 = 3*972 + 1; hence not 3 divides 2917 by NAT_4:9;
2917 = 5*583 + 2; hence not 5 divides 2917 by NAT_4:9;
2917 = 7*416 + 5; hence not 7 divides 2917 by NAT_4:9;
2917 = 11*265 + 2; hence not 11 divides 2917 by NAT_4:9;
2917 = 13*224 + 5; hence not 13 divides 2917 by NAT_4:9;
2917 = 17*171 + 10; hence not 17 divides 2917 by NAT_4:9;
2917 = 19*153 + 10; hence not 19 divides 2917 by NAT_4:9;
2917 = 23*126 + 19; hence not 23 divides 2917 by NAT_4:9;
2917 = 29*100 + 17; hence not 29 divides 2917 by NAT_4:9;
2917 = 31*94 + 3; hence not 31 divides 2917 by NAT_4:9;
2917 = 37*78 + 31; hence not 37 divides 2917 by NAT_4:9;
2917 = 41*71 + 6; hence not 41 divides 2917 by NAT_4:9;
2917 = 43*67 + 36; hence not 43 divides 2917 by NAT_4:9;
2917 = 47*62 + 3; hence not 47 divides 2917 by NAT_4:9;
2917 = 53*55 + 2; hence not 53 divides 2917 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2917 & n is prime
holds not n divides 2917 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
2927 is prime
proof
now
2927 = 2*1463 + 1; hence not 2 divides 2927 by NAT_4:9;
2927 = 3*975 + 2; hence not 3 divides 2927 by NAT_4:9;
2927 = 5*585 + 2; hence not 5 divides 2927 by NAT_4:9;
2927 = 7*418 + 1; hence not 7 divides 2927 by NAT_4:9;
2927 = 11*266 + 1; hence not 11 divides 2927 by NAT_4:9;
2927 = 13*225 + 2; hence not 13 divides 2927 by NAT_4:9;
2927 = 17*172 + 3; hence not 17 divides 2927 by NAT_4:9;
2927 = 19*154 + 1; hence not 19 divides 2927 by NAT_4:9;
2927 = 23*127 + 6; hence not 23 divides 2927 by NAT_4:9;
2927 = 29*100 + 27; hence not 29 divides 2927 by NAT_4:9;
2927 = 31*94 + 13; hence not 31 divides 2927 by NAT_4:9;
2927 = 37*79 + 4; hence not 37 divides 2927 by NAT_4:9;
2927 = 41*71 + 16; hence not 41 divides 2927 by NAT_4:9;
2927 = 43*68 + 3; hence not 43 divides 2927 by NAT_4:9;
2927 = 47*62 + 13; hence not 47 divides 2927 by NAT_4:9;
2927 = 53*55 + 12; hence not 53 divides 2927 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2927 & n is prime
holds not n divides 2927 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
2939 is prime
proof
now
2939 = 2*1469 + 1; hence not 2 divides 2939 by NAT_4:9;
2939 = 3*979 + 2; hence not 3 divides 2939 by NAT_4:9;
2939 = 5*587 + 4; hence not 5 divides 2939 by NAT_4:9;
2939 = 7*419 + 6; hence not 7 divides 2939 by NAT_4:9;
2939 = 11*267 + 2; hence not 11 divides 2939 by NAT_4:9;
2939 = 13*226 + 1; hence not 13 divides 2939 by NAT_4:9;
2939 = 17*172 + 15; hence not 17 divides 2939 by NAT_4:9;
2939 = 19*154 + 13; hence not 19 divides 2939 by NAT_4:9;
2939 = 23*127 + 18; hence not 23 divides 2939 by NAT_4:9;
2939 = 29*101 + 10; hence not 29 divides 2939 by NAT_4:9;
2939 = 31*94 + 25; hence not 31 divides 2939 by NAT_4:9;
2939 = 37*79 + 16; hence not 37 divides 2939 by NAT_4:9;
2939 = 41*71 + 28; hence not 41 divides 2939 by NAT_4:9;
2939 = 43*68 + 15; hence not 43 divides 2939 by NAT_4:9;
2939 = 47*62 + 25; hence not 47 divides 2939 by NAT_4:9;
2939 = 53*55 + 24; hence not 53 divides 2939 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2939 & n is prime
holds not n divides 2939 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
2953 is prime
proof
now
2953 = 2*1476 + 1; hence not 2 divides 2953 by NAT_4:9;
2953 = 3*984 + 1; hence not 3 divides 2953 by NAT_4:9;
2953 = 5*590 + 3; hence not 5 divides 2953 by NAT_4:9;
2953 = 7*421 + 6; hence not 7 divides 2953 by NAT_4:9;
2953 = 11*268 + 5; hence not 11 divides 2953 by NAT_4:9;
2953 = 13*227 + 2; hence not 13 divides 2953 by NAT_4:9;
2953 = 17*173 + 12; hence not 17 divides 2953 by NAT_4:9;
2953 = 19*155 + 8; hence not 19 divides 2953 by NAT_4:9;
2953 = 23*128 + 9; hence not 23 divides 2953 by NAT_4:9;
2953 = 29*101 + 24; hence not 29 divides 2953 by NAT_4:9;
2953 = 31*95 + 8; hence not 31 divides 2953 by NAT_4:9;
2953 = 37*79 + 30; hence not 37 divides 2953 by NAT_4:9;
2953 = 41*72 + 1; hence not 41 divides 2953 by NAT_4:9;
2953 = 43*68 + 29; hence not 43 divides 2953 by NAT_4:9;
2953 = 47*62 + 39; hence not 47 divides 2953 by NAT_4:9;
2953 = 53*55 + 38; hence not 53 divides 2953 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2953 & n is prime
holds not n divides 2953 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
2957 is prime
proof
now
2957 = 2*1478 + 1; hence not 2 divides 2957 by NAT_4:9;
2957 = 3*985 + 2; hence not 3 divides 2957 by NAT_4:9;
2957 = 5*591 + 2; hence not 5 divides 2957 by NAT_4:9;
2957 = 7*422 + 3; hence not 7 divides 2957 by NAT_4:9;
2957 = 11*268 + 9; hence not 11 divides 2957 by NAT_4:9;
2957 = 13*227 + 6; hence not 13 divides 2957 by NAT_4:9;
2957 = 17*173 + 16; hence not 17 divides 2957 by NAT_4:9;
2957 = 19*155 + 12; hence not 19 divides 2957 by NAT_4:9;
2957 = 23*128 + 13; hence not 23 divides 2957 by NAT_4:9;
2957 = 29*101 + 28; hence not 29 divides 2957 by NAT_4:9;
2957 = 31*95 + 12; hence not 31 divides 2957 by NAT_4:9;
2957 = 37*79 + 34; hence not 37 divides 2957 by NAT_4:9;
2957 = 41*72 + 5; hence not 41 divides 2957 by NAT_4:9;
2957 = 43*68 + 33; hence not 43 divides 2957 by NAT_4:9;
2957 = 47*62 + 43; hence not 47 divides 2957 by NAT_4:9;
2957 = 53*55 + 42; hence not 53 divides 2957 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2957 & n is prime
holds not n divides 2957 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2963 is prime
proof
now
2963 = 2*1481 + 1; hence not 2 divides 2963 by NAT_4:9;
2963 = 3*987 + 2; hence not 3 divides 2963 by NAT_4:9;
2963 = 5*592 + 3; hence not 5 divides 2963 by NAT_4:9;
2963 = 7*423 + 2; hence not 7 divides 2963 by NAT_4:9;
2963 = 11*269 + 4; hence not 11 divides 2963 by NAT_4:9;
2963 = 13*227 + 12; hence not 13 divides 2963 by NAT_4:9;
2963 = 17*174 + 5; hence not 17 divides 2963 by NAT_4:9;
2963 = 19*155 + 18; hence not 19 divides 2963 by NAT_4:9;
2963 = 23*128 + 19; hence not 23 divides 2963 by NAT_4:9;
2963 = 29*102 + 5; hence not 29 divides 2963 by NAT_4:9;
2963 = 31*95 + 18; hence not 31 divides 2963 by NAT_4:9;
2963 = 37*80 + 3; hence not 37 divides 2963 by NAT_4:9;
2963 = 41*72 + 11; hence not 41 divides 2963 by NAT_4:9;
2963 = 43*68 + 39; hence not 43 divides 2963 by NAT_4:9;
2963 = 47*63 + 2; hence not 47 divides 2963 by NAT_4:9;
2963 = 53*55 + 48; hence not 53 divides 2963 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2963 & n is prime
holds not n divides 2963 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
2969 is prime
proof
now
2969 = 2*1484 + 1; hence not 2 divides 2969 by NAT_4:9;
2969 = 3*989 + 2; hence not 3 divides 2969 by NAT_4:9;
2969 = 5*593 + 4; hence not 5 divides 2969 by NAT_4:9;
2969 = 7*424 + 1; hence not 7 divides 2969 by NAT_4:9;
2969 = 11*269 + 10; hence not 11 divides 2969 by NAT_4:9;
2969 = 13*228 + 5; hence not 13 divides 2969 by NAT_4:9;
2969 = 17*174 + 11; hence not 17 divides 2969 by NAT_4:9;
2969 = 19*156 + 5; hence not 19 divides 2969 by NAT_4:9;
2969 = 23*129 + 2; hence not 23 divides 2969 by NAT_4:9;
2969 = 29*102 + 11; hence not 29 divides 2969 by NAT_4:9;
2969 = 31*95 + 24; hence not 31 divides 2969 by NAT_4:9;
2969 = 37*80 + 9; hence not 37 divides 2969 by NAT_4:9;
2969 = 41*72 + 17; hence not 41 divides 2969 by NAT_4:9;
2969 = 43*69 + 2; hence not 43 divides 2969 by NAT_4:9;
2969 = 47*63 + 8; hence not 47 divides 2969 by NAT_4:9;
2969 = 53*56 + 1; hence not 53 divides 2969 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2969 & n is prime
holds not n divides 2969 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
2971 is prime
proof
now
2971 = 2*1485 + 1; hence not 2 divides 2971 by NAT_4:9;
2971 = 3*990 + 1; hence not 3 divides 2971 by NAT_4:9;
2971 = 5*594 + 1; hence not 5 divides 2971 by NAT_4:9;
2971 = 7*424 + 3; hence not 7 divides 2971 by NAT_4:9;
2971 = 11*270 + 1; hence not 11 divides 2971 by NAT_4:9;
2971 = 13*228 + 7; hence not 13 divides 2971 by NAT_4:9;
2971 = 17*174 + 13; hence not 17 divides 2971 by NAT_4:9;
2971 = 19*156 + 7; hence not 19 divides 2971 by NAT_4:9;
2971 = 23*129 + 4; hence not 23 divides 2971 by NAT_4:9;
2971 = 29*102 + 13; hence not 29 divides 2971 by NAT_4:9;
2971 = 31*95 + 26; hence not 31 divides 2971 by NAT_4:9;
2971 = 37*80 + 11; hence not 37 divides 2971 by NAT_4:9;
2971 = 41*72 + 19; hence not 41 divides 2971 by NAT_4:9;
2971 = 43*69 + 4; hence not 43 divides 2971 by NAT_4:9;
2971 = 47*63 + 10; hence not 47 divides 2971 by NAT_4:9;
2971 = 53*56 + 3; hence not 53 divides 2971 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2971 & n is prime
holds not n divides 2971 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 27
theorem
2999 is prime
proof
now
2999 = 2*1499 + 1; hence not 2 divides 2999 by NAT_4:9;
2999 = 3*999 + 2; hence not 3 divides 2999 by NAT_4:9;
2999 = 5*599 + 4; hence not 5 divides 2999 by NAT_4:9;
2999 = 7*428 + 3; hence not 7 divides 2999 by NAT_4:9;
2999 = 11*272 + 7; hence not 11 divides 2999 by NAT_4:9;
2999 = 13*230 + 9; hence not 13 divides 2999 by NAT_4:9;
2999 = 17*176 + 7; hence not 17 divides 2999 by NAT_4:9;
2999 = 19*157 + 16; hence not 19 divides 2999 by NAT_4:9;
2999 = 23*130 + 9; hence not 23 divides 2999 by NAT_4:9;
2999 = 29*103 + 12; hence not 29 divides 2999 by NAT_4:9;
2999 = 31*96 + 23; hence not 31 divides 2999 by NAT_4:9;
2999 = 37*81 + 2; hence not 37 divides 2999 by NAT_4:9;
2999 = 41*73 + 6; hence not 41 divides 2999 by NAT_4:9;
2999 = 43*69 + 32; hence not 43 divides 2999 by NAT_4:9;
2999 = 47*63 + 38; hence not 47 divides 2999 by NAT_4:9;
2999 = 53*56 + 31; hence not 53 divides 2999 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 2999 & n is prime
holds not n divides 2999 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3001 is prime
proof
now
3001 = 2*1500 + 1; hence not 2 divides 3001 by NAT_4:9;
3001 = 3*1000 + 1; hence not 3 divides 3001 by NAT_4:9;
3001 = 5*600 + 1; hence not 5 divides 3001 by NAT_4:9;
3001 = 7*428 + 5; hence not 7 divides 3001 by NAT_4:9;
3001 = 11*272 + 9; hence not 11 divides 3001 by NAT_4:9;
3001 = 13*230 + 11; hence not 13 divides 3001 by NAT_4:9;
3001 = 17*176 + 9; hence not 17 divides 3001 by NAT_4:9;
3001 = 19*157 + 18; hence not 19 divides 3001 by NAT_4:9;
3001 = 23*130 + 11; hence not 23 divides 3001 by NAT_4:9;
3001 = 29*103 + 14; hence not 29 divides 3001 by NAT_4:9;
3001 = 31*96 + 25; hence not 31 divides 3001 by NAT_4:9;
3001 = 37*81 + 4; hence not 37 divides 3001 by NAT_4:9;
3001 = 41*73 + 8; hence not 41 divides 3001 by NAT_4:9;
3001 = 43*69 + 34; hence not 43 divides 3001 by NAT_4:9;
3001 = 47*63 + 40; hence not 47 divides 3001 by NAT_4:9;
3001 = 53*56 + 33; hence not 53 divides 3001 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3001 & n is prime
holds not n divides 3001 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3011 is prime
proof
now
3011 = 2*1505 + 1; hence not 2 divides 3011 by NAT_4:9;
3011 = 3*1003 + 2; hence not 3 divides 3011 by NAT_4:9;
3011 = 5*602 + 1; hence not 5 divides 3011 by NAT_4:9;
3011 = 7*430 + 1; hence not 7 divides 3011 by NAT_4:9;
3011 = 11*273 + 8; hence not 11 divides 3011 by NAT_4:9;
3011 = 13*231 + 8; hence not 13 divides 3011 by NAT_4:9;
3011 = 17*177 + 2; hence not 17 divides 3011 by NAT_4:9;
3011 = 19*158 + 9; hence not 19 divides 3011 by NAT_4:9;
3011 = 23*130 + 21; hence not 23 divides 3011 by NAT_4:9;
3011 = 29*103 + 24; hence not 29 divides 3011 by NAT_4:9;
3011 = 31*97 + 4; hence not 31 divides 3011 by NAT_4:9;
3011 = 37*81 + 14; hence not 37 divides 3011 by NAT_4:9;
3011 = 41*73 + 18; hence not 41 divides 3011 by NAT_4:9;
3011 = 43*70 + 1; hence not 43 divides 3011 by NAT_4:9;
3011 = 47*64 + 3; hence not 47 divides 3011 by NAT_4:9;
3011 = 53*56 + 43; hence not 53 divides 3011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3011 & n is prime
holds not n divides 3011 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3019 is prime
proof
now
3019 = 2*1509 + 1; hence not 2 divides 3019 by NAT_4:9;
3019 = 3*1006 + 1; hence not 3 divides 3019 by NAT_4:9;
3019 = 5*603 + 4; hence not 5 divides 3019 by NAT_4:9;
3019 = 7*431 + 2; hence not 7 divides 3019 by NAT_4:9;
3019 = 11*274 + 5; hence not 11 divides 3019 by NAT_4:9;
3019 = 13*232 + 3; hence not 13 divides 3019 by NAT_4:9;
3019 = 17*177 + 10; hence not 17 divides 3019 by NAT_4:9;
3019 = 19*158 + 17; hence not 19 divides 3019 by NAT_4:9;
3019 = 23*131 + 6; hence not 23 divides 3019 by NAT_4:9;
3019 = 29*104 + 3; hence not 29 divides 3019 by NAT_4:9;
3019 = 31*97 + 12; hence not 31 divides 3019 by NAT_4:9;
3019 = 37*81 + 22; hence not 37 divides 3019 by NAT_4:9;
3019 = 41*73 + 26; hence not 41 divides 3019 by NAT_4:9;
3019 = 43*70 + 9; hence not 43 divides 3019 by NAT_4:9;
3019 = 47*64 + 11; hence not 47 divides 3019 by NAT_4:9;
3019 = 53*56 + 51; hence not 53 divides 3019 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3019 & n is prime
holds not n divides 3019 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3023 is prime
proof
now
3023 = 2*1511 + 1; hence not 2 divides 3023 by NAT_4:9;
3023 = 3*1007 + 2; hence not 3 divides 3023 by NAT_4:9;
3023 = 5*604 + 3; hence not 5 divides 3023 by NAT_4:9;
3023 = 7*431 + 6; hence not 7 divides 3023 by NAT_4:9;
3023 = 11*274 + 9; hence not 11 divides 3023 by NAT_4:9;
3023 = 13*232 + 7; hence not 13 divides 3023 by NAT_4:9;
3023 = 17*177 + 14; hence not 17 divides 3023 by NAT_4:9;
3023 = 19*159 + 2; hence not 19 divides 3023 by NAT_4:9;
3023 = 23*131 + 10; hence not 23 divides 3023 by NAT_4:9;
3023 = 29*104 + 7; hence not 29 divides 3023 by NAT_4:9;
3023 = 31*97 + 16; hence not 31 divides 3023 by NAT_4:9;
3023 = 37*81 + 26; hence not 37 divides 3023 by NAT_4:9;
3023 = 41*73 + 30; hence not 41 divides 3023 by NAT_4:9;
3023 = 43*70 + 13; hence not 43 divides 3023 by NAT_4:9;
3023 = 47*64 + 15; hence not 47 divides 3023 by NAT_4:9;
3023 = 53*57 + 2; hence not 53 divides 3023 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3023 & n is prime
holds not n divides 3023 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3037 is prime
proof
now
3037 = 2*1518 + 1; hence not 2 divides 3037 by NAT_4:9;
3037 = 3*1012 + 1; hence not 3 divides 3037 by NAT_4:9;
3037 = 5*607 + 2; hence not 5 divides 3037 by NAT_4:9;
3037 = 7*433 + 6; hence not 7 divides 3037 by NAT_4:9;
3037 = 11*276 + 1; hence not 11 divides 3037 by NAT_4:9;
3037 = 13*233 + 8; hence not 13 divides 3037 by NAT_4:9;
3037 = 17*178 + 11; hence not 17 divides 3037 by NAT_4:9;
3037 = 19*159 + 16; hence not 19 divides 3037 by NAT_4:9;
3037 = 23*132 + 1; hence not 23 divides 3037 by NAT_4:9;
3037 = 29*104 + 21; hence not 29 divides 3037 by NAT_4:9;
3037 = 31*97 + 30; hence not 31 divides 3037 by NAT_4:9;
3037 = 37*82 + 3; hence not 37 divides 3037 by NAT_4:9;
3037 = 41*74 + 3; hence not 41 divides 3037 by NAT_4:9;
3037 = 43*70 + 27; hence not 43 divides 3037 by NAT_4:9;
3037 = 47*64 + 29; hence not 47 divides 3037 by NAT_4:9;
3037 = 53*57 + 16; hence not 53 divides 3037 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3037 & n is prime
holds not n divides 3037 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3041 is prime
proof
now
3041 = 2*1520 + 1; hence not 2 divides 3041 by NAT_4:9;
3041 = 3*1013 + 2; hence not 3 divides 3041 by NAT_4:9;
3041 = 5*608 + 1; hence not 5 divides 3041 by NAT_4:9;
3041 = 7*434 + 3; hence not 7 divides 3041 by NAT_4:9;
3041 = 11*276 + 5; hence not 11 divides 3041 by NAT_4:9;
3041 = 13*233 + 12; hence not 13 divides 3041 by NAT_4:9;
3041 = 17*178 + 15; hence not 17 divides 3041 by NAT_4:9;
3041 = 19*160 + 1; hence not 19 divides 3041 by NAT_4:9;
3041 = 23*132 + 5; hence not 23 divides 3041 by NAT_4:9;
3041 = 29*104 + 25; hence not 29 divides 3041 by NAT_4:9;
3041 = 31*98 + 3; hence not 31 divides 3041 by NAT_4:9;
3041 = 37*82 + 7; hence not 37 divides 3041 by NAT_4:9;
3041 = 41*74 + 7; hence not 41 divides 3041 by NAT_4:9;
3041 = 43*70 + 31; hence not 43 divides 3041 by NAT_4:9;
3041 = 47*64 + 33; hence not 47 divides 3041 by NAT_4:9;
3041 = 53*57 + 20; hence not 53 divides 3041 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3041 & n is prime
holds not n divides 3041 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3049 is prime
proof
now
3049 = 2*1524 + 1; hence not 2 divides 3049 by NAT_4:9;
3049 = 3*1016 + 1; hence not 3 divides 3049 by NAT_4:9;
3049 = 5*609 + 4; hence not 5 divides 3049 by NAT_4:9;
3049 = 7*435 + 4; hence not 7 divides 3049 by NAT_4:9;
3049 = 11*277 + 2; hence not 11 divides 3049 by NAT_4:9;
3049 = 13*234 + 7; hence not 13 divides 3049 by NAT_4:9;
3049 = 17*179 + 6; hence not 17 divides 3049 by NAT_4:9;
3049 = 19*160 + 9; hence not 19 divides 3049 by NAT_4:9;
3049 = 23*132 + 13; hence not 23 divides 3049 by NAT_4:9;
3049 = 29*105 + 4; hence not 29 divides 3049 by NAT_4:9;
3049 = 31*98 + 11; hence not 31 divides 3049 by NAT_4:9;
3049 = 37*82 + 15; hence not 37 divides 3049 by NAT_4:9;
3049 = 41*74 + 15; hence not 41 divides 3049 by NAT_4:9;
3049 = 43*70 + 39; hence not 43 divides 3049 by NAT_4:9;
3049 = 47*64 + 41; hence not 47 divides 3049 by NAT_4:9;
3049 = 53*57 + 28; hence not 53 divides 3049 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3049 & n is prime
holds not n divides 3049 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3061 is prime
proof
now
3061 = 2*1530 + 1; hence not 2 divides 3061 by NAT_4:9;
3061 = 3*1020 + 1; hence not 3 divides 3061 by NAT_4:9;
3061 = 5*612 + 1; hence not 5 divides 3061 by NAT_4:9;
3061 = 7*437 + 2; hence not 7 divides 3061 by NAT_4:9;
3061 = 11*278 + 3; hence not 11 divides 3061 by NAT_4:9;
3061 = 13*235 + 6; hence not 13 divides 3061 by NAT_4:9;
3061 = 17*180 + 1; hence not 17 divides 3061 by NAT_4:9;
3061 = 19*161 + 2; hence not 19 divides 3061 by NAT_4:9;
3061 = 23*133 + 2; hence not 23 divides 3061 by NAT_4:9;
3061 = 29*105 + 16; hence not 29 divides 3061 by NAT_4:9;
3061 = 31*98 + 23; hence not 31 divides 3061 by NAT_4:9;
3061 = 37*82 + 27; hence not 37 divides 3061 by NAT_4:9;
3061 = 41*74 + 27; hence not 41 divides 3061 by NAT_4:9;
3061 = 43*71 + 8; hence not 43 divides 3061 by NAT_4:9;
3061 = 47*65 + 6; hence not 47 divides 3061 by NAT_4:9;
3061 = 53*57 + 40; hence not 53 divides 3061 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3061 & n is prime
holds not n divides 3061 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3067 is prime
proof
now
3067 = 2*1533 + 1; hence not 2 divides 3067 by NAT_4:9;
3067 = 3*1022 + 1; hence not 3 divides 3067 by NAT_4:9;
3067 = 5*613 + 2; hence not 5 divides 3067 by NAT_4:9;
3067 = 7*438 + 1; hence not 7 divides 3067 by NAT_4:9;
3067 = 11*278 + 9; hence not 11 divides 3067 by NAT_4:9;
3067 = 13*235 + 12; hence not 13 divides 3067 by NAT_4:9;
3067 = 17*180 + 7; hence not 17 divides 3067 by NAT_4:9;
3067 = 19*161 + 8; hence not 19 divides 3067 by NAT_4:9;
3067 = 23*133 + 8; hence not 23 divides 3067 by NAT_4:9;
3067 = 29*105 + 22; hence not 29 divides 3067 by NAT_4:9;
3067 = 31*98 + 29; hence not 31 divides 3067 by NAT_4:9;
3067 = 37*82 + 33; hence not 37 divides 3067 by NAT_4:9;
3067 = 41*74 + 33; hence not 41 divides 3067 by NAT_4:9;
3067 = 43*71 + 14; hence not 43 divides 3067 by NAT_4:9;
3067 = 47*65 + 12; hence not 47 divides 3067 by NAT_4:9;
3067 = 53*57 + 46; hence not 53 divides 3067 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3067 & n is prime
holds not n divides 3067 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3079 is prime
proof
now
3079 = 2*1539 + 1; hence not 2 divides 3079 by NAT_4:9;
3079 = 3*1026 + 1; hence not 3 divides 3079 by NAT_4:9;
3079 = 5*615 + 4; hence not 5 divides 3079 by NAT_4:9;
3079 = 7*439 + 6; hence not 7 divides 3079 by NAT_4:9;
3079 = 11*279 + 10; hence not 11 divides 3079 by NAT_4:9;
3079 = 13*236 + 11; hence not 13 divides 3079 by NAT_4:9;
3079 = 17*181 + 2; hence not 17 divides 3079 by NAT_4:9;
3079 = 19*162 + 1; hence not 19 divides 3079 by NAT_4:9;
3079 = 23*133 + 20; hence not 23 divides 3079 by NAT_4:9;
3079 = 29*106 + 5; hence not 29 divides 3079 by NAT_4:9;
3079 = 31*99 + 10; hence not 31 divides 3079 by NAT_4:9;
3079 = 37*83 + 8; hence not 37 divides 3079 by NAT_4:9;
3079 = 41*75 + 4; hence not 41 divides 3079 by NAT_4:9;
3079 = 43*71 + 26; hence not 43 divides 3079 by NAT_4:9;
3079 = 47*65 + 24; hence not 47 divides 3079 by NAT_4:9;
3079 = 53*58 + 5; hence not 53 divides 3079 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3079 & n is prime
holds not n divides 3079 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3083 is prime
proof
now
3083 = 2*1541 + 1; hence not 2 divides 3083 by NAT_4:9;
3083 = 3*1027 + 2; hence not 3 divides 3083 by NAT_4:9;
3083 = 5*616 + 3; hence not 5 divides 3083 by NAT_4:9;
3083 = 7*440 + 3; hence not 7 divides 3083 by NAT_4:9;
3083 = 11*280 + 3; hence not 11 divides 3083 by NAT_4:9;
3083 = 13*237 + 2; hence not 13 divides 3083 by NAT_4:9;
3083 = 17*181 + 6; hence not 17 divides 3083 by NAT_4:9;
3083 = 19*162 + 5; hence not 19 divides 3083 by NAT_4:9;
3083 = 23*134 + 1; hence not 23 divides 3083 by NAT_4:9;
3083 = 29*106 + 9; hence not 29 divides 3083 by NAT_4:9;
3083 = 31*99 + 14; hence not 31 divides 3083 by NAT_4:9;
3083 = 37*83 + 12; hence not 37 divides 3083 by NAT_4:9;
3083 = 41*75 + 8; hence not 41 divides 3083 by NAT_4:9;
3083 = 43*71 + 30; hence not 43 divides 3083 by NAT_4:9;
3083 = 47*65 + 28; hence not 47 divides 3083 by NAT_4:9;
3083 = 53*58 + 9; hence not 53 divides 3083 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3083 & n is prime
holds not n divides 3083 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3089 is prime
proof
now
3089 = 2*1544 + 1; hence not 2 divides 3089 by NAT_4:9;
3089 = 3*1029 + 2; hence not 3 divides 3089 by NAT_4:9;
3089 = 5*617 + 4; hence not 5 divides 3089 by NAT_4:9;
3089 = 7*441 + 2; hence not 7 divides 3089 by NAT_4:9;
3089 = 11*280 + 9; hence not 11 divides 3089 by NAT_4:9;
3089 = 13*237 + 8; hence not 13 divides 3089 by NAT_4:9;
3089 = 17*181 + 12; hence not 17 divides 3089 by NAT_4:9;
3089 = 19*162 + 11; hence not 19 divides 3089 by NAT_4:9;
3089 = 23*134 + 7; hence not 23 divides 3089 by NAT_4:9;
3089 = 29*106 + 15; hence not 29 divides 3089 by NAT_4:9;
3089 = 31*99 + 20; hence not 31 divides 3089 by NAT_4:9;
3089 = 37*83 + 18; hence not 37 divides 3089 by NAT_4:9;
3089 = 41*75 + 14; hence not 41 divides 3089 by NAT_4:9;
3089 = 43*71 + 36; hence not 43 divides 3089 by NAT_4:9;
3089 = 47*65 + 34; hence not 47 divides 3089 by NAT_4:9;
3089 = 53*58 + 15; hence not 53 divides 3089 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3089 & n is prime
holds not n divides 3089 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
3109 is prime
proof
now
3109 = 2*1554 + 1; hence not 2 divides 3109 by NAT_4:9;
3109 = 3*1036 + 1; hence not 3 divides 3109 by NAT_4:9;
3109 = 5*621 + 4; hence not 5 divides 3109 by NAT_4:9;
3109 = 7*444 + 1; hence not 7 divides 3109 by NAT_4:9;
3109 = 11*282 + 7; hence not 11 divides 3109 by NAT_4:9;
3109 = 13*239 + 2; hence not 13 divides 3109 by NAT_4:9;
3109 = 17*182 + 15; hence not 17 divides 3109 by NAT_4:9;
3109 = 19*163 + 12; hence not 19 divides 3109 by NAT_4:9;
3109 = 23*135 + 4; hence not 23 divides 3109 by NAT_4:9;
3109 = 29*107 + 6; hence not 29 divides 3109 by NAT_4:9;
3109 = 31*100 + 9; hence not 31 divides 3109 by NAT_4:9;
3109 = 37*84 + 1; hence not 37 divides 3109 by NAT_4:9;
3109 = 41*75 + 34; hence not 41 divides 3109 by NAT_4:9;
3109 = 43*72 + 13; hence not 43 divides 3109 by NAT_4:9;
3109 = 47*66 + 7; hence not 47 divides 3109 by NAT_4:9;
3109 = 53*58 + 35; hence not 53 divides 3109 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3109 & n is prime
holds not n divides 3109 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3119 is prime
proof
now
3119 = 2*1559 + 1; hence not 2 divides 3119 by NAT_4:9;
3119 = 3*1039 + 2; hence not 3 divides 3119 by NAT_4:9;
3119 = 5*623 + 4; hence not 5 divides 3119 by NAT_4:9;
3119 = 7*445 + 4; hence not 7 divides 3119 by NAT_4:9;
3119 = 11*283 + 6; hence not 11 divides 3119 by NAT_4:9;
3119 = 13*239 + 12; hence not 13 divides 3119 by NAT_4:9;
3119 = 17*183 + 8; hence not 17 divides 3119 by NAT_4:9;
3119 = 19*164 + 3; hence not 19 divides 3119 by NAT_4:9;
3119 = 23*135 + 14; hence not 23 divides 3119 by NAT_4:9;
3119 = 29*107 + 16; hence not 29 divides 3119 by NAT_4:9;
3119 = 31*100 + 19; hence not 31 divides 3119 by NAT_4:9;
3119 = 37*84 + 11; hence not 37 divides 3119 by NAT_4:9;
3119 = 41*76 + 3; hence not 41 divides 3119 by NAT_4:9;
3119 = 43*72 + 23; hence not 43 divides 3119 by NAT_4:9;
3119 = 47*66 + 17; hence not 47 divides 3119 by NAT_4:9;
3119 = 53*58 + 45; hence not 53 divides 3119 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3119 & n is prime
holds not n divides 3119 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3121 is prime
proof
now
3121 = 2*1560 + 1; hence not 2 divides 3121 by NAT_4:9;
3121 = 3*1040 + 1; hence not 3 divides 3121 by NAT_4:9;
3121 = 5*624 + 1; hence not 5 divides 3121 by NAT_4:9;
3121 = 7*445 + 6; hence not 7 divides 3121 by NAT_4:9;
3121 = 11*283 + 8; hence not 11 divides 3121 by NAT_4:9;
3121 = 13*240 + 1; hence not 13 divides 3121 by NAT_4:9;
3121 = 17*183 + 10; hence not 17 divides 3121 by NAT_4:9;
3121 = 19*164 + 5; hence not 19 divides 3121 by NAT_4:9;
3121 = 23*135 + 16; hence not 23 divides 3121 by NAT_4:9;
3121 = 29*107 + 18; hence not 29 divides 3121 by NAT_4:9;
3121 = 31*100 + 21; hence not 31 divides 3121 by NAT_4:9;
3121 = 37*84 + 13; hence not 37 divides 3121 by NAT_4:9;
3121 = 41*76 + 5; hence not 41 divides 3121 by NAT_4:9;
3121 = 43*72 + 25; hence not 43 divides 3121 by NAT_4:9;
3121 = 47*66 + 19; hence not 47 divides 3121 by NAT_4:9;
3121 = 53*58 + 47; hence not 53 divides 3121 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3121 & n is prime
holds not n divides 3121 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
3137 is prime
proof
now
3137 = 2*1568 + 1; hence not 2 divides 3137 by NAT_4:9;
3137 = 3*1045 + 2; hence not 3 divides 3137 by NAT_4:9;
3137 = 5*627 + 2; hence not 5 divides 3137 by NAT_4:9;
3137 = 7*448 + 1; hence not 7 divides 3137 by NAT_4:9;
3137 = 11*285 + 2; hence not 11 divides 3137 by NAT_4:9;
3137 = 13*241 + 4; hence not 13 divides 3137 by NAT_4:9;
3137 = 17*184 + 9; hence not 17 divides 3137 by NAT_4:9;
3137 = 19*165 + 2; hence not 19 divides 3137 by NAT_4:9;
3137 = 23*136 + 9; hence not 23 divides 3137 by NAT_4:9;
3137 = 29*108 + 5; hence not 29 divides 3137 by NAT_4:9;
3137 = 31*101 + 6; hence not 31 divides 3137 by NAT_4:9;
3137 = 37*84 + 29; hence not 37 divides 3137 by NAT_4:9;
3137 = 41*76 + 21; hence not 41 divides 3137 by NAT_4:9;
3137 = 43*72 + 41; hence not 43 divides 3137 by NAT_4:9;
3137 = 47*66 + 35; hence not 47 divides 3137 by NAT_4:9;
3137 = 53*59 + 10; hence not 53 divides 3137 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3137 & n is prime
holds not n divides 3137 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 25
theorem
3163 is prime
proof
now
3163 = 2*1581 + 1; hence not 2 divides 3163 by NAT_4:9;
3163 = 3*1054 + 1; hence not 3 divides 3163 by NAT_4:9;
3163 = 5*632 + 3; hence not 5 divides 3163 by NAT_4:9;
3163 = 7*451 + 6; hence not 7 divides 3163 by NAT_4:9;
3163 = 11*287 + 6; hence not 11 divides 3163 by NAT_4:9;
3163 = 13*243 + 4; hence not 13 divides 3163 by NAT_4:9;
3163 = 17*186 + 1; hence not 17 divides 3163 by NAT_4:9;
3163 = 19*166 + 9; hence not 19 divides 3163 by NAT_4:9;
3163 = 23*137 + 12; hence not 23 divides 3163 by NAT_4:9;
3163 = 29*109 + 2; hence not 29 divides 3163 by NAT_4:9;
3163 = 31*102 + 1; hence not 31 divides 3163 by NAT_4:9;
3163 = 37*85 + 18; hence not 37 divides 3163 by NAT_4:9;
3163 = 41*77 + 6; hence not 41 divides 3163 by NAT_4:9;
3163 = 43*73 + 24; hence not 43 divides 3163 by NAT_4:9;
3163 = 47*67 + 14; hence not 47 divides 3163 by NAT_4:9;
3163 = 53*59 + 36; hence not 53 divides 3163 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3163 & n is prime
holds not n divides 3163 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3167 is prime
proof
now
3167 = 2*1583 + 1; hence not 2 divides 3167 by NAT_4:9;
3167 = 3*1055 + 2; hence not 3 divides 3167 by NAT_4:9;
3167 = 5*633 + 2; hence not 5 divides 3167 by NAT_4:9;
3167 = 7*452 + 3; hence not 7 divides 3167 by NAT_4:9;
3167 = 11*287 + 10; hence not 11 divides 3167 by NAT_4:9;
3167 = 13*243 + 8; hence not 13 divides 3167 by NAT_4:9;
3167 = 17*186 + 5; hence not 17 divides 3167 by NAT_4:9;
3167 = 19*166 + 13; hence not 19 divides 3167 by NAT_4:9;
3167 = 23*137 + 16; hence not 23 divides 3167 by NAT_4:9;
3167 = 29*109 + 6; hence not 29 divides 3167 by NAT_4:9;
3167 = 31*102 + 5; hence not 31 divides 3167 by NAT_4:9;
3167 = 37*85 + 22; hence not 37 divides 3167 by NAT_4:9;
3167 = 41*77 + 10; hence not 41 divides 3167 by NAT_4:9;
3167 = 43*73 + 28; hence not 43 divides 3167 by NAT_4:9;
3167 = 47*67 + 18; hence not 47 divides 3167 by NAT_4:9;
3167 = 53*59 + 40; hence not 53 divides 3167 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3167 & n is prime
holds not n divides 3167 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3169 is prime
proof
now
3169 = 2*1584 + 1; hence not 2 divides 3169 by NAT_4:9;
3169 = 3*1056 + 1; hence not 3 divides 3169 by NAT_4:9;
3169 = 5*633 + 4; hence not 5 divides 3169 by NAT_4:9;
3169 = 7*452 + 5; hence not 7 divides 3169 by NAT_4:9;
3169 = 11*288 + 1; hence not 11 divides 3169 by NAT_4:9;
3169 = 13*243 + 10; hence not 13 divides 3169 by NAT_4:9;
3169 = 17*186 + 7; hence not 17 divides 3169 by NAT_4:9;
3169 = 19*166 + 15; hence not 19 divides 3169 by NAT_4:9;
3169 = 23*137 + 18; hence not 23 divides 3169 by NAT_4:9;
3169 = 29*109 + 8; hence not 29 divides 3169 by NAT_4:9;
3169 = 31*102 + 7; hence not 31 divides 3169 by NAT_4:9;
3169 = 37*85 + 24; hence not 37 divides 3169 by NAT_4:9;
3169 = 41*77 + 12; hence not 41 divides 3169 by NAT_4:9;
3169 = 43*73 + 30; hence not 43 divides 3169 by NAT_4:9;
3169 = 47*67 + 20; hence not 47 divides 3169 by NAT_4:9;
3169 = 53*59 + 42; hence not 53 divides 3169 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3169 & n is prime
holds not n divides 3169 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3181 is prime
proof
now
3181 = 2*1590 + 1; hence not 2 divides 3181 by NAT_4:9;
3181 = 3*1060 + 1; hence not 3 divides 3181 by NAT_4:9;
3181 = 5*636 + 1; hence not 5 divides 3181 by NAT_4:9;
3181 = 7*454 + 3; hence not 7 divides 3181 by NAT_4:9;
3181 = 11*289 + 2; hence not 11 divides 3181 by NAT_4:9;
3181 = 13*244 + 9; hence not 13 divides 3181 by NAT_4:9;
3181 = 17*187 + 2; hence not 17 divides 3181 by NAT_4:9;
3181 = 19*167 + 8; hence not 19 divides 3181 by NAT_4:9;
3181 = 23*138 + 7; hence not 23 divides 3181 by NAT_4:9;
3181 = 29*109 + 20; hence not 29 divides 3181 by NAT_4:9;
3181 = 31*102 + 19; hence not 31 divides 3181 by NAT_4:9;
3181 = 37*85 + 36; hence not 37 divides 3181 by NAT_4:9;
3181 = 41*77 + 24; hence not 41 divides 3181 by NAT_4:9;
3181 = 43*73 + 42; hence not 43 divides 3181 by NAT_4:9;
3181 = 47*67 + 32; hence not 47 divides 3181 by NAT_4:9;
3181 = 53*60 + 1; hence not 53 divides 3181 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3181 & n is prime
holds not n divides 3181 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3187 is prime
proof
now
3187 = 2*1593 + 1; hence not 2 divides 3187 by NAT_4:9;
3187 = 3*1062 + 1; hence not 3 divides 3187 by NAT_4:9;
3187 = 5*637 + 2; hence not 5 divides 3187 by NAT_4:9;
3187 = 7*455 + 2; hence not 7 divides 3187 by NAT_4:9;
3187 = 11*289 + 8; hence not 11 divides 3187 by NAT_4:9;
3187 = 13*245 + 2; hence not 13 divides 3187 by NAT_4:9;
3187 = 17*187 + 8; hence not 17 divides 3187 by NAT_4:9;
3187 = 19*167 + 14; hence not 19 divides 3187 by NAT_4:9;
3187 = 23*138 + 13; hence not 23 divides 3187 by NAT_4:9;
3187 = 29*109 + 26; hence not 29 divides 3187 by NAT_4:9;
3187 = 31*102 + 25; hence not 31 divides 3187 by NAT_4:9;
3187 = 37*86 + 5; hence not 37 divides 3187 by NAT_4:9;
3187 = 41*77 + 30; hence not 41 divides 3187 by NAT_4:9;
3187 = 43*74 + 5; hence not 43 divides 3187 by NAT_4:9;
3187 = 47*67 + 38; hence not 47 divides 3187 by NAT_4:9;
3187 = 53*60 + 7; hence not 53 divides 3187 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3187 & n is prime
holds not n divides 3187 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3191 is prime
proof
now
3191 = 2*1595 + 1; hence not 2 divides 3191 by NAT_4:9;
3191 = 3*1063 + 2; hence not 3 divides 3191 by NAT_4:9;
3191 = 5*638 + 1; hence not 5 divides 3191 by NAT_4:9;
3191 = 7*455 + 6; hence not 7 divides 3191 by NAT_4:9;
3191 = 11*290 + 1; hence not 11 divides 3191 by NAT_4:9;
3191 = 13*245 + 6; hence not 13 divides 3191 by NAT_4:9;
3191 = 17*187 + 12; hence not 17 divides 3191 by NAT_4:9;
3191 = 19*167 + 18; hence not 19 divides 3191 by NAT_4:9;
3191 = 23*138 + 17; hence not 23 divides 3191 by NAT_4:9;
3191 = 29*110 + 1; hence not 29 divides 3191 by NAT_4:9;
3191 = 31*102 + 29; hence not 31 divides 3191 by NAT_4:9;
3191 = 37*86 + 9; hence not 37 divides 3191 by NAT_4:9;
3191 = 41*77 + 34; hence not 41 divides 3191 by NAT_4:9;
3191 = 43*74 + 9; hence not 43 divides 3191 by NAT_4:9;
3191 = 47*67 + 42; hence not 47 divides 3191 by NAT_4:9;
3191 = 53*60 + 11; hence not 53 divides 3191 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3191 & n is prime
holds not n divides 3191 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3203 is prime
proof
now
3203 = 2*1601 + 1; hence not 2 divides 3203 by NAT_4:9;
3203 = 3*1067 + 2; hence not 3 divides 3203 by NAT_4:9;
3203 = 5*640 + 3; hence not 5 divides 3203 by NAT_4:9;
3203 = 7*457 + 4; hence not 7 divides 3203 by NAT_4:9;
3203 = 11*291 + 2; hence not 11 divides 3203 by NAT_4:9;
3203 = 13*246 + 5; hence not 13 divides 3203 by NAT_4:9;
3203 = 17*188 + 7; hence not 17 divides 3203 by NAT_4:9;
3203 = 19*168 + 11; hence not 19 divides 3203 by NAT_4:9;
3203 = 23*139 + 6; hence not 23 divides 3203 by NAT_4:9;
3203 = 29*110 + 13; hence not 29 divides 3203 by NAT_4:9;
3203 = 31*103 + 10; hence not 31 divides 3203 by NAT_4:9;
3203 = 37*86 + 21; hence not 37 divides 3203 by NAT_4:9;
3203 = 41*78 + 5; hence not 41 divides 3203 by NAT_4:9;
3203 = 43*74 + 21; hence not 43 divides 3203 by NAT_4:9;
3203 = 47*68 + 7; hence not 47 divides 3203 by NAT_4:9;
3203 = 53*60 + 23; hence not 53 divides 3203 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3203 & n is prime
holds not n divides 3203 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3209 is prime
proof
now
3209 = 2*1604 + 1; hence not 2 divides 3209 by NAT_4:9;
3209 = 3*1069 + 2; hence not 3 divides 3209 by NAT_4:9;
3209 = 5*641 + 4; hence not 5 divides 3209 by NAT_4:9;
3209 = 7*458 + 3; hence not 7 divides 3209 by NAT_4:9;
3209 = 11*291 + 8; hence not 11 divides 3209 by NAT_4:9;
3209 = 13*246 + 11; hence not 13 divides 3209 by NAT_4:9;
3209 = 17*188 + 13; hence not 17 divides 3209 by NAT_4:9;
3209 = 19*168 + 17; hence not 19 divides 3209 by NAT_4:9;
3209 = 23*139 + 12; hence not 23 divides 3209 by NAT_4:9;
3209 = 29*110 + 19; hence not 29 divides 3209 by NAT_4:9;
3209 = 31*103 + 16; hence not 31 divides 3209 by NAT_4:9;
3209 = 37*86 + 27; hence not 37 divides 3209 by NAT_4:9;
3209 = 41*78 + 11; hence not 41 divides 3209 by NAT_4:9;
3209 = 43*74 + 27; hence not 43 divides 3209 by NAT_4:9;
3209 = 47*68 + 13; hence not 47 divides 3209 by NAT_4:9;
3209 = 53*60 + 29; hence not 53 divides 3209 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3209 & n is prime
holds not n divides 3209 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3217 is prime
proof
now
3217 = 2*1608 + 1; hence not 2 divides 3217 by NAT_4:9;
3217 = 3*1072 + 1; hence not 3 divides 3217 by NAT_4:9;
3217 = 5*643 + 2; hence not 5 divides 3217 by NAT_4:9;
3217 = 7*459 + 4; hence not 7 divides 3217 by NAT_4:9;
3217 = 11*292 + 5; hence not 11 divides 3217 by NAT_4:9;
3217 = 13*247 + 6; hence not 13 divides 3217 by NAT_4:9;
3217 = 17*189 + 4; hence not 17 divides 3217 by NAT_4:9;
3217 = 19*169 + 6; hence not 19 divides 3217 by NAT_4:9;
3217 = 23*139 + 20; hence not 23 divides 3217 by NAT_4:9;
3217 = 29*110 + 27; hence not 29 divides 3217 by NAT_4:9;
3217 = 31*103 + 24; hence not 31 divides 3217 by NAT_4:9;
3217 = 37*86 + 35; hence not 37 divides 3217 by NAT_4:9;
3217 = 41*78 + 19; hence not 41 divides 3217 by NAT_4:9;
3217 = 43*74 + 35; hence not 43 divides 3217 by NAT_4:9;
3217 = 47*68 + 21; hence not 47 divides 3217 by NAT_4:9;
3217 = 53*60 + 37; hence not 53 divides 3217 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3217 & n is prime
holds not n divides 3217 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3221 is prime
proof
now
3221 = 2*1610 + 1; hence not 2 divides 3221 by NAT_4:9;
3221 = 3*1073 + 2; hence not 3 divides 3221 by NAT_4:9;
3221 = 5*644 + 1; hence not 5 divides 3221 by NAT_4:9;
3221 = 7*460 + 1; hence not 7 divides 3221 by NAT_4:9;
3221 = 11*292 + 9; hence not 11 divides 3221 by NAT_4:9;
3221 = 13*247 + 10; hence not 13 divides 3221 by NAT_4:9;
3221 = 17*189 + 8; hence not 17 divides 3221 by NAT_4:9;
3221 = 19*169 + 10; hence not 19 divides 3221 by NAT_4:9;
3221 = 23*140 + 1; hence not 23 divides 3221 by NAT_4:9;
3221 = 29*111 + 2; hence not 29 divides 3221 by NAT_4:9;
3221 = 31*103 + 28; hence not 31 divides 3221 by NAT_4:9;
3221 = 37*87 + 2; hence not 37 divides 3221 by NAT_4:9;
3221 = 41*78 + 23; hence not 41 divides 3221 by NAT_4:9;
3221 = 43*74 + 39; hence not 43 divides 3221 by NAT_4:9;
3221 = 47*68 + 25; hence not 47 divides 3221 by NAT_4:9;
3221 = 53*60 + 41; hence not 53 divides 3221 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3221 & n is prime
holds not n divides 3221 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3229 is prime
proof
now
3229 = 2*1614 + 1; hence not 2 divides 3229 by NAT_4:9;
3229 = 3*1076 + 1; hence not 3 divides 3229 by NAT_4:9;
3229 = 5*645 + 4; hence not 5 divides 3229 by NAT_4:9;
3229 = 7*461 + 2; hence not 7 divides 3229 by NAT_4:9;
3229 = 11*293 + 6; hence not 11 divides 3229 by NAT_4:9;
3229 = 13*248 + 5; hence not 13 divides 3229 by NAT_4:9;
3229 = 17*189 + 16; hence not 17 divides 3229 by NAT_4:9;
3229 = 19*169 + 18; hence not 19 divides 3229 by NAT_4:9;
3229 = 23*140 + 9; hence not 23 divides 3229 by NAT_4:9;
3229 = 29*111 + 10; hence not 29 divides 3229 by NAT_4:9;
3229 = 31*104 + 5; hence not 31 divides 3229 by NAT_4:9;
3229 = 37*87 + 10; hence not 37 divides 3229 by NAT_4:9;
3229 = 41*78 + 31; hence not 41 divides 3229 by NAT_4:9;
3229 = 43*75 + 4; hence not 43 divides 3229 by NAT_4:9;
3229 = 47*68 + 33; hence not 47 divides 3229 by NAT_4:9;
3229 = 53*60 + 49; hence not 53 divides 3229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3229 & n is prime
holds not n divides 3229 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
3251 is prime
proof
now
3251 = 2*1625 + 1; hence not 2 divides 3251 by NAT_4:9;
3251 = 3*1083 + 2; hence not 3 divides 3251 by NAT_4:9;
3251 = 5*650 + 1; hence not 5 divides 3251 by NAT_4:9;
3251 = 7*464 + 3; hence not 7 divides 3251 by NAT_4:9;
3251 = 11*295 + 6; hence not 11 divides 3251 by NAT_4:9;
3251 = 13*250 + 1; hence not 13 divides 3251 by NAT_4:9;
3251 = 17*191 + 4; hence not 17 divides 3251 by NAT_4:9;
3251 = 19*171 + 2; hence not 19 divides 3251 by NAT_4:9;
3251 = 23*141 + 8; hence not 23 divides 3251 by NAT_4:9;
3251 = 29*112 + 3; hence not 29 divides 3251 by NAT_4:9;
3251 = 31*104 + 27; hence not 31 divides 3251 by NAT_4:9;
3251 = 37*87 + 32; hence not 37 divides 3251 by NAT_4:9;
3251 = 41*79 + 12; hence not 41 divides 3251 by NAT_4:9;
3251 = 43*75 + 26; hence not 43 divides 3251 by NAT_4:9;
3251 = 47*69 + 8; hence not 47 divides 3251 by NAT_4:9;
3251 = 53*61 + 18; hence not 53 divides 3251 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3251 & n is prime
holds not n divides 3251 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3253 is prime
proof
now
3253 = 2*1626 + 1; hence not 2 divides 3253 by NAT_4:9;
3253 = 3*1084 + 1; hence not 3 divides 3253 by NAT_4:9;
3253 = 5*650 + 3; hence not 5 divides 3253 by NAT_4:9;
3253 = 7*464 + 5; hence not 7 divides 3253 by NAT_4:9;
3253 = 11*295 + 8; hence not 11 divides 3253 by NAT_4:9;
3253 = 13*250 + 3; hence not 13 divides 3253 by NAT_4:9;
3253 = 17*191 + 6; hence not 17 divides 3253 by NAT_4:9;
3253 = 19*171 + 4; hence not 19 divides 3253 by NAT_4:9;
3253 = 23*141 + 10; hence not 23 divides 3253 by NAT_4:9;
3253 = 29*112 + 5; hence not 29 divides 3253 by NAT_4:9;
3253 = 31*104 + 29; hence not 31 divides 3253 by NAT_4:9;
3253 = 37*87 + 34; hence not 37 divides 3253 by NAT_4:9;
3253 = 41*79 + 14; hence not 41 divides 3253 by NAT_4:9;
3253 = 43*75 + 28; hence not 43 divides 3253 by NAT_4:9;
3253 = 47*69 + 10; hence not 47 divides 3253 by NAT_4:9;
3253 = 53*61 + 20; hence not 53 divides 3253 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3253 & n is prime
holds not n divides 3253 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3257 is prime
proof
now
3257 = 2*1628 + 1; hence not 2 divides 3257 by NAT_4:9;
3257 = 3*1085 + 2; hence not 3 divides 3257 by NAT_4:9;
3257 = 5*651 + 2; hence not 5 divides 3257 by NAT_4:9;
3257 = 7*465 + 2; hence not 7 divides 3257 by NAT_4:9;
3257 = 11*296 + 1; hence not 11 divides 3257 by NAT_4:9;
3257 = 13*250 + 7; hence not 13 divides 3257 by NAT_4:9;
3257 = 17*191 + 10; hence not 17 divides 3257 by NAT_4:9;
3257 = 19*171 + 8; hence not 19 divides 3257 by NAT_4:9;
3257 = 23*141 + 14; hence not 23 divides 3257 by NAT_4:9;
3257 = 29*112 + 9; hence not 29 divides 3257 by NAT_4:9;
3257 = 31*105 + 2; hence not 31 divides 3257 by NAT_4:9;
3257 = 37*88 + 1; hence not 37 divides 3257 by NAT_4:9;
3257 = 41*79 + 18; hence not 41 divides 3257 by NAT_4:9;
3257 = 43*75 + 32; hence not 43 divides 3257 by NAT_4:9;
3257 = 47*69 + 14; hence not 47 divides 3257 by NAT_4:9;
3257 = 53*61 + 24; hence not 53 divides 3257 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3257 & n is prime
holds not n divides 3257 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3259 is prime
proof
now
3259 = 2*1629 + 1; hence not 2 divides 3259 by NAT_4:9;
3259 = 3*1086 + 1; hence not 3 divides 3259 by NAT_4:9;
3259 = 5*651 + 4; hence not 5 divides 3259 by NAT_4:9;
3259 = 7*465 + 4; hence not 7 divides 3259 by NAT_4:9;
3259 = 11*296 + 3; hence not 11 divides 3259 by NAT_4:9;
3259 = 13*250 + 9; hence not 13 divides 3259 by NAT_4:9;
3259 = 17*191 + 12; hence not 17 divides 3259 by NAT_4:9;
3259 = 19*171 + 10; hence not 19 divides 3259 by NAT_4:9;
3259 = 23*141 + 16; hence not 23 divides 3259 by NAT_4:9;
3259 = 29*112 + 11; hence not 29 divides 3259 by NAT_4:9;
3259 = 31*105 + 4; hence not 31 divides 3259 by NAT_4:9;
3259 = 37*88 + 3; hence not 37 divides 3259 by NAT_4:9;
3259 = 41*79 + 20; hence not 41 divides 3259 by NAT_4:9;
3259 = 43*75 + 34; hence not 43 divides 3259 by NAT_4:9;
3259 = 47*69 + 16; hence not 47 divides 3259 by NAT_4:9;
3259 = 53*61 + 26; hence not 53 divides 3259 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3259 & n is prime
holds not n divides 3259 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3271 is prime
proof
now
3271 = 2*1635 + 1; hence not 2 divides 3271 by NAT_4:9;
3271 = 3*1090 + 1; hence not 3 divides 3271 by NAT_4:9;
3271 = 5*654 + 1; hence not 5 divides 3271 by NAT_4:9;
3271 = 7*467 + 2; hence not 7 divides 3271 by NAT_4:9;
3271 = 11*297 + 4; hence not 11 divides 3271 by NAT_4:9;
3271 = 13*251 + 8; hence not 13 divides 3271 by NAT_4:9;
3271 = 17*192 + 7; hence not 17 divides 3271 by NAT_4:9;
3271 = 19*172 + 3; hence not 19 divides 3271 by NAT_4:9;
3271 = 23*142 + 5; hence not 23 divides 3271 by NAT_4:9;
3271 = 29*112 + 23; hence not 29 divides 3271 by NAT_4:9;
3271 = 31*105 + 16; hence not 31 divides 3271 by NAT_4:9;
3271 = 37*88 + 15; hence not 37 divides 3271 by NAT_4:9;
3271 = 41*79 + 32; hence not 41 divides 3271 by NAT_4:9;
3271 = 43*76 + 3; hence not 43 divides 3271 by NAT_4:9;
3271 = 47*69 + 28; hence not 47 divides 3271 by NAT_4:9;
3271 = 53*61 + 38; hence not 53 divides 3271 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3271 & n is prime
holds not n divides 3271 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 27
theorem
3299 is prime
proof
now
3299 = 2*1649 + 1; hence not 2 divides 3299 by NAT_4:9;
3299 = 3*1099 + 2; hence not 3 divides 3299 by NAT_4:9;
3299 = 5*659 + 4; hence not 5 divides 3299 by NAT_4:9;
3299 = 7*471 + 2; hence not 7 divides 3299 by NAT_4:9;
3299 = 11*299 + 10; hence not 11 divides 3299 by NAT_4:9;
3299 = 13*253 + 10; hence not 13 divides 3299 by NAT_4:9;
3299 = 17*194 + 1; hence not 17 divides 3299 by NAT_4:9;
3299 = 19*173 + 12; hence not 19 divides 3299 by NAT_4:9;
3299 = 23*143 + 10; hence not 23 divides 3299 by NAT_4:9;
3299 = 29*113 + 22; hence not 29 divides 3299 by NAT_4:9;
3299 = 31*106 + 13; hence not 31 divides 3299 by NAT_4:9;
3299 = 37*89 + 6; hence not 37 divides 3299 by NAT_4:9;
3299 = 41*80 + 19; hence not 41 divides 3299 by NAT_4:9;
3299 = 43*76 + 31; hence not 43 divides 3299 by NAT_4:9;
3299 = 47*70 + 9; hence not 47 divides 3299 by NAT_4:9;
3299 = 53*62 + 13; hence not 53 divides 3299 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3299 & n is prime
holds not n divides 3299 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3301 is prime
proof
now
3301 = 2*1650 + 1; hence not 2 divides 3301 by NAT_4:9;
3301 = 3*1100 + 1; hence not 3 divides 3301 by NAT_4:9;
3301 = 5*660 + 1; hence not 5 divides 3301 by NAT_4:9;
3301 = 7*471 + 4; hence not 7 divides 3301 by NAT_4:9;
3301 = 11*300 + 1; hence not 11 divides 3301 by NAT_4:9;
3301 = 13*253 + 12; hence not 13 divides 3301 by NAT_4:9;
3301 = 17*194 + 3; hence not 17 divides 3301 by NAT_4:9;
3301 = 19*173 + 14; hence not 19 divides 3301 by NAT_4:9;
3301 = 23*143 + 12; hence not 23 divides 3301 by NAT_4:9;
3301 = 29*113 + 24; hence not 29 divides 3301 by NAT_4:9;
3301 = 31*106 + 15; hence not 31 divides 3301 by NAT_4:9;
3301 = 37*89 + 8; hence not 37 divides 3301 by NAT_4:9;
3301 = 41*80 + 21; hence not 41 divides 3301 by NAT_4:9;
3301 = 43*76 + 33; hence not 43 divides 3301 by NAT_4:9;
3301 = 47*70 + 11; hence not 47 divides 3301 by NAT_4:9;
3301 = 53*62 + 15; hence not 53 divides 3301 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3301 & n is prime
holds not n divides 3301 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3307 is prime
proof
now
3307 = 2*1653 + 1; hence not 2 divides 3307 by NAT_4:9;
3307 = 3*1102 + 1; hence not 3 divides 3307 by NAT_4:9;
3307 = 5*661 + 2; hence not 5 divides 3307 by NAT_4:9;
3307 = 7*472 + 3; hence not 7 divides 3307 by NAT_4:9;
3307 = 11*300 + 7; hence not 11 divides 3307 by NAT_4:9;
3307 = 13*254 + 5; hence not 13 divides 3307 by NAT_4:9;
3307 = 17*194 + 9; hence not 17 divides 3307 by NAT_4:9;
3307 = 19*174 + 1; hence not 19 divides 3307 by NAT_4:9;
3307 = 23*143 + 18; hence not 23 divides 3307 by NAT_4:9;
3307 = 29*114 + 1; hence not 29 divides 3307 by NAT_4:9;
3307 = 31*106 + 21; hence not 31 divides 3307 by NAT_4:9;
3307 = 37*89 + 14; hence not 37 divides 3307 by NAT_4:9;
3307 = 41*80 + 27; hence not 41 divides 3307 by NAT_4:9;
3307 = 43*76 + 39; hence not 43 divides 3307 by NAT_4:9;
3307 = 47*70 + 17; hence not 47 divides 3307 by NAT_4:9;
3307 = 53*62 + 21; hence not 53 divides 3307 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3307 & n is prime
holds not n divides 3307 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3313 is prime
proof
now
3313 = 2*1656 + 1; hence not 2 divides 3313 by NAT_4:9;
3313 = 3*1104 + 1; hence not 3 divides 3313 by NAT_4:9;
3313 = 5*662 + 3; hence not 5 divides 3313 by NAT_4:9;
3313 = 7*473 + 2; hence not 7 divides 3313 by NAT_4:9;
3313 = 11*301 + 2; hence not 11 divides 3313 by NAT_4:9;
3313 = 13*254 + 11; hence not 13 divides 3313 by NAT_4:9;
3313 = 17*194 + 15; hence not 17 divides 3313 by NAT_4:9;
3313 = 19*174 + 7; hence not 19 divides 3313 by NAT_4:9;
3313 = 23*144 + 1; hence not 23 divides 3313 by NAT_4:9;
3313 = 29*114 + 7; hence not 29 divides 3313 by NAT_4:9;
3313 = 31*106 + 27; hence not 31 divides 3313 by NAT_4:9;
3313 = 37*89 + 20; hence not 37 divides 3313 by NAT_4:9;
3313 = 41*80 + 33; hence not 41 divides 3313 by NAT_4:9;
3313 = 43*77 + 2; hence not 43 divides 3313 by NAT_4:9;
3313 = 47*70 + 23; hence not 47 divides 3313 by NAT_4:9;
3313 = 53*62 + 27; hence not 53 divides 3313 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3313 & n is prime
holds not n divides 3313 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3319 is prime
proof
now
3319 = 2*1659 + 1; hence not 2 divides 3319 by NAT_4:9;
3319 = 3*1106 + 1; hence not 3 divides 3319 by NAT_4:9;
3319 = 5*663 + 4; hence not 5 divides 3319 by NAT_4:9;
3319 = 7*474 + 1; hence not 7 divides 3319 by NAT_4:9;
3319 = 11*301 + 8; hence not 11 divides 3319 by NAT_4:9;
3319 = 13*255 + 4; hence not 13 divides 3319 by NAT_4:9;
3319 = 17*195 + 4; hence not 17 divides 3319 by NAT_4:9;
3319 = 19*174 + 13; hence not 19 divides 3319 by NAT_4:9;
3319 = 23*144 + 7; hence not 23 divides 3319 by NAT_4:9;
3319 = 29*114 + 13; hence not 29 divides 3319 by NAT_4:9;
3319 = 31*107 + 2; hence not 31 divides 3319 by NAT_4:9;
3319 = 37*89 + 26; hence not 37 divides 3319 by NAT_4:9;
3319 = 41*80 + 39; hence not 41 divides 3319 by NAT_4:9;
3319 = 43*77 + 8; hence not 43 divides 3319 by NAT_4:9;
3319 = 47*70 + 29; hence not 47 divides 3319 by NAT_4:9;
3319 = 53*62 + 33; hence not 53 divides 3319 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3319 & n is prime
holds not n divides 3319 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3323 is prime
proof
now
3323 = 2*1661 + 1; hence not 2 divides 3323 by NAT_4:9;
3323 = 3*1107 + 2; hence not 3 divides 3323 by NAT_4:9;
3323 = 5*664 + 3; hence not 5 divides 3323 by NAT_4:9;
3323 = 7*474 + 5; hence not 7 divides 3323 by NAT_4:9;
3323 = 11*302 + 1; hence not 11 divides 3323 by NAT_4:9;
3323 = 13*255 + 8; hence not 13 divides 3323 by NAT_4:9;
3323 = 17*195 + 8; hence not 17 divides 3323 by NAT_4:9;
3323 = 19*174 + 17; hence not 19 divides 3323 by NAT_4:9;
3323 = 23*144 + 11; hence not 23 divides 3323 by NAT_4:9;
3323 = 29*114 + 17; hence not 29 divides 3323 by NAT_4:9;
3323 = 31*107 + 6; hence not 31 divides 3323 by NAT_4:9;
3323 = 37*89 + 30; hence not 37 divides 3323 by NAT_4:9;
3323 = 41*81 + 2; hence not 41 divides 3323 by NAT_4:9;
3323 = 43*77 + 12; hence not 43 divides 3323 by NAT_4:9;
3323 = 47*70 + 33; hence not 47 divides 3323 by NAT_4:9;
3323 = 53*62 + 37; hence not 53 divides 3323 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3323 & n is prime
holds not n divides 3323 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3329 is prime
proof
now
3329 = 2*1664 + 1; hence not 2 divides 3329 by NAT_4:9;
3329 = 3*1109 + 2; hence not 3 divides 3329 by NAT_4:9;
3329 = 5*665 + 4; hence not 5 divides 3329 by NAT_4:9;
3329 = 7*475 + 4; hence not 7 divides 3329 by NAT_4:9;
3329 = 11*302 + 7; hence not 11 divides 3329 by NAT_4:9;
3329 = 13*256 + 1; hence not 13 divides 3329 by NAT_4:9;
3329 = 17*195 + 14; hence not 17 divides 3329 by NAT_4:9;
3329 = 19*175 + 4; hence not 19 divides 3329 by NAT_4:9;
3329 = 23*144 + 17; hence not 23 divides 3329 by NAT_4:9;
3329 = 29*114 + 23; hence not 29 divides 3329 by NAT_4:9;
3329 = 31*107 + 12; hence not 31 divides 3329 by NAT_4:9;
3329 = 37*89 + 36; hence not 37 divides 3329 by NAT_4:9;
3329 = 41*81 + 8; hence not 41 divides 3329 by NAT_4:9;
3329 = 43*77 + 18; hence not 43 divides 3329 by NAT_4:9;
3329 = 47*70 + 39; hence not 47 divides 3329 by NAT_4:9;
3329 = 53*62 + 43; hence not 53 divides 3329 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3329 & n is prime
holds not n divides 3329 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3331 is prime
proof
now
3331 = 2*1665 + 1; hence not 2 divides 3331 by NAT_4:9;
3331 = 3*1110 + 1; hence not 3 divides 3331 by NAT_4:9;
3331 = 5*666 + 1; hence not 5 divides 3331 by NAT_4:9;
3331 = 7*475 + 6; hence not 7 divides 3331 by NAT_4:9;
3331 = 11*302 + 9; hence not 11 divides 3331 by NAT_4:9;
3331 = 13*256 + 3; hence not 13 divides 3331 by NAT_4:9;
3331 = 17*195 + 16; hence not 17 divides 3331 by NAT_4:9;
3331 = 19*175 + 6; hence not 19 divides 3331 by NAT_4:9;
3331 = 23*144 + 19; hence not 23 divides 3331 by NAT_4:9;
3331 = 29*114 + 25; hence not 29 divides 3331 by NAT_4:9;
3331 = 31*107 + 14; hence not 31 divides 3331 by NAT_4:9;
3331 = 37*90 + 1; hence not 37 divides 3331 by NAT_4:9;
3331 = 41*81 + 10; hence not 41 divides 3331 by NAT_4:9;
3331 = 43*77 + 20; hence not 43 divides 3331 by NAT_4:9;
3331 = 47*70 + 41; hence not 47 divides 3331 by NAT_4:9;
3331 = 53*62 + 45; hence not 53 divides 3331 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3331 & n is prime
holds not n divides 3331 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3343 is prime
proof
now
3343 = 2*1671 + 1; hence not 2 divides 3343 by NAT_4:9;
3343 = 3*1114 + 1; hence not 3 divides 3343 by NAT_4:9;
3343 = 5*668 + 3; hence not 5 divides 3343 by NAT_4:9;
3343 = 7*477 + 4; hence not 7 divides 3343 by NAT_4:9;
3343 = 11*303 + 10; hence not 11 divides 3343 by NAT_4:9;
3343 = 13*257 + 2; hence not 13 divides 3343 by NAT_4:9;
3343 = 17*196 + 11; hence not 17 divides 3343 by NAT_4:9;
3343 = 19*175 + 18; hence not 19 divides 3343 by NAT_4:9;
3343 = 23*145 + 8; hence not 23 divides 3343 by NAT_4:9;
3343 = 29*115 + 8; hence not 29 divides 3343 by NAT_4:9;
3343 = 31*107 + 26; hence not 31 divides 3343 by NAT_4:9;
3343 = 37*90 + 13; hence not 37 divides 3343 by NAT_4:9;
3343 = 41*81 + 22; hence not 41 divides 3343 by NAT_4:9;
3343 = 43*77 + 32; hence not 43 divides 3343 by NAT_4:9;
3343 = 47*71 + 6; hence not 47 divides 3343 by NAT_4:9;
3343 = 53*63 + 4; hence not 53 divides 3343 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3343 & n is prime
holds not n divides 3343 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3347 is prime
proof
now
3347 = 2*1673 + 1; hence not 2 divides 3347 by NAT_4:9;
3347 = 3*1115 + 2; hence not 3 divides 3347 by NAT_4:9;
3347 = 5*669 + 2; hence not 5 divides 3347 by NAT_4:9;
3347 = 7*478 + 1; hence not 7 divides 3347 by NAT_4:9;
3347 = 11*304 + 3; hence not 11 divides 3347 by NAT_4:9;
3347 = 13*257 + 6; hence not 13 divides 3347 by NAT_4:9;
3347 = 17*196 + 15; hence not 17 divides 3347 by NAT_4:9;
3347 = 19*176 + 3; hence not 19 divides 3347 by NAT_4:9;
3347 = 23*145 + 12; hence not 23 divides 3347 by NAT_4:9;
3347 = 29*115 + 12; hence not 29 divides 3347 by NAT_4:9;
3347 = 31*107 + 30; hence not 31 divides 3347 by NAT_4:9;
3347 = 37*90 + 17; hence not 37 divides 3347 by NAT_4:9;
3347 = 41*81 + 26; hence not 41 divides 3347 by NAT_4:9;
3347 = 43*77 + 36; hence not 43 divides 3347 by NAT_4:9;
3347 = 47*71 + 10; hence not 47 divides 3347 by NAT_4:9;
3347 = 53*63 + 8; hence not 53 divides 3347 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3347 & n is prime
holds not n divides 3347 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3359 is prime
proof
now
3359 = 2*1679 + 1; hence not 2 divides 3359 by NAT_4:9;
3359 = 3*1119 + 2; hence not 3 divides 3359 by NAT_4:9;
3359 = 5*671 + 4; hence not 5 divides 3359 by NAT_4:9;
3359 = 7*479 + 6; hence not 7 divides 3359 by NAT_4:9;
3359 = 11*305 + 4; hence not 11 divides 3359 by NAT_4:9;
3359 = 13*258 + 5; hence not 13 divides 3359 by NAT_4:9;
3359 = 17*197 + 10; hence not 17 divides 3359 by NAT_4:9;
3359 = 19*176 + 15; hence not 19 divides 3359 by NAT_4:9;
3359 = 23*146 + 1; hence not 23 divides 3359 by NAT_4:9;
3359 = 29*115 + 24; hence not 29 divides 3359 by NAT_4:9;
3359 = 31*108 + 11; hence not 31 divides 3359 by NAT_4:9;
3359 = 37*90 + 29; hence not 37 divides 3359 by NAT_4:9;
3359 = 41*81 + 38; hence not 41 divides 3359 by NAT_4:9;
3359 = 43*78 + 5; hence not 43 divides 3359 by NAT_4:9;
3359 = 47*71 + 22; hence not 47 divides 3359 by NAT_4:9;
3359 = 53*63 + 20; hence not 53 divides 3359 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3359 & n is prime
holds not n divides 3359 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3361 is prime
proof
now
3361 = 2*1680 + 1; hence not 2 divides 3361 by NAT_4:9;
3361 = 3*1120 + 1; hence not 3 divides 3361 by NAT_4:9;
3361 = 5*672 + 1; hence not 5 divides 3361 by NAT_4:9;
3361 = 7*480 + 1; hence not 7 divides 3361 by NAT_4:9;
3361 = 11*305 + 6; hence not 11 divides 3361 by NAT_4:9;
3361 = 13*258 + 7; hence not 13 divides 3361 by NAT_4:9;
3361 = 17*197 + 12; hence not 17 divides 3361 by NAT_4:9;
3361 = 19*176 + 17; hence not 19 divides 3361 by NAT_4:9;
3361 = 23*146 + 3; hence not 23 divides 3361 by NAT_4:9;
3361 = 29*115 + 26; hence not 29 divides 3361 by NAT_4:9;
3361 = 31*108 + 13; hence not 31 divides 3361 by NAT_4:9;
3361 = 37*90 + 31; hence not 37 divides 3361 by NAT_4:9;
3361 = 41*81 + 40; hence not 41 divides 3361 by NAT_4:9;
3361 = 43*78 + 7; hence not 43 divides 3361 by NAT_4:9;
3361 = 47*71 + 24; hence not 47 divides 3361 by NAT_4:9;
3361 = 53*63 + 22; hence not 53 divides 3361 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3361 & n is prime
holds not n divides 3361 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3371 is prime
proof
now
3371 = 2*1685 + 1; hence not 2 divides 3371 by NAT_4:9;
3371 = 3*1123 + 2; hence not 3 divides 3371 by NAT_4:9;
3371 = 5*674 + 1; hence not 5 divides 3371 by NAT_4:9;
3371 = 7*481 + 4; hence not 7 divides 3371 by NAT_4:9;
3371 = 11*306 + 5; hence not 11 divides 3371 by NAT_4:9;
3371 = 13*259 + 4; hence not 13 divides 3371 by NAT_4:9;
3371 = 17*198 + 5; hence not 17 divides 3371 by NAT_4:9;
3371 = 19*177 + 8; hence not 19 divides 3371 by NAT_4:9;
3371 = 23*146 + 13; hence not 23 divides 3371 by NAT_4:9;
3371 = 29*116 + 7; hence not 29 divides 3371 by NAT_4:9;
3371 = 31*108 + 23; hence not 31 divides 3371 by NAT_4:9;
3371 = 37*91 + 4; hence not 37 divides 3371 by NAT_4:9;
3371 = 41*82 + 9; hence not 41 divides 3371 by NAT_4:9;
3371 = 43*78 + 17; hence not 43 divides 3371 by NAT_4:9;
3371 = 47*71 + 34; hence not 47 divides 3371 by NAT_4:9;
3371 = 53*63 + 32; hence not 53 divides 3371 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3371 & n is prime
holds not n divides 3371 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3373 is prime
proof
now
3373 = 2*1686 + 1; hence not 2 divides 3373 by NAT_4:9;
3373 = 3*1124 + 1; hence not 3 divides 3373 by NAT_4:9;
3373 = 5*674 + 3; hence not 5 divides 3373 by NAT_4:9;
3373 = 7*481 + 6; hence not 7 divides 3373 by NAT_4:9;
3373 = 11*306 + 7; hence not 11 divides 3373 by NAT_4:9;
3373 = 13*259 + 6; hence not 13 divides 3373 by NAT_4:9;
3373 = 17*198 + 7; hence not 17 divides 3373 by NAT_4:9;
3373 = 19*177 + 10; hence not 19 divides 3373 by NAT_4:9;
3373 = 23*146 + 15; hence not 23 divides 3373 by NAT_4:9;
3373 = 29*116 + 9; hence not 29 divides 3373 by NAT_4:9;
3373 = 31*108 + 25; hence not 31 divides 3373 by NAT_4:9;
3373 = 37*91 + 6; hence not 37 divides 3373 by NAT_4:9;
3373 = 41*82 + 11; hence not 41 divides 3373 by NAT_4:9;
3373 = 43*78 + 19; hence not 43 divides 3373 by NAT_4:9;
3373 = 47*71 + 36; hence not 47 divides 3373 by NAT_4:9;
3373 = 53*63 + 34; hence not 53 divides 3373 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3373 & n is prime
holds not n divides 3373 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
3389 is prime
proof
now
3389 = 2*1694 + 1; hence not 2 divides 3389 by NAT_4:9;
3389 = 3*1129 + 2; hence not 3 divides 3389 by NAT_4:9;
3389 = 5*677 + 4; hence not 5 divides 3389 by NAT_4:9;
3389 = 7*484 + 1; hence not 7 divides 3389 by NAT_4:9;
3389 = 11*308 + 1; hence not 11 divides 3389 by NAT_4:9;
3389 = 13*260 + 9; hence not 13 divides 3389 by NAT_4:9;
3389 = 17*199 + 6; hence not 17 divides 3389 by NAT_4:9;
3389 = 19*178 + 7; hence not 19 divides 3389 by NAT_4:9;
3389 = 23*147 + 8; hence not 23 divides 3389 by NAT_4:9;
3389 = 29*116 + 25; hence not 29 divides 3389 by NAT_4:9;
3389 = 31*109 + 10; hence not 31 divides 3389 by NAT_4:9;
3389 = 37*91 + 22; hence not 37 divides 3389 by NAT_4:9;
3389 = 41*82 + 27; hence not 41 divides 3389 by NAT_4:9;
3389 = 43*78 + 35; hence not 43 divides 3389 by NAT_4:9;
3389 = 47*72 + 5; hence not 47 divides 3389 by NAT_4:9;
3389 = 53*63 + 50; hence not 53 divides 3389 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3389 & n is prime
holds not n divides 3389 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3391 is prime
proof
now
3391 = 2*1695 + 1; hence not 2 divides 3391 by NAT_4:9;
3391 = 3*1130 + 1; hence not 3 divides 3391 by NAT_4:9;
3391 = 5*678 + 1; hence not 5 divides 3391 by NAT_4:9;
3391 = 7*484 + 3; hence not 7 divides 3391 by NAT_4:9;
3391 = 11*308 + 3; hence not 11 divides 3391 by NAT_4:9;
3391 = 13*260 + 11; hence not 13 divides 3391 by NAT_4:9;
3391 = 17*199 + 8; hence not 17 divides 3391 by NAT_4:9;
3391 = 19*178 + 9; hence not 19 divides 3391 by NAT_4:9;
3391 = 23*147 + 10; hence not 23 divides 3391 by NAT_4:9;
3391 = 29*116 + 27; hence not 29 divides 3391 by NAT_4:9;
3391 = 31*109 + 12; hence not 31 divides 3391 by NAT_4:9;
3391 = 37*91 + 24; hence not 37 divides 3391 by NAT_4:9;
3391 = 41*82 + 29; hence not 41 divides 3391 by NAT_4:9;
3391 = 43*78 + 37; hence not 43 divides 3391 by NAT_4:9;
3391 = 47*72 + 7; hence not 47 divides 3391 by NAT_4:9;
3391 = 53*63 + 52; hence not 53 divides 3391 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3391 & n is prime
holds not n divides 3391 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
3407 is prime
proof
now
3407 = 2*1703 + 1; hence not 2 divides 3407 by NAT_4:9;
3407 = 3*1135 + 2; hence not 3 divides 3407 by NAT_4:9;
3407 = 5*681 + 2; hence not 5 divides 3407 by NAT_4:9;
3407 = 7*486 + 5; hence not 7 divides 3407 by NAT_4:9;
3407 = 11*309 + 8; hence not 11 divides 3407 by NAT_4:9;
3407 = 13*262 + 1; hence not 13 divides 3407 by NAT_4:9;
3407 = 17*200 + 7; hence not 17 divides 3407 by NAT_4:9;
3407 = 19*179 + 6; hence not 19 divides 3407 by NAT_4:9;
3407 = 23*148 + 3; hence not 23 divides 3407 by NAT_4:9;
3407 = 29*117 + 14; hence not 29 divides 3407 by NAT_4:9;
3407 = 31*109 + 28; hence not 31 divides 3407 by NAT_4:9;
3407 = 37*92 + 3; hence not 37 divides 3407 by NAT_4:9;
3407 = 41*83 + 4; hence not 41 divides 3407 by NAT_4:9;
3407 = 43*79 + 10; hence not 43 divides 3407 by NAT_4:9;
3407 = 47*72 + 23; hence not 47 divides 3407 by NAT_4:9;
3407 = 53*64 + 15; hence not 53 divides 3407 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3407 & n is prime
holds not n divides 3407 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3413 is prime
proof
now
3413 = 2*1706 + 1; hence not 2 divides 3413 by NAT_4:9;
3413 = 3*1137 + 2; hence not 3 divides 3413 by NAT_4:9;
3413 = 5*682 + 3; hence not 5 divides 3413 by NAT_4:9;
3413 = 7*487 + 4; hence not 7 divides 3413 by NAT_4:9;
3413 = 11*310 + 3; hence not 11 divides 3413 by NAT_4:9;
3413 = 13*262 + 7; hence not 13 divides 3413 by NAT_4:9;
3413 = 17*200 + 13; hence not 17 divides 3413 by NAT_4:9;
3413 = 19*179 + 12; hence not 19 divides 3413 by NAT_4:9;
3413 = 23*148 + 9; hence not 23 divides 3413 by NAT_4:9;
3413 = 29*117 + 20; hence not 29 divides 3413 by NAT_4:9;
3413 = 31*110 + 3; hence not 31 divides 3413 by NAT_4:9;
3413 = 37*92 + 9; hence not 37 divides 3413 by NAT_4:9;
3413 = 41*83 + 10; hence not 41 divides 3413 by NAT_4:9;
3413 = 43*79 + 16; hence not 43 divides 3413 by NAT_4:9;
3413 = 47*72 + 29; hence not 47 divides 3413 by NAT_4:9;
3413 = 53*64 + 21; hence not 53 divides 3413 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3413 & n is prime
holds not n divides 3413 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
3433 is prime
proof
now
3433 = 2*1716 + 1; hence not 2 divides 3433 by NAT_4:9;
3433 = 3*1144 + 1; hence not 3 divides 3433 by NAT_4:9;
3433 = 5*686 + 3; hence not 5 divides 3433 by NAT_4:9;
3433 = 7*490 + 3; hence not 7 divides 3433 by NAT_4:9;
3433 = 11*312 + 1; hence not 11 divides 3433 by NAT_4:9;
3433 = 13*264 + 1; hence not 13 divides 3433 by NAT_4:9;
3433 = 17*201 + 16; hence not 17 divides 3433 by NAT_4:9;
3433 = 19*180 + 13; hence not 19 divides 3433 by NAT_4:9;
3433 = 23*149 + 6; hence not 23 divides 3433 by NAT_4:9;
3433 = 29*118 + 11; hence not 29 divides 3433 by NAT_4:9;
3433 = 31*110 + 23; hence not 31 divides 3433 by NAT_4:9;
3433 = 37*92 + 29; hence not 37 divides 3433 by NAT_4:9;
3433 = 41*83 + 30; hence not 41 divides 3433 by NAT_4:9;
3433 = 43*79 + 36; hence not 43 divides 3433 by NAT_4:9;
3433 = 47*73 + 2; hence not 47 divides 3433 by NAT_4:9;
3433 = 53*64 + 41; hence not 53 divides 3433 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3433 & n is prime
holds not n divides 3433 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
3449 is prime
proof
now
3449 = 2*1724 + 1; hence not 2 divides 3449 by NAT_4:9;
3449 = 3*1149 + 2; hence not 3 divides 3449 by NAT_4:9;
3449 = 5*689 + 4; hence not 5 divides 3449 by NAT_4:9;
3449 = 7*492 + 5; hence not 7 divides 3449 by NAT_4:9;
3449 = 11*313 + 6; hence not 11 divides 3449 by NAT_4:9;
3449 = 13*265 + 4; hence not 13 divides 3449 by NAT_4:9;
3449 = 17*202 + 15; hence not 17 divides 3449 by NAT_4:9;
3449 = 19*181 + 10; hence not 19 divides 3449 by NAT_4:9;
3449 = 23*149 + 22; hence not 23 divides 3449 by NAT_4:9;
3449 = 29*118 + 27; hence not 29 divides 3449 by NAT_4:9;
3449 = 31*111 + 8; hence not 31 divides 3449 by NAT_4:9;
3449 = 37*93 + 8; hence not 37 divides 3449 by NAT_4:9;
3449 = 41*84 + 5; hence not 41 divides 3449 by NAT_4:9;
3449 = 43*80 + 9; hence not 43 divides 3449 by NAT_4:9;
3449 = 47*73 + 18; hence not 47 divides 3449 by NAT_4:9;
3449 = 53*65 + 4; hence not 53 divides 3449 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3449 & n is prime
holds not n divides 3449 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3457 is prime
proof
now
3457 = 2*1728 + 1; hence not 2 divides 3457 by NAT_4:9;
3457 = 3*1152 + 1; hence not 3 divides 3457 by NAT_4:9;
3457 = 5*691 + 2; hence not 5 divides 3457 by NAT_4:9;
3457 = 7*493 + 6; hence not 7 divides 3457 by NAT_4:9;
3457 = 11*314 + 3; hence not 11 divides 3457 by NAT_4:9;
3457 = 13*265 + 12; hence not 13 divides 3457 by NAT_4:9;
3457 = 17*203 + 6; hence not 17 divides 3457 by NAT_4:9;
3457 = 19*181 + 18; hence not 19 divides 3457 by NAT_4:9;
3457 = 23*150 + 7; hence not 23 divides 3457 by NAT_4:9;
3457 = 29*119 + 6; hence not 29 divides 3457 by NAT_4:9;
3457 = 31*111 + 16; hence not 31 divides 3457 by NAT_4:9;
3457 = 37*93 + 16; hence not 37 divides 3457 by NAT_4:9;
3457 = 41*84 + 13; hence not 41 divides 3457 by NAT_4:9;
3457 = 43*80 + 17; hence not 43 divides 3457 by NAT_4:9;
3457 = 47*73 + 26; hence not 47 divides 3457 by NAT_4:9;
3457 = 53*65 + 12; hence not 53 divides 3457 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3457 & n is prime
holds not n divides 3457 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3461 is prime
proof
now
3461 = 2*1730 + 1; hence not 2 divides 3461 by NAT_4:9;
3461 = 3*1153 + 2; hence not 3 divides 3461 by NAT_4:9;
3461 = 5*692 + 1; hence not 5 divides 3461 by NAT_4:9;
3461 = 7*494 + 3; hence not 7 divides 3461 by NAT_4:9;
3461 = 11*314 + 7; hence not 11 divides 3461 by NAT_4:9;
3461 = 13*266 + 3; hence not 13 divides 3461 by NAT_4:9;
3461 = 17*203 + 10; hence not 17 divides 3461 by NAT_4:9;
3461 = 19*182 + 3; hence not 19 divides 3461 by NAT_4:9;
3461 = 23*150 + 11; hence not 23 divides 3461 by NAT_4:9;
3461 = 29*119 + 10; hence not 29 divides 3461 by NAT_4:9;
3461 = 31*111 + 20; hence not 31 divides 3461 by NAT_4:9;
3461 = 37*93 + 20; hence not 37 divides 3461 by NAT_4:9;
3461 = 41*84 + 17; hence not 41 divides 3461 by NAT_4:9;
3461 = 43*80 + 21; hence not 43 divides 3461 by NAT_4:9;
3461 = 47*73 + 30; hence not 47 divides 3461 by NAT_4:9;
3461 = 53*65 + 16; hence not 53 divides 3461 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3461 & n is prime
holds not n divides 3461 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3463 is prime
proof
now
3463 = 2*1731 + 1; hence not 2 divides 3463 by NAT_4:9;
3463 = 3*1154 + 1; hence not 3 divides 3463 by NAT_4:9;
3463 = 5*692 + 3; hence not 5 divides 3463 by NAT_4:9;
3463 = 7*494 + 5; hence not 7 divides 3463 by NAT_4:9;
3463 = 11*314 + 9; hence not 11 divides 3463 by NAT_4:9;
3463 = 13*266 + 5; hence not 13 divides 3463 by NAT_4:9;
3463 = 17*203 + 12; hence not 17 divides 3463 by NAT_4:9;
3463 = 19*182 + 5; hence not 19 divides 3463 by NAT_4:9;
3463 = 23*150 + 13; hence not 23 divides 3463 by NAT_4:9;
3463 = 29*119 + 12; hence not 29 divides 3463 by NAT_4:9;
3463 = 31*111 + 22; hence not 31 divides 3463 by NAT_4:9;
3463 = 37*93 + 22; hence not 37 divides 3463 by NAT_4:9;
3463 = 41*84 + 19; hence not 41 divides 3463 by NAT_4:9;
3463 = 43*80 + 23; hence not 43 divides 3463 by NAT_4:9;
3463 = 47*73 + 32; hence not 47 divides 3463 by NAT_4:9;
3463 = 53*65 + 18; hence not 53 divides 3463 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3463 & n is prime
holds not n divides 3463 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3467 is prime
proof
now
3467 = 2*1733 + 1; hence not 2 divides 3467 by NAT_4:9;
3467 = 3*1155 + 2; hence not 3 divides 3467 by NAT_4:9;
3467 = 5*693 + 2; hence not 5 divides 3467 by NAT_4:9;
3467 = 7*495 + 2; hence not 7 divides 3467 by NAT_4:9;
3467 = 11*315 + 2; hence not 11 divides 3467 by NAT_4:9;
3467 = 13*266 + 9; hence not 13 divides 3467 by NAT_4:9;
3467 = 17*203 + 16; hence not 17 divides 3467 by NAT_4:9;
3467 = 19*182 + 9; hence not 19 divides 3467 by NAT_4:9;
3467 = 23*150 + 17; hence not 23 divides 3467 by NAT_4:9;
3467 = 29*119 + 16; hence not 29 divides 3467 by NAT_4:9;
3467 = 31*111 + 26; hence not 31 divides 3467 by NAT_4:9;
3467 = 37*93 + 26; hence not 37 divides 3467 by NAT_4:9;
3467 = 41*84 + 23; hence not 41 divides 3467 by NAT_4:9;
3467 = 43*80 + 27; hence not 43 divides 3467 by NAT_4:9;
3467 = 47*73 + 36; hence not 47 divides 3467 by NAT_4:9;
3467 = 53*65 + 22; hence not 53 divides 3467 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3467 & n is prime
holds not n divides 3467 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3469 is prime
proof
now
3469 = 2*1734 + 1; hence not 2 divides 3469 by NAT_4:9;
3469 = 3*1156 + 1; hence not 3 divides 3469 by NAT_4:9;
3469 = 5*693 + 4; hence not 5 divides 3469 by NAT_4:9;
3469 = 7*495 + 4; hence not 7 divides 3469 by NAT_4:9;
3469 = 11*315 + 4; hence not 11 divides 3469 by NAT_4:9;
3469 = 13*266 + 11; hence not 13 divides 3469 by NAT_4:9;
3469 = 17*204 + 1; hence not 17 divides 3469 by NAT_4:9;
3469 = 19*182 + 11; hence not 19 divides 3469 by NAT_4:9;
3469 = 23*150 + 19; hence not 23 divides 3469 by NAT_4:9;
3469 = 29*119 + 18; hence not 29 divides 3469 by NAT_4:9;
3469 = 31*111 + 28; hence not 31 divides 3469 by NAT_4:9;
3469 = 37*93 + 28; hence not 37 divides 3469 by NAT_4:9;
3469 = 41*84 + 25; hence not 41 divides 3469 by NAT_4:9;
3469 = 43*80 + 29; hence not 43 divides 3469 by NAT_4:9;
3469 = 47*73 + 38; hence not 47 divides 3469 by NAT_4:9;
3469 = 53*65 + 24; hence not 53 divides 3469 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3469 & n is prime
holds not n divides 3469 by XPRIMET1:32;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
3491 is prime
proof
now
3491 = 2*1745 + 1; hence not 2 divides 3491 by NAT_4:9;
3491 = 3*1163 + 2; hence not 3 divides 3491 by NAT_4:9;
3491 = 5*698 + 1; hence not 5 divides 3491 by NAT_4:9;
3491 = 7*498 + 5; hence not 7 divides 3491 by NAT_4:9;
3491 = 11*317 + 4; hence not 11 divides 3491 by NAT_4:9;
3491 = 13*268 + 7; hence not 13 divides 3491 by NAT_4:9;
3491 = 17*205 + 6; hence not 17 divides 3491 by NAT_4:9;
3491 = 19*183 + 14; hence not 19 divides 3491 by NAT_4:9;
3491 = 23*151 + 18; hence not 23 divides 3491 by NAT_4:9;
3491 = 29*120 + 11; hence not 29 divides 3491 by NAT_4:9;
3491 = 31*112 + 19; hence not 31 divides 3491 by NAT_4:9;
3491 = 37*94 + 13; hence not 37 divides 3491 by NAT_4:9;
3491 = 41*85 + 6; hence not 41 divides 3491 by NAT_4:9;
3491 = 43*81 + 8; hence not 43 divides 3491 by NAT_4:9;
3491 = 47*74 + 13; hence not 47 divides 3491 by NAT_4:9;
3491 = 53*65 + 46; hence not 53 divides 3491 by NAT_4:9;
3491 = 59*59 + 10; hence not 59 divides 3491 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3491 & n is prime
holds not n divides 3491 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3499 is prime
proof
now
3499 = 2*1749 + 1; hence not 2 divides 3499 by NAT_4:9;
3499 = 3*1166 + 1; hence not 3 divides 3499 by NAT_4:9;
3499 = 5*699 + 4; hence not 5 divides 3499 by NAT_4:9;
3499 = 7*499 + 6; hence not 7 divides 3499 by NAT_4:9;
3499 = 11*318 + 1; hence not 11 divides 3499 by NAT_4:9;
3499 = 13*269 + 2; hence not 13 divides 3499 by NAT_4:9;
3499 = 17*205 + 14; hence not 17 divides 3499 by NAT_4:9;
3499 = 19*184 + 3; hence not 19 divides 3499 by NAT_4:9;
3499 = 23*152 + 3; hence not 23 divides 3499 by NAT_4:9;
3499 = 29*120 + 19; hence not 29 divides 3499 by NAT_4:9;
3499 = 31*112 + 27; hence not 31 divides 3499 by NAT_4:9;
3499 = 37*94 + 21; hence not 37 divides 3499 by NAT_4:9;
3499 = 41*85 + 14; hence not 41 divides 3499 by NAT_4:9;
3499 = 43*81 + 16; hence not 43 divides 3499 by NAT_4:9;
3499 = 47*74 + 21; hence not 47 divides 3499 by NAT_4:9;
3499 = 53*66 + 1; hence not 53 divides 3499 by NAT_4:9;
3499 = 59*59 + 18; hence not 59 divides 3499 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3499 & n is prime
holds not n divides 3499 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3511 is prime
proof
now
3511 = 2*1755 + 1; hence not 2 divides 3511 by NAT_4:9;
3511 = 3*1170 + 1; hence not 3 divides 3511 by NAT_4:9;
3511 = 5*702 + 1; hence not 5 divides 3511 by NAT_4:9;
3511 = 7*501 + 4; hence not 7 divides 3511 by NAT_4:9;
3511 = 11*319 + 2; hence not 11 divides 3511 by NAT_4:9;
3511 = 13*270 + 1; hence not 13 divides 3511 by NAT_4:9;
3511 = 17*206 + 9; hence not 17 divides 3511 by NAT_4:9;
3511 = 19*184 + 15; hence not 19 divides 3511 by NAT_4:9;
3511 = 23*152 + 15; hence not 23 divides 3511 by NAT_4:9;
3511 = 29*121 + 2; hence not 29 divides 3511 by NAT_4:9;
3511 = 31*113 + 8; hence not 31 divides 3511 by NAT_4:9;
3511 = 37*94 + 33; hence not 37 divides 3511 by NAT_4:9;
3511 = 41*85 + 26; hence not 41 divides 3511 by NAT_4:9;
3511 = 43*81 + 28; hence not 43 divides 3511 by NAT_4:9;
3511 = 47*74 + 33; hence not 47 divides 3511 by NAT_4:9;
3511 = 53*66 + 13; hence not 53 divides 3511 by NAT_4:9;
3511 = 59*59 + 30; hence not 59 divides 3511 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3511 & n is prime
holds not n divides 3511 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3517 is prime
proof
now
3517 = 2*1758 + 1; hence not 2 divides 3517 by NAT_4:9;
3517 = 3*1172 + 1; hence not 3 divides 3517 by NAT_4:9;
3517 = 5*703 + 2; hence not 5 divides 3517 by NAT_4:9;
3517 = 7*502 + 3; hence not 7 divides 3517 by NAT_4:9;
3517 = 11*319 + 8; hence not 11 divides 3517 by NAT_4:9;
3517 = 13*270 + 7; hence not 13 divides 3517 by NAT_4:9;
3517 = 17*206 + 15; hence not 17 divides 3517 by NAT_4:9;
3517 = 19*185 + 2; hence not 19 divides 3517 by NAT_4:9;
3517 = 23*152 + 21; hence not 23 divides 3517 by NAT_4:9;
3517 = 29*121 + 8; hence not 29 divides 3517 by NAT_4:9;
3517 = 31*113 + 14; hence not 31 divides 3517 by NAT_4:9;
3517 = 37*95 + 2; hence not 37 divides 3517 by NAT_4:9;
3517 = 41*85 + 32; hence not 41 divides 3517 by NAT_4:9;
3517 = 43*81 + 34; hence not 43 divides 3517 by NAT_4:9;
3517 = 47*74 + 39; hence not 47 divides 3517 by NAT_4:9;
3517 = 53*66 + 19; hence not 53 divides 3517 by NAT_4:9;
3517 = 59*59 + 36; hence not 59 divides 3517 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3517 & n is prime
holds not n divides 3517 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3527 is prime
proof
now
3527 = 2*1763 + 1; hence not 2 divides 3527 by NAT_4:9;
3527 = 3*1175 + 2; hence not 3 divides 3527 by NAT_4:9;
3527 = 5*705 + 2; hence not 5 divides 3527 by NAT_4:9;
3527 = 7*503 + 6; hence not 7 divides 3527 by NAT_4:9;
3527 = 11*320 + 7; hence not 11 divides 3527 by NAT_4:9;
3527 = 13*271 + 4; hence not 13 divides 3527 by NAT_4:9;
3527 = 17*207 + 8; hence not 17 divides 3527 by NAT_4:9;
3527 = 19*185 + 12; hence not 19 divides 3527 by NAT_4:9;
3527 = 23*153 + 8; hence not 23 divides 3527 by NAT_4:9;
3527 = 29*121 + 18; hence not 29 divides 3527 by NAT_4:9;
3527 = 31*113 + 24; hence not 31 divides 3527 by NAT_4:9;
3527 = 37*95 + 12; hence not 37 divides 3527 by NAT_4:9;
3527 = 41*86 + 1; hence not 41 divides 3527 by NAT_4:9;
3527 = 43*82 + 1; hence not 43 divides 3527 by NAT_4:9;
3527 = 47*75 + 2; hence not 47 divides 3527 by NAT_4:9;
3527 = 53*66 + 29; hence not 53 divides 3527 by NAT_4:9;
3527 = 59*59 + 46; hence not 59 divides 3527 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3527 & n is prime
holds not n divides 3527 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3529 is prime
proof
now
3529 = 2*1764 + 1; hence not 2 divides 3529 by NAT_4:9;
3529 = 3*1176 + 1; hence not 3 divides 3529 by NAT_4:9;
3529 = 5*705 + 4; hence not 5 divides 3529 by NAT_4:9;
3529 = 7*504 + 1; hence not 7 divides 3529 by NAT_4:9;
3529 = 11*320 + 9; hence not 11 divides 3529 by NAT_4:9;
3529 = 13*271 + 6; hence not 13 divides 3529 by NAT_4:9;
3529 = 17*207 + 10; hence not 17 divides 3529 by NAT_4:9;
3529 = 19*185 + 14; hence not 19 divides 3529 by NAT_4:9;
3529 = 23*153 + 10; hence not 23 divides 3529 by NAT_4:9;
3529 = 29*121 + 20; hence not 29 divides 3529 by NAT_4:9;
3529 = 31*113 + 26; hence not 31 divides 3529 by NAT_4:9;
3529 = 37*95 + 14; hence not 37 divides 3529 by NAT_4:9;
3529 = 41*86 + 3; hence not 41 divides 3529 by NAT_4:9;
3529 = 43*82 + 3; hence not 43 divides 3529 by NAT_4:9;
3529 = 47*75 + 4; hence not 47 divides 3529 by NAT_4:9;
3529 = 53*66 + 31; hence not 53 divides 3529 by NAT_4:9;
3529 = 59*59 + 48; hence not 59 divides 3529 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3529 & n is prime
holds not n divides 3529 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3533 is prime
proof
now
3533 = 2*1766 + 1; hence not 2 divides 3533 by NAT_4:9;
3533 = 3*1177 + 2; hence not 3 divides 3533 by NAT_4:9;
3533 = 5*706 + 3; hence not 5 divides 3533 by NAT_4:9;
3533 = 7*504 + 5; hence not 7 divides 3533 by NAT_4:9;
3533 = 11*321 + 2; hence not 11 divides 3533 by NAT_4:9;
3533 = 13*271 + 10; hence not 13 divides 3533 by NAT_4:9;
3533 = 17*207 + 14; hence not 17 divides 3533 by NAT_4:9;
3533 = 19*185 + 18; hence not 19 divides 3533 by NAT_4:9;
3533 = 23*153 + 14; hence not 23 divides 3533 by NAT_4:9;
3533 = 29*121 + 24; hence not 29 divides 3533 by NAT_4:9;
3533 = 31*113 + 30; hence not 31 divides 3533 by NAT_4:9;
3533 = 37*95 + 18; hence not 37 divides 3533 by NAT_4:9;
3533 = 41*86 + 7; hence not 41 divides 3533 by NAT_4:9;
3533 = 43*82 + 7; hence not 43 divides 3533 by NAT_4:9;
3533 = 47*75 + 8; hence not 47 divides 3533 by NAT_4:9;
3533 = 53*66 + 35; hence not 53 divides 3533 by NAT_4:9;
3533 = 59*59 + 52; hence not 59 divides 3533 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3533 & n is prime
holds not n divides 3533 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3539 is prime
proof
now
3539 = 2*1769 + 1; hence not 2 divides 3539 by NAT_4:9;
3539 = 3*1179 + 2; hence not 3 divides 3539 by NAT_4:9;
3539 = 5*707 + 4; hence not 5 divides 3539 by NAT_4:9;
3539 = 7*505 + 4; hence not 7 divides 3539 by NAT_4:9;
3539 = 11*321 + 8; hence not 11 divides 3539 by NAT_4:9;
3539 = 13*272 + 3; hence not 13 divides 3539 by NAT_4:9;
3539 = 17*208 + 3; hence not 17 divides 3539 by NAT_4:9;
3539 = 19*186 + 5; hence not 19 divides 3539 by NAT_4:9;
3539 = 23*153 + 20; hence not 23 divides 3539 by NAT_4:9;
3539 = 29*122 + 1; hence not 29 divides 3539 by NAT_4:9;
3539 = 31*114 + 5; hence not 31 divides 3539 by NAT_4:9;
3539 = 37*95 + 24; hence not 37 divides 3539 by NAT_4:9;
3539 = 41*86 + 13; hence not 41 divides 3539 by NAT_4:9;
3539 = 43*82 + 13; hence not 43 divides 3539 by NAT_4:9;
3539 = 47*75 + 14; hence not 47 divides 3539 by NAT_4:9;
3539 = 53*66 + 41; hence not 53 divides 3539 by NAT_4:9;
3539 = 59*59 + 58; hence not 59 divides 3539 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3539 & n is prime
holds not n divides 3539 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3541 is prime
proof
now
3541 = 2*1770 + 1; hence not 2 divides 3541 by NAT_4:9;
3541 = 3*1180 + 1; hence not 3 divides 3541 by NAT_4:9;
3541 = 5*708 + 1; hence not 5 divides 3541 by NAT_4:9;
3541 = 7*505 + 6; hence not 7 divides 3541 by NAT_4:9;
3541 = 11*321 + 10; hence not 11 divides 3541 by NAT_4:9;
3541 = 13*272 + 5; hence not 13 divides 3541 by NAT_4:9;
3541 = 17*208 + 5; hence not 17 divides 3541 by NAT_4:9;
3541 = 19*186 + 7; hence not 19 divides 3541 by NAT_4:9;
3541 = 23*153 + 22; hence not 23 divides 3541 by NAT_4:9;
3541 = 29*122 + 3; hence not 29 divides 3541 by NAT_4:9;
3541 = 31*114 + 7; hence not 31 divides 3541 by NAT_4:9;
3541 = 37*95 + 26; hence not 37 divides 3541 by NAT_4:9;
3541 = 41*86 + 15; hence not 41 divides 3541 by NAT_4:9;
3541 = 43*82 + 15; hence not 43 divides 3541 by NAT_4:9;
3541 = 47*75 + 16; hence not 47 divides 3541 by NAT_4:9;
3541 = 53*66 + 43; hence not 53 divides 3541 by NAT_4:9;
3541 = 59*60 + 1; hence not 59 divides 3541 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3541 & n is prime
holds not n divides 3541 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3547 is prime
proof
now
3547 = 2*1773 + 1; hence not 2 divides 3547 by NAT_4:9;
3547 = 3*1182 + 1; hence not 3 divides 3547 by NAT_4:9;
3547 = 5*709 + 2; hence not 5 divides 3547 by NAT_4:9;
3547 = 7*506 + 5; hence not 7 divides 3547 by NAT_4:9;
3547 = 11*322 + 5; hence not 11 divides 3547 by NAT_4:9;
3547 = 13*272 + 11; hence not 13 divides 3547 by NAT_4:9;
3547 = 17*208 + 11; hence not 17 divides 3547 by NAT_4:9;
3547 = 19*186 + 13; hence not 19 divides 3547 by NAT_4:9;
3547 = 23*154 + 5; hence not 23 divides 3547 by NAT_4:9;
3547 = 29*122 + 9; hence not 29 divides 3547 by NAT_4:9;
3547 = 31*114 + 13; hence not 31 divides 3547 by NAT_4:9;
3547 = 37*95 + 32; hence not 37 divides 3547 by NAT_4:9;
3547 = 41*86 + 21; hence not 41 divides 3547 by NAT_4:9;
3547 = 43*82 + 21; hence not 43 divides 3547 by NAT_4:9;
3547 = 47*75 + 22; hence not 47 divides 3547 by NAT_4:9;
3547 = 53*66 + 49; hence not 53 divides 3547 by NAT_4:9;
3547 = 59*60 + 7; hence not 59 divides 3547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3547 & n is prime
holds not n divides 3547 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3557 is prime
proof
now
3557 = 2*1778 + 1; hence not 2 divides 3557 by NAT_4:9;
3557 = 3*1185 + 2; hence not 3 divides 3557 by NAT_4:9;
3557 = 5*711 + 2; hence not 5 divides 3557 by NAT_4:9;
3557 = 7*508 + 1; hence not 7 divides 3557 by NAT_4:9;
3557 = 11*323 + 4; hence not 11 divides 3557 by NAT_4:9;
3557 = 13*273 + 8; hence not 13 divides 3557 by NAT_4:9;
3557 = 17*209 + 4; hence not 17 divides 3557 by NAT_4:9;
3557 = 19*187 + 4; hence not 19 divides 3557 by NAT_4:9;
3557 = 23*154 + 15; hence not 23 divides 3557 by NAT_4:9;
3557 = 29*122 + 19; hence not 29 divides 3557 by NAT_4:9;
3557 = 31*114 + 23; hence not 31 divides 3557 by NAT_4:9;
3557 = 37*96 + 5; hence not 37 divides 3557 by NAT_4:9;
3557 = 41*86 + 31; hence not 41 divides 3557 by NAT_4:9;
3557 = 43*82 + 31; hence not 43 divides 3557 by NAT_4:9;
3557 = 47*75 + 32; hence not 47 divides 3557 by NAT_4:9;
3557 = 53*67 + 6; hence not 53 divides 3557 by NAT_4:9;
3557 = 59*60 + 17; hence not 59 divides 3557 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3557 & n is prime
holds not n divides 3557 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3559 is prime
proof
now
3559 = 2*1779 + 1; hence not 2 divides 3559 by NAT_4:9;
3559 = 3*1186 + 1; hence not 3 divides 3559 by NAT_4:9;
3559 = 5*711 + 4; hence not 5 divides 3559 by NAT_4:9;
3559 = 7*508 + 3; hence not 7 divides 3559 by NAT_4:9;
3559 = 11*323 + 6; hence not 11 divides 3559 by NAT_4:9;
3559 = 13*273 + 10; hence not 13 divides 3559 by NAT_4:9;
3559 = 17*209 + 6; hence not 17 divides 3559 by NAT_4:9;
3559 = 19*187 + 6; hence not 19 divides 3559 by NAT_4:9;
3559 = 23*154 + 17; hence not 23 divides 3559 by NAT_4:9;
3559 = 29*122 + 21; hence not 29 divides 3559 by NAT_4:9;
3559 = 31*114 + 25; hence not 31 divides 3559 by NAT_4:9;
3559 = 37*96 + 7; hence not 37 divides 3559 by NAT_4:9;
3559 = 41*86 + 33; hence not 41 divides 3559 by NAT_4:9;
3559 = 43*82 + 33; hence not 43 divides 3559 by NAT_4:9;
3559 = 47*75 + 34; hence not 47 divides 3559 by NAT_4:9;
3559 = 53*67 + 8; hence not 53 divides 3559 by NAT_4:9;
3559 = 59*60 + 19; hence not 59 divides 3559 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3559 & n is prime
holds not n divides 3559 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3571 is prime
proof
now
3571 = 2*1785 + 1; hence not 2 divides 3571 by NAT_4:9;
3571 = 3*1190 + 1; hence not 3 divides 3571 by NAT_4:9;
3571 = 5*714 + 1; hence not 5 divides 3571 by NAT_4:9;
3571 = 7*510 + 1; hence not 7 divides 3571 by NAT_4:9;
3571 = 11*324 + 7; hence not 11 divides 3571 by NAT_4:9;
3571 = 13*274 + 9; hence not 13 divides 3571 by NAT_4:9;
3571 = 17*210 + 1; hence not 17 divides 3571 by NAT_4:9;
3571 = 19*187 + 18; hence not 19 divides 3571 by NAT_4:9;
3571 = 23*155 + 6; hence not 23 divides 3571 by NAT_4:9;
3571 = 29*123 + 4; hence not 29 divides 3571 by NAT_4:9;
3571 = 31*115 + 6; hence not 31 divides 3571 by NAT_4:9;
3571 = 37*96 + 19; hence not 37 divides 3571 by NAT_4:9;
3571 = 41*87 + 4; hence not 41 divides 3571 by NAT_4:9;
3571 = 43*83 + 2; hence not 43 divides 3571 by NAT_4:9;
3571 = 47*75 + 46; hence not 47 divides 3571 by NAT_4:9;
3571 = 53*67 + 20; hence not 53 divides 3571 by NAT_4:9;
3571 = 59*60 + 31; hence not 59 divides 3571 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3571 & n is prime
holds not n divides 3571 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3581 is prime
proof
now
3581 = 2*1790 + 1; hence not 2 divides 3581 by NAT_4:9;
3581 = 3*1193 + 2; hence not 3 divides 3581 by NAT_4:9;
3581 = 5*716 + 1; hence not 5 divides 3581 by NAT_4:9;
3581 = 7*511 + 4; hence not 7 divides 3581 by NAT_4:9;
3581 = 11*325 + 6; hence not 11 divides 3581 by NAT_4:9;
3581 = 13*275 + 6; hence not 13 divides 3581 by NAT_4:9;
3581 = 17*210 + 11; hence not 17 divides 3581 by NAT_4:9;
3581 = 19*188 + 9; hence not 19 divides 3581 by NAT_4:9;
3581 = 23*155 + 16; hence not 23 divides 3581 by NAT_4:9;
3581 = 29*123 + 14; hence not 29 divides 3581 by NAT_4:9;
3581 = 31*115 + 16; hence not 31 divides 3581 by NAT_4:9;
3581 = 37*96 + 29; hence not 37 divides 3581 by NAT_4:9;
3581 = 41*87 + 14; hence not 41 divides 3581 by NAT_4:9;
3581 = 43*83 + 12; hence not 43 divides 3581 by NAT_4:9;
3581 = 47*76 + 9; hence not 47 divides 3581 by NAT_4:9;
3581 = 53*67 + 30; hence not 53 divides 3581 by NAT_4:9;
3581 = 59*60 + 41; hence not 59 divides 3581 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3581 & n is prime
holds not n divides 3581 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3583 is prime
proof
now
3583 = 2*1791 + 1; hence not 2 divides 3583 by NAT_4:9;
3583 = 3*1194 + 1; hence not 3 divides 3583 by NAT_4:9;
3583 = 5*716 + 3; hence not 5 divides 3583 by NAT_4:9;
3583 = 7*511 + 6; hence not 7 divides 3583 by NAT_4:9;
3583 = 11*325 + 8; hence not 11 divides 3583 by NAT_4:9;
3583 = 13*275 + 8; hence not 13 divides 3583 by NAT_4:9;
3583 = 17*210 + 13; hence not 17 divides 3583 by NAT_4:9;
3583 = 19*188 + 11; hence not 19 divides 3583 by NAT_4:9;
3583 = 23*155 + 18; hence not 23 divides 3583 by NAT_4:9;
3583 = 29*123 + 16; hence not 29 divides 3583 by NAT_4:9;
3583 = 31*115 + 18; hence not 31 divides 3583 by NAT_4:9;
3583 = 37*96 + 31; hence not 37 divides 3583 by NAT_4:9;
3583 = 41*87 + 16; hence not 41 divides 3583 by NAT_4:9;
3583 = 43*83 + 14; hence not 43 divides 3583 by NAT_4:9;
3583 = 47*76 + 11; hence not 47 divides 3583 by NAT_4:9;
3583 = 53*67 + 32; hence not 53 divides 3583 by NAT_4:9;
3583 = 59*60 + 43; hence not 59 divides 3583 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3583 & n is prime
holds not n divides 3583 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3593 is prime
proof
now
3593 = 2*1796 + 1; hence not 2 divides 3593 by NAT_4:9;
3593 = 3*1197 + 2; hence not 3 divides 3593 by NAT_4:9;
3593 = 5*718 + 3; hence not 5 divides 3593 by NAT_4:9;
3593 = 7*513 + 2; hence not 7 divides 3593 by NAT_4:9;
3593 = 11*326 + 7; hence not 11 divides 3593 by NAT_4:9;
3593 = 13*276 + 5; hence not 13 divides 3593 by NAT_4:9;
3593 = 17*211 + 6; hence not 17 divides 3593 by NAT_4:9;
3593 = 19*189 + 2; hence not 19 divides 3593 by NAT_4:9;
3593 = 23*156 + 5; hence not 23 divides 3593 by NAT_4:9;
3593 = 29*123 + 26; hence not 29 divides 3593 by NAT_4:9;
3593 = 31*115 + 28; hence not 31 divides 3593 by NAT_4:9;
3593 = 37*97 + 4; hence not 37 divides 3593 by NAT_4:9;
3593 = 41*87 + 26; hence not 41 divides 3593 by NAT_4:9;
3593 = 43*83 + 24; hence not 43 divides 3593 by NAT_4:9;
3593 = 47*76 + 21; hence not 47 divides 3593 by NAT_4:9;
3593 = 53*67 + 42; hence not 53 divides 3593 by NAT_4:9;
3593 = 59*60 + 53; hence not 59 divides 3593 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3593 & n is prime
holds not n divides 3593 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3607 is prime
proof
now
3607 = 2*1803 + 1; hence not 2 divides 3607 by NAT_4:9;
3607 = 3*1202 + 1; hence not 3 divides 3607 by NAT_4:9;
3607 = 5*721 + 2; hence not 5 divides 3607 by NAT_4:9;
3607 = 7*515 + 2; hence not 7 divides 3607 by NAT_4:9;
3607 = 11*327 + 10; hence not 11 divides 3607 by NAT_4:9;
3607 = 13*277 + 6; hence not 13 divides 3607 by NAT_4:9;
3607 = 17*212 + 3; hence not 17 divides 3607 by NAT_4:9;
3607 = 19*189 + 16; hence not 19 divides 3607 by NAT_4:9;
3607 = 23*156 + 19; hence not 23 divides 3607 by NAT_4:9;
3607 = 29*124 + 11; hence not 29 divides 3607 by NAT_4:9;
3607 = 31*116 + 11; hence not 31 divides 3607 by NAT_4:9;
3607 = 37*97 + 18; hence not 37 divides 3607 by NAT_4:9;
3607 = 41*87 + 40; hence not 41 divides 3607 by NAT_4:9;
3607 = 43*83 + 38; hence not 43 divides 3607 by NAT_4:9;
3607 = 47*76 + 35; hence not 47 divides 3607 by NAT_4:9;
3607 = 53*68 + 3; hence not 53 divides 3607 by NAT_4:9;
3607 = 59*61 + 8; hence not 59 divides 3607 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3607 & n is prime
holds not n divides 3607 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3613 is prime
proof
now
3613 = 2*1806 + 1; hence not 2 divides 3613 by NAT_4:9;
3613 = 3*1204 + 1; hence not 3 divides 3613 by NAT_4:9;
3613 = 5*722 + 3; hence not 5 divides 3613 by NAT_4:9;
3613 = 7*516 + 1; hence not 7 divides 3613 by NAT_4:9;
3613 = 11*328 + 5; hence not 11 divides 3613 by NAT_4:9;
3613 = 13*277 + 12; hence not 13 divides 3613 by NAT_4:9;
3613 = 17*212 + 9; hence not 17 divides 3613 by NAT_4:9;
3613 = 19*190 + 3; hence not 19 divides 3613 by NAT_4:9;
3613 = 23*157 + 2; hence not 23 divides 3613 by NAT_4:9;
3613 = 29*124 + 17; hence not 29 divides 3613 by NAT_4:9;
3613 = 31*116 + 17; hence not 31 divides 3613 by NAT_4:9;
3613 = 37*97 + 24; hence not 37 divides 3613 by NAT_4:9;
3613 = 41*88 + 5; hence not 41 divides 3613 by NAT_4:9;
3613 = 43*84 + 1; hence not 43 divides 3613 by NAT_4:9;
3613 = 47*76 + 41; hence not 47 divides 3613 by NAT_4:9;
3613 = 53*68 + 9; hence not 53 divides 3613 by NAT_4:9;
3613 = 59*61 + 14; hence not 59 divides 3613 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3613 & n is prime
holds not n divides 3613 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3617 is prime
proof
now
3617 = 2*1808 + 1; hence not 2 divides 3617 by NAT_4:9;
3617 = 3*1205 + 2; hence not 3 divides 3617 by NAT_4:9;
3617 = 5*723 + 2; hence not 5 divides 3617 by NAT_4:9;
3617 = 7*516 + 5; hence not 7 divides 3617 by NAT_4:9;
3617 = 11*328 + 9; hence not 11 divides 3617 by NAT_4:9;
3617 = 13*278 + 3; hence not 13 divides 3617 by NAT_4:9;
3617 = 17*212 + 13; hence not 17 divides 3617 by NAT_4:9;
3617 = 19*190 + 7; hence not 19 divides 3617 by NAT_4:9;
3617 = 23*157 + 6; hence not 23 divides 3617 by NAT_4:9;
3617 = 29*124 + 21; hence not 29 divides 3617 by NAT_4:9;
3617 = 31*116 + 21; hence not 31 divides 3617 by NAT_4:9;
3617 = 37*97 + 28; hence not 37 divides 3617 by NAT_4:9;
3617 = 41*88 + 9; hence not 41 divides 3617 by NAT_4:9;
3617 = 43*84 + 5; hence not 43 divides 3617 by NAT_4:9;
3617 = 47*76 + 45; hence not 47 divides 3617 by NAT_4:9;
3617 = 53*68 + 13; hence not 53 divides 3617 by NAT_4:9;
3617 = 59*61 + 18; hence not 59 divides 3617 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3617 & n is prime
holds not n divides 3617 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3623 is prime
proof
now
3623 = 2*1811 + 1; hence not 2 divides 3623 by NAT_4:9;
3623 = 3*1207 + 2; hence not 3 divides 3623 by NAT_4:9;
3623 = 5*724 + 3; hence not 5 divides 3623 by NAT_4:9;
3623 = 7*517 + 4; hence not 7 divides 3623 by NAT_4:9;
3623 = 11*329 + 4; hence not 11 divides 3623 by NAT_4:9;
3623 = 13*278 + 9; hence not 13 divides 3623 by NAT_4:9;
3623 = 17*213 + 2; hence not 17 divides 3623 by NAT_4:9;
3623 = 19*190 + 13; hence not 19 divides 3623 by NAT_4:9;
3623 = 23*157 + 12; hence not 23 divides 3623 by NAT_4:9;
3623 = 29*124 + 27; hence not 29 divides 3623 by NAT_4:9;
3623 = 31*116 + 27; hence not 31 divides 3623 by NAT_4:9;
3623 = 37*97 + 34; hence not 37 divides 3623 by NAT_4:9;
3623 = 41*88 + 15; hence not 41 divides 3623 by NAT_4:9;
3623 = 43*84 + 11; hence not 43 divides 3623 by NAT_4:9;
3623 = 47*77 + 4; hence not 47 divides 3623 by NAT_4:9;
3623 = 53*68 + 19; hence not 53 divides 3623 by NAT_4:9;
3623 = 59*61 + 24; hence not 59 divides 3623 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3623 & n is prime
holds not n divides 3623 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3631 is prime
proof
now
3631 = 2*1815 + 1; hence not 2 divides 3631 by NAT_4:9;
3631 = 3*1210 + 1; hence not 3 divides 3631 by NAT_4:9;
3631 = 5*726 + 1; hence not 5 divides 3631 by NAT_4:9;
3631 = 7*518 + 5; hence not 7 divides 3631 by NAT_4:9;
3631 = 11*330 + 1; hence not 11 divides 3631 by NAT_4:9;
3631 = 13*279 + 4; hence not 13 divides 3631 by NAT_4:9;
3631 = 17*213 + 10; hence not 17 divides 3631 by NAT_4:9;
3631 = 19*191 + 2; hence not 19 divides 3631 by NAT_4:9;
3631 = 23*157 + 20; hence not 23 divides 3631 by NAT_4:9;
3631 = 29*125 + 6; hence not 29 divides 3631 by NAT_4:9;
3631 = 31*117 + 4; hence not 31 divides 3631 by NAT_4:9;
3631 = 37*98 + 5; hence not 37 divides 3631 by NAT_4:9;
3631 = 41*88 + 23; hence not 41 divides 3631 by NAT_4:9;
3631 = 43*84 + 19; hence not 43 divides 3631 by NAT_4:9;
3631 = 47*77 + 12; hence not 47 divides 3631 by NAT_4:9;
3631 = 53*68 + 27; hence not 53 divides 3631 by NAT_4:9;
3631 = 59*61 + 32; hence not 59 divides 3631 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3631 & n is prime
holds not n divides 3631 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3637 is prime
proof
now
3637 = 2*1818 + 1; hence not 2 divides 3637 by NAT_4:9;
3637 = 3*1212 + 1; hence not 3 divides 3637 by NAT_4:9;
3637 = 5*727 + 2; hence not 5 divides 3637 by NAT_4:9;
3637 = 7*519 + 4; hence not 7 divides 3637 by NAT_4:9;
3637 = 11*330 + 7; hence not 11 divides 3637 by NAT_4:9;
3637 = 13*279 + 10; hence not 13 divides 3637 by NAT_4:9;
3637 = 17*213 + 16; hence not 17 divides 3637 by NAT_4:9;
3637 = 19*191 + 8; hence not 19 divides 3637 by NAT_4:9;
3637 = 23*158 + 3; hence not 23 divides 3637 by NAT_4:9;
3637 = 29*125 + 12; hence not 29 divides 3637 by NAT_4:9;
3637 = 31*117 + 10; hence not 31 divides 3637 by NAT_4:9;
3637 = 37*98 + 11; hence not 37 divides 3637 by NAT_4:9;
3637 = 41*88 + 29; hence not 41 divides 3637 by NAT_4:9;
3637 = 43*84 + 25; hence not 43 divides 3637 by NAT_4:9;
3637 = 47*77 + 18; hence not 47 divides 3637 by NAT_4:9;
3637 = 53*68 + 33; hence not 53 divides 3637 by NAT_4:9;
3637 = 59*61 + 38; hence not 59 divides 3637 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3637 & n is prime
holds not n divides 3637 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3643 is prime
proof
now
3643 = 2*1821 + 1; hence not 2 divides 3643 by NAT_4:9;
3643 = 3*1214 + 1; hence not 3 divides 3643 by NAT_4:9;
3643 = 5*728 + 3; hence not 5 divides 3643 by NAT_4:9;
3643 = 7*520 + 3; hence not 7 divides 3643 by NAT_4:9;
3643 = 11*331 + 2; hence not 11 divides 3643 by NAT_4:9;
3643 = 13*280 + 3; hence not 13 divides 3643 by NAT_4:9;
3643 = 17*214 + 5; hence not 17 divides 3643 by NAT_4:9;
3643 = 19*191 + 14; hence not 19 divides 3643 by NAT_4:9;
3643 = 23*158 + 9; hence not 23 divides 3643 by NAT_4:9;
3643 = 29*125 + 18; hence not 29 divides 3643 by NAT_4:9;
3643 = 31*117 + 16; hence not 31 divides 3643 by NAT_4:9;
3643 = 37*98 + 17; hence not 37 divides 3643 by NAT_4:9;
3643 = 41*88 + 35; hence not 41 divides 3643 by NAT_4:9;
3643 = 43*84 + 31; hence not 43 divides 3643 by NAT_4:9;
3643 = 47*77 + 24; hence not 47 divides 3643 by NAT_4:9;
3643 = 53*68 + 39; hence not 53 divides 3643 by NAT_4:9;
3643 = 59*61 + 44; hence not 59 divides 3643 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3643 & n is prime
holds not n divides 3643 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
3659 is prime
proof
now
3659 = 2*1829 + 1; hence not 2 divides 3659 by NAT_4:9;
3659 = 3*1219 + 2; hence not 3 divides 3659 by NAT_4:9;
3659 = 5*731 + 4; hence not 5 divides 3659 by NAT_4:9;
3659 = 7*522 + 5; hence not 7 divides 3659 by NAT_4:9;
3659 = 11*332 + 7; hence not 11 divides 3659 by NAT_4:9;
3659 = 13*281 + 6; hence not 13 divides 3659 by NAT_4:9;
3659 = 17*215 + 4; hence not 17 divides 3659 by NAT_4:9;
3659 = 19*192 + 11; hence not 19 divides 3659 by NAT_4:9;
3659 = 23*159 + 2; hence not 23 divides 3659 by NAT_4:9;
3659 = 29*126 + 5; hence not 29 divides 3659 by NAT_4:9;
3659 = 31*118 + 1; hence not 31 divides 3659 by NAT_4:9;
3659 = 37*98 + 33; hence not 37 divides 3659 by NAT_4:9;
3659 = 41*89 + 10; hence not 41 divides 3659 by NAT_4:9;
3659 = 43*85 + 4; hence not 43 divides 3659 by NAT_4:9;
3659 = 47*77 + 40; hence not 47 divides 3659 by NAT_4:9;
3659 = 53*69 + 2; hence not 53 divides 3659 by NAT_4:9;
3659 = 59*62 + 1; hence not 59 divides 3659 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3659 & n is prime
holds not n divides 3659 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3671 is prime
proof
now
3671 = 2*1835 + 1; hence not 2 divides 3671 by NAT_4:9;
3671 = 3*1223 + 2; hence not 3 divides 3671 by NAT_4:9;
3671 = 5*734 + 1; hence not 5 divides 3671 by NAT_4:9;
3671 = 7*524 + 3; hence not 7 divides 3671 by NAT_4:9;
3671 = 11*333 + 8; hence not 11 divides 3671 by NAT_4:9;
3671 = 13*282 + 5; hence not 13 divides 3671 by NAT_4:9;
3671 = 17*215 + 16; hence not 17 divides 3671 by NAT_4:9;
3671 = 19*193 + 4; hence not 19 divides 3671 by NAT_4:9;
3671 = 23*159 + 14; hence not 23 divides 3671 by NAT_4:9;
3671 = 29*126 + 17; hence not 29 divides 3671 by NAT_4:9;
3671 = 31*118 + 13; hence not 31 divides 3671 by NAT_4:9;
3671 = 37*99 + 8; hence not 37 divides 3671 by NAT_4:9;
3671 = 41*89 + 22; hence not 41 divides 3671 by NAT_4:9;
3671 = 43*85 + 16; hence not 43 divides 3671 by NAT_4:9;
3671 = 47*78 + 5; hence not 47 divides 3671 by NAT_4:9;
3671 = 53*69 + 14; hence not 53 divides 3671 by NAT_4:9;
3671 = 59*62 + 13; hence not 59 divides 3671 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3671 & n is prime
holds not n divides 3671 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3673 is prime
proof
now
3673 = 2*1836 + 1; hence not 2 divides 3673 by NAT_4:9;
3673 = 3*1224 + 1; hence not 3 divides 3673 by NAT_4:9;
3673 = 5*734 + 3; hence not 5 divides 3673 by NAT_4:9;
3673 = 7*524 + 5; hence not 7 divides 3673 by NAT_4:9;
3673 = 11*333 + 10; hence not 11 divides 3673 by NAT_4:9;
3673 = 13*282 + 7; hence not 13 divides 3673 by NAT_4:9;
3673 = 17*216 + 1; hence not 17 divides 3673 by NAT_4:9;
3673 = 19*193 + 6; hence not 19 divides 3673 by NAT_4:9;
3673 = 23*159 + 16; hence not 23 divides 3673 by NAT_4:9;
3673 = 29*126 + 19; hence not 29 divides 3673 by NAT_4:9;
3673 = 31*118 + 15; hence not 31 divides 3673 by NAT_4:9;
3673 = 37*99 + 10; hence not 37 divides 3673 by NAT_4:9;
3673 = 41*89 + 24; hence not 41 divides 3673 by NAT_4:9;
3673 = 43*85 + 18; hence not 43 divides 3673 by NAT_4:9;
3673 = 47*78 + 7; hence not 47 divides 3673 by NAT_4:9;
3673 = 53*69 + 16; hence not 53 divides 3673 by NAT_4:9;
3673 = 59*62 + 15; hence not 59 divides 3673 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3673 & n is prime
holds not n divides 3673 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3677 is prime
proof
now
3677 = 2*1838 + 1; hence not 2 divides 3677 by NAT_4:9;
3677 = 3*1225 + 2; hence not 3 divides 3677 by NAT_4:9;
3677 = 5*735 + 2; hence not 5 divides 3677 by NAT_4:9;
3677 = 7*525 + 2; hence not 7 divides 3677 by NAT_4:9;
3677 = 11*334 + 3; hence not 11 divides 3677 by NAT_4:9;
3677 = 13*282 + 11; hence not 13 divides 3677 by NAT_4:9;
3677 = 17*216 + 5; hence not 17 divides 3677 by NAT_4:9;
3677 = 19*193 + 10; hence not 19 divides 3677 by NAT_4:9;
3677 = 23*159 + 20; hence not 23 divides 3677 by NAT_4:9;
3677 = 29*126 + 23; hence not 29 divides 3677 by NAT_4:9;
3677 = 31*118 + 19; hence not 31 divides 3677 by NAT_4:9;
3677 = 37*99 + 14; hence not 37 divides 3677 by NAT_4:9;
3677 = 41*89 + 28; hence not 41 divides 3677 by NAT_4:9;
3677 = 43*85 + 22; hence not 43 divides 3677 by NAT_4:9;
3677 = 47*78 + 11; hence not 47 divides 3677 by NAT_4:9;
3677 = 53*69 + 20; hence not 53 divides 3677 by NAT_4:9;
3677 = 59*62 + 19; hence not 59 divides 3677 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3677 & n is prime
holds not n divides 3677 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3691 is prime
proof
now
3691 = 2*1845 + 1; hence not 2 divides 3691 by NAT_4:9;
3691 = 3*1230 + 1; hence not 3 divides 3691 by NAT_4:9;
3691 = 5*738 + 1; hence not 5 divides 3691 by NAT_4:9;
3691 = 7*527 + 2; hence not 7 divides 3691 by NAT_4:9;
3691 = 11*335 + 6; hence not 11 divides 3691 by NAT_4:9;
3691 = 13*283 + 12; hence not 13 divides 3691 by NAT_4:9;
3691 = 17*217 + 2; hence not 17 divides 3691 by NAT_4:9;
3691 = 19*194 + 5; hence not 19 divides 3691 by NAT_4:9;
3691 = 23*160 + 11; hence not 23 divides 3691 by NAT_4:9;
3691 = 29*127 + 8; hence not 29 divides 3691 by NAT_4:9;
3691 = 31*119 + 2; hence not 31 divides 3691 by NAT_4:9;
3691 = 37*99 + 28; hence not 37 divides 3691 by NAT_4:9;
3691 = 41*90 + 1; hence not 41 divides 3691 by NAT_4:9;
3691 = 43*85 + 36; hence not 43 divides 3691 by NAT_4:9;
3691 = 47*78 + 25; hence not 47 divides 3691 by NAT_4:9;
3691 = 53*69 + 34; hence not 53 divides 3691 by NAT_4:9;
3691 = 59*62 + 33; hence not 59 divides 3691 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3691 & n is prime
holds not n divides 3691 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3697 is prime
proof
now
3697 = 2*1848 + 1; hence not 2 divides 3697 by NAT_4:9;
3697 = 3*1232 + 1; hence not 3 divides 3697 by NAT_4:9;
3697 = 5*739 + 2; hence not 5 divides 3697 by NAT_4:9;
3697 = 7*528 + 1; hence not 7 divides 3697 by NAT_4:9;
3697 = 11*336 + 1; hence not 11 divides 3697 by NAT_4:9;
3697 = 13*284 + 5; hence not 13 divides 3697 by NAT_4:9;
3697 = 17*217 + 8; hence not 17 divides 3697 by NAT_4:9;
3697 = 19*194 + 11; hence not 19 divides 3697 by NAT_4:9;
3697 = 23*160 + 17; hence not 23 divides 3697 by NAT_4:9;
3697 = 29*127 + 14; hence not 29 divides 3697 by NAT_4:9;
3697 = 31*119 + 8; hence not 31 divides 3697 by NAT_4:9;
3697 = 37*99 + 34; hence not 37 divides 3697 by NAT_4:9;
3697 = 41*90 + 7; hence not 41 divides 3697 by NAT_4:9;
3697 = 43*85 + 42; hence not 43 divides 3697 by NAT_4:9;
3697 = 47*78 + 31; hence not 47 divides 3697 by NAT_4:9;
3697 = 53*69 + 40; hence not 53 divides 3697 by NAT_4:9;
3697 = 59*62 + 39; hence not 59 divides 3697 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3697 & n is prime
holds not n divides 3697 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3701 is prime
proof
now
3701 = 2*1850 + 1; hence not 2 divides 3701 by NAT_4:9;
3701 = 3*1233 + 2; hence not 3 divides 3701 by NAT_4:9;
3701 = 5*740 + 1; hence not 5 divides 3701 by NAT_4:9;
3701 = 7*528 + 5; hence not 7 divides 3701 by NAT_4:9;
3701 = 11*336 + 5; hence not 11 divides 3701 by NAT_4:9;
3701 = 13*284 + 9; hence not 13 divides 3701 by NAT_4:9;
3701 = 17*217 + 12; hence not 17 divides 3701 by NAT_4:9;
3701 = 19*194 + 15; hence not 19 divides 3701 by NAT_4:9;
3701 = 23*160 + 21; hence not 23 divides 3701 by NAT_4:9;
3701 = 29*127 + 18; hence not 29 divides 3701 by NAT_4:9;
3701 = 31*119 + 12; hence not 31 divides 3701 by NAT_4:9;
3701 = 37*100 + 1; hence not 37 divides 3701 by NAT_4:9;
3701 = 41*90 + 11; hence not 41 divides 3701 by NAT_4:9;
3701 = 43*86 + 3; hence not 43 divides 3701 by NAT_4:9;
3701 = 47*78 + 35; hence not 47 divides 3701 by NAT_4:9;
3701 = 53*69 + 44; hence not 53 divides 3701 by NAT_4:9;
3701 = 59*62 + 43; hence not 59 divides 3701 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3701 & n is prime
holds not n divides 3701 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3709 is prime
proof
now
3709 = 2*1854 + 1; hence not 2 divides 3709 by NAT_4:9;
3709 = 3*1236 + 1; hence not 3 divides 3709 by NAT_4:9;
3709 = 5*741 + 4; hence not 5 divides 3709 by NAT_4:9;
3709 = 7*529 + 6; hence not 7 divides 3709 by NAT_4:9;
3709 = 11*337 + 2; hence not 11 divides 3709 by NAT_4:9;
3709 = 13*285 + 4; hence not 13 divides 3709 by NAT_4:9;
3709 = 17*218 + 3; hence not 17 divides 3709 by NAT_4:9;
3709 = 19*195 + 4; hence not 19 divides 3709 by NAT_4:9;
3709 = 23*161 + 6; hence not 23 divides 3709 by NAT_4:9;
3709 = 29*127 + 26; hence not 29 divides 3709 by NAT_4:9;
3709 = 31*119 + 20; hence not 31 divides 3709 by NAT_4:9;
3709 = 37*100 + 9; hence not 37 divides 3709 by NAT_4:9;
3709 = 41*90 + 19; hence not 41 divides 3709 by NAT_4:9;
3709 = 43*86 + 11; hence not 43 divides 3709 by NAT_4:9;
3709 = 47*78 + 43; hence not 47 divides 3709 by NAT_4:9;
3709 = 53*69 + 52; hence not 53 divides 3709 by NAT_4:9;
3709 = 59*62 + 51; hence not 59 divides 3709 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3709 & n is prime
holds not n divides 3709 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3719 is prime
proof
now
3719 = 2*1859 + 1; hence not 2 divides 3719 by NAT_4:9;
3719 = 3*1239 + 2; hence not 3 divides 3719 by NAT_4:9;
3719 = 5*743 + 4; hence not 5 divides 3719 by NAT_4:9;
3719 = 7*531 + 2; hence not 7 divides 3719 by NAT_4:9;
3719 = 11*338 + 1; hence not 11 divides 3719 by NAT_4:9;
3719 = 13*286 + 1; hence not 13 divides 3719 by NAT_4:9;
3719 = 17*218 + 13; hence not 17 divides 3719 by NAT_4:9;
3719 = 19*195 + 14; hence not 19 divides 3719 by NAT_4:9;
3719 = 23*161 + 16; hence not 23 divides 3719 by NAT_4:9;
3719 = 29*128 + 7; hence not 29 divides 3719 by NAT_4:9;
3719 = 31*119 + 30; hence not 31 divides 3719 by NAT_4:9;
3719 = 37*100 + 19; hence not 37 divides 3719 by NAT_4:9;
3719 = 41*90 + 29; hence not 41 divides 3719 by NAT_4:9;
3719 = 43*86 + 21; hence not 43 divides 3719 by NAT_4:9;
3719 = 47*79 + 6; hence not 47 divides 3719 by NAT_4:9;
3719 = 53*70 + 9; hence not 53 divides 3719 by NAT_4:9;
3719 = 59*63 + 2; hence not 59 divides 3719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3719 & n is prime
holds not n divides 3719 by XPRIMET1:34;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3727 is prime
proof
now
3727 = 2*1863 + 1; hence not 2 divides 3727 by NAT_4:9;
3727 = 3*1242 + 1; hence not 3 divides 3727 by NAT_4:9;
3727 = 5*745 + 2; hence not 5 divides 3727 by NAT_4:9;
3727 = 7*532 + 3; hence not 7 divides 3727 by NAT_4:9;
3727 = 11*338 + 9; hence not 11 divides 3727 by NAT_4:9;
3727 = 13*286 + 9; hence not 13 divides 3727 by NAT_4:9;
3727 = 17*219 + 4; hence not 17 divides 3727 by NAT_4:9;
3727 = 19*196 + 3; hence not 19 divides 3727 by NAT_4:9;
3727 = 23*162 + 1; hence not 23 divides 3727 by NAT_4:9;
3727 = 29*128 + 15; hence not 29 divides 3727 by NAT_4:9;
3727 = 31*120 + 7; hence not 31 divides 3727 by NAT_4:9;
3727 = 37*100 + 27; hence not 37 divides 3727 by NAT_4:9;
3727 = 41*90 + 37; hence not 41 divides 3727 by NAT_4:9;
3727 = 43*86 + 29; hence not 43 divides 3727 by NAT_4:9;
3727 = 47*79 + 14; hence not 47 divides 3727 by NAT_4:9;
3727 = 53*70 + 17; hence not 53 divides 3727 by NAT_4:9;
3727 = 59*63 + 10; hence not 59 divides 3727 by NAT_4:9;
3727 = 61*61 + 6; hence not 61 divides 3727 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3727 & n is prime
holds not n divides 3727 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3733 is prime
proof
now
3733 = 2*1866 + 1; hence not 2 divides 3733 by NAT_4:9;
3733 = 3*1244 + 1; hence not 3 divides 3733 by NAT_4:9;
3733 = 5*746 + 3; hence not 5 divides 3733 by NAT_4:9;
3733 = 7*533 + 2; hence not 7 divides 3733 by NAT_4:9;
3733 = 11*339 + 4; hence not 11 divides 3733 by NAT_4:9;
3733 = 13*287 + 2; hence not 13 divides 3733 by NAT_4:9;
3733 = 17*219 + 10; hence not 17 divides 3733 by NAT_4:9;
3733 = 19*196 + 9; hence not 19 divides 3733 by NAT_4:9;
3733 = 23*162 + 7; hence not 23 divides 3733 by NAT_4:9;
3733 = 29*128 + 21; hence not 29 divides 3733 by NAT_4:9;
3733 = 31*120 + 13; hence not 31 divides 3733 by NAT_4:9;
3733 = 37*100 + 33; hence not 37 divides 3733 by NAT_4:9;
3733 = 41*91 + 2; hence not 41 divides 3733 by NAT_4:9;
3733 = 43*86 + 35; hence not 43 divides 3733 by NAT_4:9;
3733 = 47*79 + 20; hence not 47 divides 3733 by NAT_4:9;
3733 = 53*70 + 23; hence not 53 divides 3733 by NAT_4:9;
3733 = 59*63 + 16; hence not 59 divides 3733 by NAT_4:9;
3733 = 61*61 + 12; hence not 61 divides 3733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3733 & n is prime
holds not n divides 3733 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3739 is prime
proof
now
3739 = 2*1869 + 1; hence not 2 divides 3739 by NAT_4:9;
3739 = 3*1246 + 1; hence not 3 divides 3739 by NAT_4:9;
3739 = 5*747 + 4; hence not 5 divides 3739 by NAT_4:9;
3739 = 7*534 + 1; hence not 7 divides 3739 by NAT_4:9;
3739 = 11*339 + 10; hence not 11 divides 3739 by NAT_4:9;
3739 = 13*287 + 8; hence not 13 divides 3739 by NAT_4:9;
3739 = 17*219 + 16; hence not 17 divides 3739 by NAT_4:9;
3739 = 19*196 + 15; hence not 19 divides 3739 by NAT_4:9;
3739 = 23*162 + 13; hence not 23 divides 3739 by NAT_4:9;
3739 = 29*128 + 27; hence not 29 divides 3739 by NAT_4:9;
3739 = 31*120 + 19; hence not 31 divides 3739 by NAT_4:9;
3739 = 37*101 + 2; hence not 37 divides 3739 by NAT_4:9;
3739 = 41*91 + 8; hence not 41 divides 3739 by NAT_4:9;
3739 = 43*86 + 41; hence not 43 divides 3739 by NAT_4:9;
3739 = 47*79 + 26; hence not 47 divides 3739 by NAT_4:9;
3739 = 53*70 + 29; hence not 53 divides 3739 by NAT_4:9;
3739 = 59*63 + 22; hence not 59 divides 3739 by NAT_4:9;
3739 = 61*61 + 18; hence not 61 divides 3739 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3739 & n is prime
holds not n divides 3739 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
3761 is prime
proof
now
3761 = 2*1880 + 1; hence not 2 divides 3761 by NAT_4:9;
3761 = 3*1253 + 2; hence not 3 divides 3761 by NAT_4:9;
3761 = 5*752 + 1; hence not 5 divides 3761 by NAT_4:9;
3761 = 7*537 + 2; hence not 7 divides 3761 by NAT_4:9;
3761 = 11*341 + 10; hence not 11 divides 3761 by NAT_4:9;
3761 = 13*289 + 4; hence not 13 divides 3761 by NAT_4:9;
3761 = 17*221 + 4; hence not 17 divides 3761 by NAT_4:9;
3761 = 19*197 + 18; hence not 19 divides 3761 by NAT_4:9;
3761 = 23*163 + 12; hence not 23 divides 3761 by NAT_4:9;
3761 = 29*129 + 20; hence not 29 divides 3761 by NAT_4:9;
3761 = 31*121 + 10; hence not 31 divides 3761 by NAT_4:9;
3761 = 37*101 + 24; hence not 37 divides 3761 by NAT_4:9;
3761 = 41*91 + 30; hence not 41 divides 3761 by NAT_4:9;
3761 = 43*87 + 20; hence not 43 divides 3761 by NAT_4:9;
3761 = 47*80 + 1; hence not 47 divides 3761 by NAT_4:9;
3761 = 53*70 + 51; hence not 53 divides 3761 by NAT_4:9;
3761 = 59*63 + 44; hence not 59 divides 3761 by NAT_4:9;
3761 = 61*61 + 40; hence not 61 divides 3761 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3761 & n is prime
holds not n divides 3761 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3767 is prime
proof
now
3767 = 2*1883 + 1; hence not 2 divides 3767 by NAT_4:9;
3767 = 3*1255 + 2; hence not 3 divides 3767 by NAT_4:9;
3767 = 5*753 + 2; hence not 5 divides 3767 by NAT_4:9;
3767 = 7*538 + 1; hence not 7 divides 3767 by NAT_4:9;
3767 = 11*342 + 5; hence not 11 divides 3767 by NAT_4:9;
3767 = 13*289 + 10; hence not 13 divides 3767 by NAT_4:9;
3767 = 17*221 + 10; hence not 17 divides 3767 by NAT_4:9;
3767 = 19*198 + 5; hence not 19 divides 3767 by NAT_4:9;
3767 = 23*163 + 18; hence not 23 divides 3767 by NAT_4:9;
3767 = 29*129 + 26; hence not 29 divides 3767 by NAT_4:9;
3767 = 31*121 + 16; hence not 31 divides 3767 by NAT_4:9;
3767 = 37*101 + 30; hence not 37 divides 3767 by NAT_4:9;
3767 = 41*91 + 36; hence not 41 divides 3767 by NAT_4:9;
3767 = 43*87 + 26; hence not 43 divides 3767 by NAT_4:9;
3767 = 47*80 + 7; hence not 47 divides 3767 by NAT_4:9;
3767 = 53*71 + 4; hence not 53 divides 3767 by NAT_4:9;
3767 = 59*63 + 50; hence not 59 divides 3767 by NAT_4:9;
3767 = 61*61 + 46; hence not 61 divides 3767 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3767 & n is prime
holds not n divides 3767 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3769 is prime
proof
now
3769 = 2*1884 + 1; hence not 2 divides 3769 by NAT_4:9;
3769 = 3*1256 + 1; hence not 3 divides 3769 by NAT_4:9;
3769 = 5*753 + 4; hence not 5 divides 3769 by NAT_4:9;
3769 = 7*538 + 3; hence not 7 divides 3769 by NAT_4:9;
3769 = 11*342 + 7; hence not 11 divides 3769 by NAT_4:9;
3769 = 13*289 + 12; hence not 13 divides 3769 by NAT_4:9;
3769 = 17*221 + 12; hence not 17 divides 3769 by NAT_4:9;
3769 = 19*198 + 7; hence not 19 divides 3769 by NAT_4:9;
3769 = 23*163 + 20; hence not 23 divides 3769 by NAT_4:9;
3769 = 29*129 + 28; hence not 29 divides 3769 by NAT_4:9;
3769 = 31*121 + 18; hence not 31 divides 3769 by NAT_4:9;
3769 = 37*101 + 32; hence not 37 divides 3769 by NAT_4:9;
3769 = 41*91 + 38; hence not 41 divides 3769 by NAT_4:9;
3769 = 43*87 + 28; hence not 43 divides 3769 by NAT_4:9;
3769 = 47*80 + 9; hence not 47 divides 3769 by NAT_4:9;
3769 = 53*71 + 6; hence not 53 divides 3769 by NAT_4:9;
3769 = 59*63 + 52; hence not 59 divides 3769 by NAT_4:9;
3769 = 61*61 + 48; hence not 61 divides 3769 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3769 & n is prime
holds not n divides 3769 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3779 is prime
proof
now
3779 = 2*1889 + 1; hence not 2 divides 3779 by NAT_4:9;
3779 = 3*1259 + 2; hence not 3 divides 3779 by NAT_4:9;
3779 = 5*755 + 4; hence not 5 divides 3779 by NAT_4:9;
3779 = 7*539 + 6; hence not 7 divides 3779 by NAT_4:9;
3779 = 11*343 + 6; hence not 11 divides 3779 by NAT_4:9;
3779 = 13*290 + 9; hence not 13 divides 3779 by NAT_4:9;
3779 = 17*222 + 5; hence not 17 divides 3779 by NAT_4:9;
3779 = 19*198 + 17; hence not 19 divides 3779 by NAT_4:9;
3779 = 23*164 + 7; hence not 23 divides 3779 by NAT_4:9;
3779 = 29*130 + 9; hence not 29 divides 3779 by NAT_4:9;
3779 = 31*121 + 28; hence not 31 divides 3779 by NAT_4:9;
3779 = 37*102 + 5; hence not 37 divides 3779 by NAT_4:9;
3779 = 41*92 + 7; hence not 41 divides 3779 by NAT_4:9;
3779 = 43*87 + 38; hence not 43 divides 3779 by NAT_4:9;
3779 = 47*80 + 19; hence not 47 divides 3779 by NAT_4:9;
3779 = 53*71 + 16; hence not 53 divides 3779 by NAT_4:9;
3779 = 59*64 + 3; hence not 59 divides 3779 by NAT_4:9;
3779 = 61*61 + 58; hence not 61 divides 3779 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3779 & n is prime
holds not n divides 3779 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3793 is prime
proof
now
3793 = 2*1896 + 1; hence not 2 divides 3793 by NAT_4:9;
3793 = 3*1264 + 1; hence not 3 divides 3793 by NAT_4:9;
3793 = 5*758 + 3; hence not 5 divides 3793 by NAT_4:9;
3793 = 7*541 + 6; hence not 7 divides 3793 by NAT_4:9;
3793 = 11*344 + 9; hence not 11 divides 3793 by NAT_4:9;
3793 = 13*291 + 10; hence not 13 divides 3793 by NAT_4:9;
3793 = 17*223 + 2; hence not 17 divides 3793 by NAT_4:9;
3793 = 19*199 + 12; hence not 19 divides 3793 by NAT_4:9;
3793 = 23*164 + 21; hence not 23 divides 3793 by NAT_4:9;
3793 = 29*130 + 23; hence not 29 divides 3793 by NAT_4:9;
3793 = 31*122 + 11; hence not 31 divides 3793 by NAT_4:9;
3793 = 37*102 + 19; hence not 37 divides 3793 by NAT_4:9;
3793 = 41*92 + 21; hence not 41 divides 3793 by NAT_4:9;
3793 = 43*88 + 9; hence not 43 divides 3793 by NAT_4:9;
3793 = 47*80 + 33; hence not 47 divides 3793 by NAT_4:9;
3793 = 53*71 + 30; hence not 53 divides 3793 by NAT_4:9;
3793 = 59*64 + 17; hence not 59 divides 3793 by NAT_4:9;
3793 = 61*62 + 11; hence not 61 divides 3793 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3793 & n is prime
holds not n divides 3793 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3797 is prime
proof
now
3797 = 2*1898 + 1; hence not 2 divides 3797 by NAT_4:9;
3797 = 3*1265 + 2; hence not 3 divides 3797 by NAT_4:9;
3797 = 5*759 + 2; hence not 5 divides 3797 by NAT_4:9;
3797 = 7*542 + 3; hence not 7 divides 3797 by NAT_4:9;
3797 = 11*345 + 2; hence not 11 divides 3797 by NAT_4:9;
3797 = 13*292 + 1; hence not 13 divides 3797 by NAT_4:9;
3797 = 17*223 + 6; hence not 17 divides 3797 by NAT_4:9;
3797 = 19*199 + 16; hence not 19 divides 3797 by NAT_4:9;
3797 = 23*165 + 2; hence not 23 divides 3797 by NAT_4:9;
3797 = 29*130 + 27; hence not 29 divides 3797 by NAT_4:9;
3797 = 31*122 + 15; hence not 31 divides 3797 by NAT_4:9;
3797 = 37*102 + 23; hence not 37 divides 3797 by NAT_4:9;
3797 = 41*92 + 25; hence not 41 divides 3797 by NAT_4:9;
3797 = 43*88 + 13; hence not 43 divides 3797 by NAT_4:9;
3797 = 47*80 + 37; hence not 47 divides 3797 by NAT_4:9;
3797 = 53*71 + 34; hence not 53 divides 3797 by NAT_4:9;
3797 = 59*64 + 21; hence not 59 divides 3797 by NAT_4:9;
3797 = 61*62 + 15; hence not 61 divides 3797 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3797 & n is prime
holds not n divides 3797 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3803 is prime
proof
now
3803 = 2*1901 + 1; hence not 2 divides 3803 by NAT_4:9;
3803 = 3*1267 + 2; hence not 3 divides 3803 by NAT_4:9;
3803 = 5*760 + 3; hence not 5 divides 3803 by NAT_4:9;
3803 = 7*543 + 2; hence not 7 divides 3803 by NAT_4:9;
3803 = 11*345 + 8; hence not 11 divides 3803 by NAT_4:9;
3803 = 13*292 + 7; hence not 13 divides 3803 by NAT_4:9;
3803 = 17*223 + 12; hence not 17 divides 3803 by NAT_4:9;
3803 = 19*200 + 3; hence not 19 divides 3803 by NAT_4:9;
3803 = 23*165 + 8; hence not 23 divides 3803 by NAT_4:9;
3803 = 29*131 + 4; hence not 29 divides 3803 by NAT_4:9;
3803 = 31*122 + 21; hence not 31 divides 3803 by NAT_4:9;
3803 = 37*102 + 29; hence not 37 divides 3803 by NAT_4:9;
3803 = 41*92 + 31; hence not 41 divides 3803 by NAT_4:9;
3803 = 43*88 + 19; hence not 43 divides 3803 by NAT_4:9;
3803 = 47*80 + 43; hence not 47 divides 3803 by NAT_4:9;
3803 = 53*71 + 40; hence not 53 divides 3803 by NAT_4:9;
3803 = 59*64 + 27; hence not 59 divides 3803 by NAT_4:9;
3803 = 61*62 + 21; hence not 61 divides 3803 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3803 & n is prime
holds not n divides 3803 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
3821 is prime
proof
now
3821 = 2*1910 + 1; hence not 2 divides 3821 by NAT_4:9;
3821 = 3*1273 + 2; hence not 3 divides 3821 by NAT_4:9;
3821 = 5*764 + 1; hence not 5 divides 3821 by NAT_4:9;
3821 = 7*545 + 6; hence not 7 divides 3821 by NAT_4:9;
3821 = 11*347 + 4; hence not 11 divides 3821 by NAT_4:9;
3821 = 13*293 + 12; hence not 13 divides 3821 by NAT_4:9;
3821 = 17*224 + 13; hence not 17 divides 3821 by NAT_4:9;
3821 = 19*201 + 2; hence not 19 divides 3821 by NAT_4:9;
3821 = 23*166 + 3; hence not 23 divides 3821 by NAT_4:9;
3821 = 29*131 + 22; hence not 29 divides 3821 by NAT_4:9;
3821 = 31*123 + 8; hence not 31 divides 3821 by NAT_4:9;
3821 = 37*103 + 10; hence not 37 divides 3821 by NAT_4:9;
3821 = 41*93 + 8; hence not 41 divides 3821 by NAT_4:9;
3821 = 43*88 + 37; hence not 43 divides 3821 by NAT_4:9;
3821 = 47*81 + 14; hence not 47 divides 3821 by NAT_4:9;
3821 = 53*72 + 5; hence not 53 divides 3821 by NAT_4:9;
3821 = 59*64 + 45; hence not 59 divides 3821 by NAT_4:9;
3821 = 61*62 + 39; hence not 61 divides 3821 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3821 & n is prime
holds not n divides 3821 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3823 is prime
proof
now
3823 = 2*1911 + 1; hence not 2 divides 3823 by NAT_4:9;
3823 = 3*1274 + 1; hence not 3 divides 3823 by NAT_4:9;
3823 = 5*764 + 3; hence not 5 divides 3823 by NAT_4:9;
3823 = 7*546 + 1; hence not 7 divides 3823 by NAT_4:9;
3823 = 11*347 + 6; hence not 11 divides 3823 by NAT_4:9;
3823 = 13*294 + 1; hence not 13 divides 3823 by NAT_4:9;
3823 = 17*224 + 15; hence not 17 divides 3823 by NAT_4:9;
3823 = 19*201 + 4; hence not 19 divides 3823 by NAT_4:9;
3823 = 23*166 + 5; hence not 23 divides 3823 by NAT_4:9;
3823 = 29*131 + 24; hence not 29 divides 3823 by NAT_4:9;
3823 = 31*123 + 10; hence not 31 divides 3823 by NAT_4:9;
3823 = 37*103 + 12; hence not 37 divides 3823 by NAT_4:9;
3823 = 41*93 + 10; hence not 41 divides 3823 by NAT_4:9;
3823 = 43*88 + 39; hence not 43 divides 3823 by NAT_4:9;
3823 = 47*81 + 16; hence not 47 divides 3823 by NAT_4:9;
3823 = 53*72 + 7; hence not 53 divides 3823 by NAT_4:9;
3823 = 59*64 + 47; hence not 59 divides 3823 by NAT_4:9;
3823 = 61*62 + 41; hence not 61 divides 3823 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3823 & n is prime
holds not n divides 3823 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3833 is prime
proof
now
3833 = 2*1916 + 1; hence not 2 divides 3833 by NAT_4:9;
3833 = 3*1277 + 2; hence not 3 divides 3833 by NAT_4:9;
3833 = 5*766 + 3; hence not 5 divides 3833 by NAT_4:9;
3833 = 7*547 + 4; hence not 7 divides 3833 by NAT_4:9;
3833 = 11*348 + 5; hence not 11 divides 3833 by NAT_4:9;
3833 = 13*294 + 11; hence not 13 divides 3833 by NAT_4:9;
3833 = 17*225 + 8; hence not 17 divides 3833 by NAT_4:9;
3833 = 19*201 + 14; hence not 19 divides 3833 by NAT_4:9;
3833 = 23*166 + 15; hence not 23 divides 3833 by NAT_4:9;
3833 = 29*132 + 5; hence not 29 divides 3833 by NAT_4:9;
3833 = 31*123 + 20; hence not 31 divides 3833 by NAT_4:9;
3833 = 37*103 + 22; hence not 37 divides 3833 by NAT_4:9;
3833 = 41*93 + 20; hence not 41 divides 3833 by NAT_4:9;
3833 = 43*89 + 6; hence not 43 divides 3833 by NAT_4:9;
3833 = 47*81 + 26; hence not 47 divides 3833 by NAT_4:9;
3833 = 53*72 + 17; hence not 53 divides 3833 by NAT_4:9;
3833 = 59*64 + 57; hence not 59 divides 3833 by NAT_4:9;
3833 = 61*62 + 51; hence not 61 divides 3833 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3833 & n is prime
holds not n divides 3833 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3847 is prime
proof
now
3847 = 2*1923 + 1; hence not 2 divides 3847 by NAT_4:9;
3847 = 3*1282 + 1; hence not 3 divides 3847 by NAT_4:9;
3847 = 5*769 + 2; hence not 5 divides 3847 by NAT_4:9;
3847 = 7*549 + 4; hence not 7 divides 3847 by NAT_4:9;
3847 = 11*349 + 8; hence not 11 divides 3847 by NAT_4:9;
3847 = 13*295 + 12; hence not 13 divides 3847 by NAT_4:9;
3847 = 17*226 + 5; hence not 17 divides 3847 by NAT_4:9;
3847 = 19*202 + 9; hence not 19 divides 3847 by NAT_4:9;
3847 = 23*167 + 6; hence not 23 divides 3847 by NAT_4:9;
3847 = 29*132 + 19; hence not 29 divides 3847 by NAT_4:9;
3847 = 31*124 + 3; hence not 31 divides 3847 by NAT_4:9;
3847 = 37*103 + 36; hence not 37 divides 3847 by NAT_4:9;
3847 = 41*93 + 34; hence not 41 divides 3847 by NAT_4:9;
3847 = 43*89 + 20; hence not 43 divides 3847 by NAT_4:9;
3847 = 47*81 + 40; hence not 47 divides 3847 by NAT_4:9;
3847 = 53*72 + 31; hence not 53 divides 3847 by NAT_4:9;
3847 = 59*65 + 12; hence not 59 divides 3847 by NAT_4:9;
3847 = 61*63 + 4; hence not 61 divides 3847 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3847 & n is prime
holds not n divides 3847 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3851 is prime
proof
now
3851 = 2*1925 + 1; hence not 2 divides 3851 by NAT_4:9;
3851 = 3*1283 + 2; hence not 3 divides 3851 by NAT_4:9;
3851 = 5*770 + 1; hence not 5 divides 3851 by NAT_4:9;
3851 = 7*550 + 1; hence not 7 divides 3851 by NAT_4:9;
3851 = 11*350 + 1; hence not 11 divides 3851 by NAT_4:9;
3851 = 13*296 + 3; hence not 13 divides 3851 by NAT_4:9;
3851 = 17*226 + 9; hence not 17 divides 3851 by NAT_4:9;
3851 = 19*202 + 13; hence not 19 divides 3851 by NAT_4:9;
3851 = 23*167 + 10; hence not 23 divides 3851 by NAT_4:9;
3851 = 29*132 + 23; hence not 29 divides 3851 by NAT_4:9;
3851 = 31*124 + 7; hence not 31 divides 3851 by NAT_4:9;
3851 = 37*104 + 3; hence not 37 divides 3851 by NAT_4:9;
3851 = 41*93 + 38; hence not 41 divides 3851 by NAT_4:9;
3851 = 43*89 + 24; hence not 43 divides 3851 by NAT_4:9;
3851 = 47*81 + 44; hence not 47 divides 3851 by NAT_4:9;
3851 = 53*72 + 35; hence not 53 divides 3851 by NAT_4:9;
3851 = 59*65 + 16; hence not 59 divides 3851 by NAT_4:9;
3851 = 61*63 + 8; hence not 61 divides 3851 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3851 & n is prime
holds not n divides 3851 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3853 is prime
proof
now
3853 = 2*1926 + 1; hence not 2 divides 3853 by NAT_4:9;
3853 = 3*1284 + 1; hence not 3 divides 3853 by NAT_4:9;
3853 = 5*770 + 3; hence not 5 divides 3853 by NAT_4:9;
3853 = 7*550 + 3; hence not 7 divides 3853 by NAT_4:9;
3853 = 11*350 + 3; hence not 11 divides 3853 by NAT_4:9;
3853 = 13*296 + 5; hence not 13 divides 3853 by NAT_4:9;
3853 = 17*226 + 11; hence not 17 divides 3853 by NAT_4:9;
3853 = 19*202 + 15; hence not 19 divides 3853 by NAT_4:9;
3853 = 23*167 + 12; hence not 23 divides 3853 by NAT_4:9;
3853 = 29*132 + 25; hence not 29 divides 3853 by NAT_4:9;
3853 = 31*124 + 9; hence not 31 divides 3853 by NAT_4:9;
3853 = 37*104 + 5; hence not 37 divides 3853 by NAT_4:9;
3853 = 41*93 + 40; hence not 41 divides 3853 by NAT_4:9;
3853 = 43*89 + 26; hence not 43 divides 3853 by NAT_4:9;
3853 = 47*81 + 46; hence not 47 divides 3853 by NAT_4:9;
3853 = 53*72 + 37; hence not 53 divides 3853 by NAT_4:9;
3853 = 59*65 + 18; hence not 59 divides 3853 by NAT_4:9;
3853 = 61*63 + 10; hence not 61 divides 3853 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3853 & n is prime
holds not n divides 3853 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
3863 is prime
proof
now
3863 = 2*1931 + 1; hence not 2 divides 3863 by NAT_4:9;
3863 = 3*1287 + 2; hence not 3 divides 3863 by NAT_4:9;
3863 = 5*772 + 3; hence not 5 divides 3863 by NAT_4:9;
3863 = 7*551 + 6; hence not 7 divides 3863 by NAT_4:9;
3863 = 11*351 + 2; hence not 11 divides 3863 by NAT_4:9;
3863 = 13*297 + 2; hence not 13 divides 3863 by NAT_4:9;
3863 = 17*227 + 4; hence not 17 divides 3863 by NAT_4:9;
3863 = 19*203 + 6; hence not 19 divides 3863 by NAT_4:9;
3863 = 23*167 + 22; hence not 23 divides 3863 by NAT_4:9;
3863 = 29*133 + 6; hence not 29 divides 3863 by NAT_4:9;
3863 = 31*124 + 19; hence not 31 divides 3863 by NAT_4:9;
3863 = 37*104 + 15; hence not 37 divides 3863 by NAT_4:9;
3863 = 41*94 + 9; hence not 41 divides 3863 by NAT_4:9;
3863 = 43*89 + 36; hence not 43 divides 3863 by NAT_4:9;
3863 = 47*82 + 9; hence not 47 divides 3863 by NAT_4:9;
3863 = 53*72 + 47; hence not 53 divides 3863 by NAT_4:9;
3863 = 59*65 + 28; hence not 59 divides 3863 by NAT_4:9;
3863 = 61*63 + 20; hence not 61 divides 3863 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3863 & n is prime
holds not n divides 3863 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
3877 is prime
proof
now
3877 = 2*1938 + 1; hence not 2 divides 3877 by NAT_4:9;
3877 = 3*1292 + 1; hence not 3 divides 3877 by NAT_4:9;
3877 = 5*775 + 2; hence not 5 divides 3877 by NAT_4:9;
3877 = 7*553 + 6; hence not 7 divides 3877 by NAT_4:9;
3877 = 11*352 + 5; hence not 11 divides 3877 by NAT_4:9;
3877 = 13*298 + 3; hence not 13 divides 3877 by NAT_4:9;
3877 = 17*228 + 1; hence not 17 divides 3877 by NAT_4:9;
3877 = 19*204 + 1; hence not 19 divides 3877 by NAT_4:9;
3877 = 23*168 + 13; hence not 23 divides 3877 by NAT_4:9;
3877 = 29*133 + 20; hence not 29 divides 3877 by NAT_4:9;
3877 = 31*125 + 2; hence not 31 divides 3877 by NAT_4:9;
3877 = 37*104 + 29; hence not 37 divides 3877 by NAT_4:9;
3877 = 41*94 + 23; hence not 41 divides 3877 by NAT_4:9;
3877 = 43*90 + 7; hence not 43 divides 3877 by NAT_4:9;
3877 = 47*82 + 23; hence not 47 divides 3877 by NAT_4:9;
3877 = 53*73 + 8; hence not 53 divides 3877 by NAT_4:9;
3877 = 59*65 + 42; hence not 59 divides 3877 by NAT_4:9;
3877 = 61*63 + 34; hence not 61 divides 3877 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3877 & n is prime
holds not n divides 3877 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3881 is prime
proof
now
3881 = 2*1940 + 1; hence not 2 divides 3881 by NAT_4:9;
3881 = 3*1293 + 2; hence not 3 divides 3881 by NAT_4:9;
3881 = 5*776 + 1; hence not 5 divides 3881 by NAT_4:9;
3881 = 7*554 + 3; hence not 7 divides 3881 by NAT_4:9;
3881 = 11*352 + 9; hence not 11 divides 3881 by NAT_4:9;
3881 = 13*298 + 7; hence not 13 divides 3881 by NAT_4:9;
3881 = 17*228 + 5; hence not 17 divides 3881 by NAT_4:9;
3881 = 19*204 + 5; hence not 19 divides 3881 by NAT_4:9;
3881 = 23*168 + 17; hence not 23 divides 3881 by NAT_4:9;
3881 = 29*133 + 24; hence not 29 divides 3881 by NAT_4:9;
3881 = 31*125 + 6; hence not 31 divides 3881 by NAT_4:9;
3881 = 37*104 + 33; hence not 37 divides 3881 by NAT_4:9;
3881 = 41*94 + 27; hence not 41 divides 3881 by NAT_4:9;
3881 = 43*90 + 11; hence not 43 divides 3881 by NAT_4:9;
3881 = 47*82 + 27; hence not 47 divides 3881 by NAT_4:9;
3881 = 53*73 + 12; hence not 53 divides 3881 by NAT_4:9;
3881 = 59*65 + 46; hence not 59 divides 3881 by NAT_4:9;
3881 = 61*63 + 38; hence not 61 divides 3881 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3881 & n is prime
holds not n divides 3881 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
3889 is prime
proof
now
3889 = 2*1944 + 1; hence not 2 divides 3889 by NAT_4:9;
3889 = 3*1296 + 1; hence not 3 divides 3889 by NAT_4:9;
3889 = 5*777 + 4; hence not 5 divides 3889 by NAT_4:9;
3889 = 7*555 + 4; hence not 7 divides 3889 by NAT_4:9;
3889 = 11*353 + 6; hence not 11 divides 3889 by NAT_4:9;
3889 = 13*299 + 2; hence not 13 divides 3889 by NAT_4:9;
3889 = 17*228 + 13; hence not 17 divides 3889 by NAT_4:9;
3889 = 19*204 + 13; hence not 19 divides 3889 by NAT_4:9;
3889 = 23*169 + 2; hence not 23 divides 3889 by NAT_4:9;
3889 = 29*134 + 3; hence not 29 divides 3889 by NAT_4:9;
3889 = 31*125 + 14; hence not 31 divides 3889 by NAT_4:9;
3889 = 37*105 + 4; hence not 37 divides 3889 by NAT_4:9;
3889 = 41*94 + 35; hence not 41 divides 3889 by NAT_4:9;
3889 = 43*90 + 19; hence not 43 divides 3889 by NAT_4:9;
3889 = 47*82 + 35; hence not 47 divides 3889 by NAT_4:9;
3889 = 53*73 + 20; hence not 53 divides 3889 by NAT_4:9;
3889 = 59*65 + 54; hence not 59 divides 3889 by NAT_4:9;
3889 = 61*63 + 46; hence not 61 divides 3889 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3889 & n is prime
holds not n divides 3889 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
3907 is prime
proof
now
3907 = 2*1953 + 1; hence not 2 divides 3907 by NAT_4:9;
3907 = 3*1302 + 1; hence not 3 divides 3907 by NAT_4:9;
3907 = 5*781 + 2; hence not 5 divides 3907 by NAT_4:9;
3907 = 7*558 + 1; hence not 7 divides 3907 by NAT_4:9;
3907 = 11*355 + 2; hence not 11 divides 3907 by NAT_4:9;
3907 = 13*300 + 7; hence not 13 divides 3907 by NAT_4:9;
3907 = 17*229 + 14; hence not 17 divides 3907 by NAT_4:9;
3907 = 19*205 + 12; hence not 19 divides 3907 by NAT_4:9;
3907 = 23*169 + 20; hence not 23 divides 3907 by NAT_4:9;
3907 = 29*134 + 21; hence not 29 divides 3907 by NAT_4:9;
3907 = 31*126 + 1; hence not 31 divides 3907 by NAT_4:9;
3907 = 37*105 + 22; hence not 37 divides 3907 by NAT_4:9;
3907 = 41*95 + 12; hence not 41 divides 3907 by NAT_4:9;
3907 = 43*90 + 37; hence not 43 divides 3907 by NAT_4:9;
3907 = 47*83 + 6; hence not 47 divides 3907 by NAT_4:9;
3907 = 53*73 + 38; hence not 53 divides 3907 by NAT_4:9;
3907 = 59*66 + 13; hence not 59 divides 3907 by NAT_4:9;
3907 = 61*64 + 3; hence not 61 divides 3907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3907 & n is prime
holds not n divides 3907 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3911 is prime
proof
now
3911 = 2*1955 + 1; hence not 2 divides 3911 by NAT_4:9;
3911 = 3*1303 + 2; hence not 3 divides 3911 by NAT_4:9;
3911 = 5*782 + 1; hence not 5 divides 3911 by NAT_4:9;
3911 = 7*558 + 5; hence not 7 divides 3911 by NAT_4:9;
3911 = 11*355 + 6; hence not 11 divides 3911 by NAT_4:9;
3911 = 13*300 + 11; hence not 13 divides 3911 by NAT_4:9;
3911 = 17*230 + 1; hence not 17 divides 3911 by NAT_4:9;
3911 = 19*205 + 16; hence not 19 divides 3911 by NAT_4:9;
3911 = 23*170 + 1; hence not 23 divides 3911 by NAT_4:9;
3911 = 29*134 + 25; hence not 29 divides 3911 by NAT_4:9;
3911 = 31*126 + 5; hence not 31 divides 3911 by NAT_4:9;
3911 = 37*105 + 26; hence not 37 divides 3911 by NAT_4:9;
3911 = 41*95 + 16; hence not 41 divides 3911 by NAT_4:9;
3911 = 43*90 + 41; hence not 43 divides 3911 by NAT_4:9;
3911 = 47*83 + 10; hence not 47 divides 3911 by NAT_4:9;
3911 = 53*73 + 42; hence not 53 divides 3911 by NAT_4:9;
3911 = 59*66 + 17; hence not 59 divides 3911 by NAT_4:9;
3911 = 61*64 + 7; hence not 61 divides 3911 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3911 & n is prime
holds not n divides 3911 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3917 is prime
proof
now
3917 = 2*1958 + 1; hence not 2 divides 3917 by NAT_4:9;
3917 = 3*1305 + 2; hence not 3 divides 3917 by NAT_4:9;
3917 = 5*783 + 2; hence not 5 divides 3917 by NAT_4:9;
3917 = 7*559 + 4; hence not 7 divides 3917 by NAT_4:9;
3917 = 11*356 + 1; hence not 11 divides 3917 by NAT_4:9;
3917 = 13*301 + 4; hence not 13 divides 3917 by NAT_4:9;
3917 = 17*230 + 7; hence not 17 divides 3917 by NAT_4:9;
3917 = 19*206 + 3; hence not 19 divides 3917 by NAT_4:9;
3917 = 23*170 + 7; hence not 23 divides 3917 by NAT_4:9;
3917 = 29*135 + 2; hence not 29 divides 3917 by NAT_4:9;
3917 = 31*126 + 11; hence not 31 divides 3917 by NAT_4:9;
3917 = 37*105 + 32; hence not 37 divides 3917 by NAT_4:9;
3917 = 41*95 + 22; hence not 41 divides 3917 by NAT_4:9;
3917 = 43*91 + 4; hence not 43 divides 3917 by NAT_4:9;
3917 = 47*83 + 16; hence not 47 divides 3917 by NAT_4:9;
3917 = 53*73 + 48; hence not 53 divides 3917 by NAT_4:9;
3917 = 59*66 + 23; hence not 59 divides 3917 by NAT_4:9;
3917 = 61*64 + 13; hence not 61 divides 3917 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3917 & n is prime
holds not n divides 3917 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3919 is prime
proof
now
3919 = 2*1959 + 1; hence not 2 divides 3919 by NAT_4:9;
3919 = 3*1306 + 1; hence not 3 divides 3919 by NAT_4:9;
3919 = 5*783 + 4; hence not 5 divides 3919 by NAT_4:9;
3919 = 7*559 + 6; hence not 7 divides 3919 by NAT_4:9;
3919 = 11*356 + 3; hence not 11 divides 3919 by NAT_4:9;
3919 = 13*301 + 6; hence not 13 divides 3919 by NAT_4:9;
3919 = 17*230 + 9; hence not 17 divides 3919 by NAT_4:9;
3919 = 19*206 + 5; hence not 19 divides 3919 by NAT_4:9;
3919 = 23*170 + 9; hence not 23 divides 3919 by NAT_4:9;
3919 = 29*135 + 4; hence not 29 divides 3919 by NAT_4:9;
3919 = 31*126 + 13; hence not 31 divides 3919 by NAT_4:9;
3919 = 37*105 + 34; hence not 37 divides 3919 by NAT_4:9;
3919 = 41*95 + 24; hence not 41 divides 3919 by NAT_4:9;
3919 = 43*91 + 6; hence not 43 divides 3919 by NAT_4:9;
3919 = 47*83 + 18; hence not 47 divides 3919 by NAT_4:9;
3919 = 53*73 + 50; hence not 53 divides 3919 by NAT_4:9;
3919 = 59*66 + 25; hence not 59 divides 3919 by NAT_4:9;
3919 = 61*64 + 15; hence not 61 divides 3919 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3919 & n is prime
holds not n divides 3919 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3923 is prime
proof
now
3923 = 2*1961 + 1; hence not 2 divides 3923 by NAT_4:9;
3923 = 3*1307 + 2; hence not 3 divides 3923 by NAT_4:9;
3923 = 5*784 + 3; hence not 5 divides 3923 by NAT_4:9;
3923 = 7*560 + 3; hence not 7 divides 3923 by NAT_4:9;
3923 = 11*356 + 7; hence not 11 divides 3923 by NAT_4:9;
3923 = 13*301 + 10; hence not 13 divides 3923 by NAT_4:9;
3923 = 17*230 + 13; hence not 17 divides 3923 by NAT_4:9;
3923 = 19*206 + 9; hence not 19 divides 3923 by NAT_4:9;
3923 = 23*170 + 13; hence not 23 divides 3923 by NAT_4:9;
3923 = 29*135 + 8; hence not 29 divides 3923 by NAT_4:9;
3923 = 31*126 + 17; hence not 31 divides 3923 by NAT_4:9;
3923 = 37*106 + 1; hence not 37 divides 3923 by NAT_4:9;
3923 = 41*95 + 28; hence not 41 divides 3923 by NAT_4:9;
3923 = 43*91 + 10; hence not 43 divides 3923 by NAT_4:9;
3923 = 47*83 + 22; hence not 47 divides 3923 by NAT_4:9;
3923 = 53*74 + 1; hence not 53 divides 3923 by NAT_4:9;
3923 = 59*66 + 29; hence not 59 divides 3923 by NAT_4:9;
3923 = 61*64 + 19; hence not 61 divides 3923 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3923 & n is prime
holds not n divides 3923 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
3929 is prime
proof
now
3929 = 2*1964 + 1; hence not 2 divides 3929 by NAT_4:9;
3929 = 3*1309 + 2; hence not 3 divides 3929 by NAT_4:9;
3929 = 5*785 + 4; hence not 5 divides 3929 by NAT_4:9;
3929 = 7*561 + 2; hence not 7 divides 3929 by NAT_4:9;
3929 = 11*357 + 2; hence not 11 divides 3929 by NAT_4:9;
3929 = 13*302 + 3; hence not 13 divides 3929 by NAT_4:9;
3929 = 17*231 + 2; hence not 17 divides 3929 by NAT_4:9;
3929 = 19*206 + 15; hence not 19 divides 3929 by NAT_4:9;
3929 = 23*170 + 19; hence not 23 divides 3929 by NAT_4:9;
3929 = 29*135 + 14; hence not 29 divides 3929 by NAT_4:9;
3929 = 31*126 + 23; hence not 31 divides 3929 by NAT_4:9;
3929 = 37*106 + 7; hence not 37 divides 3929 by NAT_4:9;
3929 = 41*95 + 34; hence not 41 divides 3929 by NAT_4:9;
3929 = 43*91 + 16; hence not 43 divides 3929 by NAT_4:9;
3929 = 47*83 + 28; hence not 47 divides 3929 by NAT_4:9;
3929 = 53*74 + 7; hence not 53 divides 3929 by NAT_4:9;
3929 = 59*66 + 35; hence not 59 divides 3929 by NAT_4:9;
3929 = 61*64 + 25; hence not 61 divides 3929 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3929 & n is prime
holds not n divides 3929 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
3931 is prime
proof
now
3931 = 2*1965 + 1; hence not 2 divides 3931 by NAT_4:9;
3931 = 3*1310 + 1; hence not 3 divides 3931 by NAT_4:9;
3931 = 5*786 + 1; hence not 5 divides 3931 by NAT_4:9;
3931 = 7*561 + 4; hence not 7 divides 3931 by NAT_4:9;
3931 = 11*357 + 4; hence not 11 divides 3931 by NAT_4:9;
3931 = 13*302 + 5; hence not 13 divides 3931 by NAT_4:9;
3931 = 17*231 + 4; hence not 17 divides 3931 by NAT_4:9;
3931 = 19*206 + 17; hence not 19 divides 3931 by NAT_4:9;
3931 = 23*170 + 21; hence not 23 divides 3931 by NAT_4:9;
3931 = 29*135 + 16; hence not 29 divides 3931 by NAT_4:9;
3931 = 31*126 + 25; hence not 31 divides 3931 by NAT_4:9;
3931 = 37*106 + 9; hence not 37 divides 3931 by NAT_4:9;
3931 = 41*95 + 36; hence not 41 divides 3931 by NAT_4:9;
3931 = 43*91 + 18; hence not 43 divides 3931 by NAT_4:9;
3931 = 47*83 + 30; hence not 47 divides 3931 by NAT_4:9;
3931 = 53*74 + 9; hence not 53 divides 3931 by NAT_4:9;
3931 = 59*66 + 37; hence not 59 divides 3931 by NAT_4:9;
3931 = 61*64 + 27; hence not 61 divides 3931 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3931 & n is prime
holds not n divides 3931 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
3943 is prime
proof
now
3943 = 2*1971 + 1; hence not 2 divides 3943 by NAT_4:9;
3943 = 3*1314 + 1; hence not 3 divides 3943 by NAT_4:9;
3943 = 5*788 + 3; hence not 5 divides 3943 by NAT_4:9;
3943 = 7*563 + 2; hence not 7 divides 3943 by NAT_4:9;
3943 = 11*358 + 5; hence not 11 divides 3943 by NAT_4:9;
3943 = 13*303 + 4; hence not 13 divides 3943 by NAT_4:9;
3943 = 17*231 + 16; hence not 17 divides 3943 by NAT_4:9;
3943 = 19*207 + 10; hence not 19 divides 3943 by NAT_4:9;
3943 = 23*171 + 10; hence not 23 divides 3943 by NAT_4:9;
3943 = 29*135 + 28; hence not 29 divides 3943 by NAT_4:9;
3943 = 31*127 + 6; hence not 31 divides 3943 by NAT_4:9;
3943 = 37*106 + 21; hence not 37 divides 3943 by NAT_4:9;
3943 = 41*96 + 7; hence not 41 divides 3943 by NAT_4:9;
3943 = 43*91 + 30; hence not 43 divides 3943 by NAT_4:9;
3943 = 47*83 + 42; hence not 47 divides 3943 by NAT_4:9;
3943 = 53*74 + 21; hence not 53 divides 3943 by NAT_4:9;
3943 = 59*66 + 49; hence not 59 divides 3943 by NAT_4:9;
3943 = 61*64 + 39; hence not 61 divides 3943 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3943 & n is prime
holds not n divides 3943 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
3947 is prime
proof
now
3947 = 2*1973 + 1; hence not 2 divides 3947 by NAT_4:9;
3947 = 3*1315 + 2; hence not 3 divides 3947 by NAT_4:9;
3947 = 5*789 + 2; hence not 5 divides 3947 by NAT_4:9;
3947 = 7*563 + 6; hence not 7 divides 3947 by NAT_4:9;
3947 = 11*358 + 9; hence not 11 divides 3947 by NAT_4:9;
3947 = 13*303 + 8; hence not 13 divides 3947 by NAT_4:9;
3947 = 17*232 + 3; hence not 17 divides 3947 by NAT_4:9;
3947 = 19*207 + 14; hence not 19 divides 3947 by NAT_4:9;
3947 = 23*171 + 14; hence not 23 divides 3947 by NAT_4:9;
3947 = 29*136 + 3; hence not 29 divides 3947 by NAT_4:9;
3947 = 31*127 + 10; hence not 31 divides 3947 by NAT_4:9;
3947 = 37*106 + 25; hence not 37 divides 3947 by NAT_4:9;
3947 = 41*96 + 11; hence not 41 divides 3947 by NAT_4:9;
3947 = 43*91 + 34; hence not 43 divides 3947 by NAT_4:9;
3947 = 47*83 + 46; hence not 47 divides 3947 by NAT_4:9;
3947 = 53*74 + 25; hence not 53 divides 3947 by NAT_4:9;
3947 = 59*66 + 53; hence not 59 divides 3947 by NAT_4:9;
3947 = 61*64 + 43; hence not 61 divides 3947 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3947 & n is prime
holds not n divides 3947 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
3967 is prime
proof
now
3967 = 2*1983 + 1; hence not 2 divides 3967 by NAT_4:9;
3967 = 3*1322 + 1; hence not 3 divides 3967 by NAT_4:9;
3967 = 5*793 + 2; hence not 5 divides 3967 by NAT_4:9;
3967 = 7*566 + 5; hence not 7 divides 3967 by NAT_4:9;
3967 = 11*360 + 7; hence not 11 divides 3967 by NAT_4:9;
3967 = 13*305 + 2; hence not 13 divides 3967 by NAT_4:9;
3967 = 17*233 + 6; hence not 17 divides 3967 by NAT_4:9;
3967 = 19*208 + 15; hence not 19 divides 3967 by NAT_4:9;
3967 = 23*172 + 11; hence not 23 divides 3967 by NAT_4:9;
3967 = 29*136 + 23; hence not 29 divides 3967 by NAT_4:9;
3967 = 31*127 + 30; hence not 31 divides 3967 by NAT_4:9;
3967 = 37*107 + 8; hence not 37 divides 3967 by NAT_4:9;
3967 = 41*96 + 31; hence not 41 divides 3967 by NAT_4:9;
3967 = 43*92 + 11; hence not 43 divides 3967 by NAT_4:9;
3967 = 47*84 + 19; hence not 47 divides 3967 by NAT_4:9;
3967 = 53*74 + 45; hence not 53 divides 3967 by NAT_4:9;
3967 = 59*67 + 14; hence not 59 divides 3967 by NAT_4:9;
3967 = 61*65 + 2; hence not 61 divides 3967 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3967 & n is prime
holds not n divides 3967 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
3989 is prime
proof
now
3989 = 2*1994 + 1; hence not 2 divides 3989 by NAT_4:9;
3989 = 3*1329 + 2; hence not 3 divides 3989 by NAT_4:9;
3989 = 5*797 + 4; hence not 5 divides 3989 by NAT_4:9;
3989 = 7*569 + 6; hence not 7 divides 3989 by NAT_4:9;
3989 = 11*362 + 7; hence not 11 divides 3989 by NAT_4:9;
3989 = 13*306 + 11; hence not 13 divides 3989 by NAT_4:9;
3989 = 17*234 + 11; hence not 17 divides 3989 by NAT_4:9;
3989 = 19*209 + 18; hence not 19 divides 3989 by NAT_4:9;
3989 = 23*173 + 10; hence not 23 divides 3989 by NAT_4:9;
3989 = 29*137 + 16; hence not 29 divides 3989 by NAT_4:9;
3989 = 31*128 + 21; hence not 31 divides 3989 by NAT_4:9;
3989 = 37*107 + 30; hence not 37 divides 3989 by NAT_4:9;
3989 = 41*97 + 12; hence not 41 divides 3989 by NAT_4:9;
3989 = 43*92 + 33; hence not 43 divides 3989 by NAT_4:9;
3989 = 47*84 + 41; hence not 47 divides 3989 by NAT_4:9;
3989 = 53*75 + 14; hence not 53 divides 3989 by NAT_4:9;
3989 = 59*67 + 36; hence not 59 divides 3989 by NAT_4:9;
3989 = 61*65 + 24; hence not 61 divides 3989 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 3989 & n is prime
holds not n divides 3989 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4001 is prime
proof
now
4001 = 2*2000 + 1; hence not 2 divides 4001 by NAT_4:9;
4001 = 3*1333 + 2; hence not 3 divides 4001 by NAT_4:9;
4001 = 5*800 + 1; hence not 5 divides 4001 by NAT_4:9;
4001 = 7*571 + 4; hence not 7 divides 4001 by NAT_4:9;
4001 = 11*363 + 8; hence not 11 divides 4001 by NAT_4:9;
4001 = 13*307 + 10; hence not 13 divides 4001 by NAT_4:9;
4001 = 17*235 + 6; hence not 17 divides 4001 by NAT_4:9;
4001 = 19*210 + 11; hence not 19 divides 4001 by NAT_4:9;
4001 = 23*173 + 22; hence not 23 divides 4001 by NAT_4:9;
4001 = 29*137 + 28; hence not 29 divides 4001 by NAT_4:9;
4001 = 31*129 + 2; hence not 31 divides 4001 by NAT_4:9;
4001 = 37*108 + 5; hence not 37 divides 4001 by NAT_4:9;
4001 = 41*97 + 24; hence not 41 divides 4001 by NAT_4:9;
4001 = 43*93 + 2; hence not 43 divides 4001 by NAT_4:9;
4001 = 47*85 + 6; hence not 47 divides 4001 by NAT_4:9;
4001 = 53*75 + 26; hence not 53 divides 4001 by NAT_4:9;
4001 = 59*67 + 48; hence not 59 divides 4001 by NAT_4:9;
4001 = 61*65 + 36; hence not 61 divides 4001 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4001 & n is prime
holds not n divides 4001 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4003 is prime
proof
now
4003 = 2*2001 + 1; hence not 2 divides 4003 by NAT_4:9;
4003 = 3*1334 + 1; hence not 3 divides 4003 by NAT_4:9;
4003 = 5*800 + 3; hence not 5 divides 4003 by NAT_4:9;
4003 = 7*571 + 6; hence not 7 divides 4003 by NAT_4:9;
4003 = 11*363 + 10; hence not 11 divides 4003 by NAT_4:9;
4003 = 13*307 + 12; hence not 13 divides 4003 by NAT_4:9;
4003 = 17*235 + 8; hence not 17 divides 4003 by NAT_4:9;
4003 = 19*210 + 13; hence not 19 divides 4003 by NAT_4:9;
4003 = 23*174 + 1; hence not 23 divides 4003 by NAT_4:9;
4003 = 29*138 + 1; hence not 29 divides 4003 by NAT_4:9;
4003 = 31*129 + 4; hence not 31 divides 4003 by NAT_4:9;
4003 = 37*108 + 7; hence not 37 divides 4003 by NAT_4:9;
4003 = 41*97 + 26; hence not 41 divides 4003 by NAT_4:9;
4003 = 43*93 + 4; hence not 43 divides 4003 by NAT_4:9;
4003 = 47*85 + 8; hence not 47 divides 4003 by NAT_4:9;
4003 = 53*75 + 28; hence not 53 divides 4003 by NAT_4:9;
4003 = 59*67 + 50; hence not 59 divides 4003 by NAT_4:9;
4003 = 61*65 + 38; hence not 61 divides 4003 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4003 & n is prime
holds not n divides 4003 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4007 is prime
proof
now
4007 = 2*2003 + 1; hence not 2 divides 4007 by NAT_4:9;
4007 = 3*1335 + 2; hence not 3 divides 4007 by NAT_4:9;
4007 = 5*801 + 2; hence not 5 divides 4007 by NAT_4:9;
4007 = 7*572 + 3; hence not 7 divides 4007 by NAT_4:9;
4007 = 11*364 + 3; hence not 11 divides 4007 by NAT_4:9;
4007 = 13*308 + 3; hence not 13 divides 4007 by NAT_4:9;
4007 = 17*235 + 12; hence not 17 divides 4007 by NAT_4:9;
4007 = 19*210 + 17; hence not 19 divides 4007 by NAT_4:9;
4007 = 23*174 + 5; hence not 23 divides 4007 by NAT_4:9;
4007 = 29*138 + 5; hence not 29 divides 4007 by NAT_4:9;
4007 = 31*129 + 8; hence not 31 divides 4007 by NAT_4:9;
4007 = 37*108 + 11; hence not 37 divides 4007 by NAT_4:9;
4007 = 41*97 + 30; hence not 41 divides 4007 by NAT_4:9;
4007 = 43*93 + 8; hence not 43 divides 4007 by NAT_4:9;
4007 = 47*85 + 12; hence not 47 divides 4007 by NAT_4:9;
4007 = 53*75 + 32; hence not 53 divides 4007 by NAT_4:9;
4007 = 59*67 + 54; hence not 59 divides 4007 by NAT_4:9;
4007 = 61*65 + 42; hence not 61 divides 4007 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4007 & n is prime
holds not n divides 4007 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4013 is prime
proof
now
4013 = 2*2006 + 1; hence not 2 divides 4013 by NAT_4:9;
4013 = 3*1337 + 2; hence not 3 divides 4013 by NAT_4:9;
4013 = 5*802 + 3; hence not 5 divides 4013 by NAT_4:9;
4013 = 7*573 + 2; hence not 7 divides 4013 by NAT_4:9;
4013 = 11*364 + 9; hence not 11 divides 4013 by NAT_4:9;
4013 = 13*308 + 9; hence not 13 divides 4013 by NAT_4:9;
4013 = 17*236 + 1; hence not 17 divides 4013 by NAT_4:9;
4013 = 19*211 + 4; hence not 19 divides 4013 by NAT_4:9;
4013 = 23*174 + 11; hence not 23 divides 4013 by NAT_4:9;
4013 = 29*138 + 11; hence not 29 divides 4013 by NAT_4:9;
4013 = 31*129 + 14; hence not 31 divides 4013 by NAT_4:9;
4013 = 37*108 + 17; hence not 37 divides 4013 by NAT_4:9;
4013 = 41*97 + 36; hence not 41 divides 4013 by NAT_4:9;
4013 = 43*93 + 14; hence not 43 divides 4013 by NAT_4:9;
4013 = 47*85 + 18; hence not 47 divides 4013 by NAT_4:9;
4013 = 53*75 + 38; hence not 53 divides 4013 by NAT_4:9;
4013 = 59*68 + 1; hence not 59 divides 4013 by NAT_4:9;
4013 = 61*65 + 48; hence not 61 divides 4013 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4013 & n is prime
holds not n divides 4013 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4019 is prime
proof
now
4019 = 2*2009 + 1; hence not 2 divides 4019 by NAT_4:9;
4019 = 3*1339 + 2; hence not 3 divides 4019 by NAT_4:9;
4019 = 5*803 + 4; hence not 5 divides 4019 by NAT_4:9;
4019 = 7*574 + 1; hence not 7 divides 4019 by NAT_4:9;
4019 = 11*365 + 4; hence not 11 divides 4019 by NAT_4:9;
4019 = 13*309 + 2; hence not 13 divides 4019 by NAT_4:9;
4019 = 17*236 + 7; hence not 17 divides 4019 by NAT_4:9;
4019 = 19*211 + 10; hence not 19 divides 4019 by NAT_4:9;
4019 = 23*174 + 17; hence not 23 divides 4019 by NAT_4:9;
4019 = 29*138 + 17; hence not 29 divides 4019 by NAT_4:9;
4019 = 31*129 + 20; hence not 31 divides 4019 by NAT_4:9;
4019 = 37*108 + 23; hence not 37 divides 4019 by NAT_4:9;
4019 = 41*98 + 1; hence not 41 divides 4019 by NAT_4:9;
4019 = 43*93 + 20; hence not 43 divides 4019 by NAT_4:9;
4019 = 47*85 + 24; hence not 47 divides 4019 by NAT_4:9;
4019 = 53*75 + 44; hence not 53 divides 4019 by NAT_4:9;
4019 = 59*68 + 7; hence not 59 divides 4019 by NAT_4:9;
4019 = 61*65 + 54; hence not 61 divides 4019 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4019 & n is prime
holds not n divides 4019 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4021 is prime
proof
now
4021 = 2*2010 + 1; hence not 2 divides 4021 by NAT_4:9;
4021 = 3*1340 + 1; hence not 3 divides 4021 by NAT_4:9;
4021 = 5*804 + 1; hence not 5 divides 4021 by NAT_4:9;
4021 = 7*574 + 3; hence not 7 divides 4021 by NAT_4:9;
4021 = 11*365 + 6; hence not 11 divides 4021 by NAT_4:9;
4021 = 13*309 + 4; hence not 13 divides 4021 by NAT_4:9;
4021 = 17*236 + 9; hence not 17 divides 4021 by NAT_4:9;
4021 = 19*211 + 12; hence not 19 divides 4021 by NAT_4:9;
4021 = 23*174 + 19; hence not 23 divides 4021 by NAT_4:9;
4021 = 29*138 + 19; hence not 29 divides 4021 by NAT_4:9;
4021 = 31*129 + 22; hence not 31 divides 4021 by NAT_4:9;
4021 = 37*108 + 25; hence not 37 divides 4021 by NAT_4:9;
4021 = 41*98 + 3; hence not 41 divides 4021 by NAT_4:9;
4021 = 43*93 + 22; hence not 43 divides 4021 by NAT_4:9;
4021 = 47*85 + 26; hence not 47 divides 4021 by NAT_4:9;
4021 = 53*75 + 46; hence not 53 divides 4021 by NAT_4:9;
4021 = 59*68 + 9; hence not 59 divides 4021 by NAT_4:9;
4021 = 61*65 + 56; hence not 61 divides 4021 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4021 & n is prime
holds not n divides 4021 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4027 is prime
proof
now
4027 = 2*2013 + 1; hence not 2 divides 4027 by NAT_4:9;
4027 = 3*1342 + 1; hence not 3 divides 4027 by NAT_4:9;
4027 = 5*805 + 2; hence not 5 divides 4027 by NAT_4:9;
4027 = 7*575 + 2; hence not 7 divides 4027 by NAT_4:9;
4027 = 11*366 + 1; hence not 11 divides 4027 by NAT_4:9;
4027 = 13*309 + 10; hence not 13 divides 4027 by NAT_4:9;
4027 = 17*236 + 15; hence not 17 divides 4027 by NAT_4:9;
4027 = 19*211 + 18; hence not 19 divides 4027 by NAT_4:9;
4027 = 23*175 + 2; hence not 23 divides 4027 by NAT_4:9;
4027 = 29*138 + 25; hence not 29 divides 4027 by NAT_4:9;
4027 = 31*129 + 28; hence not 31 divides 4027 by NAT_4:9;
4027 = 37*108 + 31; hence not 37 divides 4027 by NAT_4:9;
4027 = 41*98 + 9; hence not 41 divides 4027 by NAT_4:9;
4027 = 43*93 + 28; hence not 43 divides 4027 by NAT_4:9;
4027 = 47*85 + 32; hence not 47 divides 4027 by NAT_4:9;
4027 = 53*75 + 52; hence not 53 divides 4027 by NAT_4:9;
4027 = 59*68 + 15; hence not 59 divides 4027 by NAT_4:9;
4027 = 61*66 + 1; hence not 61 divides 4027 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4027 & n is prime
holds not n divides 4027 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
4049 is prime
proof
now
4049 = 2*2024 + 1; hence not 2 divides 4049 by NAT_4:9;
4049 = 3*1349 + 2; hence not 3 divides 4049 by NAT_4:9;
4049 = 5*809 + 4; hence not 5 divides 4049 by NAT_4:9;
4049 = 7*578 + 3; hence not 7 divides 4049 by NAT_4:9;
4049 = 11*368 + 1; hence not 11 divides 4049 by NAT_4:9;
4049 = 13*311 + 6; hence not 13 divides 4049 by NAT_4:9;
4049 = 17*238 + 3; hence not 17 divides 4049 by NAT_4:9;
4049 = 19*213 + 2; hence not 19 divides 4049 by NAT_4:9;
4049 = 23*176 + 1; hence not 23 divides 4049 by NAT_4:9;
4049 = 29*139 + 18; hence not 29 divides 4049 by NAT_4:9;
4049 = 31*130 + 19; hence not 31 divides 4049 by NAT_4:9;
4049 = 37*109 + 16; hence not 37 divides 4049 by NAT_4:9;
4049 = 41*98 + 31; hence not 41 divides 4049 by NAT_4:9;
4049 = 43*94 + 7; hence not 43 divides 4049 by NAT_4:9;
4049 = 47*86 + 7; hence not 47 divides 4049 by NAT_4:9;
4049 = 53*76 + 21; hence not 53 divides 4049 by NAT_4:9;
4049 = 59*68 + 37; hence not 59 divides 4049 by NAT_4:9;
4049 = 61*66 + 23; hence not 61 divides 4049 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4049 & n is prime
holds not n divides 4049 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4051 is prime
proof
now
4051 = 2*2025 + 1; hence not 2 divides 4051 by NAT_4:9;
4051 = 3*1350 + 1; hence not 3 divides 4051 by NAT_4:9;
4051 = 5*810 + 1; hence not 5 divides 4051 by NAT_4:9;
4051 = 7*578 + 5; hence not 7 divides 4051 by NAT_4:9;
4051 = 11*368 + 3; hence not 11 divides 4051 by NAT_4:9;
4051 = 13*311 + 8; hence not 13 divides 4051 by NAT_4:9;
4051 = 17*238 + 5; hence not 17 divides 4051 by NAT_4:9;
4051 = 19*213 + 4; hence not 19 divides 4051 by NAT_4:9;
4051 = 23*176 + 3; hence not 23 divides 4051 by NAT_4:9;
4051 = 29*139 + 20; hence not 29 divides 4051 by NAT_4:9;
4051 = 31*130 + 21; hence not 31 divides 4051 by NAT_4:9;
4051 = 37*109 + 18; hence not 37 divides 4051 by NAT_4:9;
4051 = 41*98 + 33; hence not 41 divides 4051 by NAT_4:9;
4051 = 43*94 + 9; hence not 43 divides 4051 by NAT_4:9;
4051 = 47*86 + 9; hence not 47 divides 4051 by NAT_4:9;
4051 = 53*76 + 23; hence not 53 divides 4051 by NAT_4:9;
4051 = 59*68 + 39; hence not 59 divides 4051 by NAT_4:9;
4051 = 61*66 + 25; hence not 61 divides 4051 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4051 & n is prime
holds not n divides 4051 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4057 is prime
proof
now
4057 = 2*2028 + 1; hence not 2 divides 4057 by NAT_4:9;
4057 = 3*1352 + 1; hence not 3 divides 4057 by NAT_4:9;
4057 = 5*811 + 2; hence not 5 divides 4057 by NAT_4:9;
4057 = 7*579 + 4; hence not 7 divides 4057 by NAT_4:9;
4057 = 11*368 + 9; hence not 11 divides 4057 by NAT_4:9;
4057 = 13*312 + 1; hence not 13 divides 4057 by NAT_4:9;
4057 = 17*238 + 11; hence not 17 divides 4057 by NAT_4:9;
4057 = 19*213 + 10; hence not 19 divides 4057 by NAT_4:9;
4057 = 23*176 + 9; hence not 23 divides 4057 by NAT_4:9;
4057 = 29*139 + 26; hence not 29 divides 4057 by NAT_4:9;
4057 = 31*130 + 27; hence not 31 divides 4057 by NAT_4:9;
4057 = 37*109 + 24; hence not 37 divides 4057 by NAT_4:9;
4057 = 41*98 + 39; hence not 41 divides 4057 by NAT_4:9;
4057 = 43*94 + 15; hence not 43 divides 4057 by NAT_4:9;
4057 = 47*86 + 15; hence not 47 divides 4057 by NAT_4:9;
4057 = 53*76 + 29; hence not 53 divides 4057 by NAT_4:9;
4057 = 59*68 + 45; hence not 59 divides 4057 by NAT_4:9;
4057 = 61*66 + 31; hence not 61 divides 4057 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4057 & n is prime
holds not n divides 4057 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
4073 is prime
proof
now
4073 = 2*2036 + 1; hence not 2 divides 4073 by NAT_4:9;
4073 = 3*1357 + 2; hence not 3 divides 4073 by NAT_4:9;
4073 = 5*814 + 3; hence not 5 divides 4073 by NAT_4:9;
4073 = 7*581 + 6; hence not 7 divides 4073 by NAT_4:9;
4073 = 11*370 + 3; hence not 11 divides 4073 by NAT_4:9;
4073 = 13*313 + 4; hence not 13 divides 4073 by NAT_4:9;
4073 = 17*239 + 10; hence not 17 divides 4073 by NAT_4:9;
4073 = 19*214 + 7; hence not 19 divides 4073 by NAT_4:9;
4073 = 23*177 + 2; hence not 23 divides 4073 by NAT_4:9;
4073 = 29*140 + 13; hence not 29 divides 4073 by NAT_4:9;
4073 = 31*131 + 12; hence not 31 divides 4073 by NAT_4:9;
4073 = 37*110 + 3; hence not 37 divides 4073 by NAT_4:9;
4073 = 41*99 + 14; hence not 41 divides 4073 by NAT_4:9;
4073 = 43*94 + 31; hence not 43 divides 4073 by NAT_4:9;
4073 = 47*86 + 31; hence not 47 divides 4073 by NAT_4:9;
4073 = 53*76 + 45; hence not 53 divides 4073 by NAT_4:9;
4073 = 59*69 + 2; hence not 59 divides 4073 by NAT_4:9;
4073 = 61*66 + 47; hence not 61 divides 4073 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4073 & n is prime
holds not n divides 4073 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4079 is prime
proof
now
4079 = 2*2039 + 1; hence not 2 divides 4079 by NAT_4:9;
4079 = 3*1359 + 2; hence not 3 divides 4079 by NAT_4:9;
4079 = 5*815 + 4; hence not 5 divides 4079 by NAT_4:9;
4079 = 7*582 + 5; hence not 7 divides 4079 by NAT_4:9;
4079 = 11*370 + 9; hence not 11 divides 4079 by NAT_4:9;
4079 = 13*313 + 10; hence not 13 divides 4079 by NAT_4:9;
4079 = 17*239 + 16; hence not 17 divides 4079 by NAT_4:9;
4079 = 19*214 + 13; hence not 19 divides 4079 by NAT_4:9;
4079 = 23*177 + 8; hence not 23 divides 4079 by NAT_4:9;
4079 = 29*140 + 19; hence not 29 divides 4079 by NAT_4:9;
4079 = 31*131 + 18; hence not 31 divides 4079 by NAT_4:9;
4079 = 37*110 + 9; hence not 37 divides 4079 by NAT_4:9;
4079 = 41*99 + 20; hence not 41 divides 4079 by NAT_4:9;
4079 = 43*94 + 37; hence not 43 divides 4079 by NAT_4:9;
4079 = 47*86 + 37; hence not 47 divides 4079 by NAT_4:9;
4079 = 53*76 + 51; hence not 53 divides 4079 by NAT_4:9;
4079 = 59*69 + 8; hence not 59 divides 4079 by NAT_4:9;
4079 = 61*66 + 53; hence not 61 divides 4079 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4079 & n is prime
holds not n divides 4079 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4091 is prime
proof
now
4091 = 2*2045 + 1; hence not 2 divides 4091 by NAT_4:9;
4091 = 3*1363 + 2; hence not 3 divides 4091 by NAT_4:9;
4091 = 5*818 + 1; hence not 5 divides 4091 by NAT_4:9;
4091 = 7*584 + 3; hence not 7 divides 4091 by NAT_4:9;
4091 = 11*371 + 10; hence not 11 divides 4091 by NAT_4:9;
4091 = 13*314 + 9; hence not 13 divides 4091 by NAT_4:9;
4091 = 17*240 + 11; hence not 17 divides 4091 by NAT_4:9;
4091 = 19*215 + 6; hence not 19 divides 4091 by NAT_4:9;
4091 = 23*177 + 20; hence not 23 divides 4091 by NAT_4:9;
4091 = 29*141 + 2; hence not 29 divides 4091 by NAT_4:9;
4091 = 31*131 + 30; hence not 31 divides 4091 by NAT_4:9;
4091 = 37*110 + 21; hence not 37 divides 4091 by NAT_4:9;
4091 = 41*99 + 32; hence not 41 divides 4091 by NAT_4:9;
4091 = 43*95 + 6; hence not 43 divides 4091 by NAT_4:9;
4091 = 47*87 + 2; hence not 47 divides 4091 by NAT_4:9;
4091 = 53*77 + 10; hence not 53 divides 4091 by NAT_4:9;
4091 = 59*69 + 20; hence not 59 divides 4091 by NAT_4:9;
4091 = 61*67 + 4; hence not 61 divides 4091 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4091 & n is prime
holds not n divides 4091 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4093 is prime
proof
now
4093 = 2*2046 + 1; hence not 2 divides 4093 by NAT_4:9;
4093 = 3*1364 + 1; hence not 3 divides 4093 by NAT_4:9;
4093 = 5*818 + 3; hence not 5 divides 4093 by NAT_4:9;
4093 = 7*584 + 5; hence not 7 divides 4093 by NAT_4:9;
4093 = 11*372 + 1; hence not 11 divides 4093 by NAT_4:9;
4093 = 13*314 + 11; hence not 13 divides 4093 by NAT_4:9;
4093 = 17*240 + 13; hence not 17 divides 4093 by NAT_4:9;
4093 = 19*215 + 8; hence not 19 divides 4093 by NAT_4:9;
4093 = 23*177 + 22; hence not 23 divides 4093 by NAT_4:9;
4093 = 29*141 + 4; hence not 29 divides 4093 by NAT_4:9;
4093 = 31*132 + 1; hence not 31 divides 4093 by NAT_4:9;
4093 = 37*110 + 23; hence not 37 divides 4093 by NAT_4:9;
4093 = 41*99 + 34; hence not 41 divides 4093 by NAT_4:9;
4093 = 43*95 + 8; hence not 43 divides 4093 by NAT_4:9;
4093 = 47*87 + 4; hence not 47 divides 4093 by NAT_4:9;
4093 = 53*77 + 12; hence not 53 divides 4093 by NAT_4:9;
4093 = 59*69 + 22; hence not 59 divides 4093 by NAT_4:9;
4093 = 61*67 + 6; hence not 61 divides 4093 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4093 & n is prime
holds not n divides 4093 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4099 is prime
proof
now
4099 = 2*2049 + 1; hence not 2 divides 4099 by NAT_4:9;
4099 = 3*1366 + 1; hence not 3 divides 4099 by NAT_4:9;
4099 = 5*819 + 4; hence not 5 divides 4099 by NAT_4:9;
4099 = 7*585 + 4; hence not 7 divides 4099 by NAT_4:9;
4099 = 11*372 + 7; hence not 11 divides 4099 by NAT_4:9;
4099 = 13*315 + 4; hence not 13 divides 4099 by NAT_4:9;
4099 = 17*241 + 2; hence not 17 divides 4099 by NAT_4:9;
4099 = 19*215 + 14; hence not 19 divides 4099 by NAT_4:9;
4099 = 23*178 + 5; hence not 23 divides 4099 by NAT_4:9;
4099 = 29*141 + 10; hence not 29 divides 4099 by NAT_4:9;
4099 = 31*132 + 7; hence not 31 divides 4099 by NAT_4:9;
4099 = 37*110 + 29; hence not 37 divides 4099 by NAT_4:9;
4099 = 41*99 + 40; hence not 41 divides 4099 by NAT_4:9;
4099 = 43*95 + 14; hence not 43 divides 4099 by NAT_4:9;
4099 = 47*87 + 10; hence not 47 divides 4099 by NAT_4:9;
4099 = 53*77 + 18; hence not 53 divides 4099 by NAT_4:9;
4099 = 59*69 + 28; hence not 59 divides 4099 by NAT_4:9;
4099 = 61*67 + 12; hence not 61 divides 4099 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4099 & n is prime
holds not n divides 4099 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4111 is prime
proof
now
4111 = 2*2055 + 1; hence not 2 divides 4111 by NAT_4:9;
4111 = 3*1370 + 1; hence not 3 divides 4111 by NAT_4:9;
4111 = 5*822 + 1; hence not 5 divides 4111 by NAT_4:9;
4111 = 7*587 + 2; hence not 7 divides 4111 by NAT_4:9;
4111 = 11*373 + 8; hence not 11 divides 4111 by NAT_4:9;
4111 = 13*316 + 3; hence not 13 divides 4111 by NAT_4:9;
4111 = 17*241 + 14; hence not 17 divides 4111 by NAT_4:9;
4111 = 19*216 + 7; hence not 19 divides 4111 by NAT_4:9;
4111 = 23*178 + 17; hence not 23 divides 4111 by NAT_4:9;
4111 = 29*141 + 22; hence not 29 divides 4111 by NAT_4:9;
4111 = 31*132 + 19; hence not 31 divides 4111 by NAT_4:9;
4111 = 37*111 + 4; hence not 37 divides 4111 by NAT_4:9;
4111 = 41*100 + 11; hence not 41 divides 4111 by NAT_4:9;
4111 = 43*95 + 26; hence not 43 divides 4111 by NAT_4:9;
4111 = 47*87 + 22; hence not 47 divides 4111 by NAT_4:9;
4111 = 53*77 + 30; hence not 53 divides 4111 by NAT_4:9;
4111 = 59*69 + 40; hence not 59 divides 4111 by NAT_4:9;
4111 = 61*67 + 24; hence not 61 divides 4111 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4111 & n is prime
holds not n divides 4111 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
4127 is prime
proof
now
4127 = 2*2063 + 1; hence not 2 divides 4127 by NAT_4:9;
4127 = 3*1375 + 2; hence not 3 divides 4127 by NAT_4:9;
4127 = 5*825 + 2; hence not 5 divides 4127 by NAT_4:9;
4127 = 7*589 + 4; hence not 7 divides 4127 by NAT_4:9;
4127 = 11*375 + 2; hence not 11 divides 4127 by NAT_4:9;
4127 = 13*317 + 6; hence not 13 divides 4127 by NAT_4:9;
4127 = 17*242 + 13; hence not 17 divides 4127 by NAT_4:9;
4127 = 19*217 + 4; hence not 19 divides 4127 by NAT_4:9;
4127 = 23*179 + 10; hence not 23 divides 4127 by NAT_4:9;
4127 = 29*142 + 9; hence not 29 divides 4127 by NAT_4:9;
4127 = 31*133 + 4; hence not 31 divides 4127 by NAT_4:9;
4127 = 37*111 + 20; hence not 37 divides 4127 by NAT_4:9;
4127 = 41*100 + 27; hence not 41 divides 4127 by NAT_4:9;
4127 = 43*95 + 42; hence not 43 divides 4127 by NAT_4:9;
4127 = 47*87 + 38; hence not 47 divides 4127 by NAT_4:9;
4127 = 53*77 + 46; hence not 53 divides 4127 by NAT_4:9;
4127 = 59*69 + 56; hence not 59 divides 4127 by NAT_4:9;
4127 = 61*67 + 40; hence not 61 divides 4127 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4127 & n is prime
holds not n divides 4127 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4129 is prime
proof
now
4129 = 2*2064 + 1; hence not 2 divides 4129 by NAT_4:9;
4129 = 3*1376 + 1; hence not 3 divides 4129 by NAT_4:9;
4129 = 5*825 + 4; hence not 5 divides 4129 by NAT_4:9;
4129 = 7*589 + 6; hence not 7 divides 4129 by NAT_4:9;
4129 = 11*375 + 4; hence not 11 divides 4129 by NAT_4:9;
4129 = 13*317 + 8; hence not 13 divides 4129 by NAT_4:9;
4129 = 17*242 + 15; hence not 17 divides 4129 by NAT_4:9;
4129 = 19*217 + 6; hence not 19 divides 4129 by NAT_4:9;
4129 = 23*179 + 12; hence not 23 divides 4129 by NAT_4:9;
4129 = 29*142 + 11; hence not 29 divides 4129 by NAT_4:9;
4129 = 31*133 + 6; hence not 31 divides 4129 by NAT_4:9;
4129 = 37*111 + 22; hence not 37 divides 4129 by NAT_4:9;
4129 = 41*100 + 29; hence not 41 divides 4129 by NAT_4:9;
4129 = 43*96 + 1; hence not 43 divides 4129 by NAT_4:9;
4129 = 47*87 + 40; hence not 47 divides 4129 by NAT_4:9;
4129 = 53*77 + 48; hence not 53 divides 4129 by NAT_4:9;
4129 = 59*69 + 58; hence not 59 divides 4129 by NAT_4:9;
4129 = 61*67 + 42; hence not 61 divides 4129 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4129 & n is prime
holds not n divides 4129 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4133 is prime
proof
now
4133 = 2*2066 + 1; hence not 2 divides 4133 by NAT_4:9;
4133 = 3*1377 + 2; hence not 3 divides 4133 by NAT_4:9;
4133 = 5*826 + 3; hence not 5 divides 4133 by NAT_4:9;
4133 = 7*590 + 3; hence not 7 divides 4133 by NAT_4:9;
4133 = 11*375 + 8; hence not 11 divides 4133 by NAT_4:9;
4133 = 13*317 + 12; hence not 13 divides 4133 by NAT_4:9;
4133 = 17*243 + 2; hence not 17 divides 4133 by NAT_4:9;
4133 = 19*217 + 10; hence not 19 divides 4133 by NAT_4:9;
4133 = 23*179 + 16; hence not 23 divides 4133 by NAT_4:9;
4133 = 29*142 + 15; hence not 29 divides 4133 by NAT_4:9;
4133 = 31*133 + 10; hence not 31 divides 4133 by NAT_4:9;
4133 = 37*111 + 26; hence not 37 divides 4133 by NAT_4:9;
4133 = 41*100 + 33; hence not 41 divides 4133 by NAT_4:9;
4133 = 43*96 + 5; hence not 43 divides 4133 by NAT_4:9;
4133 = 47*87 + 44; hence not 47 divides 4133 by NAT_4:9;
4133 = 53*77 + 52; hence not 53 divides 4133 by NAT_4:9;
4133 = 59*70 + 3; hence not 59 divides 4133 by NAT_4:9;
4133 = 61*67 + 46; hence not 61 divides 4133 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4133 & n is prime
holds not n divides 4133 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4139 is prime
proof
now
4139 = 2*2069 + 1; hence not 2 divides 4139 by NAT_4:9;
4139 = 3*1379 + 2; hence not 3 divides 4139 by NAT_4:9;
4139 = 5*827 + 4; hence not 5 divides 4139 by NAT_4:9;
4139 = 7*591 + 2; hence not 7 divides 4139 by NAT_4:9;
4139 = 11*376 + 3; hence not 11 divides 4139 by NAT_4:9;
4139 = 13*318 + 5; hence not 13 divides 4139 by NAT_4:9;
4139 = 17*243 + 8; hence not 17 divides 4139 by NAT_4:9;
4139 = 19*217 + 16; hence not 19 divides 4139 by NAT_4:9;
4139 = 23*179 + 22; hence not 23 divides 4139 by NAT_4:9;
4139 = 29*142 + 21; hence not 29 divides 4139 by NAT_4:9;
4139 = 31*133 + 16; hence not 31 divides 4139 by NAT_4:9;
4139 = 37*111 + 32; hence not 37 divides 4139 by NAT_4:9;
4139 = 41*100 + 39; hence not 41 divides 4139 by NAT_4:9;
4139 = 43*96 + 11; hence not 43 divides 4139 by NAT_4:9;
4139 = 47*88 + 3; hence not 47 divides 4139 by NAT_4:9;
4139 = 53*78 + 5; hence not 53 divides 4139 by NAT_4:9;
4139 = 59*70 + 9; hence not 59 divides 4139 by NAT_4:9;
4139 = 61*67 + 52; hence not 61 divides 4139 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4139 & n is prime
holds not n divides 4139 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
4153 is prime
proof
now
4153 = 2*2076 + 1; hence not 2 divides 4153 by NAT_4:9;
4153 = 3*1384 + 1; hence not 3 divides 4153 by NAT_4:9;
4153 = 5*830 + 3; hence not 5 divides 4153 by NAT_4:9;
4153 = 7*593 + 2; hence not 7 divides 4153 by NAT_4:9;
4153 = 11*377 + 6; hence not 11 divides 4153 by NAT_4:9;
4153 = 13*319 + 6; hence not 13 divides 4153 by NAT_4:9;
4153 = 17*244 + 5; hence not 17 divides 4153 by NAT_4:9;
4153 = 19*218 + 11; hence not 19 divides 4153 by NAT_4:9;
4153 = 23*180 + 13; hence not 23 divides 4153 by NAT_4:9;
4153 = 29*143 + 6; hence not 29 divides 4153 by NAT_4:9;
4153 = 31*133 + 30; hence not 31 divides 4153 by NAT_4:9;
4153 = 37*112 + 9; hence not 37 divides 4153 by NAT_4:9;
4153 = 41*101 + 12; hence not 41 divides 4153 by NAT_4:9;
4153 = 43*96 + 25; hence not 43 divides 4153 by NAT_4:9;
4153 = 47*88 + 17; hence not 47 divides 4153 by NAT_4:9;
4153 = 53*78 + 19; hence not 53 divides 4153 by NAT_4:9;
4153 = 59*70 + 23; hence not 59 divides 4153 by NAT_4:9;
4153 = 61*68 + 5; hence not 61 divides 4153 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4153 & n is prime
holds not n divides 4153 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4157 is prime
proof
now
4157 = 2*2078 + 1; hence not 2 divides 4157 by NAT_4:9;
4157 = 3*1385 + 2; hence not 3 divides 4157 by NAT_4:9;
4157 = 5*831 + 2; hence not 5 divides 4157 by NAT_4:9;
4157 = 7*593 + 6; hence not 7 divides 4157 by NAT_4:9;
4157 = 11*377 + 10; hence not 11 divides 4157 by NAT_4:9;
4157 = 13*319 + 10; hence not 13 divides 4157 by NAT_4:9;
4157 = 17*244 + 9; hence not 17 divides 4157 by NAT_4:9;
4157 = 19*218 + 15; hence not 19 divides 4157 by NAT_4:9;
4157 = 23*180 + 17; hence not 23 divides 4157 by NAT_4:9;
4157 = 29*143 + 10; hence not 29 divides 4157 by NAT_4:9;
4157 = 31*134 + 3; hence not 31 divides 4157 by NAT_4:9;
4157 = 37*112 + 13; hence not 37 divides 4157 by NAT_4:9;
4157 = 41*101 + 16; hence not 41 divides 4157 by NAT_4:9;
4157 = 43*96 + 29; hence not 43 divides 4157 by NAT_4:9;
4157 = 47*88 + 21; hence not 47 divides 4157 by NAT_4:9;
4157 = 53*78 + 23; hence not 53 divides 4157 by NAT_4:9;
4157 = 59*70 + 27; hence not 59 divides 4157 by NAT_4:9;
4157 = 61*68 + 9; hence not 61 divides 4157 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4157 & n is prime
holds not n divides 4157 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4159 is prime
proof
now
4159 = 2*2079 + 1; hence not 2 divides 4159 by NAT_4:9;
4159 = 3*1386 + 1; hence not 3 divides 4159 by NAT_4:9;
4159 = 5*831 + 4; hence not 5 divides 4159 by NAT_4:9;
4159 = 7*594 + 1; hence not 7 divides 4159 by NAT_4:9;
4159 = 11*378 + 1; hence not 11 divides 4159 by NAT_4:9;
4159 = 13*319 + 12; hence not 13 divides 4159 by NAT_4:9;
4159 = 17*244 + 11; hence not 17 divides 4159 by NAT_4:9;
4159 = 19*218 + 17; hence not 19 divides 4159 by NAT_4:9;
4159 = 23*180 + 19; hence not 23 divides 4159 by NAT_4:9;
4159 = 29*143 + 12; hence not 29 divides 4159 by NAT_4:9;
4159 = 31*134 + 5; hence not 31 divides 4159 by NAT_4:9;
4159 = 37*112 + 15; hence not 37 divides 4159 by NAT_4:9;
4159 = 41*101 + 18; hence not 41 divides 4159 by NAT_4:9;
4159 = 43*96 + 31; hence not 43 divides 4159 by NAT_4:9;
4159 = 47*88 + 23; hence not 47 divides 4159 by NAT_4:9;
4159 = 53*78 + 25; hence not 53 divides 4159 by NAT_4:9;
4159 = 59*70 + 29; hence not 59 divides 4159 by NAT_4:9;
4159 = 61*68 + 11; hence not 61 divides 4159 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4159 & n is prime
holds not n divides 4159 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4177 is prime
proof
now
4177 = 2*2088 + 1; hence not 2 divides 4177 by NAT_4:9;
4177 = 3*1392 + 1; hence not 3 divides 4177 by NAT_4:9;
4177 = 5*835 + 2; hence not 5 divides 4177 by NAT_4:9;
4177 = 7*596 + 5; hence not 7 divides 4177 by NAT_4:9;
4177 = 11*379 + 8; hence not 11 divides 4177 by NAT_4:9;
4177 = 13*321 + 4; hence not 13 divides 4177 by NAT_4:9;
4177 = 17*245 + 12; hence not 17 divides 4177 by NAT_4:9;
4177 = 19*219 + 16; hence not 19 divides 4177 by NAT_4:9;
4177 = 23*181 + 14; hence not 23 divides 4177 by NAT_4:9;
4177 = 29*144 + 1; hence not 29 divides 4177 by NAT_4:9;
4177 = 31*134 + 23; hence not 31 divides 4177 by NAT_4:9;
4177 = 37*112 + 33; hence not 37 divides 4177 by NAT_4:9;
4177 = 41*101 + 36; hence not 41 divides 4177 by NAT_4:9;
4177 = 43*97 + 6; hence not 43 divides 4177 by NAT_4:9;
4177 = 47*88 + 41; hence not 47 divides 4177 by NAT_4:9;
4177 = 53*78 + 43; hence not 53 divides 4177 by NAT_4:9;
4177 = 59*70 + 47; hence not 59 divides 4177 by NAT_4:9;
4177 = 61*68 + 29; hence not 61 divides 4177 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4177 & n is prime
holds not n divides 4177 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
4201 is prime
proof
now
4201 = 2*2100 + 1; hence not 2 divides 4201 by NAT_4:9;
4201 = 3*1400 + 1; hence not 3 divides 4201 by NAT_4:9;
4201 = 5*840 + 1; hence not 5 divides 4201 by NAT_4:9;
4201 = 7*600 + 1; hence not 7 divides 4201 by NAT_4:9;
4201 = 11*381 + 10; hence not 11 divides 4201 by NAT_4:9;
4201 = 13*323 + 2; hence not 13 divides 4201 by NAT_4:9;
4201 = 17*247 + 2; hence not 17 divides 4201 by NAT_4:9;
4201 = 19*221 + 2; hence not 19 divides 4201 by NAT_4:9;
4201 = 23*182 + 15; hence not 23 divides 4201 by NAT_4:9;
4201 = 29*144 + 25; hence not 29 divides 4201 by NAT_4:9;
4201 = 31*135 + 16; hence not 31 divides 4201 by NAT_4:9;
4201 = 37*113 + 20; hence not 37 divides 4201 by NAT_4:9;
4201 = 41*102 + 19; hence not 41 divides 4201 by NAT_4:9;
4201 = 43*97 + 30; hence not 43 divides 4201 by NAT_4:9;
4201 = 47*89 + 18; hence not 47 divides 4201 by NAT_4:9;
4201 = 53*79 + 14; hence not 53 divides 4201 by NAT_4:9;
4201 = 59*71 + 12; hence not 59 divides 4201 by NAT_4:9;
4201 = 61*68 + 53; hence not 61 divides 4201 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4201 & n is prime
holds not n divides 4201 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4211 is prime
proof
now
4211 = 2*2105 + 1; hence not 2 divides 4211 by NAT_4:9;
4211 = 3*1403 + 2; hence not 3 divides 4211 by NAT_4:9;
4211 = 5*842 + 1; hence not 5 divides 4211 by NAT_4:9;
4211 = 7*601 + 4; hence not 7 divides 4211 by NAT_4:9;
4211 = 11*382 + 9; hence not 11 divides 4211 by NAT_4:9;
4211 = 13*323 + 12; hence not 13 divides 4211 by NAT_4:9;
4211 = 17*247 + 12; hence not 17 divides 4211 by NAT_4:9;
4211 = 19*221 + 12; hence not 19 divides 4211 by NAT_4:9;
4211 = 23*183 + 2; hence not 23 divides 4211 by NAT_4:9;
4211 = 29*145 + 6; hence not 29 divides 4211 by NAT_4:9;
4211 = 31*135 + 26; hence not 31 divides 4211 by NAT_4:9;
4211 = 37*113 + 30; hence not 37 divides 4211 by NAT_4:9;
4211 = 41*102 + 29; hence not 41 divides 4211 by NAT_4:9;
4211 = 43*97 + 40; hence not 43 divides 4211 by NAT_4:9;
4211 = 47*89 + 28; hence not 47 divides 4211 by NAT_4:9;
4211 = 53*79 + 24; hence not 53 divides 4211 by NAT_4:9;
4211 = 59*71 + 22; hence not 59 divides 4211 by NAT_4:9;
4211 = 61*69 + 2; hence not 61 divides 4211 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4211 & n is prime
holds not n divides 4211 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4217 is prime
proof
now
4217 = 2*2108 + 1; hence not 2 divides 4217 by NAT_4:9;
4217 = 3*1405 + 2; hence not 3 divides 4217 by NAT_4:9;
4217 = 5*843 + 2; hence not 5 divides 4217 by NAT_4:9;
4217 = 7*602 + 3; hence not 7 divides 4217 by NAT_4:9;
4217 = 11*383 + 4; hence not 11 divides 4217 by NAT_4:9;
4217 = 13*324 + 5; hence not 13 divides 4217 by NAT_4:9;
4217 = 17*248 + 1; hence not 17 divides 4217 by NAT_4:9;
4217 = 19*221 + 18; hence not 19 divides 4217 by NAT_4:9;
4217 = 23*183 + 8; hence not 23 divides 4217 by NAT_4:9;
4217 = 29*145 + 12; hence not 29 divides 4217 by NAT_4:9;
4217 = 31*136 + 1; hence not 31 divides 4217 by NAT_4:9;
4217 = 37*113 + 36; hence not 37 divides 4217 by NAT_4:9;
4217 = 41*102 + 35; hence not 41 divides 4217 by NAT_4:9;
4217 = 43*98 + 3; hence not 43 divides 4217 by NAT_4:9;
4217 = 47*89 + 34; hence not 47 divides 4217 by NAT_4:9;
4217 = 53*79 + 30; hence not 53 divides 4217 by NAT_4:9;
4217 = 59*71 + 28; hence not 59 divides 4217 by NAT_4:9;
4217 = 61*69 + 8; hence not 61 divides 4217 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4217 & n is prime
holds not n divides 4217 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4219 is prime
proof
now
4219 = 2*2109 + 1; hence not 2 divides 4219 by NAT_4:9;
4219 = 3*1406 + 1; hence not 3 divides 4219 by NAT_4:9;
4219 = 5*843 + 4; hence not 5 divides 4219 by NAT_4:9;
4219 = 7*602 + 5; hence not 7 divides 4219 by NAT_4:9;
4219 = 11*383 + 6; hence not 11 divides 4219 by NAT_4:9;
4219 = 13*324 + 7; hence not 13 divides 4219 by NAT_4:9;
4219 = 17*248 + 3; hence not 17 divides 4219 by NAT_4:9;
4219 = 19*222 + 1; hence not 19 divides 4219 by NAT_4:9;
4219 = 23*183 + 10; hence not 23 divides 4219 by NAT_4:9;
4219 = 29*145 + 14; hence not 29 divides 4219 by NAT_4:9;
4219 = 31*136 + 3; hence not 31 divides 4219 by NAT_4:9;
4219 = 37*114 + 1; hence not 37 divides 4219 by NAT_4:9;
4219 = 41*102 + 37; hence not 41 divides 4219 by NAT_4:9;
4219 = 43*98 + 5; hence not 43 divides 4219 by NAT_4:9;
4219 = 47*89 + 36; hence not 47 divides 4219 by NAT_4:9;
4219 = 53*79 + 32; hence not 53 divides 4219 by NAT_4:9;
4219 = 59*71 + 30; hence not 59 divides 4219 by NAT_4:9;
4219 = 61*69 + 10; hence not 61 divides 4219 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4219 & n is prime
holds not n divides 4219 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4229 is prime
proof
now
4229 = 2*2114 + 1; hence not 2 divides 4229 by NAT_4:9;
4229 = 3*1409 + 2; hence not 3 divides 4229 by NAT_4:9;
4229 = 5*845 + 4; hence not 5 divides 4229 by NAT_4:9;
4229 = 7*604 + 1; hence not 7 divides 4229 by NAT_4:9;
4229 = 11*384 + 5; hence not 11 divides 4229 by NAT_4:9;
4229 = 13*325 + 4; hence not 13 divides 4229 by NAT_4:9;
4229 = 17*248 + 13; hence not 17 divides 4229 by NAT_4:9;
4229 = 19*222 + 11; hence not 19 divides 4229 by NAT_4:9;
4229 = 23*183 + 20; hence not 23 divides 4229 by NAT_4:9;
4229 = 29*145 + 24; hence not 29 divides 4229 by NAT_4:9;
4229 = 31*136 + 13; hence not 31 divides 4229 by NAT_4:9;
4229 = 37*114 + 11; hence not 37 divides 4229 by NAT_4:9;
4229 = 41*103 + 6; hence not 41 divides 4229 by NAT_4:9;
4229 = 43*98 + 15; hence not 43 divides 4229 by NAT_4:9;
4229 = 47*89 + 46; hence not 47 divides 4229 by NAT_4:9;
4229 = 53*79 + 42; hence not 53 divides 4229 by NAT_4:9;
4229 = 59*71 + 40; hence not 59 divides 4229 by NAT_4:9;
4229 = 61*69 + 20; hence not 61 divides 4229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4229 & n is prime
holds not n divides 4229 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4231 is prime
proof
now
4231 = 2*2115 + 1; hence not 2 divides 4231 by NAT_4:9;
4231 = 3*1410 + 1; hence not 3 divides 4231 by NAT_4:9;
4231 = 5*846 + 1; hence not 5 divides 4231 by NAT_4:9;
4231 = 7*604 + 3; hence not 7 divides 4231 by NAT_4:9;
4231 = 11*384 + 7; hence not 11 divides 4231 by NAT_4:9;
4231 = 13*325 + 6; hence not 13 divides 4231 by NAT_4:9;
4231 = 17*248 + 15; hence not 17 divides 4231 by NAT_4:9;
4231 = 19*222 + 13; hence not 19 divides 4231 by NAT_4:9;
4231 = 23*183 + 22; hence not 23 divides 4231 by NAT_4:9;
4231 = 29*145 + 26; hence not 29 divides 4231 by NAT_4:9;
4231 = 31*136 + 15; hence not 31 divides 4231 by NAT_4:9;
4231 = 37*114 + 13; hence not 37 divides 4231 by NAT_4:9;
4231 = 41*103 + 8; hence not 41 divides 4231 by NAT_4:9;
4231 = 43*98 + 17; hence not 43 divides 4231 by NAT_4:9;
4231 = 47*90 + 1; hence not 47 divides 4231 by NAT_4:9;
4231 = 53*79 + 44; hence not 53 divides 4231 by NAT_4:9;
4231 = 59*71 + 42; hence not 59 divides 4231 by NAT_4:9;
4231 = 61*69 + 22; hence not 61 divides 4231 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4231 & n is prime
holds not n divides 4231 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4241 is prime
proof
now
4241 = 2*2120 + 1; hence not 2 divides 4241 by NAT_4:9;
4241 = 3*1413 + 2; hence not 3 divides 4241 by NAT_4:9;
4241 = 5*848 + 1; hence not 5 divides 4241 by NAT_4:9;
4241 = 7*605 + 6; hence not 7 divides 4241 by NAT_4:9;
4241 = 11*385 + 6; hence not 11 divides 4241 by NAT_4:9;
4241 = 13*326 + 3; hence not 13 divides 4241 by NAT_4:9;
4241 = 17*249 + 8; hence not 17 divides 4241 by NAT_4:9;
4241 = 19*223 + 4; hence not 19 divides 4241 by NAT_4:9;
4241 = 23*184 + 9; hence not 23 divides 4241 by NAT_4:9;
4241 = 29*146 + 7; hence not 29 divides 4241 by NAT_4:9;
4241 = 31*136 + 25; hence not 31 divides 4241 by NAT_4:9;
4241 = 37*114 + 23; hence not 37 divides 4241 by NAT_4:9;
4241 = 41*103 + 18; hence not 41 divides 4241 by NAT_4:9;
4241 = 43*98 + 27; hence not 43 divides 4241 by NAT_4:9;
4241 = 47*90 + 11; hence not 47 divides 4241 by NAT_4:9;
4241 = 53*80 + 1; hence not 53 divides 4241 by NAT_4:9;
4241 = 59*71 + 52; hence not 59 divides 4241 by NAT_4:9;
4241 = 61*69 + 32; hence not 61 divides 4241 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4241 & n is prime
holds not n divides 4241 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4243 is prime
proof
now
4243 = 2*2121 + 1; hence not 2 divides 4243 by NAT_4:9;
4243 = 3*1414 + 1; hence not 3 divides 4243 by NAT_4:9;
4243 = 5*848 + 3; hence not 5 divides 4243 by NAT_4:9;
4243 = 7*606 + 1; hence not 7 divides 4243 by NAT_4:9;
4243 = 11*385 + 8; hence not 11 divides 4243 by NAT_4:9;
4243 = 13*326 + 5; hence not 13 divides 4243 by NAT_4:9;
4243 = 17*249 + 10; hence not 17 divides 4243 by NAT_4:9;
4243 = 19*223 + 6; hence not 19 divides 4243 by NAT_4:9;
4243 = 23*184 + 11; hence not 23 divides 4243 by NAT_4:9;
4243 = 29*146 + 9; hence not 29 divides 4243 by NAT_4:9;
4243 = 31*136 + 27; hence not 31 divides 4243 by NAT_4:9;
4243 = 37*114 + 25; hence not 37 divides 4243 by NAT_4:9;
4243 = 41*103 + 20; hence not 41 divides 4243 by NAT_4:9;
4243 = 43*98 + 29; hence not 43 divides 4243 by NAT_4:9;
4243 = 47*90 + 13; hence not 47 divides 4243 by NAT_4:9;
4243 = 53*80 + 3; hence not 53 divides 4243 by NAT_4:9;
4243 = 59*71 + 54; hence not 59 divides 4243 by NAT_4:9;
4243 = 61*69 + 34; hence not 61 divides 4243 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4243 & n is prime
holds not n divides 4243 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4253 is prime
proof
now
4253 = 2*2126 + 1; hence not 2 divides 4253 by NAT_4:9;
4253 = 3*1417 + 2; hence not 3 divides 4253 by NAT_4:9;
4253 = 5*850 + 3; hence not 5 divides 4253 by NAT_4:9;
4253 = 7*607 + 4; hence not 7 divides 4253 by NAT_4:9;
4253 = 11*386 + 7; hence not 11 divides 4253 by NAT_4:9;
4253 = 13*327 + 2; hence not 13 divides 4253 by NAT_4:9;
4253 = 17*250 + 3; hence not 17 divides 4253 by NAT_4:9;
4253 = 19*223 + 16; hence not 19 divides 4253 by NAT_4:9;
4253 = 23*184 + 21; hence not 23 divides 4253 by NAT_4:9;
4253 = 29*146 + 19; hence not 29 divides 4253 by NAT_4:9;
4253 = 31*137 + 6; hence not 31 divides 4253 by NAT_4:9;
4253 = 37*114 + 35; hence not 37 divides 4253 by NAT_4:9;
4253 = 41*103 + 30; hence not 41 divides 4253 by NAT_4:9;
4253 = 43*98 + 39; hence not 43 divides 4253 by NAT_4:9;
4253 = 47*90 + 23; hence not 47 divides 4253 by NAT_4:9;
4253 = 53*80 + 13; hence not 53 divides 4253 by NAT_4:9;
4253 = 59*72 + 5; hence not 59 divides 4253 by NAT_4:9;
4253 = 61*69 + 44; hence not 61 divides 4253 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4253 & n is prime
holds not n divides 4253 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4259 is prime
proof
now
4259 = 2*2129 + 1; hence not 2 divides 4259 by NAT_4:9;
4259 = 3*1419 + 2; hence not 3 divides 4259 by NAT_4:9;
4259 = 5*851 + 4; hence not 5 divides 4259 by NAT_4:9;
4259 = 7*608 + 3; hence not 7 divides 4259 by NAT_4:9;
4259 = 11*387 + 2; hence not 11 divides 4259 by NAT_4:9;
4259 = 13*327 + 8; hence not 13 divides 4259 by NAT_4:9;
4259 = 17*250 + 9; hence not 17 divides 4259 by NAT_4:9;
4259 = 19*224 + 3; hence not 19 divides 4259 by NAT_4:9;
4259 = 23*185 + 4; hence not 23 divides 4259 by NAT_4:9;
4259 = 29*146 + 25; hence not 29 divides 4259 by NAT_4:9;
4259 = 31*137 + 12; hence not 31 divides 4259 by NAT_4:9;
4259 = 37*115 + 4; hence not 37 divides 4259 by NAT_4:9;
4259 = 41*103 + 36; hence not 41 divides 4259 by NAT_4:9;
4259 = 43*99 + 2; hence not 43 divides 4259 by NAT_4:9;
4259 = 47*90 + 29; hence not 47 divides 4259 by NAT_4:9;
4259 = 53*80 + 19; hence not 53 divides 4259 by NAT_4:9;
4259 = 59*72 + 11; hence not 59 divides 4259 by NAT_4:9;
4259 = 61*69 + 50; hence not 61 divides 4259 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4259 & n is prime
holds not n divides 4259 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4261 is prime
proof
now
4261 = 2*2130 + 1; hence not 2 divides 4261 by NAT_4:9;
4261 = 3*1420 + 1; hence not 3 divides 4261 by NAT_4:9;
4261 = 5*852 + 1; hence not 5 divides 4261 by NAT_4:9;
4261 = 7*608 + 5; hence not 7 divides 4261 by NAT_4:9;
4261 = 11*387 + 4; hence not 11 divides 4261 by NAT_4:9;
4261 = 13*327 + 10; hence not 13 divides 4261 by NAT_4:9;
4261 = 17*250 + 11; hence not 17 divides 4261 by NAT_4:9;
4261 = 19*224 + 5; hence not 19 divides 4261 by NAT_4:9;
4261 = 23*185 + 6; hence not 23 divides 4261 by NAT_4:9;
4261 = 29*146 + 27; hence not 29 divides 4261 by NAT_4:9;
4261 = 31*137 + 14; hence not 31 divides 4261 by NAT_4:9;
4261 = 37*115 + 6; hence not 37 divides 4261 by NAT_4:9;
4261 = 41*103 + 38; hence not 41 divides 4261 by NAT_4:9;
4261 = 43*99 + 4; hence not 43 divides 4261 by NAT_4:9;
4261 = 47*90 + 31; hence not 47 divides 4261 by NAT_4:9;
4261 = 53*80 + 21; hence not 53 divides 4261 by NAT_4:9;
4261 = 59*72 + 13; hence not 59 divides 4261 by NAT_4:9;
4261 = 61*69 + 52; hence not 61 divides 4261 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4261 & n is prime
holds not n divides 4261 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4271 is prime
proof
now
4271 = 2*2135 + 1; hence not 2 divides 4271 by NAT_4:9;
4271 = 3*1423 + 2; hence not 3 divides 4271 by NAT_4:9;
4271 = 5*854 + 1; hence not 5 divides 4271 by NAT_4:9;
4271 = 7*610 + 1; hence not 7 divides 4271 by NAT_4:9;
4271 = 11*388 + 3; hence not 11 divides 4271 by NAT_4:9;
4271 = 13*328 + 7; hence not 13 divides 4271 by NAT_4:9;
4271 = 17*251 + 4; hence not 17 divides 4271 by NAT_4:9;
4271 = 19*224 + 15; hence not 19 divides 4271 by NAT_4:9;
4271 = 23*185 + 16; hence not 23 divides 4271 by NAT_4:9;
4271 = 29*147 + 8; hence not 29 divides 4271 by NAT_4:9;
4271 = 31*137 + 24; hence not 31 divides 4271 by NAT_4:9;
4271 = 37*115 + 16; hence not 37 divides 4271 by NAT_4:9;
4271 = 41*104 + 7; hence not 41 divides 4271 by NAT_4:9;
4271 = 43*99 + 14; hence not 43 divides 4271 by NAT_4:9;
4271 = 47*90 + 41; hence not 47 divides 4271 by NAT_4:9;
4271 = 53*80 + 31; hence not 53 divides 4271 by NAT_4:9;
4271 = 59*72 + 23; hence not 59 divides 4271 by NAT_4:9;
4271 = 61*70 + 1; hence not 61 divides 4271 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4271 & n is prime
holds not n divides 4271 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4273 is prime
proof
now
4273 = 2*2136 + 1; hence not 2 divides 4273 by NAT_4:9;
4273 = 3*1424 + 1; hence not 3 divides 4273 by NAT_4:9;
4273 = 5*854 + 3; hence not 5 divides 4273 by NAT_4:9;
4273 = 7*610 + 3; hence not 7 divides 4273 by NAT_4:9;
4273 = 11*388 + 5; hence not 11 divides 4273 by NAT_4:9;
4273 = 13*328 + 9; hence not 13 divides 4273 by NAT_4:9;
4273 = 17*251 + 6; hence not 17 divides 4273 by NAT_4:9;
4273 = 19*224 + 17; hence not 19 divides 4273 by NAT_4:9;
4273 = 23*185 + 18; hence not 23 divides 4273 by NAT_4:9;
4273 = 29*147 + 10; hence not 29 divides 4273 by NAT_4:9;
4273 = 31*137 + 26; hence not 31 divides 4273 by NAT_4:9;
4273 = 37*115 + 18; hence not 37 divides 4273 by NAT_4:9;
4273 = 41*104 + 9; hence not 41 divides 4273 by NAT_4:9;
4273 = 43*99 + 16; hence not 43 divides 4273 by NAT_4:9;
4273 = 47*90 + 43; hence not 47 divides 4273 by NAT_4:9;
4273 = 53*80 + 33; hence not 53 divides 4273 by NAT_4:9;
4273 = 59*72 + 25; hence not 59 divides 4273 by NAT_4:9;
4273 = 61*70 + 3; hence not 61 divides 4273 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4273 & n is prime
holds not n divides 4273 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4283 is prime
proof
now
4283 = 2*2141 + 1; hence not 2 divides 4283 by NAT_4:9;
4283 = 3*1427 + 2; hence not 3 divides 4283 by NAT_4:9;
4283 = 5*856 + 3; hence not 5 divides 4283 by NAT_4:9;
4283 = 7*611 + 6; hence not 7 divides 4283 by NAT_4:9;
4283 = 11*389 + 4; hence not 11 divides 4283 by NAT_4:9;
4283 = 13*329 + 6; hence not 13 divides 4283 by NAT_4:9;
4283 = 17*251 + 16; hence not 17 divides 4283 by NAT_4:9;
4283 = 19*225 + 8; hence not 19 divides 4283 by NAT_4:9;
4283 = 23*186 + 5; hence not 23 divides 4283 by NAT_4:9;
4283 = 29*147 + 20; hence not 29 divides 4283 by NAT_4:9;
4283 = 31*138 + 5; hence not 31 divides 4283 by NAT_4:9;
4283 = 37*115 + 28; hence not 37 divides 4283 by NAT_4:9;
4283 = 41*104 + 19; hence not 41 divides 4283 by NAT_4:9;
4283 = 43*99 + 26; hence not 43 divides 4283 by NAT_4:9;
4283 = 47*91 + 6; hence not 47 divides 4283 by NAT_4:9;
4283 = 53*80 + 43; hence not 53 divides 4283 by NAT_4:9;
4283 = 59*72 + 35; hence not 59 divides 4283 by NAT_4:9;
4283 = 61*70 + 13; hence not 61 divides 4283 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4283 & n is prime
holds not n divides 4283 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4289 is prime
proof
now
4289 = 2*2144 + 1; hence not 2 divides 4289 by NAT_4:9;
4289 = 3*1429 + 2; hence not 3 divides 4289 by NAT_4:9;
4289 = 5*857 + 4; hence not 5 divides 4289 by NAT_4:9;
4289 = 7*612 + 5; hence not 7 divides 4289 by NAT_4:9;
4289 = 11*389 + 10; hence not 11 divides 4289 by NAT_4:9;
4289 = 13*329 + 12; hence not 13 divides 4289 by NAT_4:9;
4289 = 17*252 + 5; hence not 17 divides 4289 by NAT_4:9;
4289 = 19*225 + 14; hence not 19 divides 4289 by NAT_4:9;
4289 = 23*186 + 11; hence not 23 divides 4289 by NAT_4:9;
4289 = 29*147 + 26; hence not 29 divides 4289 by NAT_4:9;
4289 = 31*138 + 11; hence not 31 divides 4289 by NAT_4:9;
4289 = 37*115 + 34; hence not 37 divides 4289 by NAT_4:9;
4289 = 41*104 + 25; hence not 41 divides 4289 by NAT_4:9;
4289 = 43*99 + 32; hence not 43 divides 4289 by NAT_4:9;
4289 = 47*91 + 12; hence not 47 divides 4289 by NAT_4:9;
4289 = 53*80 + 49; hence not 53 divides 4289 by NAT_4:9;
4289 = 59*72 + 41; hence not 59 divides 4289 by NAT_4:9;
4289 = 61*70 + 19; hence not 61 divides 4289 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4289 & n is prime
holds not n divides 4289 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
4297 is prime
proof
now
4297 = 2*2148 + 1; hence not 2 divides 4297 by NAT_4:9;
4297 = 3*1432 + 1; hence not 3 divides 4297 by NAT_4:9;
4297 = 5*859 + 2; hence not 5 divides 4297 by NAT_4:9;
4297 = 7*613 + 6; hence not 7 divides 4297 by NAT_4:9;
4297 = 11*390 + 7; hence not 11 divides 4297 by NAT_4:9;
4297 = 13*330 + 7; hence not 13 divides 4297 by NAT_4:9;
4297 = 17*252 + 13; hence not 17 divides 4297 by NAT_4:9;
4297 = 19*226 + 3; hence not 19 divides 4297 by NAT_4:9;
4297 = 23*186 + 19; hence not 23 divides 4297 by NAT_4:9;
4297 = 29*148 + 5; hence not 29 divides 4297 by NAT_4:9;
4297 = 31*138 + 19; hence not 31 divides 4297 by NAT_4:9;
4297 = 37*116 + 5; hence not 37 divides 4297 by NAT_4:9;
4297 = 41*104 + 33; hence not 41 divides 4297 by NAT_4:9;
4297 = 43*99 + 40; hence not 43 divides 4297 by NAT_4:9;
4297 = 47*91 + 20; hence not 47 divides 4297 by NAT_4:9;
4297 = 53*81 + 4; hence not 53 divides 4297 by NAT_4:9;
4297 = 59*72 + 49; hence not 59 divides 4297 by NAT_4:9;
4297 = 61*70 + 27; hence not 61 divides 4297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4297 & n is prime
holds not n divides 4297 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
4327 is prime
proof
now
4327 = 2*2163 + 1; hence not 2 divides 4327 by NAT_4:9;
4327 = 3*1442 + 1; hence not 3 divides 4327 by NAT_4:9;
4327 = 5*865 + 2; hence not 5 divides 4327 by NAT_4:9;
4327 = 7*618 + 1; hence not 7 divides 4327 by NAT_4:9;
4327 = 11*393 + 4; hence not 11 divides 4327 by NAT_4:9;
4327 = 13*332 + 11; hence not 13 divides 4327 by NAT_4:9;
4327 = 17*254 + 9; hence not 17 divides 4327 by NAT_4:9;
4327 = 19*227 + 14; hence not 19 divides 4327 by NAT_4:9;
4327 = 23*188 + 3; hence not 23 divides 4327 by NAT_4:9;
4327 = 29*149 + 6; hence not 29 divides 4327 by NAT_4:9;
4327 = 31*139 + 18; hence not 31 divides 4327 by NAT_4:9;
4327 = 37*116 + 35; hence not 37 divides 4327 by NAT_4:9;
4327 = 41*105 + 22; hence not 41 divides 4327 by NAT_4:9;
4327 = 43*100 + 27; hence not 43 divides 4327 by NAT_4:9;
4327 = 47*92 + 3; hence not 47 divides 4327 by NAT_4:9;
4327 = 53*81 + 34; hence not 53 divides 4327 by NAT_4:9;
4327 = 59*73 + 20; hence not 59 divides 4327 by NAT_4:9;
4327 = 61*70 + 57; hence not 61 divides 4327 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4327 & n is prime
holds not n divides 4327 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4337 is prime
proof
now
4337 = 2*2168 + 1; hence not 2 divides 4337 by NAT_4:9;
4337 = 3*1445 + 2; hence not 3 divides 4337 by NAT_4:9;
4337 = 5*867 + 2; hence not 5 divides 4337 by NAT_4:9;
4337 = 7*619 + 4; hence not 7 divides 4337 by NAT_4:9;
4337 = 11*394 + 3; hence not 11 divides 4337 by NAT_4:9;
4337 = 13*333 + 8; hence not 13 divides 4337 by NAT_4:9;
4337 = 17*255 + 2; hence not 17 divides 4337 by NAT_4:9;
4337 = 19*228 + 5; hence not 19 divides 4337 by NAT_4:9;
4337 = 23*188 + 13; hence not 23 divides 4337 by NAT_4:9;
4337 = 29*149 + 16; hence not 29 divides 4337 by NAT_4:9;
4337 = 31*139 + 28; hence not 31 divides 4337 by NAT_4:9;
4337 = 37*117 + 8; hence not 37 divides 4337 by NAT_4:9;
4337 = 41*105 + 32; hence not 41 divides 4337 by NAT_4:9;
4337 = 43*100 + 37; hence not 43 divides 4337 by NAT_4:9;
4337 = 47*92 + 13; hence not 47 divides 4337 by NAT_4:9;
4337 = 53*81 + 44; hence not 53 divides 4337 by NAT_4:9;
4337 = 59*73 + 30; hence not 59 divides 4337 by NAT_4:9;
4337 = 61*71 + 6; hence not 61 divides 4337 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4337 & n is prime
holds not n divides 4337 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4339 is prime
proof
now
4339 = 2*2169 + 1; hence not 2 divides 4339 by NAT_4:9;
4339 = 3*1446 + 1; hence not 3 divides 4339 by NAT_4:9;
4339 = 5*867 + 4; hence not 5 divides 4339 by NAT_4:9;
4339 = 7*619 + 6; hence not 7 divides 4339 by NAT_4:9;
4339 = 11*394 + 5; hence not 11 divides 4339 by NAT_4:9;
4339 = 13*333 + 10; hence not 13 divides 4339 by NAT_4:9;
4339 = 17*255 + 4; hence not 17 divides 4339 by NAT_4:9;
4339 = 19*228 + 7; hence not 19 divides 4339 by NAT_4:9;
4339 = 23*188 + 15; hence not 23 divides 4339 by NAT_4:9;
4339 = 29*149 + 18; hence not 29 divides 4339 by NAT_4:9;
4339 = 31*139 + 30; hence not 31 divides 4339 by NAT_4:9;
4339 = 37*117 + 10; hence not 37 divides 4339 by NAT_4:9;
4339 = 41*105 + 34; hence not 41 divides 4339 by NAT_4:9;
4339 = 43*100 + 39; hence not 43 divides 4339 by NAT_4:9;
4339 = 47*92 + 15; hence not 47 divides 4339 by NAT_4:9;
4339 = 53*81 + 46; hence not 53 divides 4339 by NAT_4:9;
4339 = 59*73 + 32; hence not 59 divides 4339 by NAT_4:9;
4339 = 61*71 + 8; hence not 61 divides 4339 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4339 & n is prime
holds not n divides 4339 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4349 is prime
proof
now
4349 = 2*2174 + 1; hence not 2 divides 4349 by NAT_4:9;
4349 = 3*1449 + 2; hence not 3 divides 4349 by NAT_4:9;
4349 = 5*869 + 4; hence not 5 divides 4349 by NAT_4:9;
4349 = 7*621 + 2; hence not 7 divides 4349 by NAT_4:9;
4349 = 11*395 + 4; hence not 11 divides 4349 by NAT_4:9;
4349 = 13*334 + 7; hence not 13 divides 4349 by NAT_4:9;
4349 = 17*255 + 14; hence not 17 divides 4349 by NAT_4:9;
4349 = 19*228 + 17; hence not 19 divides 4349 by NAT_4:9;
4349 = 23*189 + 2; hence not 23 divides 4349 by NAT_4:9;
4349 = 29*149 + 28; hence not 29 divides 4349 by NAT_4:9;
4349 = 31*140 + 9; hence not 31 divides 4349 by NAT_4:9;
4349 = 37*117 + 20; hence not 37 divides 4349 by NAT_4:9;
4349 = 41*106 + 3; hence not 41 divides 4349 by NAT_4:9;
4349 = 43*101 + 6; hence not 43 divides 4349 by NAT_4:9;
4349 = 47*92 + 25; hence not 47 divides 4349 by NAT_4:9;
4349 = 53*82 + 3; hence not 53 divides 4349 by NAT_4:9;
4349 = 59*73 + 42; hence not 59 divides 4349 by NAT_4:9;
4349 = 61*71 + 18; hence not 61 divides 4349 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4349 & n is prime
holds not n divides 4349 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
4357 is prime
proof
now
4357 = 2*2178 + 1; hence not 2 divides 4357 by NAT_4:9;
4357 = 3*1452 + 1; hence not 3 divides 4357 by NAT_4:9;
4357 = 5*871 + 2; hence not 5 divides 4357 by NAT_4:9;
4357 = 7*622 + 3; hence not 7 divides 4357 by NAT_4:9;
4357 = 11*396 + 1; hence not 11 divides 4357 by NAT_4:9;
4357 = 13*335 + 2; hence not 13 divides 4357 by NAT_4:9;
4357 = 17*256 + 5; hence not 17 divides 4357 by NAT_4:9;
4357 = 19*229 + 6; hence not 19 divides 4357 by NAT_4:9;
4357 = 23*189 + 10; hence not 23 divides 4357 by NAT_4:9;
4357 = 29*150 + 7; hence not 29 divides 4357 by NAT_4:9;
4357 = 31*140 + 17; hence not 31 divides 4357 by NAT_4:9;
4357 = 37*117 + 28; hence not 37 divides 4357 by NAT_4:9;
4357 = 41*106 + 11; hence not 41 divides 4357 by NAT_4:9;
4357 = 43*101 + 14; hence not 43 divides 4357 by NAT_4:9;
4357 = 47*92 + 33; hence not 47 divides 4357 by NAT_4:9;
4357 = 53*82 + 11; hence not 53 divides 4357 by NAT_4:9;
4357 = 59*73 + 50; hence not 59 divides 4357 by NAT_4:9;
4357 = 61*71 + 26; hence not 61 divides 4357 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4357 & n is prime
holds not n divides 4357 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4363 is prime
proof
now
4363 = 2*2181 + 1; hence not 2 divides 4363 by NAT_4:9;
4363 = 3*1454 + 1; hence not 3 divides 4363 by NAT_4:9;
4363 = 5*872 + 3; hence not 5 divides 4363 by NAT_4:9;
4363 = 7*623 + 2; hence not 7 divides 4363 by NAT_4:9;
4363 = 11*396 + 7; hence not 11 divides 4363 by NAT_4:9;
4363 = 13*335 + 8; hence not 13 divides 4363 by NAT_4:9;
4363 = 17*256 + 11; hence not 17 divides 4363 by NAT_4:9;
4363 = 19*229 + 12; hence not 19 divides 4363 by NAT_4:9;
4363 = 23*189 + 16; hence not 23 divides 4363 by NAT_4:9;
4363 = 29*150 + 13; hence not 29 divides 4363 by NAT_4:9;
4363 = 31*140 + 23; hence not 31 divides 4363 by NAT_4:9;
4363 = 37*117 + 34; hence not 37 divides 4363 by NAT_4:9;
4363 = 41*106 + 17; hence not 41 divides 4363 by NAT_4:9;
4363 = 43*101 + 20; hence not 43 divides 4363 by NAT_4:9;
4363 = 47*92 + 39; hence not 47 divides 4363 by NAT_4:9;
4363 = 53*82 + 17; hence not 53 divides 4363 by NAT_4:9;
4363 = 59*73 + 56; hence not 59 divides 4363 by NAT_4:9;
4363 = 61*71 + 32; hence not 61 divides 4363 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4363 & n is prime
holds not n divides 4363 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4373 is prime
proof
now
4373 = 2*2186 + 1; hence not 2 divides 4373 by NAT_4:9;
4373 = 3*1457 + 2; hence not 3 divides 4373 by NAT_4:9;
4373 = 5*874 + 3; hence not 5 divides 4373 by NAT_4:9;
4373 = 7*624 + 5; hence not 7 divides 4373 by NAT_4:9;
4373 = 11*397 + 6; hence not 11 divides 4373 by NAT_4:9;
4373 = 13*336 + 5; hence not 13 divides 4373 by NAT_4:9;
4373 = 17*257 + 4; hence not 17 divides 4373 by NAT_4:9;
4373 = 19*230 + 3; hence not 19 divides 4373 by NAT_4:9;
4373 = 23*190 + 3; hence not 23 divides 4373 by NAT_4:9;
4373 = 29*150 + 23; hence not 29 divides 4373 by NAT_4:9;
4373 = 31*141 + 2; hence not 31 divides 4373 by NAT_4:9;
4373 = 37*118 + 7; hence not 37 divides 4373 by NAT_4:9;
4373 = 41*106 + 27; hence not 41 divides 4373 by NAT_4:9;
4373 = 43*101 + 30; hence not 43 divides 4373 by NAT_4:9;
4373 = 47*93 + 2; hence not 47 divides 4373 by NAT_4:9;
4373 = 53*82 + 27; hence not 53 divides 4373 by NAT_4:9;
4373 = 59*74 + 7; hence not 59 divides 4373 by NAT_4:9;
4373 = 61*71 + 42; hence not 61 divides 4373 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4373 & n is prime
holds not n divides 4373 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4391 is prime
proof
now
4391 = 2*2195 + 1; hence not 2 divides 4391 by NAT_4:9;
4391 = 3*1463 + 2; hence not 3 divides 4391 by NAT_4:9;
4391 = 5*878 + 1; hence not 5 divides 4391 by NAT_4:9;
4391 = 7*627 + 2; hence not 7 divides 4391 by NAT_4:9;
4391 = 11*399 + 2; hence not 11 divides 4391 by NAT_4:9;
4391 = 13*337 + 10; hence not 13 divides 4391 by NAT_4:9;
4391 = 17*258 + 5; hence not 17 divides 4391 by NAT_4:9;
4391 = 19*231 + 2; hence not 19 divides 4391 by NAT_4:9;
4391 = 23*190 + 21; hence not 23 divides 4391 by NAT_4:9;
4391 = 29*151 + 12; hence not 29 divides 4391 by NAT_4:9;
4391 = 31*141 + 20; hence not 31 divides 4391 by NAT_4:9;
4391 = 37*118 + 25; hence not 37 divides 4391 by NAT_4:9;
4391 = 41*107 + 4; hence not 41 divides 4391 by NAT_4:9;
4391 = 43*102 + 5; hence not 43 divides 4391 by NAT_4:9;
4391 = 47*93 + 20; hence not 47 divides 4391 by NAT_4:9;
4391 = 53*82 + 45; hence not 53 divides 4391 by NAT_4:9;
4391 = 59*74 + 25; hence not 59 divides 4391 by NAT_4:9;
4391 = 61*71 + 60; hence not 61 divides 4391 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4391 & n is prime
holds not n divides 4391 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4397 is prime
proof
now
4397 = 2*2198 + 1; hence not 2 divides 4397 by NAT_4:9;
4397 = 3*1465 + 2; hence not 3 divides 4397 by NAT_4:9;
4397 = 5*879 + 2; hence not 5 divides 4397 by NAT_4:9;
4397 = 7*628 + 1; hence not 7 divides 4397 by NAT_4:9;
4397 = 11*399 + 8; hence not 11 divides 4397 by NAT_4:9;
4397 = 13*338 + 3; hence not 13 divides 4397 by NAT_4:9;
4397 = 17*258 + 11; hence not 17 divides 4397 by NAT_4:9;
4397 = 19*231 + 8; hence not 19 divides 4397 by NAT_4:9;
4397 = 23*191 + 4; hence not 23 divides 4397 by NAT_4:9;
4397 = 29*151 + 18; hence not 29 divides 4397 by NAT_4:9;
4397 = 31*141 + 26; hence not 31 divides 4397 by NAT_4:9;
4397 = 37*118 + 31; hence not 37 divides 4397 by NAT_4:9;
4397 = 41*107 + 10; hence not 41 divides 4397 by NAT_4:9;
4397 = 43*102 + 11; hence not 43 divides 4397 by NAT_4:9;
4397 = 47*93 + 26; hence not 47 divides 4397 by NAT_4:9;
4397 = 53*82 + 51; hence not 53 divides 4397 by NAT_4:9;
4397 = 59*74 + 31; hence not 59 divides 4397 by NAT_4:9;
4397 = 61*72 + 5; hence not 61 divides 4397 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4397 & n is prime
holds not n divides 4397 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4409 is prime
proof
now
4409 = 2*2204 + 1; hence not 2 divides 4409 by NAT_4:9;
4409 = 3*1469 + 2; hence not 3 divides 4409 by NAT_4:9;
4409 = 5*881 + 4; hence not 5 divides 4409 by NAT_4:9;
4409 = 7*629 + 6; hence not 7 divides 4409 by NAT_4:9;
4409 = 11*400 + 9; hence not 11 divides 4409 by NAT_4:9;
4409 = 13*339 + 2; hence not 13 divides 4409 by NAT_4:9;
4409 = 17*259 + 6; hence not 17 divides 4409 by NAT_4:9;
4409 = 19*232 + 1; hence not 19 divides 4409 by NAT_4:9;
4409 = 23*191 + 16; hence not 23 divides 4409 by NAT_4:9;
4409 = 29*152 + 1; hence not 29 divides 4409 by NAT_4:9;
4409 = 31*142 + 7; hence not 31 divides 4409 by NAT_4:9;
4409 = 37*119 + 6; hence not 37 divides 4409 by NAT_4:9;
4409 = 41*107 + 22; hence not 41 divides 4409 by NAT_4:9;
4409 = 43*102 + 23; hence not 43 divides 4409 by NAT_4:9;
4409 = 47*93 + 38; hence not 47 divides 4409 by NAT_4:9;
4409 = 53*83 + 10; hence not 53 divides 4409 by NAT_4:9;
4409 = 59*74 + 43; hence not 59 divides 4409 by NAT_4:9;
4409 = 61*72 + 17; hence not 61 divides 4409 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4409 & n is prime
holds not n divides 4409 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4421 is prime
proof
now
4421 = 2*2210 + 1; hence not 2 divides 4421 by NAT_4:9;
4421 = 3*1473 + 2; hence not 3 divides 4421 by NAT_4:9;
4421 = 5*884 + 1; hence not 5 divides 4421 by NAT_4:9;
4421 = 7*631 + 4; hence not 7 divides 4421 by NAT_4:9;
4421 = 11*401 + 10; hence not 11 divides 4421 by NAT_4:9;
4421 = 13*340 + 1; hence not 13 divides 4421 by NAT_4:9;
4421 = 17*260 + 1; hence not 17 divides 4421 by NAT_4:9;
4421 = 19*232 + 13; hence not 19 divides 4421 by NAT_4:9;
4421 = 23*192 + 5; hence not 23 divides 4421 by NAT_4:9;
4421 = 29*152 + 13; hence not 29 divides 4421 by NAT_4:9;
4421 = 31*142 + 19; hence not 31 divides 4421 by NAT_4:9;
4421 = 37*119 + 18; hence not 37 divides 4421 by NAT_4:9;
4421 = 41*107 + 34; hence not 41 divides 4421 by NAT_4:9;
4421 = 43*102 + 35; hence not 43 divides 4421 by NAT_4:9;
4421 = 47*94 + 3; hence not 47 divides 4421 by NAT_4:9;
4421 = 53*83 + 22; hence not 53 divides 4421 by NAT_4:9;
4421 = 59*74 + 55; hence not 59 divides 4421 by NAT_4:9;
4421 = 61*72 + 29; hence not 61 divides 4421 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4421 & n is prime
holds not n divides 4421 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4423 is prime
proof
now
4423 = 2*2211 + 1; hence not 2 divides 4423 by NAT_4:9;
4423 = 3*1474 + 1; hence not 3 divides 4423 by NAT_4:9;
4423 = 5*884 + 3; hence not 5 divides 4423 by NAT_4:9;
4423 = 7*631 + 6; hence not 7 divides 4423 by NAT_4:9;
4423 = 11*402 + 1; hence not 11 divides 4423 by NAT_4:9;
4423 = 13*340 + 3; hence not 13 divides 4423 by NAT_4:9;
4423 = 17*260 + 3; hence not 17 divides 4423 by NAT_4:9;
4423 = 19*232 + 15; hence not 19 divides 4423 by NAT_4:9;
4423 = 23*192 + 7; hence not 23 divides 4423 by NAT_4:9;
4423 = 29*152 + 15; hence not 29 divides 4423 by NAT_4:9;
4423 = 31*142 + 21; hence not 31 divides 4423 by NAT_4:9;
4423 = 37*119 + 20; hence not 37 divides 4423 by NAT_4:9;
4423 = 41*107 + 36; hence not 41 divides 4423 by NAT_4:9;
4423 = 43*102 + 37; hence not 43 divides 4423 by NAT_4:9;
4423 = 47*94 + 5; hence not 47 divides 4423 by NAT_4:9;
4423 = 53*83 + 24; hence not 53 divides 4423 by NAT_4:9;
4423 = 59*74 + 57; hence not 59 divides 4423 by NAT_4:9;
4423 = 61*72 + 31; hence not 61 divides 4423 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4423 & n is prime
holds not n divides 4423 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4441 is prime
proof
now
4441 = 2*2220 + 1; hence not 2 divides 4441 by NAT_4:9;
4441 = 3*1480 + 1; hence not 3 divides 4441 by NAT_4:9;
4441 = 5*888 + 1; hence not 5 divides 4441 by NAT_4:9;
4441 = 7*634 + 3; hence not 7 divides 4441 by NAT_4:9;
4441 = 11*403 + 8; hence not 11 divides 4441 by NAT_4:9;
4441 = 13*341 + 8; hence not 13 divides 4441 by NAT_4:9;
4441 = 17*261 + 4; hence not 17 divides 4441 by NAT_4:9;
4441 = 19*233 + 14; hence not 19 divides 4441 by NAT_4:9;
4441 = 23*193 + 2; hence not 23 divides 4441 by NAT_4:9;
4441 = 29*153 + 4; hence not 29 divides 4441 by NAT_4:9;
4441 = 31*143 + 8; hence not 31 divides 4441 by NAT_4:9;
4441 = 37*120 + 1; hence not 37 divides 4441 by NAT_4:9;
4441 = 41*108 + 13; hence not 41 divides 4441 by NAT_4:9;
4441 = 43*103 + 12; hence not 43 divides 4441 by NAT_4:9;
4441 = 47*94 + 23; hence not 47 divides 4441 by NAT_4:9;
4441 = 53*83 + 42; hence not 53 divides 4441 by NAT_4:9;
4441 = 59*75 + 16; hence not 59 divides 4441 by NAT_4:9;
4441 = 61*72 + 49; hence not 61 divides 4441 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4441 & n is prime
holds not n divides 4441 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4447 is prime
proof
now
4447 = 2*2223 + 1; hence not 2 divides 4447 by NAT_4:9;
4447 = 3*1482 + 1; hence not 3 divides 4447 by NAT_4:9;
4447 = 5*889 + 2; hence not 5 divides 4447 by NAT_4:9;
4447 = 7*635 + 2; hence not 7 divides 4447 by NAT_4:9;
4447 = 11*404 + 3; hence not 11 divides 4447 by NAT_4:9;
4447 = 13*342 + 1; hence not 13 divides 4447 by NAT_4:9;
4447 = 17*261 + 10; hence not 17 divides 4447 by NAT_4:9;
4447 = 19*234 + 1; hence not 19 divides 4447 by NAT_4:9;
4447 = 23*193 + 8; hence not 23 divides 4447 by NAT_4:9;
4447 = 29*153 + 10; hence not 29 divides 4447 by NAT_4:9;
4447 = 31*143 + 14; hence not 31 divides 4447 by NAT_4:9;
4447 = 37*120 + 7; hence not 37 divides 4447 by NAT_4:9;
4447 = 41*108 + 19; hence not 41 divides 4447 by NAT_4:9;
4447 = 43*103 + 18; hence not 43 divides 4447 by NAT_4:9;
4447 = 47*94 + 29; hence not 47 divides 4447 by NAT_4:9;
4447 = 53*83 + 48; hence not 53 divides 4447 by NAT_4:9;
4447 = 59*75 + 22; hence not 59 divides 4447 by NAT_4:9;
4447 = 61*72 + 55; hence not 61 divides 4447 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4447 & n is prime
holds not n divides 4447 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4451 is prime
proof
now
4451 = 2*2225 + 1; hence not 2 divides 4451 by NAT_4:9;
4451 = 3*1483 + 2; hence not 3 divides 4451 by NAT_4:9;
4451 = 5*890 + 1; hence not 5 divides 4451 by NAT_4:9;
4451 = 7*635 + 6; hence not 7 divides 4451 by NAT_4:9;
4451 = 11*404 + 7; hence not 11 divides 4451 by NAT_4:9;
4451 = 13*342 + 5; hence not 13 divides 4451 by NAT_4:9;
4451 = 17*261 + 14; hence not 17 divides 4451 by NAT_4:9;
4451 = 19*234 + 5; hence not 19 divides 4451 by NAT_4:9;
4451 = 23*193 + 12; hence not 23 divides 4451 by NAT_4:9;
4451 = 29*153 + 14; hence not 29 divides 4451 by NAT_4:9;
4451 = 31*143 + 18; hence not 31 divides 4451 by NAT_4:9;
4451 = 37*120 + 11; hence not 37 divides 4451 by NAT_4:9;
4451 = 41*108 + 23; hence not 41 divides 4451 by NAT_4:9;
4451 = 43*103 + 22; hence not 43 divides 4451 by NAT_4:9;
4451 = 47*94 + 33; hence not 47 divides 4451 by NAT_4:9;
4451 = 53*83 + 52; hence not 53 divides 4451 by NAT_4:9;
4451 = 59*75 + 26; hence not 59 divides 4451 by NAT_4:9;
4451 = 61*72 + 59; hence not 61 divides 4451 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4451 & n is prime
holds not n divides 4451 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4457 is prime
proof
now
4457 = 2*2228 + 1; hence not 2 divides 4457 by NAT_4:9;
4457 = 3*1485 + 2; hence not 3 divides 4457 by NAT_4:9;
4457 = 5*891 + 2; hence not 5 divides 4457 by NAT_4:9;
4457 = 7*636 + 5; hence not 7 divides 4457 by NAT_4:9;
4457 = 11*405 + 2; hence not 11 divides 4457 by NAT_4:9;
4457 = 13*342 + 11; hence not 13 divides 4457 by NAT_4:9;
4457 = 17*262 + 3; hence not 17 divides 4457 by NAT_4:9;
4457 = 19*234 + 11; hence not 19 divides 4457 by NAT_4:9;
4457 = 23*193 + 18; hence not 23 divides 4457 by NAT_4:9;
4457 = 29*153 + 20; hence not 29 divides 4457 by NAT_4:9;
4457 = 31*143 + 24; hence not 31 divides 4457 by NAT_4:9;
4457 = 37*120 + 17; hence not 37 divides 4457 by NAT_4:9;
4457 = 41*108 + 29; hence not 41 divides 4457 by NAT_4:9;
4457 = 43*103 + 28; hence not 43 divides 4457 by NAT_4:9;
4457 = 47*94 + 39; hence not 47 divides 4457 by NAT_4:9;
4457 = 53*84 + 5; hence not 53 divides 4457 by NAT_4:9;
4457 = 59*75 + 32; hence not 59 divides 4457 by NAT_4:9;
4457 = 61*73 + 4; hence not 61 divides 4457 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4457 & n is prime
holds not n divides 4457 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4463 is prime
proof
now
4463 = 2*2231 + 1; hence not 2 divides 4463 by NAT_4:9;
4463 = 3*1487 + 2; hence not 3 divides 4463 by NAT_4:9;
4463 = 5*892 + 3; hence not 5 divides 4463 by NAT_4:9;
4463 = 7*637 + 4; hence not 7 divides 4463 by NAT_4:9;
4463 = 11*405 + 8; hence not 11 divides 4463 by NAT_4:9;
4463 = 13*343 + 4; hence not 13 divides 4463 by NAT_4:9;
4463 = 17*262 + 9; hence not 17 divides 4463 by NAT_4:9;
4463 = 19*234 + 17; hence not 19 divides 4463 by NAT_4:9;
4463 = 23*194 + 1; hence not 23 divides 4463 by NAT_4:9;
4463 = 29*153 + 26; hence not 29 divides 4463 by NAT_4:9;
4463 = 31*143 + 30; hence not 31 divides 4463 by NAT_4:9;
4463 = 37*120 + 23; hence not 37 divides 4463 by NAT_4:9;
4463 = 41*108 + 35; hence not 41 divides 4463 by NAT_4:9;
4463 = 43*103 + 34; hence not 43 divides 4463 by NAT_4:9;
4463 = 47*94 + 45; hence not 47 divides 4463 by NAT_4:9;
4463 = 53*84 + 11; hence not 53 divides 4463 by NAT_4:9;
4463 = 59*75 + 38; hence not 59 divides 4463 by NAT_4:9;
4463 = 61*73 + 10; hence not 61 divides 4463 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4463 & n is prime
holds not n divides 4463 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4481 is prime
proof
now
4481 = 2*2240 + 1; hence not 2 divides 4481 by NAT_4:9;
4481 = 3*1493 + 2; hence not 3 divides 4481 by NAT_4:9;
4481 = 5*896 + 1; hence not 5 divides 4481 by NAT_4:9;
4481 = 7*640 + 1; hence not 7 divides 4481 by NAT_4:9;
4481 = 11*407 + 4; hence not 11 divides 4481 by NAT_4:9;
4481 = 13*344 + 9; hence not 13 divides 4481 by NAT_4:9;
4481 = 17*263 + 10; hence not 17 divides 4481 by NAT_4:9;
4481 = 19*235 + 16; hence not 19 divides 4481 by NAT_4:9;
4481 = 23*194 + 19; hence not 23 divides 4481 by NAT_4:9;
4481 = 29*154 + 15; hence not 29 divides 4481 by NAT_4:9;
4481 = 31*144 + 17; hence not 31 divides 4481 by NAT_4:9;
4481 = 37*121 + 4; hence not 37 divides 4481 by NAT_4:9;
4481 = 41*109 + 12; hence not 41 divides 4481 by NAT_4:9;
4481 = 43*104 + 9; hence not 43 divides 4481 by NAT_4:9;
4481 = 47*95 + 16; hence not 47 divides 4481 by NAT_4:9;
4481 = 53*84 + 29; hence not 53 divides 4481 by NAT_4:9;
4481 = 59*75 + 56; hence not 59 divides 4481 by NAT_4:9;
4481 = 61*73 + 28; hence not 61 divides 4481 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4481 & n is prime
holds not n divides 4481 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4483 is prime
proof
now
4483 = 2*2241 + 1; hence not 2 divides 4483 by NAT_4:9;
4483 = 3*1494 + 1; hence not 3 divides 4483 by NAT_4:9;
4483 = 5*896 + 3; hence not 5 divides 4483 by NAT_4:9;
4483 = 7*640 + 3; hence not 7 divides 4483 by NAT_4:9;
4483 = 11*407 + 6; hence not 11 divides 4483 by NAT_4:9;
4483 = 13*344 + 11; hence not 13 divides 4483 by NAT_4:9;
4483 = 17*263 + 12; hence not 17 divides 4483 by NAT_4:9;
4483 = 19*235 + 18; hence not 19 divides 4483 by NAT_4:9;
4483 = 23*194 + 21; hence not 23 divides 4483 by NAT_4:9;
4483 = 29*154 + 17; hence not 29 divides 4483 by NAT_4:9;
4483 = 31*144 + 19; hence not 31 divides 4483 by NAT_4:9;
4483 = 37*121 + 6; hence not 37 divides 4483 by NAT_4:9;
4483 = 41*109 + 14; hence not 41 divides 4483 by NAT_4:9;
4483 = 43*104 + 11; hence not 43 divides 4483 by NAT_4:9;
4483 = 47*95 + 18; hence not 47 divides 4483 by NAT_4:9;
4483 = 53*84 + 31; hence not 53 divides 4483 by NAT_4:9;
4483 = 59*75 + 58; hence not 59 divides 4483 by NAT_4:9;
4483 = 61*73 + 30; hence not 61 divides 4483 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4483 & n is prime
holds not n divides 4483 by XPRIMET1:36;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4493 is prime
proof
now
4493 = 2*2246 + 1; hence not 2 divides 4493 by NAT_4:9;
4493 = 3*1497 + 2; hence not 3 divides 4493 by NAT_4:9;
4493 = 5*898 + 3; hence not 5 divides 4493 by NAT_4:9;
4493 = 7*641 + 6; hence not 7 divides 4493 by NAT_4:9;
4493 = 11*408 + 5; hence not 11 divides 4493 by NAT_4:9;
4493 = 13*345 + 8; hence not 13 divides 4493 by NAT_4:9;
4493 = 17*264 + 5; hence not 17 divides 4493 by NAT_4:9;
4493 = 19*236 + 9; hence not 19 divides 4493 by NAT_4:9;
4493 = 23*195 + 8; hence not 23 divides 4493 by NAT_4:9;
4493 = 29*154 + 27; hence not 29 divides 4493 by NAT_4:9;
4493 = 31*144 + 29; hence not 31 divides 4493 by NAT_4:9;
4493 = 37*121 + 16; hence not 37 divides 4493 by NAT_4:9;
4493 = 41*109 + 24; hence not 41 divides 4493 by NAT_4:9;
4493 = 43*104 + 21; hence not 43 divides 4493 by NAT_4:9;
4493 = 47*95 + 28; hence not 47 divides 4493 by NAT_4:9;
4493 = 53*84 + 41; hence not 53 divides 4493 by NAT_4:9;
4493 = 59*76 + 9; hence not 59 divides 4493 by NAT_4:9;
4493 = 61*73 + 40; hence not 61 divides 4493 by NAT_4:9;
4493 = 67*67 + 4; hence not 67 divides 4493 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4493 & n is prime
holds not n divides 4493 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
4507 is prime
proof
now
4507 = 2*2253 + 1; hence not 2 divides 4507 by NAT_4:9;
4507 = 3*1502 + 1; hence not 3 divides 4507 by NAT_4:9;
4507 = 5*901 + 2; hence not 5 divides 4507 by NAT_4:9;
4507 = 7*643 + 6; hence not 7 divides 4507 by NAT_4:9;
4507 = 11*409 + 8; hence not 11 divides 4507 by NAT_4:9;
4507 = 13*346 + 9; hence not 13 divides 4507 by NAT_4:9;
4507 = 17*265 + 2; hence not 17 divides 4507 by NAT_4:9;
4507 = 19*237 + 4; hence not 19 divides 4507 by NAT_4:9;
4507 = 23*195 + 22; hence not 23 divides 4507 by NAT_4:9;
4507 = 29*155 + 12; hence not 29 divides 4507 by NAT_4:9;
4507 = 31*145 + 12; hence not 31 divides 4507 by NAT_4:9;
4507 = 37*121 + 30; hence not 37 divides 4507 by NAT_4:9;
4507 = 41*109 + 38; hence not 41 divides 4507 by NAT_4:9;
4507 = 43*104 + 35; hence not 43 divides 4507 by NAT_4:9;
4507 = 47*95 + 42; hence not 47 divides 4507 by NAT_4:9;
4507 = 53*85 + 2; hence not 53 divides 4507 by NAT_4:9;
4507 = 59*76 + 23; hence not 59 divides 4507 by NAT_4:9;
4507 = 61*73 + 54; hence not 61 divides 4507 by NAT_4:9;
4507 = 67*67 + 18; hence not 67 divides 4507 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4507 & n is prime
holds not n divides 4507 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4513 is prime
proof
now
4513 = 2*2256 + 1; hence not 2 divides 4513 by NAT_4:9;
4513 = 3*1504 + 1; hence not 3 divides 4513 by NAT_4:9;
4513 = 5*902 + 3; hence not 5 divides 4513 by NAT_4:9;
4513 = 7*644 + 5; hence not 7 divides 4513 by NAT_4:9;
4513 = 11*410 + 3; hence not 11 divides 4513 by NAT_4:9;
4513 = 13*347 + 2; hence not 13 divides 4513 by NAT_4:9;
4513 = 17*265 + 8; hence not 17 divides 4513 by NAT_4:9;
4513 = 19*237 + 10; hence not 19 divides 4513 by NAT_4:9;
4513 = 23*196 + 5; hence not 23 divides 4513 by NAT_4:9;
4513 = 29*155 + 18; hence not 29 divides 4513 by NAT_4:9;
4513 = 31*145 + 18; hence not 31 divides 4513 by NAT_4:9;
4513 = 37*121 + 36; hence not 37 divides 4513 by NAT_4:9;
4513 = 41*110 + 3; hence not 41 divides 4513 by NAT_4:9;
4513 = 43*104 + 41; hence not 43 divides 4513 by NAT_4:9;
4513 = 47*96 + 1; hence not 47 divides 4513 by NAT_4:9;
4513 = 53*85 + 8; hence not 53 divides 4513 by NAT_4:9;
4513 = 59*76 + 29; hence not 59 divides 4513 by NAT_4:9;
4513 = 61*73 + 60; hence not 61 divides 4513 by NAT_4:9;
4513 = 67*67 + 24; hence not 67 divides 4513 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4513 & n is prime
holds not n divides 4513 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4517 is prime
proof
now
4517 = 2*2258 + 1; hence not 2 divides 4517 by NAT_4:9;
4517 = 3*1505 + 2; hence not 3 divides 4517 by NAT_4:9;
4517 = 5*903 + 2; hence not 5 divides 4517 by NAT_4:9;
4517 = 7*645 + 2; hence not 7 divides 4517 by NAT_4:9;
4517 = 11*410 + 7; hence not 11 divides 4517 by NAT_4:9;
4517 = 13*347 + 6; hence not 13 divides 4517 by NAT_4:9;
4517 = 17*265 + 12; hence not 17 divides 4517 by NAT_4:9;
4517 = 19*237 + 14; hence not 19 divides 4517 by NAT_4:9;
4517 = 23*196 + 9; hence not 23 divides 4517 by NAT_4:9;
4517 = 29*155 + 22; hence not 29 divides 4517 by NAT_4:9;
4517 = 31*145 + 22; hence not 31 divides 4517 by NAT_4:9;
4517 = 37*122 + 3; hence not 37 divides 4517 by NAT_4:9;
4517 = 41*110 + 7; hence not 41 divides 4517 by NAT_4:9;
4517 = 43*105 + 2; hence not 43 divides 4517 by NAT_4:9;
4517 = 47*96 + 5; hence not 47 divides 4517 by NAT_4:9;
4517 = 53*85 + 12; hence not 53 divides 4517 by NAT_4:9;
4517 = 59*76 + 33; hence not 59 divides 4517 by NAT_4:9;
4517 = 61*74 + 3; hence not 61 divides 4517 by NAT_4:9;
4517 = 67*67 + 28; hence not 67 divides 4517 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4517 & n is prime
holds not n divides 4517 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4519 is prime
proof
now
4519 = 2*2259 + 1; hence not 2 divides 4519 by NAT_4:9;
4519 = 3*1506 + 1; hence not 3 divides 4519 by NAT_4:9;
4519 = 5*903 + 4; hence not 5 divides 4519 by NAT_4:9;
4519 = 7*645 + 4; hence not 7 divides 4519 by NAT_4:9;
4519 = 11*410 + 9; hence not 11 divides 4519 by NAT_4:9;
4519 = 13*347 + 8; hence not 13 divides 4519 by NAT_4:9;
4519 = 17*265 + 14; hence not 17 divides 4519 by NAT_4:9;
4519 = 19*237 + 16; hence not 19 divides 4519 by NAT_4:9;
4519 = 23*196 + 11; hence not 23 divides 4519 by NAT_4:9;
4519 = 29*155 + 24; hence not 29 divides 4519 by NAT_4:9;
4519 = 31*145 + 24; hence not 31 divides 4519 by NAT_4:9;
4519 = 37*122 + 5; hence not 37 divides 4519 by NAT_4:9;
4519 = 41*110 + 9; hence not 41 divides 4519 by NAT_4:9;
4519 = 43*105 + 4; hence not 43 divides 4519 by NAT_4:9;
4519 = 47*96 + 7; hence not 47 divides 4519 by NAT_4:9;
4519 = 53*85 + 14; hence not 53 divides 4519 by NAT_4:9;
4519 = 59*76 + 35; hence not 59 divides 4519 by NAT_4:9;
4519 = 61*74 + 5; hence not 61 divides 4519 by NAT_4:9;
4519 = 67*67 + 30; hence not 67 divides 4519 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4519 & n is prime
holds not n divides 4519 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4523 is prime
proof
now
4523 = 2*2261 + 1; hence not 2 divides 4523 by NAT_4:9;
4523 = 3*1507 + 2; hence not 3 divides 4523 by NAT_4:9;
4523 = 5*904 + 3; hence not 5 divides 4523 by NAT_4:9;
4523 = 7*646 + 1; hence not 7 divides 4523 by NAT_4:9;
4523 = 11*411 + 2; hence not 11 divides 4523 by NAT_4:9;
4523 = 13*347 + 12; hence not 13 divides 4523 by NAT_4:9;
4523 = 17*266 + 1; hence not 17 divides 4523 by NAT_4:9;
4523 = 19*238 + 1; hence not 19 divides 4523 by NAT_4:9;
4523 = 23*196 + 15; hence not 23 divides 4523 by NAT_4:9;
4523 = 29*155 + 28; hence not 29 divides 4523 by NAT_4:9;
4523 = 31*145 + 28; hence not 31 divides 4523 by NAT_4:9;
4523 = 37*122 + 9; hence not 37 divides 4523 by NAT_4:9;
4523 = 41*110 + 13; hence not 41 divides 4523 by NAT_4:9;
4523 = 43*105 + 8; hence not 43 divides 4523 by NAT_4:9;
4523 = 47*96 + 11; hence not 47 divides 4523 by NAT_4:9;
4523 = 53*85 + 18; hence not 53 divides 4523 by NAT_4:9;
4523 = 59*76 + 39; hence not 59 divides 4523 by NAT_4:9;
4523 = 61*74 + 9; hence not 61 divides 4523 by NAT_4:9;
4523 = 67*67 + 34; hence not 67 divides 4523 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4523 & n is prime
holds not n divides 4523 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
4547 is prime
proof
now
4547 = 2*2273 + 1; hence not 2 divides 4547 by NAT_4:9;
4547 = 3*1515 + 2; hence not 3 divides 4547 by NAT_4:9;
4547 = 5*909 + 2; hence not 5 divides 4547 by NAT_4:9;
4547 = 7*649 + 4; hence not 7 divides 4547 by NAT_4:9;
4547 = 11*413 + 4; hence not 11 divides 4547 by NAT_4:9;
4547 = 13*349 + 10; hence not 13 divides 4547 by NAT_4:9;
4547 = 17*267 + 8; hence not 17 divides 4547 by NAT_4:9;
4547 = 19*239 + 6; hence not 19 divides 4547 by NAT_4:9;
4547 = 23*197 + 16; hence not 23 divides 4547 by NAT_4:9;
4547 = 29*156 + 23; hence not 29 divides 4547 by NAT_4:9;
4547 = 31*146 + 21; hence not 31 divides 4547 by NAT_4:9;
4547 = 37*122 + 33; hence not 37 divides 4547 by NAT_4:9;
4547 = 41*110 + 37; hence not 41 divides 4547 by NAT_4:9;
4547 = 43*105 + 32; hence not 43 divides 4547 by NAT_4:9;
4547 = 47*96 + 35; hence not 47 divides 4547 by NAT_4:9;
4547 = 53*85 + 42; hence not 53 divides 4547 by NAT_4:9;
4547 = 59*77 + 4; hence not 59 divides 4547 by NAT_4:9;
4547 = 61*74 + 33; hence not 61 divides 4547 by NAT_4:9;
4547 = 67*67 + 58; hence not 67 divides 4547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4547 & n is prime
holds not n divides 4547 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4549 is prime
proof
now
4549 = 2*2274 + 1; hence not 2 divides 4549 by NAT_4:9;
4549 = 3*1516 + 1; hence not 3 divides 4549 by NAT_4:9;
4549 = 5*909 + 4; hence not 5 divides 4549 by NAT_4:9;
4549 = 7*649 + 6; hence not 7 divides 4549 by NAT_4:9;
4549 = 11*413 + 6; hence not 11 divides 4549 by NAT_4:9;
4549 = 13*349 + 12; hence not 13 divides 4549 by NAT_4:9;
4549 = 17*267 + 10; hence not 17 divides 4549 by NAT_4:9;
4549 = 19*239 + 8; hence not 19 divides 4549 by NAT_4:9;
4549 = 23*197 + 18; hence not 23 divides 4549 by NAT_4:9;
4549 = 29*156 + 25; hence not 29 divides 4549 by NAT_4:9;
4549 = 31*146 + 23; hence not 31 divides 4549 by NAT_4:9;
4549 = 37*122 + 35; hence not 37 divides 4549 by NAT_4:9;
4549 = 41*110 + 39; hence not 41 divides 4549 by NAT_4:9;
4549 = 43*105 + 34; hence not 43 divides 4549 by NAT_4:9;
4549 = 47*96 + 37; hence not 47 divides 4549 by NAT_4:9;
4549 = 53*85 + 44; hence not 53 divides 4549 by NAT_4:9;
4549 = 59*77 + 6; hence not 59 divides 4549 by NAT_4:9;
4549 = 61*74 + 35; hence not 61 divides 4549 by NAT_4:9;
4549 = 67*67 + 60; hence not 67 divides 4549 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4549 & n is prime
holds not n divides 4549 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4561 is prime
proof
now
4561 = 2*2280 + 1; hence not 2 divides 4561 by NAT_4:9;
4561 = 3*1520 + 1; hence not 3 divides 4561 by NAT_4:9;
4561 = 5*912 + 1; hence not 5 divides 4561 by NAT_4:9;
4561 = 7*651 + 4; hence not 7 divides 4561 by NAT_4:9;
4561 = 11*414 + 7; hence not 11 divides 4561 by NAT_4:9;
4561 = 13*350 + 11; hence not 13 divides 4561 by NAT_4:9;
4561 = 17*268 + 5; hence not 17 divides 4561 by NAT_4:9;
4561 = 19*240 + 1; hence not 19 divides 4561 by NAT_4:9;
4561 = 23*198 + 7; hence not 23 divides 4561 by NAT_4:9;
4561 = 29*157 + 8; hence not 29 divides 4561 by NAT_4:9;
4561 = 31*147 + 4; hence not 31 divides 4561 by NAT_4:9;
4561 = 37*123 + 10; hence not 37 divides 4561 by NAT_4:9;
4561 = 41*111 + 10; hence not 41 divides 4561 by NAT_4:9;
4561 = 43*106 + 3; hence not 43 divides 4561 by NAT_4:9;
4561 = 47*97 + 2; hence not 47 divides 4561 by NAT_4:9;
4561 = 53*86 + 3; hence not 53 divides 4561 by NAT_4:9;
4561 = 59*77 + 18; hence not 59 divides 4561 by NAT_4:9;
4561 = 61*74 + 47; hence not 61 divides 4561 by NAT_4:9;
4561 = 67*68 + 5; hence not 67 divides 4561 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4561 & n is prime
holds not n divides 4561 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4567 is prime
proof
now
4567 = 2*2283 + 1; hence not 2 divides 4567 by NAT_4:9;
4567 = 3*1522 + 1; hence not 3 divides 4567 by NAT_4:9;
4567 = 5*913 + 2; hence not 5 divides 4567 by NAT_4:9;
4567 = 7*652 + 3; hence not 7 divides 4567 by NAT_4:9;
4567 = 11*415 + 2; hence not 11 divides 4567 by NAT_4:9;
4567 = 13*351 + 4; hence not 13 divides 4567 by NAT_4:9;
4567 = 17*268 + 11; hence not 17 divides 4567 by NAT_4:9;
4567 = 19*240 + 7; hence not 19 divides 4567 by NAT_4:9;
4567 = 23*198 + 13; hence not 23 divides 4567 by NAT_4:9;
4567 = 29*157 + 14; hence not 29 divides 4567 by NAT_4:9;
4567 = 31*147 + 10; hence not 31 divides 4567 by NAT_4:9;
4567 = 37*123 + 16; hence not 37 divides 4567 by NAT_4:9;
4567 = 41*111 + 16; hence not 41 divides 4567 by NAT_4:9;
4567 = 43*106 + 9; hence not 43 divides 4567 by NAT_4:9;
4567 = 47*97 + 8; hence not 47 divides 4567 by NAT_4:9;
4567 = 53*86 + 9; hence not 53 divides 4567 by NAT_4:9;
4567 = 59*77 + 24; hence not 59 divides 4567 by NAT_4:9;
4567 = 61*74 + 53; hence not 61 divides 4567 by NAT_4:9;
4567 = 67*68 + 11; hence not 67 divides 4567 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4567 & n is prime
holds not n divides 4567 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
4583 is prime
proof
now
4583 = 2*2291 + 1; hence not 2 divides 4583 by NAT_4:9;
4583 = 3*1527 + 2; hence not 3 divides 4583 by NAT_4:9;
4583 = 5*916 + 3; hence not 5 divides 4583 by NAT_4:9;
4583 = 7*654 + 5; hence not 7 divides 4583 by NAT_4:9;
4583 = 11*416 + 7; hence not 11 divides 4583 by NAT_4:9;
4583 = 13*352 + 7; hence not 13 divides 4583 by NAT_4:9;
4583 = 17*269 + 10; hence not 17 divides 4583 by NAT_4:9;
4583 = 19*241 + 4; hence not 19 divides 4583 by NAT_4:9;
4583 = 23*199 + 6; hence not 23 divides 4583 by NAT_4:9;
4583 = 29*158 + 1; hence not 29 divides 4583 by NAT_4:9;
4583 = 31*147 + 26; hence not 31 divides 4583 by NAT_4:9;
4583 = 37*123 + 32; hence not 37 divides 4583 by NAT_4:9;
4583 = 41*111 + 32; hence not 41 divides 4583 by NAT_4:9;
4583 = 43*106 + 25; hence not 43 divides 4583 by NAT_4:9;
4583 = 47*97 + 24; hence not 47 divides 4583 by NAT_4:9;
4583 = 53*86 + 25; hence not 53 divides 4583 by NAT_4:9;
4583 = 59*77 + 40; hence not 59 divides 4583 by NAT_4:9;
4583 = 61*75 + 8; hence not 61 divides 4583 by NAT_4:9;
4583 = 67*68 + 27; hence not 67 divides 4583 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4583 & n is prime
holds not n divides 4583 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
4591 is prime
proof
now
4591 = 2*2295 + 1; hence not 2 divides 4591 by NAT_4:9;
4591 = 3*1530 + 1; hence not 3 divides 4591 by NAT_4:9;
4591 = 5*918 + 1; hence not 5 divides 4591 by NAT_4:9;
4591 = 7*655 + 6; hence not 7 divides 4591 by NAT_4:9;
4591 = 11*417 + 4; hence not 11 divides 4591 by NAT_4:9;
4591 = 13*353 + 2; hence not 13 divides 4591 by NAT_4:9;
4591 = 17*270 + 1; hence not 17 divides 4591 by NAT_4:9;
4591 = 19*241 + 12; hence not 19 divides 4591 by NAT_4:9;
4591 = 23*199 + 14; hence not 23 divides 4591 by NAT_4:9;
4591 = 29*158 + 9; hence not 29 divides 4591 by NAT_4:9;
4591 = 31*148 + 3; hence not 31 divides 4591 by NAT_4:9;
4591 = 37*124 + 3; hence not 37 divides 4591 by NAT_4:9;
4591 = 41*111 + 40; hence not 41 divides 4591 by NAT_4:9;
4591 = 43*106 + 33; hence not 43 divides 4591 by NAT_4:9;
4591 = 47*97 + 32; hence not 47 divides 4591 by NAT_4:9;
4591 = 53*86 + 33; hence not 53 divides 4591 by NAT_4:9;
4591 = 59*77 + 48; hence not 59 divides 4591 by NAT_4:9;
4591 = 61*75 + 16; hence not 61 divides 4591 by NAT_4:9;
4591 = 67*68 + 35; hence not 67 divides 4591 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4591 & n is prime
holds not n divides 4591 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4597 is prime
proof
now
4597 = 2*2298 + 1; hence not 2 divides 4597 by NAT_4:9;
4597 = 3*1532 + 1; hence not 3 divides 4597 by NAT_4:9;
4597 = 5*919 + 2; hence not 5 divides 4597 by NAT_4:9;
4597 = 7*656 + 5; hence not 7 divides 4597 by NAT_4:9;
4597 = 11*417 + 10; hence not 11 divides 4597 by NAT_4:9;
4597 = 13*353 + 8; hence not 13 divides 4597 by NAT_4:9;
4597 = 17*270 + 7; hence not 17 divides 4597 by NAT_4:9;
4597 = 19*241 + 18; hence not 19 divides 4597 by NAT_4:9;
4597 = 23*199 + 20; hence not 23 divides 4597 by NAT_4:9;
4597 = 29*158 + 15; hence not 29 divides 4597 by NAT_4:9;
4597 = 31*148 + 9; hence not 31 divides 4597 by NAT_4:9;
4597 = 37*124 + 9; hence not 37 divides 4597 by NAT_4:9;
4597 = 41*112 + 5; hence not 41 divides 4597 by NAT_4:9;
4597 = 43*106 + 39; hence not 43 divides 4597 by NAT_4:9;
4597 = 47*97 + 38; hence not 47 divides 4597 by NAT_4:9;
4597 = 53*86 + 39; hence not 53 divides 4597 by NAT_4:9;
4597 = 59*77 + 54; hence not 59 divides 4597 by NAT_4:9;
4597 = 61*75 + 22; hence not 61 divides 4597 by NAT_4:9;
4597 = 67*68 + 41; hence not 67 divides 4597 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4597 & n is prime
holds not n divides 4597 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4603 is prime
proof
now
4603 = 2*2301 + 1; hence not 2 divides 4603 by NAT_4:9;
4603 = 3*1534 + 1; hence not 3 divides 4603 by NAT_4:9;
4603 = 5*920 + 3; hence not 5 divides 4603 by NAT_4:9;
4603 = 7*657 + 4; hence not 7 divides 4603 by NAT_4:9;
4603 = 11*418 + 5; hence not 11 divides 4603 by NAT_4:9;
4603 = 13*354 + 1; hence not 13 divides 4603 by NAT_4:9;
4603 = 17*270 + 13; hence not 17 divides 4603 by NAT_4:9;
4603 = 19*242 + 5; hence not 19 divides 4603 by NAT_4:9;
4603 = 23*200 + 3; hence not 23 divides 4603 by NAT_4:9;
4603 = 29*158 + 21; hence not 29 divides 4603 by NAT_4:9;
4603 = 31*148 + 15; hence not 31 divides 4603 by NAT_4:9;
4603 = 37*124 + 15; hence not 37 divides 4603 by NAT_4:9;
4603 = 41*112 + 11; hence not 41 divides 4603 by NAT_4:9;
4603 = 43*107 + 2; hence not 43 divides 4603 by NAT_4:9;
4603 = 47*97 + 44; hence not 47 divides 4603 by NAT_4:9;
4603 = 53*86 + 45; hence not 53 divides 4603 by NAT_4:9;
4603 = 59*78 + 1; hence not 59 divides 4603 by NAT_4:9;
4603 = 61*75 + 28; hence not 61 divides 4603 by NAT_4:9;
4603 = 67*68 + 47; hence not 67 divides 4603 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4603 & n is prime
holds not n divides 4603 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4621 is prime
proof
now
4621 = 2*2310 + 1; hence not 2 divides 4621 by NAT_4:9;
4621 = 3*1540 + 1; hence not 3 divides 4621 by NAT_4:9;
4621 = 5*924 + 1; hence not 5 divides 4621 by NAT_4:9;
4621 = 7*660 + 1; hence not 7 divides 4621 by NAT_4:9;
4621 = 11*420 + 1; hence not 11 divides 4621 by NAT_4:9;
4621 = 13*355 + 6; hence not 13 divides 4621 by NAT_4:9;
4621 = 17*271 + 14; hence not 17 divides 4621 by NAT_4:9;
4621 = 19*243 + 4; hence not 19 divides 4621 by NAT_4:9;
4621 = 23*200 + 21; hence not 23 divides 4621 by NAT_4:9;
4621 = 29*159 + 10; hence not 29 divides 4621 by NAT_4:9;
4621 = 31*149 + 2; hence not 31 divides 4621 by NAT_4:9;
4621 = 37*124 + 33; hence not 37 divides 4621 by NAT_4:9;
4621 = 41*112 + 29; hence not 41 divides 4621 by NAT_4:9;
4621 = 43*107 + 20; hence not 43 divides 4621 by NAT_4:9;
4621 = 47*98 + 15; hence not 47 divides 4621 by NAT_4:9;
4621 = 53*87 + 10; hence not 53 divides 4621 by NAT_4:9;
4621 = 59*78 + 19; hence not 59 divides 4621 by NAT_4:9;
4621 = 61*75 + 46; hence not 61 divides 4621 by NAT_4:9;
4621 = 67*68 + 65; hence not 67 divides 4621 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4621 & n is prime
holds not n divides 4621 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
4637 is prime
proof
now
4637 = 2*2318 + 1; hence not 2 divides 4637 by NAT_4:9;
4637 = 3*1545 + 2; hence not 3 divides 4637 by NAT_4:9;
4637 = 5*927 + 2; hence not 5 divides 4637 by NAT_4:9;
4637 = 7*662 + 3; hence not 7 divides 4637 by NAT_4:9;
4637 = 11*421 + 6; hence not 11 divides 4637 by NAT_4:9;
4637 = 13*356 + 9; hence not 13 divides 4637 by NAT_4:9;
4637 = 17*272 + 13; hence not 17 divides 4637 by NAT_4:9;
4637 = 19*244 + 1; hence not 19 divides 4637 by NAT_4:9;
4637 = 23*201 + 14; hence not 23 divides 4637 by NAT_4:9;
4637 = 29*159 + 26; hence not 29 divides 4637 by NAT_4:9;
4637 = 31*149 + 18; hence not 31 divides 4637 by NAT_4:9;
4637 = 37*125 + 12; hence not 37 divides 4637 by NAT_4:9;
4637 = 41*113 + 4; hence not 41 divides 4637 by NAT_4:9;
4637 = 43*107 + 36; hence not 43 divides 4637 by NAT_4:9;
4637 = 47*98 + 31; hence not 47 divides 4637 by NAT_4:9;
4637 = 53*87 + 26; hence not 53 divides 4637 by NAT_4:9;
4637 = 59*78 + 35; hence not 59 divides 4637 by NAT_4:9;
4637 = 61*76 + 1; hence not 61 divides 4637 by NAT_4:9;
4637 = 67*69 + 14; hence not 67 divides 4637 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4637 & n is prime
holds not n divides 4637 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4639 is prime
proof
now
4639 = 2*2319 + 1; hence not 2 divides 4639 by NAT_4:9;
4639 = 3*1546 + 1; hence not 3 divides 4639 by NAT_4:9;
4639 = 5*927 + 4; hence not 5 divides 4639 by NAT_4:9;
4639 = 7*662 + 5; hence not 7 divides 4639 by NAT_4:9;
4639 = 11*421 + 8; hence not 11 divides 4639 by NAT_4:9;
4639 = 13*356 + 11; hence not 13 divides 4639 by NAT_4:9;
4639 = 17*272 + 15; hence not 17 divides 4639 by NAT_4:9;
4639 = 19*244 + 3; hence not 19 divides 4639 by NAT_4:9;
4639 = 23*201 + 16; hence not 23 divides 4639 by NAT_4:9;
4639 = 29*159 + 28; hence not 29 divides 4639 by NAT_4:9;
4639 = 31*149 + 20; hence not 31 divides 4639 by NAT_4:9;
4639 = 37*125 + 14; hence not 37 divides 4639 by NAT_4:9;
4639 = 41*113 + 6; hence not 41 divides 4639 by NAT_4:9;
4639 = 43*107 + 38; hence not 43 divides 4639 by NAT_4:9;
4639 = 47*98 + 33; hence not 47 divides 4639 by NAT_4:9;
4639 = 53*87 + 28; hence not 53 divides 4639 by NAT_4:9;
4639 = 59*78 + 37; hence not 59 divides 4639 by NAT_4:9;
4639 = 61*76 + 3; hence not 61 divides 4639 by NAT_4:9;
4639 = 67*69 + 16; hence not 67 divides 4639 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4639 & n is prime
holds not n divides 4639 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4643 is prime
proof
now
4643 = 2*2321 + 1; hence not 2 divides 4643 by NAT_4:9;
4643 = 3*1547 + 2; hence not 3 divides 4643 by NAT_4:9;
4643 = 5*928 + 3; hence not 5 divides 4643 by NAT_4:9;
4643 = 7*663 + 2; hence not 7 divides 4643 by NAT_4:9;
4643 = 11*422 + 1; hence not 11 divides 4643 by NAT_4:9;
4643 = 13*357 + 2; hence not 13 divides 4643 by NAT_4:9;
4643 = 17*273 + 2; hence not 17 divides 4643 by NAT_4:9;
4643 = 19*244 + 7; hence not 19 divides 4643 by NAT_4:9;
4643 = 23*201 + 20; hence not 23 divides 4643 by NAT_4:9;
4643 = 29*160 + 3; hence not 29 divides 4643 by NAT_4:9;
4643 = 31*149 + 24; hence not 31 divides 4643 by NAT_4:9;
4643 = 37*125 + 18; hence not 37 divides 4643 by NAT_4:9;
4643 = 41*113 + 10; hence not 41 divides 4643 by NAT_4:9;
4643 = 43*107 + 42; hence not 43 divides 4643 by NAT_4:9;
4643 = 47*98 + 37; hence not 47 divides 4643 by NAT_4:9;
4643 = 53*87 + 32; hence not 53 divides 4643 by NAT_4:9;
4643 = 59*78 + 41; hence not 59 divides 4643 by NAT_4:9;
4643 = 61*76 + 7; hence not 61 divides 4643 by NAT_4:9;
4643 = 67*69 + 20; hence not 67 divides 4643 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4643 & n is prime
holds not n divides 4643 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4649 is prime
proof
now
4649 = 2*2324 + 1; hence not 2 divides 4649 by NAT_4:9;
4649 = 3*1549 + 2; hence not 3 divides 4649 by NAT_4:9;
4649 = 5*929 + 4; hence not 5 divides 4649 by NAT_4:9;
4649 = 7*664 + 1; hence not 7 divides 4649 by NAT_4:9;
4649 = 11*422 + 7; hence not 11 divides 4649 by NAT_4:9;
4649 = 13*357 + 8; hence not 13 divides 4649 by NAT_4:9;
4649 = 17*273 + 8; hence not 17 divides 4649 by NAT_4:9;
4649 = 19*244 + 13; hence not 19 divides 4649 by NAT_4:9;
4649 = 23*202 + 3; hence not 23 divides 4649 by NAT_4:9;
4649 = 29*160 + 9; hence not 29 divides 4649 by NAT_4:9;
4649 = 31*149 + 30; hence not 31 divides 4649 by NAT_4:9;
4649 = 37*125 + 24; hence not 37 divides 4649 by NAT_4:9;
4649 = 41*113 + 16; hence not 41 divides 4649 by NAT_4:9;
4649 = 43*108 + 5; hence not 43 divides 4649 by NAT_4:9;
4649 = 47*98 + 43; hence not 47 divides 4649 by NAT_4:9;
4649 = 53*87 + 38; hence not 53 divides 4649 by NAT_4:9;
4649 = 59*78 + 47; hence not 59 divides 4649 by NAT_4:9;
4649 = 61*76 + 13; hence not 61 divides 4649 by NAT_4:9;
4649 = 67*69 + 26; hence not 67 divides 4649 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4649 & n is prime
holds not n divides 4649 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4651 is prime
proof
now
4651 = 2*2325 + 1; hence not 2 divides 4651 by NAT_4:9;
4651 = 3*1550 + 1; hence not 3 divides 4651 by NAT_4:9;
4651 = 5*930 + 1; hence not 5 divides 4651 by NAT_4:9;
4651 = 7*664 + 3; hence not 7 divides 4651 by NAT_4:9;
4651 = 11*422 + 9; hence not 11 divides 4651 by NAT_4:9;
4651 = 13*357 + 10; hence not 13 divides 4651 by NAT_4:9;
4651 = 17*273 + 10; hence not 17 divides 4651 by NAT_4:9;
4651 = 19*244 + 15; hence not 19 divides 4651 by NAT_4:9;
4651 = 23*202 + 5; hence not 23 divides 4651 by NAT_4:9;
4651 = 29*160 + 11; hence not 29 divides 4651 by NAT_4:9;
4651 = 31*150 + 1; hence not 31 divides 4651 by NAT_4:9;
4651 = 37*125 + 26; hence not 37 divides 4651 by NAT_4:9;
4651 = 41*113 + 18; hence not 41 divides 4651 by NAT_4:9;
4651 = 43*108 + 7; hence not 43 divides 4651 by NAT_4:9;
4651 = 47*98 + 45; hence not 47 divides 4651 by NAT_4:9;
4651 = 53*87 + 40; hence not 53 divides 4651 by NAT_4:9;
4651 = 59*78 + 49; hence not 59 divides 4651 by NAT_4:9;
4651 = 61*76 + 15; hence not 61 divides 4651 by NAT_4:9;
4651 = 67*69 + 28; hence not 67 divides 4651 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4651 & n is prime
holds not n divides 4651 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4657 is prime
proof
now
4657 = 2*2328 + 1; hence not 2 divides 4657 by NAT_4:9;
4657 = 3*1552 + 1; hence not 3 divides 4657 by NAT_4:9;
4657 = 5*931 + 2; hence not 5 divides 4657 by NAT_4:9;
4657 = 7*665 + 2; hence not 7 divides 4657 by NAT_4:9;
4657 = 11*423 + 4; hence not 11 divides 4657 by NAT_4:9;
4657 = 13*358 + 3; hence not 13 divides 4657 by NAT_4:9;
4657 = 17*273 + 16; hence not 17 divides 4657 by NAT_4:9;
4657 = 19*245 + 2; hence not 19 divides 4657 by NAT_4:9;
4657 = 23*202 + 11; hence not 23 divides 4657 by NAT_4:9;
4657 = 29*160 + 17; hence not 29 divides 4657 by NAT_4:9;
4657 = 31*150 + 7; hence not 31 divides 4657 by NAT_4:9;
4657 = 37*125 + 32; hence not 37 divides 4657 by NAT_4:9;
4657 = 41*113 + 24; hence not 41 divides 4657 by NAT_4:9;
4657 = 43*108 + 13; hence not 43 divides 4657 by NAT_4:9;
4657 = 47*99 + 4; hence not 47 divides 4657 by NAT_4:9;
4657 = 53*87 + 46; hence not 53 divides 4657 by NAT_4:9;
4657 = 59*78 + 55; hence not 59 divides 4657 by NAT_4:9;
4657 = 61*76 + 21; hence not 61 divides 4657 by NAT_4:9;
4657 = 67*69 + 34; hence not 67 divides 4657 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4657 & n is prime
holds not n divides 4657 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4663 is prime
proof
now
4663 = 2*2331 + 1; hence not 2 divides 4663 by NAT_4:9;
4663 = 3*1554 + 1; hence not 3 divides 4663 by NAT_4:9;
4663 = 5*932 + 3; hence not 5 divides 4663 by NAT_4:9;
4663 = 7*666 + 1; hence not 7 divides 4663 by NAT_4:9;
4663 = 11*423 + 10; hence not 11 divides 4663 by NAT_4:9;
4663 = 13*358 + 9; hence not 13 divides 4663 by NAT_4:9;
4663 = 17*274 + 5; hence not 17 divides 4663 by NAT_4:9;
4663 = 19*245 + 8; hence not 19 divides 4663 by NAT_4:9;
4663 = 23*202 + 17; hence not 23 divides 4663 by NAT_4:9;
4663 = 29*160 + 23; hence not 29 divides 4663 by NAT_4:9;
4663 = 31*150 + 13; hence not 31 divides 4663 by NAT_4:9;
4663 = 37*126 + 1; hence not 37 divides 4663 by NAT_4:9;
4663 = 41*113 + 30; hence not 41 divides 4663 by NAT_4:9;
4663 = 43*108 + 19; hence not 43 divides 4663 by NAT_4:9;
4663 = 47*99 + 10; hence not 47 divides 4663 by NAT_4:9;
4663 = 53*87 + 52; hence not 53 divides 4663 by NAT_4:9;
4663 = 59*79 + 2; hence not 59 divides 4663 by NAT_4:9;
4663 = 61*76 + 27; hence not 61 divides 4663 by NAT_4:9;
4663 = 67*69 + 40; hence not 67 divides 4663 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4663 & n is prime
holds not n divides 4663 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4673 is prime
proof
now
4673 = 2*2336 + 1; hence not 2 divides 4673 by NAT_4:9;
4673 = 3*1557 + 2; hence not 3 divides 4673 by NAT_4:9;
4673 = 5*934 + 3; hence not 5 divides 4673 by NAT_4:9;
4673 = 7*667 + 4; hence not 7 divides 4673 by NAT_4:9;
4673 = 11*424 + 9; hence not 11 divides 4673 by NAT_4:9;
4673 = 13*359 + 6; hence not 13 divides 4673 by NAT_4:9;
4673 = 17*274 + 15; hence not 17 divides 4673 by NAT_4:9;
4673 = 19*245 + 18; hence not 19 divides 4673 by NAT_4:9;
4673 = 23*203 + 4; hence not 23 divides 4673 by NAT_4:9;
4673 = 29*161 + 4; hence not 29 divides 4673 by NAT_4:9;
4673 = 31*150 + 23; hence not 31 divides 4673 by NAT_4:9;
4673 = 37*126 + 11; hence not 37 divides 4673 by NAT_4:9;
4673 = 41*113 + 40; hence not 41 divides 4673 by NAT_4:9;
4673 = 43*108 + 29; hence not 43 divides 4673 by NAT_4:9;
4673 = 47*99 + 20; hence not 47 divides 4673 by NAT_4:9;
4673 = 53*88 + 9; hence not 53 divides 4673 by NAT_4:9;
4673 = 59*79 + 12; hence not 59 divides 4673 by NAT_4:9;
4673 = 61*76 + 37; hence not 61 divides 4673 by NAT_4:9;
4673 = 67*69 + 50; hence not 67 divides 4673 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4673 & n is prime
holds not n divides 4673 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4679 is prime
proof
now
4679 = 2*2339 + 1; hence not 2 divides 4679 by NAT_4:9;
4679 = 3*1559 + 2; hence not 3 divides 4679 by NAT_4:9;
4679 = 5*935 + 4; hence not 5 divides 4679 by NAT_4:9;
4679 = 7*668 + 3; hence not 7 divides 4679 by NAT_4:9;
4679 = 11*425 + 4; hence not 11 divides 4679 by NAT_4:9;
4679 = 13*359 + 12; hence not 13 divides 4679 by NAT_4:9;
4679 = 17*275 + 4; hence not 17 divides 4679 by NAT_4:9;
4679 = 19*246 + 5; hence not 19 divides 4679 by NAT_4:9;
4679 = 23*203 + 10; hence not 23 divides 4679 by NAT_4:9;
4679 = 29*161 + 10; hence not 29 divides 4679 by NAT_4:9;
4679 = 31*150 + 29; hence not 31 divides 4679 by NAT_4:9;
4679 = 37*126 + 17; hence not 37 divides 4679 by NAT_4:9;
4679 = 41*114 + 5; hence not 41 divides 4679 by NAT_4:9;
4679 = 43*108 + 35; hence not 43 divides 4679 by NAT_4:9;
4679 = 47*99 + 26; hence not 47 divides 4679 by NAT_4:9;
4679 = 53*88 + 15; hence not 53 divides 4679 by NAT_4:9;
4679 = 59*79 + 18; hence not 59 divides 4679 by NAT_4:9;
4679 = 61*76 + 43; hence not 61 divides 4679 by NAT_4:9;
4679 = 67*69 + 56; hence not 67 divides 4679 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4679 & n is prime
holds not n divides 4679 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4691 is prime
proof
now
4691 = 2*2345 + 1; hence not 2 divides 4691 by NAT_4:9;
4691 = 3*1563 + 2; hence not 3 divides 4691 by NAT_4:9;
4691 = 5*938 + 1; hence not 5 divides 4691 by NAT_4:9;
4691 = 7*670 + 1; hence not 7 divides 4691 by NAT_4:9;
4691 = 11*426 + 5; hence not 11 divides 4691 by NAT_4:9;
4691 = 13*360 + 11; hence not 13 divides 4691 by NAT_4:9;
4691 = 17*275 + 16; hence not 17 divides 4691 by NAT_4:9;
4691 = 19*246 + 17; hence not 19 divides 4691 by NAT_4:9;
4691 = 23*203 + 22; hence not 23 divides 4691 by NAT_4:9;
4691 = 29*161 + 22; hence not 29 divides 4691 by NAT_4:9;
4691 = 31*151 + 10; hence not 31 divides 4691 by NAT_4:9;
4691 = 37*126 + 29; hence not 37 divides 4691 by NAT_4:9;
4691 = 41*114 + 17; hence not 41 divides 4691 by NAT_4:9;
4691 = 43*109 + 4; hence not 43 divides 4691 by NAT_4:9;
4691 = 47*99 + 38; hence not 47 divides 4691 by NAT_4:9;
4691 = 53*88 + 27; hence not 53 divides 4691 by NAT_4:9;
4691 = 59*79 + 30; hence not 59 divides 4691 by NAT_4:9;
4691 = 61*76 + 55; hence not 61 divides 4691 by NAT_4:9;
4691 = 67*70 + 1; hence not 67 divides 4691 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4691 & n is prime
holds not n divides 4691 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4703 is prime
proof
now
4703 = 2*2351 + 1; hence not 2 divides 4703 by NAT_4:9;
4703 = 3*1567 + 2; hence not 3 divides 4703 by NAT_4:9;
4703 = 5*940 + 3; hence not 5 divides 4703 by NAT_4:9;
4703 = 7*671 + 6; hence not 7 divides 4703 by NAT_4:9;
4703 = 11*427 + 6; hence not 11 divides 4703 by NAT_4:9;
4703 = 13*361 + 10; hence not 13 divides 4703 by NAT_4:9;
4703 = 17*276 + 11; hence not 17 divides 4703 by NAT_4:9;
4703 = 19*247 + 10; hence not 19 divides 4703 by NAT_4:9;
4703 = 23*204 + 11; hence not 23 divides 4703 by NAT_4:9;
4703 = 29*162 + 5; hence not 29 divides 4703 by NAT_4:9;
4703 = 31*151 + 22; hence not 31 divides 4703 by NAT_4:9;
4703 = 37*127 + 4; hence not 37 divides 4703 by NAT_4:9;
4703 = 41*114 + 29; hence not 41 divides 4703 by NAT_4:9;
4703 = 43*109 + 16; hence not 43 divides 4703 by NAT_4:9;
4703 = 47*100 + 3; hence not 47 divides 4703 by NAT_4:9;
4703 = 53*88 + 39; hence not 53 divides 4703 by NAT_4:9;
4703 = 59*79 + 42; hence not 59 divides 4703 by NAT_4:9;
4703 = 61*77 + 6; hence not 61 divides 4703 by NAT_4:9;
4703 = 67*70 + 13; hence not 67 divides 4703 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4703 & n is prime
holds not n divides 4703 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4721 is prime
proof
now
4721 = 2*2360 + 1; hence not 2 divides 4721 by NAT_4:9;
4721 = 3*1573 + 2; hence not 3 divides 4721 by NAT_4:9;
4721 = 5*944 + 1; hence not 5 divides 4721 by NAT_4:9;
4721 = 7*674 + 3; hence not 7 divides 4721 by NAT_4:9;
4721 = 11*429 + 2; hence not 11 divides 4721 by NAT_4:9;
4721 = 13*363 + 2; hence not 13 divides 4721 by NAT_4:9;
4721 = 17*277 + 12; hence not 17 divides 4721 by NAT_4:9;
4721 = 19*248 + 9; hence not 19 divides 4721 by NAT_4:9;
4721 = 23*205 + 6; hence not 23 divides 4721 by NAT_4:9;
4721 = 29*162 + 23; hence not 29 divides 4721 by NAT_4:9;
4721 = 31*152 + 9; hence not 31 divides 4721 by NAT_4:9;
4721 = 37*127 + 22; hence not 37 divides 4721 by NAT_4:9;
4721 = 41*115 + 6; hence not 41 divides 4721 by NAT_4:9;
4721 = 43*109 + 34; hence not 43 divides 4721 by NAT_4:9;
4721 = 47*100 + 21; hence not 47 divides 4721 by NAT_4:9;
4721 = 53*89 + 4; hence not 53 divides 4721 by NAT_4:9;
4721 = 59*80 + 1; hence not 59 divides 4721 by NAT_4:9;
4721 = 61*77 + 24; hence not 61 divides 4721 by NAT_4:9;
4721 = 67*70 + 31; hence not 67 divides 4721 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4721 & n is prime
holds not n divides 4721 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4723 is prime
proof
now
4723 = 2*2361 + 1; hence not 2 divides 4723 by NAT_4:9;
4723 = 3*1574 + 1; hence not 3 divides 4723 by NAT_4:9;
4723 = 5*944 + 3; hence not 5 divides 4723 by NAT_4:9;
4723 = 7*674 + 5; hence not 7 divides 4723 by NAT_4:9;
4723 = 11*429 + 4; hence not 11 divides 4723 by NAT_4:9;
4723 = 13*363 + 4; hence not 13 divides 4723 by NAT_4:9;
4723 = 17*277 + 14; hence not 17 divides 4723 by NAT_4:9;
4723 = 19*248 + 11; hence not 19 divides 4723 by NAT_4:9;
4723 = 23*205 + 8; hence not 23 divides 4723 by NAT_4:9;
4723 = 29*162 + 25; hence not 29 divides 4723 by NAT_4:9;
4723 = 31*152 + 11; hence not 31 divides 4723 by NAT_4:9;
4723 = 37*127 + 24; hence not 37 divides 4723 by NAT_4:9;
4723 = 41*115 + 8; hence not 41 divides 4723 by NAT_4:9;
4723 = 43*109 + 36; hence not 43 divides 4723 by NAT_4:9;
4723 = 47*100 + 23; hence not 47 divides 4723 by NAT_4:9;
4723 = 53*89 + 6; hence not 53 divides 4723 by NAT_4:9;
4723 = 59*80 + 3; hence not 59 divides 4723 by NAT_4:9;
4723 = 61*77 + 26; hence not 61 divides 4723 by NAT_4:9;
4723 = 67*70 + 33; hence not 67 divides 4723 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4723 & n is prime
holds not n divides 4723 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4729 is prime
proof
now
4729 = 2*2364 + 1; hence not 2 divides 4729 by NAT_4:9;
4729 = 3*1576 + 1; hence not 3 divides 4729 by NAT_4:9;
4729 = 5*945 + 4; hence not 5 divides 4729 by NAT_4:9;
4729 = 7*675 + 4; hence not 7 divides 4729 by NAT_4:9;
4729 = 11*429 + 10; hence not 11 divides 4729 by NAT_4:9;
4729 = 13*363 + 10; hence not 13 divides 4729 by NAT_4:9;
4729 = 17*278 + 3; hence not 17 divides 4729 by NAT_4:9;
4729 = 19*248 + 17; hence not 19 divides 4729 by NAT_4:9;
4729 = 23*205 + 14; hence not 23 divides 4729 by NAT_4:9;
4729 = 29*163 + 2; hence not 29 divides 4729 by NAT_4:9;
4729 = 31*152 + 17; hence not 31 divides 4729 by NAT_4:9;
4729 = 37*127 + 30; hence not 37 divides 4729 by NAT_4:9;
4729 = 41*115 + 14; hence not 41 divides 4729 by NAT_4:9;
4729 = 43*109 + 42; hence not 43 divides 4729 by NAT_4:9;
4729 = 47*100 + 29; hence not 47 divides 4729 by NAT_4:9;
4729 = 53*89 + 12; hence not 53 divides 4729 by NAT_4:9;
4729 = 59*80 + 9; hence not 59 divides 4729 by NAT_4:9;
4729 = 61*77 + 32; hence not 61 divides 4729 by NAT_4:9;
4729 = 67*70 + 39; hence not 67 divides 4729 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4729 & n is prime
holds not n divides 4729 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4733 is prime
proof
now
4733 = 2*2366 + 1; hence not 2 divides 4733 by NAT_4:9;
4733 = 3*1577 + 2; hence not 3 divides 4733 by NAT_4:9;
4733 = 5*946 + 3; hence not 5 divides 4733 by NAT_4:9;
4733 = 7*676 + 1; hence not 7 divides 4733 by NAT_4:9;
4733 = 11*430 + 3; hence not 11 divides 4733 by NAT_4:9;
4733 = 13*364 + 1; hence not 13 divides 4733 by NAT_4:9;
4733 = 17*278 + 7; hence not 17 divides 4733 by NAT_4:9;
4733 = 19*249 + 2; hence not 19 divides 4733 by NAT_4:9;
4733 = 23*205 + 18; hence not 23 divides 4733 by NAT_4:9;
4733 = 29*163 + 6; hence not 29 divides 4733 by NAT_4:9;
4733 = 31*152 + 21; hence not 31 divides 4733 by NAT_4:9;
4733 = 37*127 + 34; hence not 37 divides 4733 by NAT_4:9;
4733 = 41*115 + 18; hence not 41 divides 4733 by NAT_4:9;
4733 = 43*110 + 3; hence not 43 divides 4733 by NAT_4:9;
4733 = 47*100 + 33; hence not 47 divides 4733 by NAT_4:9;
4733 = 53*89 + 16; hence not 53 divides 4733 by NAT_4:9;
4733 = 59*80 + 13; hence not 59 divides 4733 by NAT_4:9;
4733 = 61*77 + 36; hence not 61 divides 4733 by NAT_4:9;
4733 = 67*70 + 43; hence not 67 divides 4733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4733 & n is prime
holds not n divides 4733 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
4751 is prime
proof
now
4751 = 2*2375 + 1; hence not 2 divides 4751 by NAT_4:9;
4751 = 3*1583 + 2; hence not 3 divides 4751 by NAT_4:9;
4751 = 5*950 + 1; hence not 5 divides 4751 by NAT_4:9;
4751 = 7*678 + 5; hence not 7 divides 4751 by NAT_4:9;
4751 = 11*431 + 10; hence not 11 divides 4751 by NAT_4:9;
4751 = 13*365 + 6; hence not 13 divides 4751 by NAT_4:9;
4751 = 17*279 + 8; hence not 17 divides 4751 by NAT_4:9;
4751 = 19*250 + 1; hence not 19 divides 4751 by NAT_4:9;
4751 = 23*206 + 13; hence not 23 divides 4751 by NAT_4:9;
4751 = 29*163 + 24; hence not 29 divides 4751 by NAT_4:9;
4751 = 31*153 + 8; hence not 31 divides 4751 by NAT_4:9;
4751 = 37*128 + 15; hence not 37 divides 4751 by NAT_4:9;
4751 = 41*115 + 36; hence not 41 divides 4751 by NAT_4:9;
4751 = 43*110 + 21; hence not 43 divides 4751 by NAT_4:9;
4751 = 47*101 + 4; hence not 47 divides 4751 by NAT_4:9;
4751 = 53*89 + 34; hence not 53 divides 4751 by NAT_4:9;
4751 = 59*80 + 31; hence not 59 divides 4751 by NAT_4:9;
4751 = 61*77 + 54; hence not 61 divides 4751 by NAT_4:9;
4751 = 67*70 + 61; hence not 67 divides 4751 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4751 & n is prime
holds not n divides 4751 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
4759 is prime
proof
now
4759 = 2*2379 + 1; hence not 2 divides 4759 by NAT_4:9;
4759 = 3*1586 + 1; hence not 3 divides 4759 by NAT_4:9;
4759 = 5*951 + 4; hence not 5 divides 4759 by NAT_4:9;
4759 = 7*679 + 6; hence not 7 divides 4759 by NAT_4:9;
4759 = 11*432 + 7; hence not 11 divides 4759 by NAT_4:9;
4759 = 13*366 + 1; hence not 13 divides 4759 by NAT_4:9;
4759 = 17*279 + 16; hence not 17 divides 4759 by NAT_4:9;
4759 = 19*250 + 9; hence not 19 divides 4759 by NAT_4:9;
4759 = 23*206 + 21; hence not 23 divides 4759 by NAT_4:9;
4759 = 29*164 + 3; hence not 29 divides 4759 by NAT_4:9;
4759 = 31*153 + 16; hence not 31 divides 4759 by NAT_4:9;
4759 = 37*128 + 23; hence not 37 divides 4759 by NAT_4:9;
4759 = 41*116 + 3; hence not 41 divides 4759 by NAT_4:9;
4759 = 43*110 + 29; hence not 43 divides 4759 by NAT_4:9;
4759 = 47*101 + 12; hence not 47 divides 4759 by NAT_4:9;
4759 = 53*89 + 42; hence not 53 divides 4759 by NAT_4:9;
4759 = 59*80 + 39; hence not 59 divides 4759 by NAT_4:9;
4759 = 61*78 + 1; hence not 61 divides 4759 by NAT_4:9;
4759 = 67*71 + 2; hence not 67 divides 4759 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4759 & n is prime
holds not n divides 4759 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
4783 is prime
proof
now
4783 = 2*2391 + 1; hence not 2 divides 4783 by NAT_4:9;
4783 = 3*1594 + 1; hence not 3 divides 4783 by NAT_4:9;
4783 = 5*956 + 3; hence not 5 divides 4783 by NAT_4:9;
4783 = 7*683 + 2; hence not 7 divides 4783 by NAT_4:9;
4783 = 11*434 + 9; hence not 11 divides 4783 by NAT_4:9;
4783 = 13*367 + 12; hence not 13 divides 4783 by NAT_4:9;
4783 = 17*281 + 6; hence not 17 divides 4783 by NAT_4:9;
4783 = 19*251 + 14; hence not 19 divides 4783 by NAT_4:9;
4783 = 23*207 + 22; hence not 23 divides 4783 by NAT_4:9;
4783 = 29*164 + 27; hence not 29 divides 4783 by NAT_4:9;
4783 = 31*154 + 9; hence not 31 divides 4783 by NAT_4:9;
4783 = 37*129 + 10; hence not 37 divides 4783 by NAT_4:9;
4783 = 41*116 + 27; hence not 41 divides 4783 by NAT_4:9;
4783 = 43*111 + 10; hence not 43 divides 4783 by NAT_4:9;
4783 = 47*101 + 36; hence not 47 divides 4783 by NAT_4:9;
4783 = 53*90 + 13; hence not 53 divides 4783 by NAT_4:9;
4783 = 59*81 + 4; hence not 59 divides 4783 by NAT_4:9;
4783 = 61*78 + 25; hence not 61 divides 4783 by NAT_4:9;
4783 = 67*71 + 26; hence not 67 divides 4783 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4783 & n is prime
holds not n divides 4783 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4787 is prime
proof
now
4787 = 2*2393 + 1; hence not 2 divides 4787 by NAT_4:9;
4787 = 3*1595 + 2; hence not 3 divides 4787 by NAT_4:9;
4787 = 5*957 + 2; hence not 5 divides 4787 by NAT_4:9;
4787 = 7*683 + 6; hence not 7 divides 4787 by NAT_4:9;
4787 = 11*435 + 2; hence not 11 divides 4787 by NAT_4:9;
4787 = 13*368 + 3; hence not 13 divides 4787 by NAT_4:9;
4787 = 17*281 + 10; hence not 17 divides 4787 by NAT_4:9;
4787 = 19*251 + 18; hence not 19 divides 4787 by NAT_4:9;
4787 = 23*208 + 3; hence not 23 divides 4787 by NAT_4:9;
4787 = 29*165 + 2; hence not 29 divides 4787 by NAT_4:9;
4787 = 31*154 + 13; hence not 31 divides 4787 by NAT_4:9;
4787 = 37*129 + 14; hence not 37 divides 4787 by NAT_4:9;
4787 = 41*116 + 31; hence not 41 divides 4787 by NAT_4:9;
4787 = 43*111 + 14; hence not 43 divides 4787 by NAT_4:9;
4787 = 47*101 + 40; hence not 47 divides 4787 by NAT_4:9;
4787 = 53*90 + 17; hence not 53 divides 4787 by NAT_4:9;
4787 = 59*81 + 8; hence not 59 divides 4787 by NAT_4:9;
4787 = 61*78 + 29; hence not 61 divides 4787 by NAT_4:9;
4787 = 67*71 + 30; hence not 67 divides 4787 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4787 & n is prime
holds not n divides 4787 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4789 is prime
proof
now
4789 = 2*2394 + 1; hence not 2 divides 4789 by NAT_4:9;
4789 = 3*1596 + 1; hence not 3 divides 4789 by NAT_4:9;
4789 = 5*957 + 4; hence not 5 divides 4789 by NAT_4:9;
4789 = 7*684 + 1; hence not 7 divides 4789 by NAT_4:9;
4789 = 11*435 + 4; hence not 11 divides 4789 by NAT_4:9;
4789 = 13*368 + 5; hence not 13 divides 4789 by NAT_4:9;
4789 = 17*281 + 12; hence not 17 divides 4789 by NAT_4:9;
4789 = 19*252 + 1; hence not 19 divides 4789 by NAT_4:9;
4789 = 23*208 + 5; hence not 23 divides 4789 by NAT_4:9;
4789 = 29*165 + 4; hence not 29 divides 4789 by NAT_4:9;
4789 = 31*154 + 15; hence not 31 divides 4789 by NAT_4:9;
4789 = 37*129 + 16; hence not 37 divides 4789 by NAT_4:9;
4789 = 41*116 + 33; hence not 41 divides 4789 by NAT_4:9;
4789 = 43*111 + 16; hence not 43 divides 4789 by NAT_4:9;
4789 = 47*101 + 42; hence not 47 divides 4789 by NAT_4:9;
4789 = 53*90 + 19; hence not 53 divides 4789 by NAT_4:9;
4789 = 59*81 + 10; hence not 59 divides 4789 by NAT_4:9;
4789 = 61*78 + 31; hence not 61 divides 4789 by NAT_4:9;
4789 = 67*71 + 32; hence not 67 divides 4789 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4789 & n is prime
holds not n divides 4789 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4793 is prime
proof
now
4793 = 2*2396 + 1; hence not 2 divides 4793 by NAT_4:9;
4793 = 3*1597 + 2; hence not 3 divides 4793 by NAT_4:9;
4793 = 5*958 + 3; hence not 5 divides 4793 by NAT_4:9;
4793 = 7*684 + 5; hence not 7 divides 4793 by NAT_4:9;
4793 = 11*435 + 8; hence not 11 divides 4793 by NAT_4:9;
4793 = 13*368 + 9; hence not 13 divides 4793 by NAT_4:9;
4793 = 17*281 + 16; hence not 17 divides 4793 by NAT_4:9;
4793 = 19*252 + 5; hence not 19 divides 4793 by NAT_4:9;
4793 = 23*208 + 9; hence not 23 divides 4793 by NAT_4:9;
4793 = 29*165 + 8; hence not 29 divides 4793 by NAT_4:9;
4793 = 31*154 + 19; hence not 31 divides 4793 by NAT_4:9;
4793 = 37*129 + 20; hence not 37 divides 4793 by NAT_4:9;
4793 = 41*116 + 37; hence not 41 divides 4793 by NAT_4:9;
4793 = 43*111 + 20; hence not 43 divides 4793 by NAT_4:9;
4793 = 47*101 + 46; hence not 47 divides 4793 by NAT_4:9;
4793 = 53*90 + 23; hence not 53 divides 4793 by NAT_4:9;
4793 = 59*81 + 14; hence not 59 divides 4793 by NAT_4:9;
4793 = 61*78 + 35; hence not 61 divides 4793 by NAT_4:9;
4793 = 67*71 + 36; hence not 67 divides 4793 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4793 & n is prime
holds not n divides 4793 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4799 is prime
proof
now
4799 = 2*2399 + 1; hence not 2 divides 4799 by NAT_4:9;
4799 = 3*1599 + 2; hence not 3 divides 4799 by NAT_4:9;
4799 = 5*959 + 4; hence not 5 divides 4799 by NAT_4:9;
4799 = 7*685 + 4; hence not 7 divides 4799 by NAT_4:9;
4799 = 11*436 + 3; hence not 11 divides 4799 by NAT_4:9;
4799 = 13*369 + 2; hence not 13 divides 4799 by NAT_4:9;
4799 = 17*282 + 5; hence not 17 divides 4799 by NAT_4:9;
4799 = 19*252 + 11; hence not 19 divides 4799 by NAT_4:9;
4799 = 23*208 + 15; hence not 23 divides 4799 by NAT_4:9;
4799 = 29*165 + 14; hence not 29 divides 4799 by NAT_4:9;
4799 = 31*154 + 25; hence not 31 divides 4799 by NAT_4:9;
4799 = 37*129 + 26; hence not 37 divides 4799 by NAT_4:9;
4799 = 41*117 + 2; hence not 41 divides 4799 by NAT_4:9;
4799 = 43*111 + 26; hence not 43 divides 4799 by NAT_4:9;
4799 = 47*102 + 5; hence not 47 divides 4799 by NAT_4:9;
4799 = 53*90 + 29; hence not 53 divides 4799 by NAT_4:9;
4799 = 59*81 + 20; hence not 59 divides 4799 by NAT_4:9;
4799 = 61*78 + 41; hence not 61 divides 4799 by NAT_4:9;
4799 = 67*71 + 42; hence not 67 divides 4799 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4799 & n is prime
holds not n divides 4799 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4801 is prime
proof
now
4801 = 2*2400 + 1; hence not 2 divides 4801 by NAT_4:9;
4801 = 3*1600 + 1; hence not 3 divides 4801 by NAT_4:9;
4801 = 5*960 + 1; hence not 5 divides 4801 by NAT_4:9;
4801 = 7*685 + 6; hence not 7 divides 4801 by NAT_4:9;
4801 = 11*436 + 5; hence not 11 divides 4801 by NAT_4:9;
4801 = 13*369 + 4; hence not 13 divides 4801 by NAT_4:9;
4801 = 17*282 + 7; hence not 17 divides 4801 by NAT_4:9;
4801 = 19*252 + 13; hence not 19 divides 4801 by NAT_4:9;
4801 = 23*208 + 17; hence not 23 divides 4801 by NAT_4:9;
4801 = 29*165 + 16; hence not 29 divides 4801 by NAT_4:9;
4801 = 31*154 + 27; hence not 31 divides 4801 by NAT_4:9;
4801 = 37*129 + 28; hence not 37 divides 4801 by NAT_4:9;
4801 = 41*117 + 4; hence not 41 divides 4801 by NAT_4:9;
4801 = 43*111 + 28; hence not 43 divides 4801 by NAT_4:9;
4801 = 47*102 + 7; hence not 47 divides 4801 by NAT_4:9;
4801 = 53*90 + 31; hence not 53 divides 4801 by NAT_4:9;
4801 = 59*81 + 22; hence not 59 divides 4801 by NAT_4:9;
4801 = 61*78 + 43; hence not 61 divides 4801 by NAT_4:9;
4801 = 67*71 + 44; hence not 67 divides 4801 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4801 & n is prime
holds not n divides 4801 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4813 is prime
proof
now
4813 = 2*2406 + 1; hence not 2 divides 4813 by NAT_4:9;
4813 = 3*1604 + 1; hence not 3 divides 4813 by NAT_4:9;
4813 = 5*962 + 3; hence not 5 divides 4813 by NAT_4:9;
4813 = 7*687 + 4; hence not 7 divides 4813 by NAT_4:9;
4813 = 11*437 + 6; hence not 11 divides 4813 by NAT_4:9;
4813 = 13*370 + 3; hence not 13 divides 4813 by NAT_4:9;
4813 = 17*283 + 2; hence not 17 divides 4813 by NAT_4:9;
4813 = 19*253 + 6; hence not 19 divides 4813 by NAT_4:9;
4813 = 23*209 + 6; hence not 23 divides 4813 by NAT_4:9;
4813 = 29*165 + 28; hence not 29 divides 4813 by NAT_4:9;
4813 = 31*155 + 8; hence not 31 divides 4813 by NAT_4:9;
4813 = 37*130 + 3; hence not 37 divides 4813 by NAT_4:9;
4813 = 41*117 + 16; hence not 41 divides 4813 by NAT_4:9;
4813 = 43*111 + 40; hence not 43 divides 4813 by NAT_4:9;
4813 = 47*102 + 19; hence not 47 divides 4813 by NAT_4:9;
4813 = 53*90 + 43; hence not 53 divides 4813 by NAT_4:9;
4813 = 59*81 + 34; hence not 59 divides 4813 by NAT_4:9;
4813 = 61*78 + 55; hence not 61 divides 4813 by NAT_4:9;
4813 = 67*71 + 56; hence not 67 divides 4813 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4813 & n is prime
holds not n divides 4813 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4817 is prime
proof
now
4817 = 2*2408 + 1; hence not 2 divides 4817 by NAT_4:9;
4817 = 3*1605 + 2; hence not 3 divides 4817 by NAT_4:9;
4817 = 5*963 + 2; hence not 5 divides 4817 by NAT_4:9;
4817 = 7*688 + 1; hence not 7 divides 4817 by NAT_4:9;
4817 = 11*437 + 10; hence not 11 divides 4817 by NAT_4:9;
4817 = 13*370 + 7; hence not 13 divides 4817 by NAT_4:9;
4817 = 17*283 + 6; hence not 17 divides 4817 by NAT_4:9;
4817 = 19*253 + 10; hence not 19 divides 4817 by NAT_4:9;
4817 = 23*209 + 10; hence not 23 divides 4817 by NAT_4:9;
4817 = 29*166 + 3; hence not 29 divides 4817 by NAT_4:9;
4817 = 31*155 + 12; hence not 31 divides 4817 by NAT_4:9;
4817 = 37*130 + 7; hence not 37 divides 4817 by NAT_4:9;
4817 = 41*117 + 20; hence not 41 divides 4817 by NAT_4:9;
4817 = 43*112 + 1; hence not 43 divides 4817 by NAT_4:9;
4817 = 47*102 + 23; hence not 47 divides 4817 by NAT_4:9;
4817 = 53*90 + 47; hence not 53 divides 4817 by NAT_4:9;
4817 = 59*81 + 38; hence not 59 divides 4817 by NAT_4:9;
4817 = 61*78 + 59; hence not 61 divides 4817 by NAT_4:9;
4817 = 67*71 + 60; hence not 67 divides 4817 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4817 & n is prime
holds not n divides 4817 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
4831 is prime
proof
now
4831 = 2*2415 + 1; hence not 2 divides 4831 by NAT_4:9;
4831 = 3*1610 + 1; hence not 3 divides 4831 by NAT_4:9;
4831 = 5*966 + 1; hence not 5 divides 4831 by NAT_4:9;
4831 = 7*690 + 1; hence not 7 divides 4831 by NAT_4:9;
4831 = 11*439 + 2; hence not 11 divides 4831 by NAT_4:9;
4831 = 13*371 + 8; hence not 13 divides 4831 by NAT_4:9;
4831 = 17*284 + 3; hence not 17 divides 4831 by NAT_4:9;
4831 = 19*254 + 5; hence not 19 divides 4831 by NAT_4:9;
4831 = 23*210 + 1; hence not 23 divides 4831 by NAT_4:9;
4831 = 29*166 + 17; hence not 29 divides 4831 by NAT_4:9;
4831 = 31*155 + 26; hence not 31 divides 4831 by NAT_4:9;
4831 = 37*130 + 21; hence not 37 divides 4831 by NAT_4:9;
4831 = 41*117 + 34; hence not 41 divides 4831 by NAT_4:9;
4831 = 43*112 + 15; hence not 43 divides 4831 by NAT_4:9;
4831 = 47*102 + 37; hence not 47 divides 4831 by NAT_4:9;
4831 = 53*91 + 8; hence not 53 divides 4831 by NAT_4:9;
4831 = 59*81 + 52; hence not 59 divides 4831 by NAT_4:9;
4831 = 61*79 + 12; hence not 61 divides 4831 by NAT_4:9;
4831 = 67*72 + 7; hence not 67 divides 4831 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4831 & n is prime
holds not n divides 4831 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
4861 is prime
proof
now
4861 = 2*2430 + 1; hence not 2 divides 4861 by NAT_4:9;
4861 = 3*1620 + 1; hence not 3 divides 4861 by NAT_4:9;
4861 = 5*972 + 1; hence not 5 divides 4861 by NAT_4:9;
4861 = 7*694 + 3; hence not 7 divides 4861 by NAT_4:9;
4861 = 11*441 + 10; hence not 11 divides 4861 by NAT_4:9;
4861 = 13*373 + 12; hence not 13 divides 4861 by NAT_4:9;
4861 = 17*285 + 16; hence not 17 divides 4861 by NAT_4:9;
4861 = 19*255 + 16; hence not 19 divides 4861 by NAT_4:9;
4861 = 23*211 + 8; hence not 23 divides 4861 by NAT_4:9;
4861 = 29*167 + 18; hence not 29 divides 4861 by NAT_4:9;
4861 = 31*156 + 25; hence not 31 divides 4861 by NAT_4:9;
4861 = 37*131 + 14; hence not 37 divides 4861 by NAT_4:9;
4861 = 41*118 + 23; hence not 41 divides 4861 by NAT_4:9;
4861 = 43*113 + 2; hence not 43 divides 4861 by NAT_4:9;
4861 = 47*103 + 20; hence not 47 divides 4861 by NAT_4:9;
4861 = 53*91 + 38; hence not 53 divides 4861 by NAT_4:9;
4861 = 59*82 + 23; hence not 59 divides 4861 by NAT_4:9;
4861 = 61*79 + 42; hence not 61 divides 4861 by NAT_4:9;
4861 = 67*72 + 37; hence not 67 divides 4861 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4861 & n is prime
holds not n divides 4861 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4871 is prime
proof
now
4871 = 2*2435 + 1; hence not 2 divides 4871 by NAT_4:9;
4871 = 3*1623 + 2; hence not 3 divides 4871 by NAT_4:9;
4871 = 5*974 + 1; hence not 5 divides 4871 by NAT_4:9;
4871 = 7*695 + 6; hence not 7 divides 4871 by NAT_4:9;
4871 = 11*442 + 9; hence not 11 divides 4871 by NAT_4:9;
4871 = 13*374 + 9; hence not 13 divides 4871 by NAT_4:9;
4871 = 17*286 + 9; hence not 17 divides 4871 by NAT_4:9;
4871 = 19*256 + 7; hence not 19 divides 4871 by NAT_4:9;
4871 = 23*211 + 18; hence not 23 divides 4871 by NAT_4:9;
4871 = 29*167 + 28; hence not 29 divides 4871 by NAT_4:9;
4871 = 31*157 + 4; hence not 31 divides 4871 by NAT_4:9;
4871 = 37*131 + 24; hence not 37 divides 4871 by NAT_4:9;
4871 = 41*118 + 33; hence not 41 divides 4871 by NAT_4:9;
4871 = 43*113 + 12; hence not 43 divides 4871 by NAT_4:9;
4871 = 47*103 + 30; hence not 47 divides 4871 by NAT_4:9;
4871 = 53*91 + 48; hence not 53 divides 4871 by NAT_4:9;
4871 = 59*82 + 33; hence not 59 divides 4871 by NAT_4:9;
4871 = 61*79 + 52; hence not 61 divides 4871 by NAT_4:9;
4871 = 67*72 + 47; hence not 67 divides 4871 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4871 & n is prime
holds not n divides 4871 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4877 is prime
proof
now
4877 = 2*2438 + 1; hence not 2 divides 4877 by NAT_4:9;
4877 = 3*1625 + 2; hence not 3 divides 4877 by NAT_4:9;
4877 = 5*975 + 2; hence not 5 divides 4877 by NAT_4:9;
4877 = 7*696 + 5; hence not 7 divides 4877 by NAT_4:9;
4877 = 11*443 + 4; hence not 11 divides 4877 by NAT_4:9;
4877 = 13*375 + 2; hence not 13 divides 4877 by NAT_4:9;
4877 = 17*286 + 15; hence not 17 divides 4877 by NAT_4:9;
4877 = 19*256 + 13; hence not 19 divides 4877 by NAT_4:9;
4877 = 23*212 + 1; hence not 23 divides 4877 by NAT_4:9;
4877 = 29*168 + 5; hence not 29 divides 4877 by NAT_4:9;
4877 = 31*157 + 10; hence not 31 divides 4877 by NAT_4:9;
4877 = 37*131 + 30; hence not 37 divides 4877 by NAT_4:9;
4877 = 41*118 + 39; hence not 41 divides 4877 by NAT_4:9;
4877 = 43*113 + 18; hence not 43 divides 4877 by NAT_4:9;
4877 = 47*103 + 36; hence not 47 divides 4877 by NAT_4:9;
4877 = 53*92 + 1; hence not 53 divides 4877 by NAT_4:9;
4877 = 59*82 + 39; hence not 59 divides 4877 by NAT_4:9;
4877 = 61*79 + 58; hence not 61 divides 4877 by NAT_4:9;
4877 = 67*72 + 53; hence not 67 divides 4877 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4877 & n is prime
holds not n divides 4877 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4889 is prime
proof
now
4889 = 2*2444 + 1; hence not 2 divides 4889 by NAT_4:9;
4889 = 3*1629 + 2; hence not 3 divides 4889 by NAT_4:9;
4889 = 5*977 + 4; hence not 5 divides 4889 by NAT_4:9;
4889 = 7*698 + 3; hence not 7 divides 4889 by NAT_4:9;
4889 = 11*444 + 5; hence not 11 divides 4889 by NAT_4:9;
4889 = 13*376 + 1; hence not 13 divides 4889 by NAT_4:9;
4889 = 17*287 + 10; hence not 17 divides 4889 by NAT_4:9;
4889 = 19*257 + 6; hence not 19 divides 4889 by NAT_4:9;
4889 = 23*212 + 13; hence not 23 divides 4889 by NAT_4:9;
4889 = 29*168 + 17; hence not 29 divides 4889 by NAT_4:9;
4889 = 31*157 + 22; hence not 31 divides 4889 by NAT_4:9;
4889 = 37*132 + 5; hence not 37 divides 4889 by NAT_4:9;
4889 = 41*119 + 10; hence not 41 divides 4889 by NAT_4:9;
4889 = 43*113 + 30; hence not 43 divides 4889 by NAT_4:9;
4889 = 47*104 + 1; hence not 47 divides 4889 by NAT_4:9;
4889 = 53*92 + 13; hence not 53 divides 4889 by NAT_4:9;
4889 = 59*82 + 51; hence not 59 divides 4889 by NAT_4:9;
4889 = 61*80 + 9; hence not 61 divides 4889 by NAT_4:9;
4889 = 67*72 + 65; hence not 67 divides 4889 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4889 & n is prime
holds not n divides 4889 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
4903 is prime
proof
now
4903 = 2*2451 + 1; hence not 2 divides 4903 by NAT_4:9;
4903 = 3*1634 + 1; hence not 3 divides 4903 by NAT_4:9;
4903 = 5*980 + 3; hence not 5 divides 4903 by NAT_4:9;
4903 = 7*700 + 3; hence not 7 divides 4903 by NAT_4:9;
4903 = 11*445 + 8; hence not 11 divides 4903 by NAT_4:9;
4903 = 13*377 + 2; hence not 13 divides 4903 by NAT_4:9;
4903 = 17*288 + 7; hence not 17 divides 4903 by NAT_4:9;
4903 = 19*258 + 1; hence not 19 divides 4903 by NAT_4:9;
4903 = 23*213 + 4; hence not 23 divides 4903 by NAT_4:9;
4903 = 29*169 + 2; hence not 29 divides 4903 by NAT_4:9;
4903 = 31*158 + 5; hence not 31 divides 4903 by NAT_4:9;
4903 = 37*132 + 19; hence not 37 divides 4903 by NAT_4:9;
4903 = 41*119 + 24; hence not 41 divides 4903 by NAT_4:9;
4903 = 43*114 + 1; hence not 43 divides 4903 by NAT_4:9;
4903 = 47*104 + 15; hence not 47 divides 4903 by NAT_4:9;
4903 = 53*92 + 27; hence not 53 divides 4903 by NAT_4:9;
4903 = 59*83 + 6; hence not 59 divides 4903 by NAT_4:9;
4903 = 61*80 + 23; hence not 61 divides 4903 by NAT_4:9;
4903 = 67*73 + 12; hence not 67 divides 4903 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4903 & n is prime
holds not n divides 4903 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4909 is prime
proof
now
4909 = 2*2454 + 1; hence not 2 divides 4909 by NAT_4:9;
4909 = 3*1636 + 1; hence not 3 divides 4909 by NAT_4:9;
4909 = 5*981 + 4; hence not 5 divides 4909 by NAT_4:9;
4909 = 7*701 + 2; hence not 7 divides 4909 by NAT_4:9;
4909 = 11*446 + 3; hence not 11 divides 4909 by NAT_4:9;
4909 = 13*377 + 8; hence not 13 divides 4909 by NAT_4:9;
4909 = 17*288 + 13; hence not 17 divides 4909 by NAT_4:9;
4909 = 19*258 + 7; hence not 19 divides 4909 by NAT_4:9;
4909 = 23*213 + 10; hence not 23 divides 4909 by NAT_4:9;
4909 = 29*169 + 8; hence not 29 divides 4909 by NAT_4:9;
4909 = 31*158 + 11; hence not 31 divides 4909 by NAT_4:9;
4909 = 37*132 + 25; hence not 37 divides 4909 by NAT_4:9;
4909 = 41*119 + 30; hence not 41 divides 4909 by NAT_4:9;
4909 = 43*114 + 7; hence not 43 divides 4909 by NAT_4:9;
4909 = 47*104 + 21; hence not 47 divides 4909 by NAT_4:9;
4909 = 53*92 + 33; hence not 53 divides 4909 by NAT_4:9;
4909 = 59*83 + 12; hence not 59 divides 4909 by NAT_4:9;
4909 = 61*80 + 29; hence not 61 divides 4909 by NAT_4:9;
4909 = 67*73 + 18; hence not 67 divides 4909 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4909 & n is prime
holds not n divides 4909 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4919 is prime
proof
now
4919 = 2*2459 + 1; hence not 2 divides 4919 by NAT_4:9;
4919 = 3*1639 + 2; hence not 3 divides 4919 by NAT_4:9;
4919 = 5*983 + 4; hence not 5 divides 4919 by NAT_4:9;
4919 = 7*702 + 5; hence not 7 divides 4919 by NAT_4:9;
4919 = 11*447 + 2; hence not 11 divides 4919 by NAT_4:9;
4919 = 13*378 + 5; hence not 13 divides 4919 by NAT_4:9;
4919 = 17*289 + 6; hence not 17 divides 4919 by NAT_4:9;
4919 = 19*258 + 17; hence not 19 divides 4919 by NAT_4:9;
4919 = 23*213 + 20; hence not 23 divides 4919 by NAT_4:9;
4919 = 29*169 + 18; hence not 29 divides 4919 by NAT_4:9;
4919 = 31*158 + 21; hence not 31 divides 4919 by NAT_4:9;
4919 = 37*132 + 35; hence not 37 divides 4919 by NAT_4:9;
4919 = 41*119 + 40; hence not 41 divides 4919 by NAT_4:9;
4919 = 43*114 + 17; hence not 43 divides 4919 by NAT_4:9;
4919 = 47*104 + 31; hence not 47 divides 4919 by NAT_4:9;
4919 = 53*92 + 43; hence not 53 divides 4919 by NAT_4:9;
4919 = 59*83 + 22; hence not 59 divides 4919 by NAT_4:9;
4919 = 61*80 + 39; hence not 61 divides 4919 by NAT_4:9;
4919 = 67*73 + 28; hence not 67 divides 4919 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4919 & n is prime
holds not n divides 4919 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
4931 is prime
proof
now
4931 = 2*2465 + 1; hence not 2 divides 4931 by NAT_4:9;
4931 = 3*1643 + 2; hence not 3 divides 4931 by NAT_4:9;
4931 = 5*986 + 1; hence not 5 divides 4931 by NAT_4:9;
4931 = 7*704 + 3; hence not 7 divides 4931 by NAT_4:9;
4931 = 11*448 + 3; hence not 11 divides 4931 by NAT_4:9;
4931 = 13*379 + 4; hence not 13 divides 4931 by NAT_4:9;
4931 = 17*290 + 1; hence not 17 divides 4931 by NAT_4:9;
4931 = 19*259 + 10; hence not 19 divides 4931 by NAT_4:9;
4931 = 23*214 + 9; hence not 23 divides 4931 by NAT_4:9;
4931 = 29*170 + 1; hence not 29 divides 4931 by NAT_4:9;
4931 = 31*159 + 2; hence not 31 divides 4931 by NAT_4:9;
4931 = 37*133 + 10; hence not 37 divides 4931 by NAT_4:9;
4931 = 41*120 + 11; hence not 41 divides 4931 by NAT_4:9;
4931 = 43*114 + 29; hence not 43 divides 4931 by NAT_4:9;
4931 = 47*104 + 43; hence not 47 divides 4931 by NAT_4:9;
4931 = 53*93 + 2; hence not 53 divides 4931 by NAT_4:9;
4931 = 59*83 + 34; hence not 59 divides 4931 by NAT_4:9;
4931 = 61*80 + 51; hence not 61 divides 4931 by NAT_4:9;
4931 = 67*73 + 40; hence not 67 divides 4931 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4931 & n is prime
holds not n divides 4931 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4933 is prime
proof
now
4933 = 2*2466 + 1; hence not 2 divides 4933 by NAT_4:9;
4933 = 3*1644 + 1; hence not 3 divides 4933 by NAT_4:9;
4933 = 5*986 + 3; hence not 5 divides 4933 by NAT_4:9;
4933 = 7*704 + 5; hence not 7 divides 4933 by NAT_4:9;
4933 = 11*448 + 5; hence not 11 divides 4933 by NAT_4:9;
4933 = 13*379 + 6; hence not 13 divides 4933 by NAT_4:9;
4933 = 17*290 + 3; hence not 17 divides 4933 by NAT_4:9;
4933 = 19*259 + 12; hence not 19 divides 4933 by NAT_4:9;
4933 = 23*214 + 11; hence not 23 divides 4933 by NAT_4:9;
4933 = 29*170 + 3; hence not 29 divides 4933 by NAT_4:9;
4933 = 31*159 + 4; hence not 31 divides 4933 by NAT_4:9;
4933 = 37*133 + 12; hence not 37 divides 4933 by NAT_4:9;
4933 = 41*120 + 13; hence not 41 divides 4933 by NAT_4:9;
4933 = 43*114 + 31; hence not 43 divides 4933 by NAT_4:9;
4933 = 47*104 + 45; hence not 47 divides 4933 by NAT_4:9;
4933 = 53*93 + 4; hence not 53 divides 4933 by NAT_4:9;
4933 = 59*83 + 36; hence not 59 divides 4933 by NAT_4:9;
4933 = 61*80 + 53; hence not 61 divides 4933 by NAT_4:9;
4933 = 67*73 + 42; hence not 67 divides 4933 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4933 & n is prime
holds not n divides 4933 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4937 is prime
proof
now
4937 = 2*2468 + 1; hence not 2 divides 4937 by NAT_4:9;
4937 = 3*1645 + 2; hence not 3 divides 4937 by NAT_4:9;
4937 = 5*987 + 2; hence not 5 divides 4937 by NAT_4:9;
4937 = 7*705 + 2; hence not 7 divides 4937 by NAT_4:9;
4937 = 11*448 + 9; hence not 11 divides 4937 by NAT_4:9;
4937 = 13*379 + 10; hence not 13 divides 4937 by NAT_4:9;
4937 = 17*290 + 7; hence not 17 divides 4937 by NAT_4:9;
4937 = 19*259 + 16; hence not 19 divides 4937 by NAT_4:9;
4937 = 23*214 + 15; hence not 23 divides 4937 by NAT_4:9;
4937 = 29*170 + 7; hence not 29 divides 4937 by NAT_4:9;
4937 = 31*159 + 8; hence not 31 divides 4937 by NAT_4:9;
4937 = 37*133 + 16; hence not 37 divides 4937 by NAT_4:9;
4937 = 41*120 + 17; hence not 41 divides 4937 by NAT_4:9;
4937 = 43*114 + 35; hence not 43 divides 4937 by NAT_4:9;
4937 = 47*105 + 2; hence not 47 divides 4937 by NAT_4:9;
4937 = 53*93 + 8; hence not 53 divides 4937 by NAT_4:9;
4937 = 59*83 + 40; hence not 59 divides 4937 by NAT_4:9;
4937 = 61*80 + 57; hence not 61 divides 4937 by NAT_4:9;
4937 = 67*73 + 46; hence not 67 divides 4937 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4937 & n is prime
holds not n divides 4937 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4943 is prime
proof
now
4943 = 2*2471 + 1; hence not 2 divides 4943 by NAT_4:9;
4943 = 3*1647 + 2; hence not 3 divides 4943 by NAT_4:9;
4943 = 5*988 + 3; hence not 5 divides 4943 by NAT_4:9;
4943 = 7*706 + 1; hence not 7 divides 4943 by NAT_4:9;
4943 = 11*449 + 4; hence not 11 divides 4943 by NAT_4:9;
4943 = 13*380 + 3; hence not 13 divides 4943 by NAT_4:9;
4943 = 17*290 + 13; hence not 17 divides 4943 by NAT_4:9;
4943 = 19*260 + 3; hence not 19 divides 4943 by NAT_4:9;
4943 = 23*214 + 21; hence not 23 divides 4943 by NAT_4:9;
4943 = 29*170 + 13; hence not 29 divides 4943 by NAT_4:9;
4943 = 31*159 + 14; hence not 31 divides 4943 by NAT_4:9;
4943 = 37*133 + 22; hence not 37 divides 4943 by NAT_4:9;
4943 = 41*120 + 23; hence not 41 divides 4943 by NAT_4:9;
4943 = 43*114 + 41; hence not 43 divides 4943 by NAT_4:9;
4943 = 47*105 + 8; hence not 47 divides 4943 by NAT_4:9;
4943 = 53*93 + 14; hence not 53 divides 4943 by NAT_4:9;
4943 = 59*83 + 46; hence not 59 divides 4943 by NAT_4:9;
4943 = 61*81 + 2; hence not 61 divides 4943 by NAT_4:9;
4943 = 67*73 + 52; hence not 67 divides 4943 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4943 & n is prime
holds not n divides 4943 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
4951 is prime
proof
now
4951 = 2*2475 + 1; hence not 2 divides 4951 by NAT_4:9;
4951 = 3*1650 + 1; hence not 3 divides 4951 by NAT_4:9;
4951 = 5*990 + 1; hence not 5 divides 4951 by NAT_4:9;
4951 = 7*707 + 2; hence not 7 divides 4951 by NAT_4:9;
4951 = 11*450 + 1; hence not 11 divides 4951 by NAT_4:9;
4951 = 13*380 + 11; hence not 13 divides 4951 by NAT_4:9;
4951 = 17*291 + 4; hence not 17 divides 4951 by NAT_4:9;
4951 = 19*260 + 11; hence not 19 divides 4951 by NAT_4:9;
4951 = 23*215 + 6; hence not 23 divides 4951 by NAT_4:9;
4951 = 29*170 + 21; hence not 29 divides 4951 by NAT_4:9;
4951 = 31*159 + 22; hence not 31 divides 4951 by NAT_4:9;
4951 = 37*133 + 30; hence not 37 divides 4951 by NAT_4:9;
4951 = 41*120 + 31; hence not 41 divides 4951 by NAT_4:9;
4951 = 43*115 + 6; hence not 43 divides 4951 by NAT_4:9;
4951 = 47*105 + 16; hence not 47 divides 4951 by NAT_4:9;
4951 = 53*93 + 22; hence not 53 divides 4951 by NAT_4:9;
4951 = 59*83 + 54; hence not 59 divides 4951 by NAT_4:9;
4951 = 61*81 + 10; hence not 61 divides 4951 by NAT_4:9;
4951 = 67*73 + 60; hence not 67 divides 4951 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4951 & n is prime
holds not n divides 4951 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4957 is prime
proof
now
4957 = 2*2478 + 1; hence not 2 divides 4957 by NAT_4:9;
4957 = 3*1652 + 1; hence not 3 divides 4957 by NAT_4:9;
4957 = 5*991 + 2; hence not 5 divides 4957 by NAT_4:9;
4957 = 7*708 + 1; hence not 7 divides 4957 by NAT_4:9;
4957 = 11*450 + 7; hence not 11 divides 4957 by NAT_4:9;
4957 = 13*381 + 4; hence not 13 divides 4957 by NAT_4:9;
4957 = 17*291 + 10; hence not 17 divides 4957 by NAT_4:9;
4957 = 19*260 + 17; hence not 19 divides 4957 by NAT_4:9;
4957 = 23*215 + 12; hence not 23 divides 4957 by NAT_4:9;
4957 = 29*170 + 27; hence not 29 divides 4957 by NAT_4:9;
4957 = 31*159 + 28; hence not 31 divides 4957 by NAT_4:9;
4957 = 37*133 + 36; hence not 37 divides 4957 by NAT_4:9;
4957 = 41*120 + 37; hence not 41 divides 4957 by NAT_4:9;
4957 = 43*115 + 12; hence not 43 divides 4957 by NAT_4:9;
4957 = 47*105 + 22; hence not 47 divides 4957 by NAT_4:9;
4957 = 53*93 + 28; hence not 53 divides 4957 by NAT_4:9;
4957 = 59*84 + 1; hence not 59 divides 4957 by NAT_4:9;
4957 = 61*81 + 16; hence not 61 divides 4957 by NAT_4:9;
4957 = 67*73 + 66; hence not 67 divides 4957 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4957 & n is prime
holds not n divides 4957 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
4967 is prime
proof
now
4967 = 2*2483 + 1; hence not 2 divides 4967 by NAT_4:9;
4967 = 3*1655 + 2; hence not 3 divides 4967 by NAT_4:9;
4967 = 5*993 + 2; hence not 5 divides 4967 by NAT_4:9;
4967 = 7*709 + 4; hence not 7 divides 4967 by NAT_4:9;
4967 = 11*451 + 6; hence not 11 divides 4967 by NAT_4:9;
4967 = 13*382 + 1; hence not 13 divides 4967 by NAT_4:9;
4967 = 17*292 + 3; hence not 17 divides 4967 by NAT_4:9;
4967 = 19*261 + 8; hence not 19 divides 4967 by NAT_4:9;
4967 = 23*215 + 22; hence not 23 divides 4967 by NAT_4:9;
4967 = 29*171 + 8; hence not 29 divides 4967 by NAT_4:9;
4967 = 31*160 + 7; hence not 31 divides 4967 by NAT_4:9;
4967 = 37*134 + 9; hence not 37 divides 4967 by NAT_4:9;
4967 = 41*121 + 6; hence not 41 divides 4967 by NAT_4:9;
4967 = 43*115 + 22; hence not 43 divides 4967 by NAT_4:9;
4967 = 47*105 + 32; hence not 47 divides 4967 by NAT_4:9;
4967 = 53*93 + 38; hence not 53 divides 4967 by NAT_4:9;
4967 = 59*84 + 11; hence not 59 divides 4967 by NAT_4:9;
4967 = 61*81 + 26; hence not 61 divides 4967 by NAT_4:9;
4967 = 67*74 + 9; hence not 67 divides 4967 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4967 & n is prime
holds not n divides 4967 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
4969 is prime
proof
now
4969 = 2*2484 + 1; hence not 2 divides 4969 by NAT_4:9;
4969 = 3*1656 + 1; hence not 3 divides 4969 by NAT_4:9;
4969 = 5*993 + 4; hence not 5 divides 4969 by NAT_4:9;
4969 = 7*709 + 6; hence not 7 divides 4969 by NAT_4:9;
4969 = 11*451 + 8; hence not 11 divides 4969 by NAT_4:9;
4969 = 13*382 + 3; hence not 13 divides 4969 by NAT_4:9;
4969 = 17*292 + 5; hence not 17 divides 4969 by NAT_4:9;
4969 = 19*261 + 10; hence not 19 divides 4969 by NAT_4:9;
4969 = 23*216 + 1; hence not 23 divides 4969 by NAT_4:9;
4969 = 29*171 + 10; hence not 29 divides 4969 by NAT_4:9;
4969 = 31*160 + 9; hence not 31 divides 4969 by NAT_4:9;
4969 = 37*134 + 11; hence not 37 divides 4969 by NAT_4:9;
4969 = 41*121 + 8; hence not 41 divides 4969 by NAT_4:9;
4969 = 43*115 + 24; hence not 43 divides 4969 by NAT_4:9;
4969 = 47*105 + 34; hence not 47 divides 4969 by NAT_4:9;
4969 = 53*93 + 40; hence not 53 divides 4969 by NAT_4:9;
4969 = 59*84 + 13; hence not 59 divides 4969 by NAT_4:9;
4969 = 61*81 + 28; hence not 61 divides 4969 by NAT_4:9;
4969 = 67*74 + 11; hence not 67 divides 4969 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4969 & n is prime
holds not n divides 4969 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
4973 is prime
proof
now
4973 = 2*2486 + 1; hence not 2 divides 4973 by NAT_4:9;
4973 = 3*1657 + 2; hence not 3 divides 4973 by NAT_4:9;
4973 = 5*994 + 3; hence not 5 divides 4973 by NAT_4:9;
4973 = 7*710 + 3; hence not 7 divides 4973 by NAT_4:9;
4973 = 11*452 + 1; hence not 11 divides 4973 by NAT_4:9;
4973 = 13*382 + 7; hence not 13 divides 4973 by NAT_4:9;
4973 = 17*292 + 9; hence not 17 divides 4973 by NAT_4:9;
4973 = 19*261 + 14; hence not 19 divides 4973 by NAT_4:9;
4973 = 23*216 + 5; hence not 23 divides 4973 by NAT_4:9;
4973 = 29*171 + 14; hence not 29 divides 4973 by NAT_4:9;
4973 = 31*160 + 13; hence not 31 divides 4973 by NAT_4:9;
4973 = 37*134 + 15; hence not 37 divides 4973 by NAT_4:9;
4973 = 41*121 + 12; hence not 41 divides 4973 by NAT_4:9;
4973 = 43*115 + 28; hence not 43 divides 4973 by NAT_4:9;
4973 = 47*105 + 38; hence not 47 divides 4973 by NAT_4:9;
4973 = 53*93 + 44; hence not 53 divides 4973 by NAT_4:9;
4973 = 59*84 + 17; hence not 59 divides 4973 by NAT_4:9;
4973 = 61*81 + 32; hence not 61 divides 4973 by NAT_4:9;
4973 = 67*74 + 15; hence not 67 divides 4973 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4973 & n is prime
holds not n divides 4973 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
4987 is prime
proof
now
4987 = 2*2493 + 1; hence not 2 divides 4987 by NAT_4:9;
4987 = 3*1662 + 1; hence not 3 divides 4987 by NAT_4:9;
4987 = 5*997 + 2; hence not 5 divides 4987 by NAT_4:9;
4987 = 7*712 + 3; hence not 7 divides 4987 by NAT_4:9;
4987 = 11*453 + 4; hence not 11 divides 4987 by NAT_4:9;
4987 = 13*383 + 8; hence not 13 divides 4987 by NAT_4:9;
4987 = 17*293 + 6; hence not 17 divides 4987 by NAT_4:9;
4987 = 19*262 + 9; hence not 19 divides 4987 by NAT_4:9;
4987 = 23*216 + 19; hence not 23 divides 4987 by NAT_4:9;
4987 = 29*171 + 28; hence not 29 divides 4987 by NAT_4:9;
4987 = 31*160 + 27; hence not 31 divides 4987 by NAT_4:9;
4987 = 37*134 + 29; hence not 37 divides 4987 by NAT_4:9;
4987 = 41*121 + 26; hence not 41 divides 4987 by NAT_4:9;
4987 = 43*115 + 42; hence not 43 divides 4987 by NAT_4:9;
4987 = 47*106 + 5; hence not 47 divides 4987 by NAT_4:9;
4987 = 53*94 + 5; hence not 53 divides 4987 by NAT_4:9;
4987 = 59*84 + 31; hence not 59 divides 4987 by NAT_4:9;
4987 = 61*81 + 46; hence not 61 divides 4987 by NAT_4:9;
4987 = 67*74 + 29; hence not 67 divides 4987 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4987 & n is prime
holds not n divides 4987 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4993 is prime
proof
now
4993 = 2*2496 + 1; hence not 2 divides 4993 by NAT_4:9;
4993 = 3*1664 + 1; hence not 3 divides 4993 by NAT_4:9;
4993 = 5*998 + 3; hence not 5 divides 4993 by NAT_4:9;
4993 = 7*713 + 2; hence not 7 divides 4993 by NAT_4:9;
4993 = 11*453 + 10; hence not 11 divides 4993 by NAT_4:9;
4993 = 13*384 + 1; hence not 13 divides 4993 by NAT_4:9;
4993 = 17*293 + 12; hence not 17 divides 4993 by NAT_4:9;
4993 = 19*262 + 15; hence not 19 divides 4993 by NAT_4:9;
4993 = 23*217 + 2; hence not 23 divides 4993 by NAT_4:9;
4993 = 29*172 + 5; hence not 29 divides 4993 by NAT_4:9;
4993 = 31*161 + 2; hence not 31 divides 4993 by NAT_4:9;
4993 = 37*134 + 35; hence not 37 divides 4993 by NAT_4:9;
4993 = 41*121 + 32; hence not 41 divides 4993 by NAT_4:9;
4993 = 43*116 + 5; hence not 43 divides 4993 by NAT_4:9;
4993 = 47*106 + 11; hence not 47 divides 4993 by NAT_4:9;
4993 = 53*94 + 11; hence not 53 divides 4993 by NAT_4:9;
4993 = 59*84 + 37; hence not 59 divides 4993 by NAT_4:9;
4993 = 61*81 + 52; hence not 61 divides 4993 by NAT_4:9;
4993 = 67*74 + 35; hence not 67 divides 4993 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4993 & n is prime
holds not n divides 4993 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
4999 is prime
proof
now
4999 = 2*2499 + 1; hence not 2 divides 4999 by NAT_4:9;
4999 = 3*1666 + 1; hence not 3 divides 4999 by NAT_4:9;
4999 = 5*999 + 4; hence not 5 divides 4999 by NAT_4:9;
4999 = 7*714 + 1; hence not 7 divides 4999 by NAT_4:9;
4999 = 11*454 + 5; hence not 11 divides 4999 by NAT_4:9;
4999 = 13*384 + 7; hence not 13 divides 4999 by NAT_4:9;
4999 = 17*294 + 1; hence not 17 divides 4999 by NAT_4:9;
4999 = 19*263 + 2; hence not 19 divides 4999 by NAT_4:9;
4999 = 23*217 + 8; hence not 23 divides 4999 by NAT_4:9;
4999 = 29*172 + 11; hence not 29 divides 4999 by NAT_4:9;
4999 = 31*161 + 8; hence not 31 divides 4999 by NAT_4:9;
4999 = 37*135 + 4; hence not 37 divides 4999 by NAT_4:9;
4999 = 41*121 + 38; hence not 41 divides 4999 by NAT_4:9;
4999 = 43*116 + 11; hence not 43 divides 4999 by NAT_4:9;
4999 = 47*106 + 17; hence not 47 divides 4999 by NAT_4:9;
4999 = 53*94 + 17; hence not 53 divides 4999 by NAT_4:9;
4999 = 59*84 + 43; hence not 59 divides 4999 by NAT_4:9;
4999 = 61*81 + 58; hence not 61 divides 4999 by NAT_4:9;
4999 = 67*74 + 41; hence not 67 divides 4999 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 4999 & n is prime
holds not n divides 4999 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5003 is prime
proof
now
5003 = 2*2501 + 1; hence not 2 divides 5003 by NAT_4:9;
5003 = 3*1667 + 2; hence not 3 divides 5003 by NAT_4:9;
5003 = 5*1000 + 3; hence not 5 divides 5003 by NAT_4:9;
5003 = 7*714 + 5; hence not 7 divides 5003 by NAT_4:9;
5003 = 11*454 + 9; hence not 11 divides 5003 by NAT_4:9;
5003 = 13*384 + 11; hence not 13 divides 5003 by NAT_4:9;
5003 = 17*294 + 5; hence not 17 divides 5003 by NAT_4:9;
5003 = 19*263 + 6; hence not 19 divides 5003 by NAT_4:9;
5003 = 23*217 + 12; hence not 23 divides 5003 by NAT_4:9;
5003 = 29*172 + 15; hence not 29 divides 5003 by NAT_4:9;
5003 = 31*161 + 12; hence not 31 divides 5003 by NAT_4:9;
5003 = 37*135 + 8; hence not 37 divides 5003 by NAT_4:9;
5003 = 41*122 + 1; hence not 41 divides 5003 by NAT_4:9;
5003 = 43*116 + 15; hence not 43 divides 5003 by NAT_4:9;
5003 = 47*106 + 21; hence not 47 divides 5003 by NAT_4:9;
5003 = 53*94 + 21; hence not 53 divides 5003 by NAT_4:9;
5003 = 59*84 + 47; hence not 59 divides 5003 by NAT_4:9;
5003 = 61*82 + 1; hence not 61 divides 5003 by NAT_4:9;
5003 = 67*74 + 45; hence not 67 divides 5003 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5003 & n is prime
holds not n divides 5003 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5009 is prime
proof
now
5009 = 2*2504 + 1; hence not 2 divides 5009 by NAT_4:9;
5009 = 3*1669 + 2; hence not 3 divides 5009 by NAT_4:9;
5009 = 5*1001 + 4; hence not 5 divides 5009 by NAT_4:9;
5009 = 7*715 + 4; hence not 7 divides 5009 by NAT_4:9;
5009 = 11*455 + 4; hence not 11 divides 5009 by NAT_4:9;
5009 = 13*385 + 4; hence not 13 divides 5009 by NAT_4:9;
5009 = 17*294 + 11; hence not 17 divides 5009 by NAT_4:9;
5009 = 19*263 + 12; hence not 19 divides 5009 by NAT_4:9;
5009 = 23*217 + 18; hence not 23 divides 5009 by NAT_4:9;
5009 = 29*172 + 21; hence not 29 divides 5009 by NAT_4:9;
5009 = 31*161 + 18; hence not 31 divides 5009 by NAT_4:9;
5009 = 37*135 + 14; hence not 37 divides 5009 by NAT_4:9;
5009 = 41*122 + 7; hence not 41 divides 5009 by NAT_4:9;
5009 = 43*116 + 21; hence not 43 divides 5009 by NAT_4:9;
5009 = 47*106 + 27; hence not 47 divides 5009 by NAT_4:9;
5009 = 53*94 + 27; hence not 53 divides 5009 by NAT_4:9;
5009 = 59*84 + 53; hence not 59 divides 5009 by NAT_4:9;
5009 = 61*82 + 7; hence not 61 divides 5009 by NAT_4:9;
5009 = 67*74 + 51; hence not 67 divides 5009 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5009 & n is prime
holds not n divides 5009 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5011 is prime
proof
now
5011 = 2*2505 + 1; hence not 2 divides 5011 by NAT_4:9;
5011 = 3*1670 + 1; hence not 3 divides 5011 by NAT_4:9;
5011 = 5*1002 + 1; hence not 5 divides 5011 by NAT_4:9;
5011 = 7*715 + 6; hence not 7 divides 5011 by NAT_4:9;
5011 = 11*455 + 6; hence not 11 divides 5011 by NAT_4:9;
5011 = 13*385 + 6; hence not 13 divides 5011 by NAT_4:9;
5011 = 17*294 + 13; hence not 17 divides 5011 by NAT_4:9;
5011 = 19*263 + 14; hence not 19 divides 5011 by NAT_4:9;
5011 = 23*217 + 20; hence not 23 divides 5011 by NAT_4:9;
5011 = 29*172 + 23; hence not 29 divides 5011 by NAT_4:9;
5011 = 31*161 + 20; hence not 31 divides 5011 by NAT_4:9;
5011 = 37*135 + 16; hence not 37 divides 5011 by NAT_4:9;
5011 = 41*122 + 9; hence not 41 divides 5011 by NAT_4:9;
5011 = 43*116 + 23; hence not 43 divides 5011 by NAT_4:9;
5011 = 47*106 + 29; hence not 47 divides 5011 by NAT_4:9;
5011 = 53*94 + 29; hence not 53 divides 5011 by NAT_4:9;
5011 = 59*84 + 55; hence not 59 divides 5011 by NAT_4:9;
5011 = 61*82 + 9; hence not 61 divides 5011 by NAT_4:9;
5011 = 67*74 + 53; hence not 67 divides 5011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5011 & n is prime
holds not n divides 5011 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5021 is prime
proof
now
5021 = 2*2510 + 1; hence not 2 divides 5021 by NAT_4:9;
5021 = 3*1673 + 2; hence not 3 divides 5021 by NAT_4:9;
5021 = 5*1004 + 1; hence not 5 divides 5021 by NAT_4:9;
5021 = 7*717 + 2; hence not 7 divides 5021 by NAT_4:9;
5021 = 11*456 + 5; hence not 11 divides 5021 by NAT_4:9;
5021 = 13*386 + 3; hence not 13 divides 5021 by NAT_4:9;
5021 = 17*295 + 6; hence not 17 divides 5021 by NAT_4:9;
5021 = 19*264 + 5; hence not 19 divides 5021 by NAT_4:9;
5021 = 23*218 + 7; hence not 23 divides 5021 by NAT_4:9;
5021 = 29*173 + 4; hence not 29 divides 5021 by NAT_4:9;
5021 = 31*161 + 30; hence not 31 divides 5021 by NAT_4:9;
5021 = 37*135 + 26; hence not 37 divides 5021 by NAT_4:9;
5021 = 41*122 + 19; hence not 41 divides 5021 by NAT_4:9;
5021 = 43*116 + 33; hence not 43 divides 5021 by NAT_4:9;
5021 = 47*106 + 39; hence not 47 divides 5021 by NAT_4:9;
5021 = 53*94 + 39; hence not 53 divides 5021 by NAT_4:9;
5021 = 59*85 + 6; hence not 59 divides 5021 by NAT_4:9;
5021 = 61*82 + 19; hence not 61 divides 5021 by NAT_4:9;
5021 = 67*74 + 63; hence not 67 divides 5021 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5021 & n is prime
holds not n divides 5021 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5023 is prime
proof
now
5023 = 2*2511 + 1; hence not 2 divides 5023 by NAT_4:9;
5023 = 3*1674 + 1; hence not 3 divides 5023 by NAT_4:9;
5023 = 5*1004 + 3; hence not 5 divides 5023 by NAT_4:9;
5023 = 7*717 + 4; hence not 7 divides 5023 by NAT_4:9;
5023 = 11*456 + 7; hence not 11 divides 5023 by NAT_4:9;
5023 = 13*386 + 5; hence not 13 divides 5023 by NAT_4:9;
5023 = 17*295 + 8; hence not 17 divides 5023 by NAT_4:9;
5023 = 19*264 + 7; hence not 19 divides 5023 by NAT_4:9;
5023 = 23*218 + 9; hence not 23 divides 5023 by NAT_4:9;
5023 = 29*173 + 6; hence not 29 divides 5023 by NAT_4:9;
5023 = 31*162 + 1; hence not 31 divides 5023 by NAT_4:9;
5023 = 37*135 + 28; hence not 37 divides 5023 by NAT_4:9;
5023 = 41*122 + 21; hence not 41 divides 5023 by NAT_4:9;
5023 = 43*116 + 35; hence not 43 divides 5023 by NAT_4:9;
5023 = 47*106 + 41; hence not 47 divides 5023 by NAT_4:9;
5023 = 53*94 + 41; hence not 53 divides 5023 by NAT_4:9;
5023 = 59*85 + 8; hence not 59 divides 5023 by NAT_4:9;
5023 = 61*82 + 21; hence not 61 divides 5023 by NAT_4:9;
5023 = 67*74 + 65; hence not 67 divides 5023 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5023 & n is prime
holds not n divides 5023 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
5039 is prime
proof
now
5039 = 2*2519 + 1; hence not 2 divides 5039 by NAT_4:9;
5039 = 3*1679 + 2; hence not 3 divides 5039 by NAT_4:9;
5039 = 5*1007 + 4; hence not 5 divides 5039 by NAT_4:9;
5039 = 7*719 + 6; hence not 7 divides 5039 by NAT_4:9;
5039 = 11*458 + 1; hence not 11 divides 5039 by NAT_4:9;
5039 = 13*387 + 8; hence not 13 divides 5039 by NAT_4:9;
5039 = 17*296 + 7; hence not 17 divides 5039 by NAT_4:9;
5039 = 19*265 + 4; hence not 19 divides 5039 by NAT_4:9;
5039 = 23*219 + 2; hence not 23 divides 5039 by NAT_4:9;
5039 = 29*173 + 22; hence not 29 divides 5039 by NAT_4:9;
5039 = 31*162 + 17; hence not 31 divides 5039 by NAT_4:9;
5039 = 37*136 + 7; hence not 37 divides 5039 by NAT_4:9;
5039 = 41*122 + 37; hence not 41 divides 5039 by NAT_4:9;
5039 = 43*117 + 8; hence not 43 divides 5039 by NAT_4:9;
5039 = 47*107 + 10; hence not 47 divides 5039 by NAT_4:9;
5039 = 53*95 + 4; hence not 53 divides 5039 by NAT_4:9;
5039 = 59*85 + 24; hence not 59 divides 5039 by NAT_4:9;
5039 = 61*82 + 37; hence not 61 divides 5039 by NAT_4:9;
5039 = 67*75 + 14; hence not 67 divides 5039 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5039 & n is prime
holds not n divides 5039 by XPRIMET1:38;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5051 is prime
proof
now
5051 = 2*2525 + 1; hence not 2 divides 5051 by NAT_4:9;
5051 = 3*1683 + 2; hence not 3 divides 5051 by NAT_4:9;
5051 = 5*1010 + 1; hence not 5 divides 5051 by NAT_4:9;
5051 = 7*721 + 4; hence not 7 divides 5051 by NAT_4:9;
5051 = 11*459 + 2; hence not 11 divides 5051 by NAT_4:9;
5051 = 13*388 + 7; hence not 13 divides 5051 by NAT_4:9;
5051 = 17*297 + 2; hence not 17 divides 5051 by NAT_4:9;
5051 = 19*265 + 16; hence not 19 divides 5051 by NAT_4:9;
5051 = 23*219 + 14; hence not 23 divides 5051 by NAT_4:9;
5051 = 29*174 + 5; hence not 29 divides 5051 by NAT_4:9;
5051 = 31*162 + 29; hence not 31 divides 5051 by NAT_4:9;
5051 = 37*136 + 19; hence not 37 divides 5051 by NAT_4:9;
5051 = 41*123 + 8; hence not 41 divides 5051 by NAT_4:9;
5051 = 43*117 + 20; hence not 43 divides 5051 by NAT_4:9;
5051 = 47*107 + 22; hence not 47 divides 5051 by NAT_4:9;
5051 = 53*95 + 16; hence not 53 divides 5051 by NAT_4:9;
5051 = 59*85 + 36; hence not 59 divides 5051 by NAT_4:9;
5051 = 61*82 + 49; hence not 61 divides 5051 by NAT_4:9;
5051 = 67*75 + 26; hence not 67 divides 5051 by NAT_4:9;
5051 = 71*71 + 10; hence not 71 divides 5051 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5051 & n is prime
holds not n divides 5051 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5059 is prime
proof
now
5059 = 2*2529 + 1; hence not 2 divides 5059 by NAT_4:9;
5059 = 3*1686 + 1; hence not 3 divides 5059 by NAT_4:9;
5059 = 5*1011 + 4; hence not 5 divides 5059 by NAT_4:9;
5059 = 7*722 + 5; hence not 7 divides 5059 by NAT_4:9;
5059 = 11*459 + 10; hence not 11 divides 5059 by NAT_4:9;
5059 = 13*389 + 2; hence not 13 divides 5059 by NAT_4:9;
5059 = 17*297 + 10; hence not 17 divides 5059 by NAT_4:9;
5059 = 19*266 + 5; hence not 19 divides 5059 by NAT_4:9;
5059 = 23*219 + 22; hence not 23 divides 5059 by NAT_4:9;
5059 = 29*174 + 13; hence not 29 divides 5059 by NAT_4:9;
5059 = 31*163 + 6; hence not 31 divides 5059 by NAT_4:9;
5059 = 37*136 + 27; hence not 37 divides 5059 by NAT_4:9;
5059 = 41*123 + 16; hence not 41 divides 5059 by NAT_4:9;
5059 = 43*117 + 28; hence not 43 divides 5059 by NAT_4:9;
5059 = 47*107 + 30; hence not 47 divides 5059 by NAT_4:9;
5059 = 53*95 + 24; hence not 53 divides 5059 by NAT_4:9;
5059 = 59*85 + 44; hence not 59 divides 5059 by NAT_4:9;
5059 = 61*82 + 57; hence not 61 divides 5059 by NAT_4:9;
5059 = 67*75 + 34; hence not 67 divides 5059 by NAT_4:9;
5059 = 71*71 + 18; hence not 71 divides 5059 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5059 & n is prime
holds not n divides 5059 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
5077 is prime
proof
now
5077 = 2*2538 + 1; hence not 2 divides 5077 by NAT_4:9;
5077 = 3*1692 + 1; hence not 3 divides 5077 by NAT_4:9;
5077 = 5*1015 + 2; hence not 5 divides 5077 by NAT_4:9;
5077 = 7*725 + 2; hence not 7 divides 5077 by NAT_4:9;
5077 = 11*461 + 6; hence not 11 divides 5077 by NAT_4:9;
5077 = 13*390 + 7; hence not 13 divides 5077 by NAT_4:9;
5077 = 17*298 + 11; hence not 17 divides 5077 by NAT_4:9;
5077 = 19*267 + 4; hence not 19 divides 5077 by NAT_4:9;
5077 = 23*220 + 17; hence not 23 divides 5077 by NAT_4:9;
5077 = 29*175 + 2; hence not 29 divides 5077 by NAT_4:9;
5077 = 31*163 + 24; hence not 31 divides 5077 by NAT_4:9;
5077 = 37*137 + 8; hence not 37 divides 5077 by NAT_4:9;
5077 = 41*123 + 34; hence not 41 divides 5077 by NAT_4:9;
5077 = 43*118 + 3; hence not 43 divides 5077 by NAT_4:9;
5077 = 47*108 + 1; hence not 47 divides 5077 by NAT_4:9;
5077 = 53*95 + 42; hence not 53 divides 5077 by NAT_4:9;
5077 = 59*86 + 3; hence not 59 divides 5077 by NAT_4:9;
5077 = 61*83 + 14; hence not 61 divides 5077 by NAT_4:9;
5077 = 67*75 + 52; hence not 67 divides 5077 by NAT_4:9;
5077 = 71*71 + 36; hence not 71 divides 5077 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5077 & n is prime
holds not n divides 5077 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5081 is prime
proof
now
5081 = 2*2540 + 1; hence not 2 divides 5081 by NAT_4:9;
5081 = 3*1693 + 2; hence not 3 divides 5081 by NAT_4:9;
5081 = 5*1016 + 1; hence not 5 divides 5081 by NAT_4:9;
5081 = 7*725 + 6; hence not 7 divides 5081 by NAT_4:9;
5081 = 11*461 + 10; hence not 11 divides 5081 by NAT_4:9;
5081 = 13*390 + 11; hence not 13 divides 5081 by NAT_4:9;
5081 = 17*298 + 15; hence not 17 divides 5081 by NAT_4:9;
5081 = 19*267 + 8; hence not 19 divides 5081 by NAT_4:9;
5081 = 23*220 + 21; hence not 23 divides 5081 by NAT_4:9;
5081 = 29*175 + 6; hence not 29 divides 5081 by NAT_4:9;
5081 = 31*163 + 28; hence not 31 divides 5081 by NAT_4:9;
5081 = 37*137 + 12; hence not 37 divides 5081 by NAT_4:9;
5081 = 41*123 + 38; hence not 41 divides 5081 by NAT_4:9;
5081 = 43*118 + 7; hence not 43 divides 5081 by NAT_4:9;
5081 = 47*108 + 5; hence not 47 divides 5081 by NAT_4:9;
5081 = 53*95 + 46; hence not 53 divides 5081 by NAT_4:9;
5081 = 59*86 + 7; hence not 59 divides 5081 by NAT_4:9;
5081 = 61*83 + 18; hence not 61 divides 5081 by NAT_4:9;
5081 = 67*75 + 56; hence not 67 divides 5081 by NAT_4:9;
5081 = 71*71 + 40; hence not 71 divides 5081 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5081 & n is prime
holds not n divides 5081 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5087 is prime
proof
now
5087 = 2*2543 + 1; hence not 2 divides 5087 by NAT_4:9;
5087 = 3*1695 + 2; hence not 3 divides 5087 by NAT_4:9;
5087 = 5*1017 + 2; hence not 5 divides 5087 by NAT_4:9;
5087 = 7*726 + 5; hence not 7 divides 5087 by NAT_4:9;
5087 = 11*462 + 5; hence not 11 divides 5087 by NAT_4:9;
5087 = 13*391 + 4; hence not 13 divides 5087 by NAT_4:9;
5087 = 17*299 + 4; hence not 17 divides 5087 by NAT_4:9;
5087 = 19*267 + 14; hence not 19 divides 5087 by NAT_4:9;
5087 = 23*221 + 4; hence not 23 divides 5087 by NAT_4:9;
5087 = 29*175 + 12; hence not 29 divides 5087 by NAT_4:9;
5087 = 31*164 + 3; hence not 31 divides 5087 by NAT_4:9;
5087 = 37*137 + 18; hence not 37 divides 5087 by NAT_4:9;
5087 = 41*124 + 3; hence not 41 divides 5087 by NAT_4:9;
5087 = 43*118 + 13; hence not 43 divides 5087 by NAT_4:9;
5087 = 47*108 + 11; hence not 47 divides 5087 by NAT_4:9;
5087 = 53*95 + 52; hence not 53 divides 5087 by NAT_4:9;
5087 = 59*86 + 13; hence not 59 divides 5087 by NAT_4:9;
5087 = 61*83 + 24; hence not 61 divides 5087 by NAT_4:9;
5087 = 67*75 + 62; hence not 67 divides 5087 by NAT_4:9;
5087 = 71*71 + 46; hence not 71 divides 5087 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5087 & n is prime
holds not n divides 5087 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5099 is prime
proof
now
5099 = 2*2549 + 1; hence not 2 divides 5099 by NAT_4:9;
5099 = 3*1699 + 2; hence not 3 divides 5099 by NAT_4:9;
5099 = 5*1019 + 4; hence not 5 divides 5099 by NAT_4:9;
5099 = 7*728 + 3; hence not 7 divides 5099 by NAT_4:9;
5099 = 11*463 + 6; hence not 11 divides 5099 by NAT_4:9;
5099 = 13*392 + 3; hence not 13 divides 5099 by NAT_4:9;
5099 = 17*299 + 16; hence not 17 divides 5099 by NAT_4:9;
5099 = 19*268 + 7; hence not 19 divides 5099 by NAT_4:9;
5099 = 23*221 + 16; hence not 23 divides 5099 by NAT_4:9;
5099 = 29*175 + 24; hence not 29 divides 5099 by NAT_4:9;
5099 = 31*164 + 15; hence not 31 divides 5099 by NAT_4:9;
5099 = 37*137 + 30; hence not 37 divides 5099 by NAT_4:9;
5099 = 41*124 + 15; hence not 41 divides 5099 by NAT_4:9;
5099 = 43*118 + 25; hence not 43 divides 5099 by NAT_4:9;
5099 = 47*108 + 23; hence not 47 divides 5099 by NAT_4:9;
5099 = 53*96 + 11; hence not 53 divides 5099 by NAT_4:9;
5099 = 59*86 + 25; hence not 59 divides 5099 by NAT_4:9;
5099 = 61*83 + 36; hence not 61 divides 5099 by NAT_4:9;
5099 = 67*76 + 7; hence not 67 divides 5099 by NAT_4:9;
5099 = 71*71 + 58; hence not 71 divides 5099 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5099 & n is prime
holds not n divides 5099 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5101 is prime
proof
now
5101 = 2*2550 + 1; hence not 2 divides 5101 by NAT_4:9;
5101 = 3*1700 + 1; hence not 3 divides 5101 by NAT_4:9;
5101 = 5*1020 + 1; hence not 5 divides 5101 by NAT_4:9;
5101 = 7*728 + 5; hence not 7 divides 5101 by NAT_4:9;
5101 = 11*463 + 8; hence not 11 divides 5101 by NAT_4:9;
5101 = 13*392 + 5; hence not 13 divides 5101 by NAT_4:9;
5101 = 17*300 + 1; hence not 17 divides 5101 by NAT_4:9;
5101 = 19*268 + 9; hence not 19 divides 5101 by NAT_4:9;
5101 = 23*221 + 18; hence not 23 divides 5101 by NAT_4:9;
5101 = 29*175 + 26; hence not 29 divides 5101 by NAT_4:9;
5101 = 31*164 + 17; hence not 31 divides 5101 by NAT_4:9;
5101 = 37*137 + 32; hence not 37 divides 5101 by NAT_4:9;
5101 = 41*124 + 17; hence not 41 divides 5101 by NAT_4:9;
5101 = 43*118 + 27; hence not 43 divides 5101 by NAT_4:9;
5101 = 47*108 + 25; hence not 47 divides 5101 by NAT_4:9;
5101 = 53*96 + 13; hence not 53 divides 5101 by NAT_4:9;
5101 = 59*86 + 27; hence not 59 divides 5101 by NAT_4:9;
5101 = 61*83 + 38; hence not 61 divides 5101 by NAT_4:9;
5101 = 67*76 + 9; hence not 67 divides 5101 by NAT_4:9;
5101 = 71*71 + 60; hence not 71 divides 5101 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5101 & n is prime
holds not n divides 5101 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5107 is prime
proof
now
5107 = 2*2553 + 1; hence not 2 divides 5107 by NAT_4:9;
5107 = 3*1702 + 1; hence not 3 divides 5107 by NAT_4:9;
5107 = 5*1021 + 2; hence not 5 divides 5107 by NAT_4:9;
5107 = 7*729 + 4; hence not 7 divides 5107 by NAT_4:9;
5107 = 11*464 + 3; hence not 11 divides 5107 by NAT_4:9;
5107 = 13*392 + 11; hence not 13 divides 5107 by NAT_4:9;
5107 = 17*300 + 7; hence not 17 divides 5107 by NAT_4:9;
5107 = 19*268 + 15; hence not 19 divides 5107 by NAT_4:9;
5107 = 23*222 + 1; hence not 23 divides 5107 by NAT_4:9;
5107 = 29*176 + 3; hence not 29 divides 5107 by NAT_4:9;
5107 = 31*164 + 23; hence not 31 divides 5107 by NAT_4:9;
5107 = 37*138 + 1; hence not 37 divides 5107 by NAT_4:9;
5107 = 41*124 + 23; hence not 41 divides 5107 by NAT_4:9;
5107 = 43*118 + 33; hence not 43 divides 5107 by NAT_4:9;
5107 = 47*108 + 31; hence not 47 divides 5107 by NAT_4:9;
5107 = 53*96 + 19; hence not 53 divides 5107 by NAT_4:9;
5107 = 59*86 + 33; hence not 59 divides 5107 by NAT_4:9;
5107 = 61*83 + 44; hence not 61 divides 5107 by NAT_4:9;
5107 = 67*76 + 15; hence not 67 divides 5107 by NAT_4:9;
5107 = 71*71 + 66; hence not 71 divides 5107 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5107 & n is prime
holds not n divides 5107 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5113 is prime
proof
now
5113 = 2*2556 + 1; hence not 2 divides 5113 by NAT_4:9;
5113 = 3*1704 + 1; hence not 3 divides 5113 by NAT_4:9;
5113 = 5*1022 + 3; hence not 5 divides 5113 by NAT_4:9;
5113 = 7*730 + 3; hence not 7 divides 5113 by NAT_4:9;
5113 = 11*464 + 9; hence not 11 divides 5113 by NAT_4:9;
5113 = 13*393 + 4; hence not 13 divides 5113 by NAT_4:9;
5113 = 17*300 + 13; hence not 17 divides 5113 by NAT_4:9;
5113 = 19*269 + 2; hence not 19 divides 5113 by NAT_4:9;
5113 = 23*222 + 7; hence not 23 divides 5113 by NAT_4:9;
5113 = 29*176 + 9; hence not 29 divides 5113 by NAT_4:9;
5113 = 31*164 + 29; hence not 31 divides 5113 by NAT_4:9;
5113 = 37*138 + 7; hence not 37 divides 5113 by NAT_4:9;
5113 = 41*124 + 29; hence not 41 divides 5113 by NAT_4:9;
5113 = 43*118 + 39; hence not 43 divides 5113 by NAT_4:9;
5113 = 47*108 + 37; hence not 47 divides 5113 by NAT_4:9;
5113 = 53*96 + 25; hence not 53 divides 5113 by NAT_4:9;
5113 = 59*86 + 39; hence not 59 divides 5113 by NAT_4:9;
5113 = 61*83 + 50; hence not 61 divides 5113 by NAT_4:9;
5113 = 67*76 + 21; hence not 67 divides 5113 by NAT_4:9;
5113 = 71*72 + 1; hence not 71 divides 5113 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5113 & n is prime
holds not n divides 5113 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5119 is prime
proof
now
5119 = 2*2559 + 1; hence not 2 divides 5119 by NAT_4:9;
5119 = 3*1706 + 1; hence not 3 divides 5119 by NAT_4:9;
5119 = 5*1023 + 4; hence not 5 divides 5119 by NAT_4:9;
5119 = 7*731 + 2; hence not 7 divides 5119 by NAT_4:9;
5119 = 11*465 + 4; hence not 11 divides 5119 by NAT_4:9;
5119 = 13*393 + 10; hence not 13 divides 5119 by NAT_4:9;
5119 = 17*301 + 2; hence not 17 divides 5119 by NAT_4:9;
5119 = 19*269 + 8; hence not 19 divides 5119 by NAT_4:9;
5119 = 23*222 + 13; hence not 23 divides 5119 by NAT_4:9;
5119 = 29*176 + 15; hence not 29 divides 5119 by NAT_4:9;
5119 = 31*165 + 4; hence not 31 divides 5119 by NAT_4:9;
5119 = 37*138 + 13; hence not 37 divides 5119 by NAT_4:9;
5119 = 41*124 + 35; hence not 41 divides 5119 by NAT_4:9;
5119 = 43*119 + 2; hence not 43 divides 5119 by NAT_4:9;
5119 = 47*108 + 43; hence not 47 divides 5119 by NAT_4:9;
5119 = 53*96 + 31; hence not 53 divides 5119 by NAT_4:9;
5119 = 59*86 + 45; hence not 59 divides 5119 by NAT_4:9;
5119 = 61*83 + 56; hence not 61 divides 5119 by NAT_4:9;
5119 = 67*76 + 27; hence not 67 divides 5119 by NAT_4:9;
5119 = 71*72 + 7; hence not 71 divides 5119 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5119 & n is prime
holds not n divides 5119 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 27
theorem
5147 is prime
proof
now
5147 = 2*2573 + 1; hence not 2 divides 5147 by NAT_4:9;
5147 = 3*1715 + 2; hence not 3 divides 5147 by NAT_4:9;
5147 = 5*1029 + 2; hence not 5 divides 5147 by NAT_4:9;
5147 = 7*735 + 2; hence not 7 divides 5147 by NAT_4:9;
5147 = 11*467 + 10; hence not 11 divides 5147 by NAT_4:9;
5147 = 13*395 + 12; hence not 13 divides 5147 by NAT_4:9;
5147 = 17*302 + 13; hence not 17 divides 5147 by NAT_4:9;
5147 = 19*270 + 17; hence not 19 divides 5147 by NAT_4:9;
5147 = 23*223 + 18; hence not 23 divides 5147 by NAT_4:9;
5147 = 29*177 + 14; hence not 29 divides 5147 by NAT_4:9;
5147 = 31*166 + 1; hence not 31 divides 5147 by NAT_4:9;
5147 = 37*139 + 4; hence not 37 divides 5147 by NAT_4:9;
5147 = 41*125 + 22; hence not 41 divides 5147 by NAT_4:9;
5147 = 43*119 + 30; hence not 43 divides 5147 by NAT_4:9;
5147 = 47*109 + 24; hence not 47 divides 5147 by NAT_4:9;
5147 = 53*97 + 6; hence not 53 divides 5147 by NAT_4:9;
5147 = 59*87 + 14; hence not 59 divides 5147 by NAT_4:9;
5147 = 61*84 + 23; hence not 61 divides 5147 by NAT_4:9;
5147 = 67*76 + 55; hence not 67 divides 5147 by NAT_4:9;
5147 = 71*72 + 35; hence not 71 divides 5147 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5147 & n is prime
holds not n divides 5147 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5153 is prime
proof
now
5153 = 2*2576 + 1; hence not 2 divides 5153 by NAT_4:9;
5153 = 3*1717 + 2; hence not 3 divides 5153 by NAT_4:9;
5153 = 5*1030 + 3; hence not 5 divides 5153 by NAT_4:9;
5153 = 7*736 + 1; hence not 7 divides 5153 by NAT_4:9;
5153 = 11*468 + 5; hence not 11 divides 5153 by NAT_4:9;
5153 = 13*396 + 5; hence not 13 divides 5153 by NAT_4:9;
5153 = 17*303 + 2; hence not 17 divides 5153 by NAT_4:9;
5153 = 19*271 + 4; hence not 19 divides 5153 by NAT_4:9;
5153 = 23*224 + 1; hence not 23 divides 5153 by NAT_4:9;
5153 = 29*177 + 20; hence not 29 divides 5153 by NAT_4:9;
5153 = 31*166 + 7; hence not 31 divides 5153 by NAT_4:9;
5153 = 37*139 + 10; hence not 37 divides 5153 by NAT_4:9;
5153 = 41*125 + 28; hence not 41 divides 5153 by NAT_4:9;
5153 = 43*119 + 36; hence not 43 divides 5153 by NAT_4:9;
5153 = 47*109 + 30; hence not 47 divides 5153 by NAT_4:9;
5153 = 53*97 + 12; hence not 53 divides 5153 by NAT_4:9;
5153 = 59*87 + 20; hence not 59 divides 5153 by NAT_4:9;
5153 = 61*84 + 29; hence not 61 divides 5153 by NAT_4:9;
5153 = 67*76 + 61; hence not 67 divides 5153 by NAT_4:9;
5153 = 71*72 + 41; hence not 71 divides 5153 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5153 & n is prime
holds not n divides 5153 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
5167 is prime
proof
now
5167 = 2*2583 + 1; hence not 2 divides 5167 by NAT_4:9;
5167 = 3*1722 + 1; hence not 3 divides 5167 by NAT_4:9;
5167 = 5*1033 + 2; hence not 5 divides 5167 by NAT_4:9;
5167 = 7*738 + 1; hence not 7 divides 5167 by NAT_4:9;
5167 = 11*469 + 8; hence not 11 divides 5167 by NAT_4:9;
5167 = 13*397 + 6; hence not 13 divides 5167 by NAT_4:9;
5167 = 17*303 + 16; hence not 17 divides 5167 by NAT_4:9;
5167 = 19*271 + 18; hence not 19 divides 5167 by NAT_4:9;
5167 = 23*224 + 15; hence not 23 divides 5167 by NAT_4:9;
5167 = 29*178 + 5; hence not 29 divides 5167 by NAT_4:9;
5167 = 31*166 + 21; hence not 31 divides 5167 by NAT_4:9;
5167 = 37*139 + 24; hence not 37 divides 5167 by NAT_4:9;
5167 = 41*126 + 1; hence not 41 divides 5167 by NAT_4:9;
5167 = 43*120 + 7; hence not 43 divides 5167 by NAT_4:9;
5167 = 47*109 + 44; hence not 47 divides 5167 by NAT_4:9;
5167 = 53*97 + 26; hence not 53 divides 5167 by NAT_4:9;
5167 = 59*87 + 34; hence not 59 divides 5167 by NAT_4:9;
5167 = 61*84 + 43; hence not 61 divides 5167 by NAT_4:9;
5167 = 67*77 + 8; hence not 67 divides 5167 by NAT_4:9;
5167 = 71*72 + 55; hence not 71 divides 5167 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5167 & n is prime
holds not n divides 5167 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5171 is prime
proof
now
5171 = 2*2585 + 1; hence not 2 divides 5171 by NAT_4:9;
5171 = 3*1723 + 2; hence not 3 divides 5171 by NAT_4:9;
5171 = 5*1034 + 1; hence not 5 divides 5171 by NAT_4:9;
5171 = 7*738 + 5; hence not 7 divides 5171 by NAT_4:9;
5171 = 11*470 + 1; hence not 11 divides 5171 by NAT_4:9;
5171 = 13*397 + 10; hence not 13 divides 5171 by NAT_4:9;
5171 = 17*304 + 3; hence not 17 divides 5171 by NAT_4:9;
5171 = 19*272 + 3; hence not 19 divides 5171 by NAT_4:9;
5171 = 23*224 + 19; hence not 23 divides 5171 by NAT_4:9;
5171 = 29*178 + 9; hence not 29 divides 5171 by NAT_4:9;
5171 = 31*166 + 25; hence not 31 divides 5171 by NAT_4:9;
5171 = 37*139 + 28; hence not 37 divides 5171 by NAT_4:9;
5171 = 41*126 + 5; hence not 41 divides 5171 by NAT_4:9;
5171 = 43*120 + 11; hence not 43 divides 5171 by NAT_4:9;
5171 = 47*110 + 1; hence not 47 divides 5171 by NAT_4:9;
5171 = 53*97 + 30; hence not 53 divides 5171 by NAT_4:9;
5171 = 59*87 + 38; hence not 59 divides 5171 by NAT_4:9;
5171 = 61*84 + 47; hence not 61 divides 5171 by NAT_4:9;
5171 = 67*77 + 12; hence not 67 divides 5171 by NAT_4:9;
5171 = 71*72 + 59; hence not 71 divides 5171 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5171 & n is prime
holds not n divides 5171 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5179 is prime
proof
now
5179 = 2*2589 + 1; hence not 2 divides 5179 by NAT_4:9;
5179 = 3*1726 + 1; hence not 3 divides 5179 by NAT_4:9;
5179 = 5*1035 + 4; hence not 5 divides 5179 by NAT_4:9;
5179 = 7*739 + 6; hence not 7 divides 5179 by NAT_4:9;
5179 = 11*470 + 9; hence not 11 divides 5179 by NAT_4:9;
5179 = 13*398 + 5; hence not 13 divides 5179 by NAT_4:9;
5179 = 17*304 + 11; hence not 17 divides 5179 by NAT_4:9;
5179 = 19*272 + 11; hence not 19 divides 5179 by NAT_4:9;
5179 = 23*225 + 4; hence not 23 divides 5179 by NAT_4:9;
5179 = 29*178 + 17; hence not 29 divides 5179 by NAT_4:9;
5179 = 31*167 + 2; hence not 31 divides 5179 by NAT_4:9;
5179 = 37*139 + 36; hence not 37 divides 5179 by NAT_4:9;
5179 = 41*126 + 13; hence not 41 divides 5179 by NAT_4:9;
5179 = 43*120 + 19; hence not 43 divides 5179 by NAT_4:9;
5179 = 47*110 + 9; hence not 47 divides 5179 by NAT_4:9;
5179 = 53*97 + 38; hence not 53 divides 5179 by NAT_4:9;
5179 = 59*87 + 46; hence not 59 divides 5179 by NAT_4:9;
5179 = 61*84 + 55; hence not 61 divides 5179 by NAT_4:9;
5179 = 67*77 + 20; hence not 67 divides 5179 by NAT_4:9;
5179 = 71*72 + 67; hence not 71 divides 5179 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5179 & n is prime
holds not n divides 5179 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5189 is prime
proof
now
5189 = 2*2594 + 1; hence not 2 divides 5189 by NAT_4:9;
5189 = 3*1729 + 2; hence not 3 divides 5189 by NAT_4:9;
5189 = 5*1037 + 4; hence not 5 divides 5189 by NAT_4:9;
5189 = 7*741 + 2; hence not 7 divides 5189 by NAT_4:9;
5189 = 11*471 + 8; hence not 11 divides 5189 by NAT_4:9;
5189 = 13*399 + 2; hence not 13 divides 5189 by NAT_4:9;
5189 = 17*305 + 4; hence not 17 divides 5189 by NAT_4:9;
5189 = 19*273 + 2; hence not 19 divides 5189 by NAT_4:9;
5189 = 23*225 + 14; hence not 23 divides 5189 by NAT_4:9;
5189 = 29*178 + 27; hence not 29 divides 5189 by NAT_4:9;
5189 = 31*167 + 12; hence not 31 divides 5189 by NAT_4:9;
5189 = 37*140 + 9; hence not 37 divides 5189 by NAT_4:9;
5189 = 41*126 + 23; hence not 41 divides 5189 by NAT_4:9;
5189 = 43*120 + 29; hence not 43 divides 5189 by NAT_4:9;
5189 = 47*110 + 19; hence not 47 divides 5189 by NAT_4:9;
5189 = 53*97 + 48; hence not 53 divides 5189 by NAT_4:9;
5189 = 59*87 + 56; hence not 59 divides 5189 by NAT_4:9;
5189 = 61*85 + 4; hence not 61 divides 5189 by NAT_4:9;
5189 = 67*77 + 30; hence not 67 divides 5189 by NAT_4:9;
5189 = 71*73 + 6; hence not 71 divides 5189 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5189 & n is prime
holds not n divides 5189 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5197 is prime
proof
now
5197 = 2*2598 + 1; hence not 2 divides 5197 by NAT_4:9;
5197 = 3*1732 + 1; hence not 3 divides 5197 by NAT_4:9;
5197 = 5*1039 + 2; hence not 5 divides 5197 by NAT_4:9;
5197 = 7*742 + 3; hence not 7 divides 5197 by NAT_4:9;
5197 = 11*472 + 5; hence not 11 divides 5197 by NAT_4:9;
5197 = 13*399 + 10; hence not 13 divides 5197 by NAT_4:9;
5197 = 17*305 + 12; hence not 17 divides 5197 by NAT_4:9;
5197 = 19*273 + 10; hence not 19 divides 5197 by NAT_4:9;
5197 = 23*225 + 22; hence not 23 divides 5197 by NAT_4:9;
5197 = 29*179 + 6; hence not 29 divides 5197 by NAT_4:9;
5197 = 31*167 + 20; hence not 31 divides 5197 by NAT_4:9;
5197 = 37*140 + 17; hence not 37 divides 5197 by NAT_4:9;
5197 = 41*126 + 31; hence not 41 divides 5197 by NAT_4:9;
5197 = 43*120 + 37; hence not 43 divides 5197 by NAT_4:9;
5197 = 47*110 + 27; hence not 47 divides 5197 by NAT_4:9;
5197 = 53*98 + 3; hence not 53 divides 5197 by NAT_4:9;
5197 = 59*88 + 5; hence not 59 divides 5197 by NAT_4:9;
5197 = 61*85 + 12; hence not 61 divides 5197 by NAT_4:9;
5197 = 67*77 + 38; hence not 67 divides 5197 by NAT_4:9;
5197 = 71*73 + 14; hence not 71 divides 5197 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5197 & n is prime
holds not n divides 5197 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5209 is prime
proof
now
5209 = 2*2604 + 1; hence not 2 divides 5209 by NAT_4:9;
5209 = 3*1736 + 1; hence not 3 divides 5209 by NAT_4:9;
5209 = 5*1041 + 4; hence not 5 divides 5209 by NAT_4:9;
5209 = 7*744 + 1; hence not 7 divides 5209 by NAT_4:9;
5209 = 11*473 + 6; hence not 11 divides 5209 by NAT_4:9;
5209 = 13*400 + 9; hence not 13 divides 5209 by NAT_4:9;
5209 = 17*306 + 7; hence not 17 divides 5209 by NAT_4:9;
5209 = 19*274 + 3; hence not 19 divides 5209 by NAT_4:9;
5209 = 23*226 + 11; hence not 23 divides 5209 by NAT_4:9;
5209 = 29*179 + 18; hence not 29 divides 5209 by NAT_4:9;
5209 = 31*168 + 1; hence not 31 divides 5209 by NAT_4:9;
5209 = 37*140 + 29; hence not 37 divides 5209 by NAT_4:9;
5209 = 41*127 + 2; hence not 41 divides 5209 by NAT_4:9;
5209 = 43*121 + 6; hence not 43 divides 5209 by NAT_4:9;
5209 = 47*110 + 39; hence not 47 divides 5209 by NAT_4:9;
5209 = 53*98 + 15; hence not 53 divides 5209 by NAT_4:9;
5209 = 59*88 + 17; hence not 59 divides 5209 by NAT_4:9;
5209 = 61*85 + 24; hence not 61 divides 5209 by NAT_4:9;
5209 = 67*77 + 50; hence not 67 divides 5209 by NAT_4:9;
5209 = 71*73 + 26; hence not 71 divides 5209 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5209 & n is prime
holds not n divides 5209 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
5227 is prime
proof
now
5227 = 2*2613 + 1; hence not 2 divides 5227 by NAT_4:9;
5227 = 3*1742 + 1; hence not 3 divides 5227 by NAT_4:9;
5227 = 5*1045 + 2; hence not 5 divides 5227 by NAT_4:9;
5227 = 7*746 + 5; hence not 7 divides 5227 by NAT_4:9;
5227 = 11*475 + 2; hence not 11 divides 5227 by NAT_4:9;
5227 = 13*402 + 1; hence not 13 divides 5227 by NAT_4:9;
5227 = 17*307 + 8; hence not 17 divides 5227 by NAT_4:9;
5227 = 19*275 + 2; hence not 19 divides 5227 by NAT_4:9;
5227 = 23*227 + 6; hence not 23 divides 5227 by NAT_4:9;
5227 = 29*180 + 7; hence not 29 divides 5227 by NAT_4:9;
5227 = 31*168 + 19; hence not 31 divides 5227 by NAT_4:9;
5227 = 37*141 + 10; hence not 37 divides 5227 by NAT_4:9;
5227 = 41*127 + 20; hence not 41 divides 5227 by NAT_4:9;
5227 = 43*121 + 24; hence not 43 divides 5227 by NAT_4:9;
5227 = 47*111 + 10; hence not 47 divides 5227 by NAT_4:9;
5227 = 53*98 + 33; hence not 53 divides 5227 by NAT_4:9;
5227 = 59*88 + 35; hence not 59 divides 5227 by NAT_4:9;
5227 = 61*85 + 42; hence not 61 divides 5227 by NAT_4:9;
5227 = 67*78 + 1; hence not 67 divides 5227 by NAT_4:9;
5227 = 71*73 + 44; hence not 71 divides 5227 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5227 & n is prime
holds not n divides 5227 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5231 is prime
proof
now
5231 = 2*2615 + 1; hence not 2 divides 5231 by NAT_4:9;
5231 = 3*1743 + 2; hence not 3 divides 5231 by NAT_4:9;
5231 = 5*1046 + 1; hence not 5 divides 5231 by NAT_4:9;
5231 = 7*747 + 2; hence not 7 divides 5231 by NAT_4:9;
5231 = 11*475 + 6; hence not 11 divides 5231 by NAT_4:9;
5231 = 13*402 + 5; hence not 13 divides 5231 by NAT_4:9;
5231 = 17*307 + 12; hence not 17 divides 5231 by NAT_4:9;
5231 = 19*275 + 6; hence not 19 divides 5231 by NAT_4:9;
5231 = 23*227 + 10; hence not 23 divides 5231 by NAT_4:9;
5231 = 29*180 + 11; hence not 29 divides 5231 by NAT_4:9;
5231 = 31*168 + 23; hence not 31 divides 5231 by NAT_4:9;
5231 = 37*141 + 14; hence not 37 divides 5231 by NAT_4:9;
5231 = 41*127 + 24; hence not 41 divides 5231 by NAT_4:9;
5231 = 43*121 + 28; hence not 43 divides 5231 by NAT_4:9;
5231 = 47*111 + 14; hence not 47 divides 5231 by NAT_4:9;
5231 = 53*98 + 37; hence not 53 divides 5231 by NAT_4:9;
5231 = 59*88 + 39; hence not 59 divides 5231 by NAT_4:9;
5231 = 61*85 + 46; hence not 61 divides 5231 by NAT_4:9;
5231 = 67*78 + 5; hence not 67 divides 5231 by NAT_4:9;
5231 = 71*73 + 48; hence not 71 divides 5231 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5231 & n is prime
holds not n divides 5231 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5233 is prime
proof
now
5233 = 2*2616 + 1; hence not 2 divides 5233 by NAT_4:9;
5233 = 3*1744 + 1; hence not 3 divides 5233 by NAT_4:9;
5233 = 5*1046 + 3; hence not 5 divides 5233 by NAT_4:9;
5233 = 7*747 + 4; hence not 7 divides 5233 by NAT_4:9;
5233 = 11*475 + 8; hence not 11 divides 5233 by NAT_4:9;
5233 = 13*402 + 7; hence not 13 divides 5233 by NAT_4:9;
5233 = 17*307 + 14; hence not 17 divides 5233 by NAT_4:9;
5233 = 19*275 + 8; hence not 19 divides 5233 by NAT_4:9;
5233 = 23*227 + 12; hence not 23 divides 5233 by NAT_4:9;
5233 = 29*180 + 13; hence not 29 divides 5233 by NAT_4:9;
5233 = 31*168 + 25; hence not 31 divides 5233 by NAT_4:9;
5233 = 37*141 + 16; hence not 37 divides 5233 by NAT_4:9;
5233 = 41*127 + 26; hence not 41 divides 5233 by NAT_4:9;
5233 = 43*121 + 30; hence not 43 divides 5233 by NAT_4:9;
5233 = 47*111 + 16; hence not 47 divides 5233 by NAT_4:9;
5233 = 53*98 + 39; hence not 53 divides 5233 by NAT_4:9;
5233 = 59*88 + 41; hence not 59 divides 5233 by NAT_4:9;
5233 = 61*85 + 48; hence not 61 divides 5233 by NAT_4:9;
5233 = 67*78 + 7; hence not 67 divides 5233 by NAT_4:9;
5233 = 71*73 + 50; hence not 71 divides 5233 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5233 & n is prime
holds not n divides 5233 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5237 is prime
proof
now
5237 = 2*2618 + 1; hence not 2 divides 5237 by NAT_4:9;
5237 = 3*1745 + 2; hence not 3 divides 5237 by NAT_4:9;
5237 = 5*1047 + 2; hence not 5 divides 5237 by NAT_4:9;
5237 = 7*748 + 1; hence not 7 divides 5237 by NAT_4:9;
5237 = 11*476 + 1; hence not 11 divides 5237 by NAT_4:9;
5237 = 13*402 + 11; hence not 13 divides 5237 by NAT_4:9;
5237 = 17*308 + 1; hence not 17 divides 5237 by NAT_4:9;
5237 = 19*275 + 12; hence not 19 divides 5237 by NAT_4:9;
5237 = 23*227 + 16; hence not 23 divides 5237 by NAT_4:9;
5237 = 29*180 + 17; hence not 29 divides 5237 by NAT_4:9;
5237 = 31*168 + 29; hence not 31 divides 5237 by NAT_4:9;
5237 = 37*141 + 20; hence not 37 divides 5237 by NAT_4:9;
5237 = 41*127 + 30; hence not 41 divides 5237 by NAT_4:9;
5237 = 43*121 + 34; hence not 43 divides 5237 by NAT_4:9;
5237 = 47*111 + 20; hence not 47 divides 5237 by NAT_4:9;
5237 = 53*98 + 43; hence not 53 divides 5237 by NAT_4:9;
5237 = 59*88 + 45; hence not 59 divides 5237 by NAT_4:9;
5237 = 61*85 + 52; hence not 61 divides 5237 by NAT_4:9;
5237 = 67*78 + 11; hence not 67 divides 5237 by NAT_4:9;
5237 = 71*73 + 54; hence not 71 divides 5237 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5237 & n is prime
holds not n divides 5237 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
5261 is prime
proof
now
5261 = 2*2630 + 1; hence not 2 divides 5261 by NAT_4:9;
5261 = 3*1753 + 2; hence not 3 divides 5261 by NAT_4:9;
5261 = 5*1052 + 1; hence not 5 divides 5261 by NAT_4:9;
5261 = 7*751 + 4; hence not 7 divides 5261 by NAT_4:9;
5261 = 11*478 + 3; hence not 11 divides 5261 by NAT_4:9;
5261 = 13*404 + 9; hence not 13 divides 5261 by NAT_4:9;
5261 = 17*309 + 8; hence not 17 divides 5261 by NAT_4:9;
5261 = 19*276 + 17; hence not 19 divides 5261 by NAT_4:9;
5261 = 23*228 + 17; hence not 23 divides 5261 by NAT_4:9;
5261 = 29*181 + 12; hence not 29 divides 5261 by NAT_4:9;
5261 = 31*169 + 22; hence not 31 divides 5261 by NAT_4:9;
5261 = 37*142 + 7; hence not 37 divides 5261 by NAT_4:9;
5261 = 41*128 + 13; hence not 41 divides 5261 by NAT_4:9;
5261 = 43*122 + 15; hence not 43 divides 5261 by NAT_4:9;
5261 = 47*111 + 44; hence not 47 divides 5261 by NAT_4:9;
5261 = 53*99 + 14; hence not 53 divides 5261 by NAT_4:9;
5261 = 59*89 + 10; hence not 59 divides 5261 by NAT_4:9;
5261 = 61*86 + 15; hence not 61 divides 5261 by NAT_4:9;
5261 = 67*78 + 35; hence not 67 divides 5261 by NAT_4:9;
5261 = 71*74 + 7; hence not 71 divides 5261 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5261 & n is prime
holds not n divides 5261 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5273 is prime
proof
now
5273 = 2*2636 + 1; hence not 2 divides 5273 by NAT_4:9;
5273 = 3*1757 + 2; hence not 3 divides 5273 by NAT_4:9;
5273 = 5*1054 + 3; hence not 5 divides 5273 by NAT_4:9;
5273 = 7*753 + 2; hence not 7 divides 5273 by NAT_4:9;
5273 = 11*479 + 4; hence not 11 divides 5273 by NAT_4:9;
5273 = 13*405 + 8; hence not 13 divides 5273 by NAT_4:9;
5273 = 17*310 + 3; hence not 17 divides 5273 by NAT_4:9;
5273 = 19*277 + 10; hence not 19 divides 5273 by NAT_4:9;
5273 = 23*229 + 6; hence not 23 divides 5273 by NAT_4:9;
5273 = 29*181 + 24; hence not 29 divides 5273 by NAT_4:9;
5273 = 31*170 + 3; hence not 31 divides 5273 by NAT_4:9;
5273 = 37*142 + 19; hence not 37 divides 5273 by NAT_4:9;
5273 = 41*128 + 25; hence not 41 divides 5273 by NAT_4:9;
5273 = 43*122 + 27; hence not 43 divides 5273 by NAT_4:9;
5273 = 47*112 + 9; hence not 47 divides 5273 by NAT_4:9;
5273 = 53*99 + 26; hence not 53 divides 5273 by NAT_4:9;
5273 = 59*89 + 22; hence not 59 divides 5273 by NAT_4:9;
5273 = 61*86 + 27; hence not 61 divides 5273 by NAT_4:9;
5273 = 67*78 + 47; hence not 67 divides 5273 by NAT_4:9;
5273 = 71*74 + 19; hence not 71 divides 5273 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5273 & n is prime
holds not n divides 5273 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5279 is prime
proof
now
5279 = 2*2639 + 1; hence not 2 divides 5279 by NAT_4:9;
5279 = 3*1759 + 2; hence not 3 divides 5279 by NAT_4:9;
5279 = 5*1055 + 4; hence not 5 divides 5279 by NAT_4:9;
5279 = 7*754 + 1; hence not 7 divides 5279 by NAT_4:9;
5279 = 11*479 + 10; hence not 11 divides 5279 by NAT_4:9;
5279 = 13*406 + 1; hence not 13 divides 5279 by NAT_4:9;
5279 = 17*310 + 9; hence not 17 divides 5279 by NAT_4:9;
5279 = 19*277 + 16; hence not 19 divides 5279 by NAT_4:9;
5279 = 23*229 + 12; hence not 23 divides 5279 by NAT_4:9;
5279 = 29*182 + 1; hence not 29 divides 5279 by NAT_4:9;
5279 = 31*170 + 9; hence not 31 divides 5279 by NAT_4:9;
5279 = 37*142 + 25; hence not 37 divides 5279 by NAT_4:9;
5279 = 41*128 + 31; hence not 41 divides 5279 by NAT_4:9;
5279 = 43*122 + 33; hence not 43 divides 5279 by NAT_4:9;
5279 = 47*112 + 15; hence not 47 divides 5279 by NAT_4:9;
5279 = 53*99 + 32; hence not 53 divides 5279 by NAT_4:9;
5279 = 59*89 + 28; hence not 59 divides 5279 by NAT_4:9;
5279 = 61*86 + 33; hence not 61 divides 5279 by NAT_4:9;
5279 = 67*78 + 53; hence not 67 divides 5279 by NAT_4:9;
5279 = 71*74 + 25; hence not 71 divides 5279 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5279 & n is prime
holds not n divides 5279 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5281 is prime
proof
now
5281 = 2*2640 + 1; hence not 2 divides 5281 by NAT_4:9;
5281 = 3*1760 + 1; hence not 3 divides 5281 by NAT_4:9;
5281 = 5*1056 + 1; hence not 5 divides 5281 by NAT_4:9;
5281 = 7*754 + 3; hence not 7 divides 5281 by NAT_4:9;
5281 = 11*480 + 1; hence not 11 divides 5281 by NAT_4:9;
5281 = 13*406 + 3; hence not 13 divides 5281 by NAT_4:9;
5281 = 17*310 + 11; hence not 17 divides 5281 by NAT_4:9;
5281 = 19*277 + 18; hence not 19 divides 5281 by NAT_4:9;
5281 = 23*229 + 14; hence not 23 divides 5281 by NAT_4:9;
5281 = 29*182 + 3; hence not 29 divides 5281 by NAT_4:9;
5281 = 31*170 + 11; hence not 31 divides 5281 by NAT_4:9;
5281 = 37*142 + 27; hence not 37 divides 5281 by NAT_4:9;
5281 = 41*128 + 33; hence not 41 divides 5281 by NAT_4:9;
5281 = 43*122 + 35; hence not 43 divides 5281 by NAT_4:9;
5281 = 47*112 + 17; hence not 47 divides 5281 by NAT_4:9;
5281 = 53*99 + 34; hence not 53 divides 5281 by NAT_4:9;
5281 = 59*89 + 30; hence not 59 divides 5281 by NAT_4:9;
5281 = 61*86 + 35; hence not 61 divides 5281 by NAT_4:9;
5281 = 67*78 + 55; hence not 67 divides 5281 by NAT_4:9;
5281 = 71*74 + 27; hence not 71 divides 5281 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5281 & n is prime
holds not n divides 5281 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
5297 is prime
proof
now
5297 = 2*2648 + 1; hence not 2 divides 5297 by NAT_4:9;
5297 = 3*1765 + 2; hence not 3 divides 5297 by NAT_4:9;
5297 = 5*1059 + 2; hence not 5 divides 5297 by NAT_4:9;
5297 = 7*756 + 5; hence not 7 divides 5297 by NAT_4:9;
5297 = 11*481 + 6; hence not 11 divides 5297 by NAT_4:9;
5297 = 13*407 + 6; hence not 13 divides 5297 by NAT_4:9;
5297 = 17*311 + 10; hence not 17 divides 5297 by NAT_4:9;
5297 = 19*278 + 15; hence not 19 divides 5297 by NAT_4:9;
5297 = 23*230 + 7; hence not 23 divides 5297 by NAT_4:9;
5297 = 29*182 + 19; hence not 29 divides 5297 by NAT_4:9;
5297 = 31*170 + 27; hence not 31 divides 5297 by NAT_4:9;
5297 = 37*143 + 6; hence not 37 divides 5297 by NAT_4:9;
5297 = 41*129 + 8; hence not 41 divides 5297 by NAT_4:9;
5297 = 43*123 + 8; hence not 43 divides 5297 by NAT_4:9;
5297 = 47*112 + 33; hence not 47 divides 5297 by NAT_4:9;
5297 = 53*99 + 50; hence not 53 divides 5297 by NAT_4:9;
5297 = 59*89 + 46; hence not 59 divides 5297 by NAT_4:9;
5297 = 61*86 + 51; hence not 61 divides 5297 by NAT_4:9;
5297 = 67*79 + 4; hence not 67 divides 5297 by NAT_4:9;
5297 = 71*74 + 43; hence not 71 divides 5297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5297 & n is prime
holds not n divides 5297 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5303 is prime
proof
now
5303 = 2*2651 + 1; hence not 2 divides 5303 by NAT_4:9;
5303 = 3*1767 + 2; hence not 3 divides 5303 by NAT_4:9;
5303 = 5*1060 + 3; hence not 5 divides 5303 by NAT_4:9;
5303 = 7*757 + 4; hence not 7 divides 5303 by NAT_4:9;
5303 = 11*482 + 1; hence not 11 divides 5303 by NAT_4:9;
5303 = 13*407 + 12; hence not 13 divides 5303 by NAT_4:9;
5303 = 17*311 + 16; hence not 17 divides 5303 by NAT_4:9;
5303 = 19*279 + 2; hence not 19 divides 5303 by NAT_4:9;
5303 = 23*230 + 13; hence not 23 divides 5303 by NAT_4:9;
5303 = 29*182 + 25; hence not 29 divides 5303 by NAT_4:9;
5303 = 31*171 + 2; hence not 31 divides 5303 by NAT_4:9;
5303 = 37*143 + 12; hence not 37 divides 5303 by NAT_4:9;
5303 = 41*129 + 14; hence not 41 divides 5303 by NAT_4:9;
5303 = 43*123 + 14; hence not 43 divides 5303 by NAT_4:9;
5303 = 47*112 + 39; hence not 47 divides 5303 by NAT_4:9;
5303 = 53*100 + 3; hence not 53 divides 5303 by NAT_4:9;
5303 = 59*89 + 52; hence not 59 divides 5303 by NAT_4:9;
5303 = 61*86 + 57; hence not 61 divides 5303 by NAT_4:9;
5303 = 67*79 + 10; hence not 67 divides 5303 by NAT_4:9;
5303 = 71*74 + 49; hence not 71 divides 5303 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5303 & n is prime
holds not n divides 5303 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5309 is prime
proof
now
5309 = 2*2654 + 1; hence not 2 divides 5309 by NAT_4:9;
5309 = 3*1769 + 2; hence not 3 divides 5309 by NAT_4:9;
5309 = 5*1061 + 4; hence not 5 divides 5309 by NAT_4:9;
5309 = 7*758 + 3; hence not 7 divides 5309 by NAT_4:9;
5309 = 11*482 + 7; hence not 11 divides 5309 by NAT_4:9;
5309 = 13*408 + 5; hence not 13 divides 5309 by NAT_4:9;
5309 = 17*312 + 5; hence not 17 divides 5309 by NAT_4:9;
5309 = 19*279 + 8; hence not 19 divides 5309 by NAT_4:9;
5309 = 23*230 + 19; hence not 23 divides 5309 by NAT_4:9;
5309 = 29*183 + 2; hence not 29 divides 5309 by NAT_4:9;
5309 = 31*171 + 8; hence not 31 divides 5309 by NAT_4:9;
5309 = 37*143 + 18; hence not 37 divides 5309 by NAT_4:9;
5309 = 41*129 + 20; hence not 41 divides 5309 by NAT_4:9;
5309 = 43*123 + 20; hence not 43 divides 5309 by NAT_4:9;
5309 = 47*112 + 45; hence not 47 divides 5309 by NAT_4:9;
5309 = 53*100 + 9; hence not 53 divides 5309 by NAT_4:9;
5309 = 59*89 + 58; hence not 59 divides 5309 by NAT_4:9;
5309 = 61*87 + 2; hence not 61 divides 5309 by NAT_4:9;
5309 = 67*79 + 16; hence not 67 divides 5309 by NAT_4:9;
5309 = 71*74 + 55; hence not 71 divides 5309 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5309 & n is prime
holds not n divides 5309 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
5323 is prime
proof
now
5323 = 2*2661 + 1; hence not 2 divides 5323 by NAT_4:9;
5323 = 3*1774 + 1; hence not 3 divides 5323 by NAT_4:9;
5323 = 5*1064 + 3; hence not 5 divides 5323 by NAT_4:9;
5323 = 7*760 + 3; hence not 7 divides 5323 by NAT_4:9;
5323 = 11*483 + 10; hence not 11 divides 5323 by NAT_4:9;
5323 = 13*409 + 6; hence not 13 divides 5323 by NAT_4:9;
5323 = 17*313 + 2; hence not 17 divides 5323 by NAT_4:9;
5323 = 19*280 + 3; hence not 19 divides 5323 by NAT_4:9;
5323 = 23*231 + 10; hence not 23 divides 5323 by NAT_4:9;
5323 = 29*183 + 16; hence not 29 divides 5323 by NAT_4:9;
5323 = 31*171 + 22; hence not 31 divides 5323 by NAT_4:9;
5323 = 37*143 + 32; hence not 37 divides 5323 by NAT_4:9;
5323 = 41*129 + 34; hence not 41 divides 5323 by NAT_4:9;
5323 = 43*123 + 34; hence not 43 divides 5323 by NAT_4:9;
5323 = 47*113 + 12; hence not 47 divides 5323 by NAT_4:9;
5323 = 53*100 + 23; hence not 53 divides 5323 by NAT_4:9;
5323 = 59*90 + 13; hence not 59 divides 5323 by NAT_4:9;
5323 = 61*87 + 16; hence not 61 divides 5323 by NAT_4:9;
5323 = 67*79 + 30; hence not 67 divides 5323 by NAT_4:9;
5323 = 71*74 + 69; hence not 71 divides 5323 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5323 & n is prime
holds not n divides 5323 by XPRIMET1:40;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5333 is prime
proof
now
5333 = 2*2666 + 1; hence not 2 divides 5333 by NAT_4:9;
5333 = 3*1777 + 2; hence not 3 divides 5333 by NAT_4:9;
5333 = 5*1066 + 3; hence not 5 divides 5333 by NAT_4:9;
5333 = 7*761 + 6; hence not 7 divides 5333 by NAT_4:9;
5333 = 11*484 + 9; hence not 11 divides 5333 by NAT_4:9;
5333 = 13*410 + 3; hence not 13 divides 5333 by NAT_4:9;
5333 = 17*313 + 12; hence not 17 divides 5333 by NAT_4:9;
5333 = 19*280 + 13; hence not 19 divides 5333 by NAT_4:9;
5333 = 23*231 + 20; hence not 23 divides 5333 by NAT_4:9;
5333 = 29*183 + 26; hence not 29 divides 5333 by NAT_4:9;
5333 = 31*172 + 1; hence not 31 divides 5333 by NAT_4:9;
5333 = 37*144 + 5; hence not 37 divides 5333 by NAT_4:9;
5333 = 41*130 + 3; hence not 41 divides 5333 by NAT_4:9;
5333 = 43*124 + 1; hence not 43 divides 5333 by NAT_4:9;
5333 = 47*113 + 22; hence not 47 divides 5333 by NAT_4:9;
5333 = 53*100 + 33; hence not 53 divides 5333 by NAT_4:9;
5333 = 59*90 + 23; hence not 59 divides 5333 by NAT_4:9;
5333 = 61*87 + 26; hence not 61 divides 5333 by NAT_4:9;
5333 = 67*79 + 40; hence not 67 divides 5333 by NAT_4:9;
5333 = 71*75 + 8; hence not 71 divides 5333 by NAT_4:9;
5333 = 73*73 + 4; hence not 73 divides 5333 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5333 & n is prime
holds not n divides 5333 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
5347 is prime
proof
now
5347 = 2*2673 + 1; hence not 2 divides 5347 by NAT_4:9;
5347 = 3*1782 + 1; hence not 3 divides 5347 by NAT_4:9;
5347 = 5*1069 + 2; hence not 5 divides 5347 by NAT_4:9;
5347 = 7*763 + 6; hence not 7 divides 5347 by NAT_4:9;
5347 = 11*486 + 1; hence not 11 divides 5347 by NAT_4:9;
5347 = 13*411 + 4; hence not 13 divides 5347 by NAT_4:9;
5347 = 17*314 + 9; hence not 17 divides 5347 by NAT_4:9;
5347 = 19*281 + 8; hence not 19 divides 5347 by NAT_4:9;
5347 = 23*232 + 11; hence not 23 divides 5347 by NAT_4:9;
5347 = 29*184 + 11; hence not 29 divides 5347 by NAT_4:9;
5347 = 31*172 + 15; hence not 31 divides 5347 by NAT_4:9;
5347 = 37*144 + 19; hence not 37 divides 5347 by NAT_4:9;
5347 = 41*130 + 17; hence not 41 divides 5347 by NAT_4:9;
5347 = 43*124 + 15; hence not 43 divides 5347 by NAT_4:9;
5347 = 47*113 + 36; hence not 47 divides 5347 by NAT_4:9;
5347 = 53*100 + 47; hence not 53 divides 5347 by NAT_4:9;
5347 = 59*90 + 37; hence not 59 divides 5347 by NAT_4:9;
5347 = 61*87 + 40; hence not 61 divides 5347 by NAT_4:9;
5347 = 67*79 + 54; hence not 67 divides 5347 by NAT_4:9;
5347 = 71*75 + 22; hence not 71 divides 5347 by NAT_4:9;
5347 = 73*73 + 18; hence not 73 divides 5347 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5347 & n is prime
holds not n divides 5347 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5351 is prime
proof
now
5351 = 2*2675 + 1; hence not 2 divides 5351 by NAT_4:9;
5351 = 3*1783 + 2; hence not 3 divides 5351 by NAT_4:9;
5351 = 5*1070 + 1; hence not 5 divides 5351 by NAT_4:9;
5351 = 7*764 + 3; hence not 7 divides 5351 by NAT_4:9;
5351 = 11*486 + 5; hence not 11 divides 5351 by NAT_4:9;
5351 = 13*411 + 8; hence not 13 divides 5351 by NAT_4:9;
5351 = 17*314 + 13; hence not 17 divides 5351 by NAT_4:9;
5351 = 19*281 + 12; hence not 19 divides 5351 by NAT_4:9;
5351 = 23*232 + 15; hence not 23 divides 5351 by NAT_4:9;
5351 = 29*184 + 15; hence not 29 divides 5351 by NAT_4:9;
5351 = 31*172 + 19; hence not 31 divides 5351 by NAT_4:9;
5351 = 37*144 + 23; hence not 37 divides 5351 by NAT_4:9;
5351 = 41*130 + 21; hence not 41 divides 5351 by NAT_4:9;
5351 = 43*124 + 19; hence not 43 divides 5351 by NAT_4:9;
5351 = 47*113 + 40; hence not 47 divides 5351 by NAT_4:9;
5351 = 53*100 + 51; hence not 53 divides 5351 by NAT_4:9;
5351 = 59*90 + 41; hence not 59 divides 5351 by NAT_4:9;
5351 = 61*87 + 44; hence not 61 divides 5351 by NAT_4:9;
5351 = 67*79 + 58; hence not 67 divides 5351 by NAT_4:9;
5351 = 71*75 + 26; hence not 71 divides 5351 by NAT_4:9;
5351 = 73*73 + 22; hence not 73 divides 5351 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5351 & n is prime
holds not n divides 5351 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
5381 is prime
proof
now
5381 = 2*2690 + 1; hence not 2 divides 5381 by NAT_4:9;
5381 = 3*1793 + 2; hence not 3 divides 5381 by NAT_4:9;
5381 = 5*1076 + 1; hence not 5 divides 5381 by NAT_4:9;
5381 = 7*768 + 5; hence not 7 divides 5381 by NAT_4:9;
5381 = 11*489 + 2; hence not 11 divides 5381 by NAT_4:9;
5381 = 13*413 + 12; hence not 13 divides 5381 by NAT_4:9;
5381 = 17*316 + 9; hence not 17 divides 5381 by NAT_4:9;
5381 = 19*283 + 4; hence not 19 divides 5381 by NAT_4:9;
5381 = 23*233 + 22; hence not 23 divides 5381 by NAT_4:9;
5381 = 29*185 + 16; hence not 29 divides 5381 by NAT_4:9;
5381 = 31*173 + 18; hence not 31 divides 5381 by NAT_4:9;
5381 = 37*145 + 16; hence not 37 divides 5381 by NAT_4:9;
5381 = 41*131 + 10; hence not 41 divides 5381 by NAT_4:9;
5381 = 43*125 + 6; hence not 43 divides 5381 by NAT_4:9;
5381 = 47*114 + 23; hence not 47 divides 5381 by NAT_4:9;
5381 = 53*101 + 28; hence not 53 divides 5381 by NAT_4:9;
5381 = 59*91 + 12; hence not 59 divides 5381 by NAT_4:9;
5381 = 61*88 + 13; hence not 61 divides 5381 by NAT_4:9;
5381 = 67*80 + 21; hence not 67 divides 5381 by NAT_4:9;
5381 = 71*75 + 56; hence not 71 divides 5381 by NAT_4:9;
5381 = 73*73 + 52; hence not 73 divides 5381 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5381 & n is prime
holds not n divides 5381 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5387 is prime
proof
now
5387 = 2*2693 + 1; hence not 2 divides 5387 by NAT_4:9;
5387 = 3*1795 + 2; hence not 3 divides 5387 by NAT_4:9;
5387 = 5*1077 + 2; hence not 5 divides 5387 by NAT_4:9;
5387 = 7*769 + 4; hence not 7 divides 5387 by NAT_4:9;
5387 = 11*489 + 8; hence not 11 divides 5387 by NAT_4:9;
5387 = 13*414 + 5; hence not 13 divides 5387 by NAT_4:9;
5387 = 17*316 + 15; hence not 17 divides 5387 by NAT_4:9;
5387 = 19*283 + 10; hence not 19 divides 5387 by NAT_4:9;
5387 = 23*234 + 5; hence not 23 divides 5387 by NAT_4:9;
5387 = 29*185 + 22; hence not 29 divides 5387 by NAT_4:9;
5387 = 31*173 + 24; hence not 31 divides 5387 by NAT_4:9;
5387 = 37*145 + 22; hence not 37 divides 5387 by NAT_4:9;
5387 = 41*131 + 16; hence not 41 divides 5387 by NAT_4:9;
5387 = 43*125 + 12; hence not 43 divides 5387 by NAT_4:9;
5387 = 47*114 + 29; hence not 47 divides 5387 by NAT_4:9;
5387 = 53*101 + 34; hence not 53 divides 5387 by NAT_4:9;
5387 = 59*91 + 18; hence not 59 divides 5387 by NAT_4:9;
5387 = 61*88 + 19; hence not 61 divides 5387 by NAT_4:9;
5387 = 67*80 + 27; hence not 67 divides 5387 by NAT_4:9;
5387 = 71*75 + 62; hence not 71 divides 5387 by NAT_4:9;
5387 = 73*73 + 58; hence not 73 divides 5387 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5387 & n is prime
holds not n divides 5387 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5393 is prime
proof
now
5393 = 2*2696 + 1; hence not 2 divides 5393 by NAT_4:9;
5393 = 3*1797 + 2; hence not 3 divides 5393 by NAT_4:9;
5393 = 5*1078 + 3; hence not 5 divides 5393 by NAT_4:9;
5393 = 7*770 + 3; hence not 7 divides 5393 by NAT_4:9;
5393 = 11*490 + 3; hence not 11 divides 5393 by NAT_4:9;
5393 = 13*414 + 11; hence not 13 divides 5393 by NAT_4:9;
5393 = 17*317 + 4; hence not 17 divides 5393 by NAT_4:9;
5393 = 19*283 + 16; hence not 19 divides 5393 by NAT_4:9;
5393 = 23*234 + 11; hence not 23 divides 5393 by NAT_4:9;
5393 = 29*185 + 28; hence not 29 divides 5393 by NAT_4:9;
5393 = 31*173 + 30; hence not 31 divides 5393 by NAT_4:9;
5393 = 37*145 + 28; hence not 37 divides 5393 by NAT_4:9;
5393 = 41*131 + 22; hence not 41 divides 5393 by NAT_4:9;
5393 = 43*125 + 18; hence not 43 divides 5393 by NAT_4:9;
5393 = 47*114 + 35; hence not 47 divides 5393 by NAT_4:9;
5393 = 53*101 + 40; hence not 53 divides 5393 by NAT_4:9;
5393 = 59*91 + 24; hence not 59 divides 5393 by NAT_4:9;
5393 = 61*88 + 25; hence not 61 divides 5393 by NAT_4:9;
5393 = 67*80 + 33; hence not 67 divides 5393 by NAT_4:9;
5393 = 71*75 + 68; hence not 71 divides 5393 by NAT_4:9;
5393 = 73*73 + 64; hence not 73 divides 5393 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5393 & n is prime
holds not n divides 5393 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5399 is prime
proof
now
5399 = 2*2699 + 1; hence not 2 divides 5399 by NAT_4:9;
5399 = 3*1799 + 2; hence not 3 divides 5399 by NAT_4:9;
5399 = 5*1079 + 4; hence not 5 divides 5399 by NAT_4:9;
5399 = 7*771 + 2; hence not 7 divides 5399 by NAT_4:9;
5399 = 11*490 + 9; hence not 11 divides 5399 by NAT_4:9;
5399 = 13*415 + 4; hence not 13 divides 5399 by NAT_4:9;
5399 = 17*317 + 10; hence not 17 divides 5399 by NAT_4:9;
5399 = 19*284 + 3; hence not 19 divides 5399 by NAT_4:9;
5399 = 23*234 + 17; hence not 23 divides 5399 by NAT_4:9;
5399 = 29*186 + 5; hence not 29 divides 5399 by NAT_4:9;
5399 = 31*174 + 5; hence not 31 divides 5399 by NAT_4:9;
5399 = 37*145 + 34; hence not 37 divides 5399 by NAT_4:9;
5399 = 41*131 + 28; hence not 41 divides 5399 by NAT_4:9;
5399 = 43*125 + 24; hence not 43 divides 5399 by NAT_4:9;
5399 = 47*114 + 41; hence not 47 divides 5399 by NAT_4:9;
5399 = 53*101 + 46; hence not 53 divides 5399 by NAT_4:9;
5399 = 59*91 + 30; hence not 59 divides 5399 by NAT_4:9;
5399 = 61*88 + 31; hence not 61 divides 5399 by NAT_4:9;
5399 = 67*80 + 39; hence not 67 divides 5399 by NAT_4:9;
5399 = 71*76 + 3; hence not 71 divides 5399 by NAT_4:9;
5399 = 73*73 + 70; hence not 73 divides 5399 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5399 & n is prime
holds not n divides 5399 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5407 is prime
proof
now
5407 = 2*2703 + 1; hence not 2 divides 5407 by NAT_4:9;
5407 = 3*1802 + 1; hence not 3 divides 5407 by NAT_4:9;
5407 = 5*1081 + 2; hence not 5 divides 5407 by NAT_4:9;
5407 = 7*772 + 3; hence not 7 divides 5407 by NAT_4:9;
5407 = 11*491 + 6; hence not 11 divides 5407 by NAT_4:9;
5407 = 13*415 + 12; hence not 13 divides 5407 by NAT_4:9;
5407 = 17*318 + 1; hence not 17 divides 5407 by NAT_4:9;
5407 = 19*284 + 11; hence not 19 divides 5407 by NAT_4:9;
5407 = 23*235 + 2; hence not 23 divides 5407 by NAT_4:9;
5407 = 29*186 + 13; hence not 29 divides 5407 by NAT_4:9;
5407 = 31*174 + 13; hence not 31 divides 5407 by NAT_4:9;
5407 = 37*146 + 5; hence not 37 divides 5407 by NAT_4:9;
5407 = 41*131 + 36; hence not 41 divides 5407 by NAT_4:9;
5407 = 43*125 + 32; hence not 43 divides 5407 by NAT_4:9;
5407 = 47*115 + 2; hence not 47 divides 5407 by NAT_4:9;
5407 = 53*102 + 1; hence not 53 divides 5407 by NAT_4:9;
5407 = 59*91 + 38; hence not 59 divides 5407 by NAT_4:9;
5407 = 61*88 + 39; hence not 61 divides 5407 by NAT_4:9;
5407 = 67*80 + 47; hence not 67 divides 5407 by NAT_4:9;
5407 = 71*76 + 11; hence not 71 divides 5407 by NAT_4:9;
5407 = 73*74 + 5; hence not 73 divides 5407 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5407 & n is prime
holds not n divides 5407 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5413 is prime
proof
now
5413 = 2*2706 + 1; hence not 2 divides 5413 by NAT_4:9;
5413 = 3*1804 + 1; hence not 3 divides 5413 by NAT_4:9;
5413 = 5*1082 + 3; hence not 5 divides 5413 by NAT_4:9;
5413 = 7*773 + 2; hence not 7 divides 5413 by NAT_4:9;
5413 = 11*492 + 1; hence not 11 divides 5413 by NAT_4:9;
5413 = 13*416 + 5; hence not 13 divides 5413 by NAT_4:9;
5413 = 17*318 + 7; hence not 17 divides 5413 by NAT_4:9;
5413 = 19*284 + 17; hence not 19 divides 5413 by NAT_4:9;
5413 = 23*235 + 8; hence not 23 divides 5413 by NAT_4:9;
5413 = 29*186 + 19; hence not 29 divides 5413 by NAT_4:9;
5413 = 31*174 + 19; hence not 31 divides 5413 by NAT_4:9;
5413 = 37*146 + 11; hence not 37 divides 5413 by NAT_4:9;
5413 = 41*132 + 1; hence not 41 divides 5413 by NAT_4:9;
5413 = 43*125 + 38; hence not 43 divides 5413 by NAT_4:9;
5413 = 47*115 + 8; hence not 47 divides 5413 by NAT_4:9;
5413 = 53*102 + 7; hence not 53 divides 5413 by NAT_4:9;
5413 = 59*91 + 44; hence not 59 divides 5413 by NAT_4:9;
5413 = 61*88 + 45; hence not 61 divides 5413 by NAT_4:9;
5413 = 67*80 + 53; hence not 67 divides 5413 by NAT_4:9;
5413 = 71*76 + 17; hence not 71 divides 5413 by NAT_4:9;
5413 = 73*74 + 11; hence not 73 divides 5413 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5413 & n is prime
holds not n divides 5413 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5417 is prime
proof
now
5417 = 2*2708 + 1; hence not 2 divides 5417 by NAT_4:9;
5417 = 3*1805 + 2; hence not 3 divides 5417 by NAT_4:9;
5417 = 5*1083 + 2; hence not 5 divides 5417 by NAT_4:9;
5417 = 7*773 + 6; hence not 7 divides 5417 by NAT_4:9;
5417 = 11*492 + 5; hence not 11 divides 5417 by NAT_4:9;
5417 = 13*416 + 9; hence not 13 divides 5417 by NAT_4:9;
5417 = 17*318 + 11; hence not 17 divides 5417 by NAT_4:9;
5417 = 19*285 + 2; hence not 19 divides 5417 by NAT_4:9;
5417 = 23*235 + 12; hence not 23 divides 5417 by NAT_4:9;
5417 = 29*186 + 23; hence not 29 divides 5417 by NAT_4:9;
5417 = 31*174 + 23; hence not 31 divides 5417 by NAT_4:9;
5417 = 37*146 + 15; hence not 37 divides 5417 by NAT_4:9;
5417 = 41*132 + 5; hence not 41 divides 5417 by NAT_4:9;
5417 = 43*125 + 42; hence not 43 divides 5417 by NAT_4:9;
5417 = 47*115 + 12; hence not 47 divides 5417 by NAT_4:9;
5417 = 53*102 + 11; hence not 53 divides 5417 by NAT_4:9;
5417 = 59*91 + 48; hence not 59 divides 5417 by NAT_4:9;
5417 = 61*88 + 49; hence not 61 divides 5417 by NAT_4:9;
5417 = 67*80 + 57; hence not 67 divides 5417 by NAT_4:9;
5417 = 71*76 + 21; hence not 71 divides 5417 by NAT_4:9;
5417 = 73*74 + 15; hence not 73 divides 5417 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5417 & n is prime
holds not n divides 5417 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5419 is prime
proof
now
5419 = 2*2709 + 1; hence not 2 divides 5419 by NAT_4:9;
5419 = 3*1806 + 1; hence not 3 divides 5419 by NAT_4:9;
5419 = 5*1083 + 4; hence not 5 divides 5419 by NAT_4:9;
5419 = 7*774 + 1; hence not 7 divides 5419 by NAT_4:9;
5419 = 11*492 + 7; hence not 11 divides 5419 by NAT_4:9;
5419 = 13*416 + 11; hence not 13 divides 5419 by NAT_4:9;
5419 = 17*318 + 13; hence not 17 divides 5419 by NAT_4:9;
5419 = 19*285 + 4; hence not 19 divides 5419 by NAT_4:9;
5419 = 23*235 + 14; hence not 23 divides 5419 by NAT_4:9;
5419 = 29*186 + 25; hence not 29 divides 5419 by NAT_4:9;
5419 = 31*174 + 25; hence not 31 divides 5419 by NAT_4:9;
5419 = 37*146 + 17; hence not 37 divides 5419 by NAT_4:9;
5419 = 41*132 + 7; hence not 41 divides 5419 by NAT_4:9;
5419 = 43*126 + 1; hence not 43 divides 5419 by NAT_4:9;
5419 = 47*115 + 14; hence not 47 divides 5419 by NAT_4:9;
5419 = 53*102 + 13; hence not 53 divides 5419 by NAT_4:9;
5419 = 59*91 + 50; hence not 59 divides 5419 by NAT_4:9;
5419 = 61*88 + 51; hence not 61 divides 5419 by NAT_4:9;
5419 = 67*80 + 59; hence not 67 divides 5419 by NAT_4:9;
5419 = 71*76 + 23; hence not 71 divides 5419 by NAT_4:9;
5419 = 73*74 + 17; hence not 73 divides 5419 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5419 & n is prime
holds not n divides 5419 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5431 is prime
proof
now
5431 = 2*2715 + 1; hence not 2 divides 5431 by NAT_4:9;
5431 = 3*1810 + 1; hence not 3 divides 5431 by NAT_4:9;
5431 = 5*1086 + 1; hence not 5 divides 5431 by NAT_4:9;
5431 = 7*775 + 6; hence not 7 divides 5431 by NAT_4:9;
5431 = 11*493 + 8; hence not 11 divides 5431 by NAT_4:9;
5431 = 13*417 + 10; hence not 13 divides 5431 by NAT_4:9;
5431 = 17*319 + 8; hence not 17 divides 5431 by NAT_4:9;
5431 = 19*285 + 16; hence not 19 divides 5431 by NAT_4:9;
5431 = 23*236 + 3; hence not 23 divides 5431 by NAT_4:9;
5431 = 29*187 + 8; hence not 29 divides 5431 by NAT_4:9;
5431 = 31*175 + 6; hence not 31 divides 5431 by NAT_4:9;
5431 = 37*146 + 29; hence not 37 divides 5431 by NAT_4:9;
5431 = 41*132 + 19; hence not 41 divides 5431 by NAT_4:9;
5431 = 43*126 + 13; hence not 43 divides 5431 by NAT_4:9;
5431 = 47*115 + 26; hence not 47 divides 5431 by NAT_4:9;
5431 = 53*102 + 25; hence not 53 divides 5431 by NAT_4:9;
5431 = 59*92 + 3; hence not 59 divides 5431 by NAT_4:9;
5431 = 61*89 + 2; hence not 61 divides 5431 by NAT_4:9;
5431 = 67*81 + 4; hence not 67 divides 5431 by NAT_4:9;
5431 = 71*76 + 35; hence not 71 divides 5431 by NAT_4:9;
5431 = 73*74 + 29; hence not 73 divides 5431 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5431 & n is prime
holds not n divides 5431 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5437 is prime
proof
now
5437 = 2*2718 + 1; hence not 2 divides 5437 by NAT_4:9;
5437 = 3*1812 + 1; hence not 3 divides 5437 by NAT_4:9;
5437 = 5*1087 + 2; hence not 5 divides 5437 by NAT_4:9;
5437 = 7*776 + 5; hence not 7 divides 5437 by NAT_4:9;
5437 = 11*494 + 3; hence not 11 divides 5437 by NAT_4:9;
5437 = 13*418 + 3; hence not 13 divides 5437 by NAT_4:9;
5437 = 17*319 + 14; hence not 17 divides 5437 by NAT_4:9;
5437 = 19*286 + 3; hence not 19 divides 5437 by NAT_4:9;
5437 = 23*236 + 9; hence not 23 divides 5437 by NAT_4:9;
5437 = 29*187 + 14; hence not 29 divides 5437 by NAT_4:9;
5437 = 31*175 + 12; hence not 31 divides 5437 by NAT_4:9;
5437 = 37*146 + 35; hence not 37 divides 5437 by NAT_4:9;
5437 = 41*132 + 25; hence not 41 divides 5437 by NAT_4:9;
5437 = 43*126 + 19; hence not 43 divides 5437 by NAT_4:9;
5437 = 47*115 + 32; hence not 47 divides 5437 by NAT_4:9;
5437 = 53*102 + 31; hence not 53 divides 5437 by NAT_4:9;
5437 = 59*92 + 9; hence not 59 divides 5437 by NAT_4:9;
5437 = 61*89 + 8; hence not 61 divides 5437 by NAT_4:9;
5437 = 67*81 + 10; hence not 67 divides 5437 by NAT_4:9;
5437 = 71*76 + 41; hence not 71 divides 5437 by NAT_4:9;
5437 = 73*74 + 35; hence not 73 divides 5437 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5437 & n is prime
holds not n divides 5437 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5441 is prime
proof
now
5441 = 2*2720 + 1; hence not 2 divides 5441 by NAT_4:9;
5441 = 3*1813 + 2; hence not 3 divides 5441 by NAT_4:9;
5441 = 5*1088 + 1; hence not 5 divides 5441 by NAT_4:9;
5441 = 7*777 + 2; hence not 7 divides 5441 by NAT_4:9;
5441 = 11*494 + 7; hence not 11 divides 5441 by NAT_4:9;
5441 = 13*418 + 7; hence not 13 divides 5441 by NAT_4:9;
5441 = 17*320 + 1; hence not 17 divides 5441 by NAT_4:9;
5441 = 19*286 + 7; hence not 19 divides 5441 by NAT_4:9;
5441 = 23*236 + 13; hence not 23 divides 5441 by NAT_4:9;
5441 = 29*187 + 18; hence not 29 divides 5441 by NAT_4:9;
5441 = 31*175 + 16; hence not 31 divides 5441 by NAT_4:9;
5441 = 37*147 + 2; hence not 37 divides 5441 by NAT_4:9;
5441 = 41*132 + 29; hence not 41 divides 5441 by NAT_4:9;
5441 = 43*126 + 23; hence not 43 divides 5441 by NAT_4:9;
5441 = 47*115 + 36; hence not 47 divides 5441 by NAT_4:9;
5441 = 53*102 + 35; hence not 53 divides 5441 by NAT_4:9;
5441 = 59*92 + 13; hence not 59 divides 5441 by NAT_4:9;
5441 = 61*89 + 12; hence not 61 divides 5441 by NAT_4:9;
5441 = 67*81 + 14; hence not 67 divides 5441 by NAT_4:9;
5441 = 71*76 + 45; hence not 71 divides 5441 by NAT_4:9;
5441 = 73*74 + 39; hence not 73 divides 5441 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5441 & n is prime
holds not n divides 5441 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5443 is prime
proof
now
5443 = 2*2721 + 1; hence not 2 divides 5443 by NAT_4:9;
5443 = 3*1814 + 1; hence not 3 divides 5443 by NAT_4:9;
5443 = 5*1088 + 3; hence not 5 divides 5443 by NAT_4:9;
5443 = 7*777 + 4; hence not 7 divides 5443 by NAT_4:9;
5443 = 11*494 + 9; hence not 11 divides 5443 by NAT_4:9;
5443 = 13*418 + 9; hence not 13 divides 5443 by NAT_4:9;
5443 = 17*320 + 3; hence not 17 divides 5443 by NAT_4:9;
5443 = 19*286 + 9; hence not 19 divides 5443 by NAT_4:9;
5443 = 23*236 + 15; hence not 23 divides 5443 by NAT_4:9;
5443 = 29*187 + 20; hence not 29 divides 5443 by NAT_4:9;
5443 = 31*175 + 18; hence not 31 divides 5443 by NAT_4:9;
5443 = 37*147 + 4; hence not 37 divides 5443 by NAT_4:9;
5443 = 41*132 + 31; hence not 41 divides 5443 by NAT_4:9;
5443 = 43*126 + 25; hence not 43 divides 5443 by NAT_4:9;
5443 = 47*115 + 38; hence not 47 divides 5443 by NAT_4:9;
5443 = 53*102 + 37; hence not 53 divides 5443 by NAT_4:9;
5443 = 59*92 + 15; hence not 59 divides 5443 by NAT_4:9;
5443 = 61*89 + 14; hence not 61 divides 5443 by NAT_4:9;
5443 = 67*81 + 16; hence not 67 divides 5443 by NAT_4:9;
5443 = 71*76 + 47; hence not 71 divides 5443 by NAT_4:9;
5443 = 73*74 + 41; hence not 73 divides 5443 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5443 & n is prime
holds not n divides 5443 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5449 is prime
proof
now
5449 = 2*2724 + 1; hence not 2 divides 5449 by NAT_4:9;
5449 = 3*1816 + 1; hence not 3 divides 5449 by NAT_4:9;
5449 = 5*1089 + 4; hence not 5 divides 5449 by NAT_4:9;
5449 = 7*778 + 3; hence not 7 divides 5449 by NAT_4:9;
5449 = 11*495 + 4; hence not 11 divides 5449 by NAT_4:9;
5449 = 13*419 + 2; hence not 13 divides 5449 by NAT_4:9;
5449 = 17*320 + 9; hence not 17 divides 5449 by NAT_4:9;
5449 = 19*286 + 15; hence not 19 divides 5449 by NAT_4:9;
5449 = 23*236 + 21; hence not 23 divides 5449 by NAT_4:9;
5449 = 29*187 + 26; hence not 29 divides 5449 by NAT_4:9;
5449 = 31*175 + 24; hence not 31 divides 5449 by NAT_4:9;
5449 = 37*147 + 10; hence not 37 divides 5449 by NAT_4:9;
5449 = 41*132 + 37; hence not 41 divides 5449 by NAT_4:9;
5449 = 43*126 + 31; hence not 43 divides 5449 by NAT_4:9;
5449 = 47*115 + 44; hence not 47 divides 5449 by NAT_4:9;
5449 = 53*102 + 43; hence not 53 divides 5449 by NAT_4:9;
5449 = 59*92 + 21; hence not 59 divides 5449 by NAT_4:9;
5449 = 61*89 + 20; hence not 61 divides 5449 by NAT_4:9;
5449 = 67*81 + 22; hence not 67 divides 5449 by NAT_4:9;
5449 = 71*76 + 53; hence not 71 divides 5449 by NAT_4:9;
5449 = 73*74 + 47; hence not 73 divides 5449 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5449 & n is prime
holds not n divides 5449 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
5471 is prime
proof
now
5471 = 2*2735 + 1; hence not 2 divides 5471 by NAT_4:9;
5471 = 3*1823 + 2; hence not 3 divides 5471 by NAT_4:9;
5471 = 5*1094 + 1; hence not 5 divides 5471 by NAT_4:9;
5471 = 7*781 + 4; hence not 7 divides 5471 by NAT_4:9;
5471 = 11*497 + 4; hence not 11 divides 5471 by NAT_4:9;
5471 = 13*420 + 11; hence not 13 divides 5471 by NAT_4:9;
5471 = 17*321 + 14; hence not 17 divides 5471 by NAT_4:9;
5471 = 19*287 + 18; hence not 19 divides 5471 by NAT_4:9;
5471 = 23*237 + 20; hence not 23 divides 5471 by NAT_4:9;
5471 = 29*188 + 19; hence not 29 divides 5471 by NAT_4:9;
5471 = 31*176 + 15; hence not 31 divides 5471 by NAT_4:9;
5471 = 37*147 + 32; hence not 37 divides 5471 by NAT_4:9;
5471 = 41*133 + 18; hence not 41 divides 5471 by NAT_4:9;
5471 = 43*127 + 10; hence not 43 divides 5471 by NAT_4:9;
5471 = 47*116 + 19; hence not 47 divides 5471 by NAT_4:9;
5471 = 53*103 + 12; hence not 53 divides 5471 by NAT_4:9;
5471 = 59*92 + 43; hence not 59 divides 5471 by NAT_4:9;
5471 = 61*89 + 42; hence not 61 divides 5471 by NAT_4:9;
5471 = 67*81 + 44; hence not 67 divides 5471 by NAT_4:9;
5471 = 71*77 + 4; hence not 71 divides 5471 by NAT_4:9;
5471 = 73*74 + 69; hence not 73 divides 5471 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5471 & n is prime
holds not n divides 5471 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5477 is prime
proof
now
5477 = 2*2738 + 1; hence not 2 divides 5477 by NAT_4:9;
5477 = 3*1825 + 2; hence not 3 divides 5477 by NAT_4:9;
5477 = 5*1095 + 2; hence not 5 divides 5477 by NAT_4:9;
5477 = 7*782 + 3; hence not 7 divides 5477 by NAT_4:9;
5477 = 11*497 + 10; hence not 11 divides 5477 by NAT_4:9;
5477 = 13*421 + 4; hence not 13 divides 5477 by NAT_4:9;
5477 = 17*322 + 3; hence not 17 divides 5477 by NAT_4:9;
5477 = 19*288 + 5; hence not 19 divides 5477 by NAT_4:9;
5477 = 23*238 + 3; hence not 23 divides 5477 by NAT_4:9;
5477 = 29*188 + 25; hence not 29 divides 5477 by NAT_4:9;
5477 = 31*176 + 21; hence not 31 divides 5477 by NAT_4:9;
5477 = 37*148 + 1; hence not 37 divides 5477 by NAT_4:9;
5477 = 41*133 + 24; hence not 41 divides 5477 by NAT_4:9;
5477 = 43*127 + 16; hence not 43 divides 5477 by NAT_4:9;
5477 = 47*116 + 25; hence not 47 divides 5477 by NAT_4:9;
5477 = 53*103 + 18; hence not 53 divides 5477 by NAT_4:9;
5477 = 59*92 + 49; hence not 59 divides 5477 by NAT_4:9;
5477 = 61*89 + 48; hence not 61 divides 5477 by NAT_4:9;
5477 = 67*81 + 50; hence not 67 divides 5477 by NAT_4:9;
5477 = 71*77 + 10; hence not 71 divides 5477 by NAT_4:9;
5477 = 73*75 + 2; hence not 73 divides 5477 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5477 & n is prime
holds not n divides 5477 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5479 is prime
proof
now
5479 = 2*2739 + 1; hence not 2 divides 5479 by NAT_4:9;
5479 = 3*1826 + 1; hence not 3 divides 5479 by NAT_4:9;
5479 = 5*1095 + 4; hence not 5 divides 5479 by NAT_4:9;
5479 = 7*782 + 5; hence not 7 divides 5479 by NAT_4:9;
5479 = 11*498 + 1; hence not 11 divides 5479 by NAT_4:9;
5479 = 13*421 + 6; hence not 13 divides 5479 by NAT_4:9;
5479 = 17*322 + 5; hence not 17 divides 5479 by NAT_4:9;
5479 = 19*288 + 7; hence not 19 divides 5479 by NAT_4:9;
5479 = 23*238 + 5; hence not 23 divides 5479 by NAT_4:9;
5479 = 29*188 + 27; hence not 29 divides 5479 by NAT_4:9;
5479 = 31*176 + 23; hence not 31 divides 5479 by NAT_4:9;
5479 = 37*148 + 3; hence not 37 divides 5479 by NAT_4:9;
5479 = 41*133 + 26; hence not 41 divides 5479 by NAT_4:9;
5479 = 43*127 + 18; hence not 43 divides 5479 by NAT_4:9;
5479 = 47*116 + 27; hence not 47 divides 5479 by NAT_4:9;
5479 = 53*103 + 20; hence not 53 divides 5479 by NAT_4:9;
5479 = 59*92 + 51; hence not 59 divides 5479 by NAT_4:9;
5479 = 61*89 + 50; hence not 61 divides 5479 by NAT_4:9;
5479 = 67*81 + 52; hence not 67 divides 5479 by NAT_4:9;
5479 = 71*77 + 12; hence not 71 divides 5479 by NAT_4:9;
5479 = 73*75 + 4; hence not 73 divides 5479 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5479 & n is prime
holds not n divides 5479 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5483 is prime
proof
now
5483 = 2*2741 + 1; hence not 2 divides 5483 by NAT_4:9;
5483 = 3*1827 + 2; hence not 3 divides 5483 by NAT_4:9;
5483 = 5*1096 + 3; hence not 5 divides 5483 by NAT_4:9;
5483 = 7*783 + 2; hence not 7 divides 5483 by NAT_4:9;
5483 = 11*498 + 5; hence not 11 divides 5483 by NAT_4:9;
5483 = 13*421 + 10; hence not 13 divides 5483 by NAT_4:9;
5483 = 17*322 + 9; hence not 17 divides 5483 by NAT_4:9;
5483 = 19*288 + 11; hence not 19 divides 5483 by NAT_4:9;
5483 = 23*238 + 9; hence not 23 divides 5483 by NAT_4:9;
5483 = 29*189 + 2; hence not 29 divides 5483 by NAT_4:9;
5483 = 31*176 + 27; hence not 31 divides 5483 by NAT_4:9;
5483 = 37*148 + 7; hence not 37 divides 5483 by NAT_4:9;
5483 = 41*133 + 30; hence not 41 divides 5483 by NAT_4:9;
5483 = 43*127 + 22; hence not 43 divides 5483 by NAT_4:9;
5483 = 47*116 + 31; hence not 47 divides 5483 by NAT_4:9;
5483 = 53*103 + 24; hence not 53 divides 5483 by NAT_4:9;
5483 = 59*92 + 55; hence not 59 divides 5483 by NAT_4:9;
5483 = 61*89 + 54; hence not 61 divides 5483 by NAT_4:9;
5483 = 67*81 + 56; hence not 67 divides 5483 by NAT_4:9;
5483 = 71*77 + 16; hence not 71 divides 5483 by NAT_4:9;
5483 = 73*75 + 8; hence not 73 divides 5483 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5483 & n is prime
holds not n divides 5483 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
5501 is prime
proof
now
5501 = 2*2750 + 1; hence not 2 divides 5501 by NAT_4:9;
5501 = 3*1833 + 2; hence not 3 divides 5501 by NAT_4:9;
5501 = 5*1100 + 1; hence not 5 divides 5501 by NAT_4:9;
5501 = 7*785 + 6; hence not 7 divides 5501 by NAT_4:9;
5501 = 11*500 + 1; hence not 11 divides 5501 by NAT_4:9;
5501 = 13*423 + 2; hence not 13 divides 5501 by NAT_4:9;
5501 = 17*323 + 10; hence not 17 divides 5501 by NAT_4:9;
5501 = 19*289 + 10; hence not 19 divides 5501 by NAT_4:9;
5501 = 23*239 + 4; hence not 23 divides 5501 by NAT_4:9;
5501 = 29*189 + 20; hence not 29 divides 5501 by NAT_4:9;
5501 = 31*177 + 14; hence not 31 divides 5501 by NAT_4:9;
5501 = 37*148 + 25; hence not 37 divides 5501 by NAT_4:9;
5501 = 41*134 + 7; hence not 41 divides 5501 by NAT_4:9;
5501 = 43*127 + 40; hence not 43 divides 5501 by NAT_4:9;
5501 = 47*117 + 2; hence not 47 divides 5501 by NAT_4:9;
5501 = 53*103 + 42; hence not 53 divides 5501 by NAT_4:9;
5501 = 59*93 + 14; hence not 59 divides 5501 by NAT_4:9;
5501 = 61*90 + 11; hence not 61 divides 5501 by NAT_4:9;
5501 = 67*82 + 7; hence not 67 divides 5501 by NAT_4:9;
5501 = 71*77 + 34; hence not 71 divides 5501 by NAT_4:9;
5501 = 73*75 + 26; hence not 73 divides 5501 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5501 & n is prime
holds not n divides 5501 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5503 is prime
proof
now
5503 = 2*2751 + 1; hence not 2 divides 5503 by NAT_4:9;
5503 = 3*1834 + 1; hence not 3 divides 5503 by NAT_4:9;
5503 = 5*1100 + 3; hence not 5 divides 5503 by NAT_4:9;
5503 = 7*786 + 1; hence not 7 divides 5503 by NAT_4:9;
5503 = 11*500 + 3; hence not 11 divides 5503 by NAT_4:9;
5503 = 13*423 + 4; hence not 13 divides 5503 by NAT_4:9;
5503 = 17*323 + 12; hence not 17 divides 5503 by NAT_4:9;
5503 = 19*289 + 12; hence not 19 divides 5503 by NAT_4:9;
5503 = 23*239 + 6; hence not 23 divides 5503 by NAT_4:9;
5503 = 29*189 + 22; hence not 29 divides 5503 by NAT_4:9;
5503 = 31*177 + 16; hence not 31 divides 5503 by NAT_4:9;
5503 = 37*148 + 27; hence not 37 divides 5503 by NAT_4:9;
5503 = 41*134 + 9; hence not 41 divides 5503 by NAT_4:9;
5503 = 43*127 + 42; hence not 43 divides 5503 by NAT_4:9;
5503 = 47*117 + 4; hence not 47 divides 5503 by NAT_4:9;
5503 = 53*103 + 44; hence not 53 divides 5503 by NAT_4:9;
5503 = 59*93 + 16; hence not 59 divides 5503 by NAT_4:9;
5503 = 61*90 + 13; hence not 61 divides 5503 by NAT_4:9;
5503 = 67*82 + 9; hence not 67 divides 5503 by NAT_4:9;
5503 = 71*77 + 36; hence not 71 divides 5503 by NAT_4:9;
5503 = 73*75 + 28; hence not 73 divides 5503 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5503 & n is prime
holds not n divides 5503 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5507 is prime
proof
now
5507 = 2*2753 + 1; hence not 2 divides 5507 by NAT_4:9;
5507 = 3*1835 + 2; hence not 3 divides 5507 by NAT_4:9;
5507 = 5*1101 + 2; hence not 5 divides 5507 by NAT_4:9;
5507 = 7*786 + 5; hence not 7 divides 5507 by NAT_4:9;
5507 = 11*500 + 7; hence not 11 divides 5507 by NAT_4:9;
5507 = 13*423 + 8; hence not 13 divides 5507 by NAT_4:9;
5507 = 17*323 + 16; hence not 17 divides 5507 by NAT_4:9;
5507 = 19*289 + 16; hence not 19 divides 5507 by NAT_4:9;
5507 = 23*239 + 10; hence not 23 divides 5507 by NAT_4:9;
5507 = 29*189 + 26; hence not 29 divides 5507 by NAT_4:9;
5507 = 31*177 + 20; hence not 31 divides 5507 by NAT_4:9;
5507 = 37*148 + 31; hence not 37 divides 5507 by NAT_4:9;
5507 = 41*134 + 13; hence not 41 divides 5507 by NAT_4:9;
5507 = 43*128 + 3; hence not 43 divides 5507 by NAT_4:9;
5507 = 47*117 + 8; hence not 47 divides 5507 by NAT_4:9;
5507 = 53*103 + 48; hence not 53 divides 5507 by NAT_4:9;
5507 = 59*93 + 20; hence not 59 divides 5507 by NAT_4:9;
5507 = 61*90 + 17; hence not 61 divides 5507 by NAT_4:9;
5507 = 67*82 + 13; hence not 67 divides 5507 by NAT_4:9;
5507 = 71*77 + 40; hence not 71 divides 5507 by NAT_4:9;
5507 = 73*75 + 32; hence not 73 divides 5507 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5507 & n is prime
holds not n divides 5507 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5519 is prime
proof
now
5519 = 2*2759 + 1; hence not 2 divides 5519 by NAT_4:9;
5519 = 3*1839 + 2; hence not 3 divides 5519 by NAT_4:9;
5519 = 5*1103 + 4; hence not 5 divides 5519 by NAT_4:9;
5519 = 7*788 + 3; hence not 7 divides 5519 by NAT_4:9;
5519 = 11*501 + 8; hence not 11 divides 5519 by NAT_4:9;
5519 = 13*424 + 7; hence not 13 divides 5519 by NAT_4:9;
5519 = 17*324 + 11; hence not 17 divides 5519 by NAT_4:9;
5519 = 19*290 + 9; hence not 19 divides 5519 by NAT_4:9;
5519 = 23*239 + 22; hence not 23 divides 5519 by NAT_4:9;
5519 = 29*190 + 9; hence not 29 divides 5519 by NAT_4:9;
5519 = 31*178 + 1; hence not 31 divides 5519 by NAT_4:9;
5519 = 37*149 + 6; hence not 37 divides 5519 by NAT_4:9;
5519 = 41*134 + 25; hence not 41 divides 5519 by NAT_4:9;
5519 = 43*128 + 15; hence not 43 divides 5519 by NAT_4:9;
5519 = 47*117 + 20; hence not 47 divides 5519 by NAT_4:9;
5519 = 53*104 + 7; hence not 53 divides 5519 by NAT_4:9;
5519 = 59*93 + 32; hence not 59 divides 5519 by NAT_4:9;
5519 = 61*90 + 29; hence not 61 divides 5519 by NAT_4:9;
5519 = 67*82 + 25; hence not 67 divides 5519 by NAT_4:9;
5519 = 71*77 + 52; hence not 71 divides 5519 by NAT_4:9;
5519 = 73*75 + 44; hence not 73 divides 5519 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5519 & n is prime
holds not n divides 5519 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5521 is prime
proof
now
5521 = 2*2760 + 1; hence not 2 divides 5521 by NAT_4:9;
5521 = 3*1840 + 1; hence not 3 divides 5521 by NAT_4:9;
5521 = 5*1104 + 1; hence not 5 divides 5521 by NAT_4:9;
5521 = 7*788 + 5; hence not 7 divides 5521 by NAT_4:9;
5521 = 11*501 + 10; hence not 11 divides 5521 by NAT_4:9;
5521 = 13*424 + 9; hence not 13 divides 5521 by NAT_4:9;
5521 = 17*324 + 13; hence not 17 divides 5521 by NAT_4:9;
5521 = 19*290 + 11; hence not 19 divides 5521 by NAT_4:9;
5521 = 23*240 + 1; hence not 23 divides 5521 by NAT_4:9;
5521 = 29*190 + 11; hence not 29 divides 5521 by NAT_4:9;
5521 = 31*178 + 3; hence not 31 divides 5521 by NAT_4:9;
5521 = 37*149 + 8; hence not 37 divides 5521 by NAT_4:9;
5521 = 41*134 + 27; hence not 41 divides 5521 by NAT_4:9;
5521 = 43*128 + 17; hence not 43 divides 5521 by NAT_4:9;
5521 = 47*117 + 22; hence not 47 divides 5521 by NAT_4:9;
5521 = 53*104 + 9; hence not 53 divides 5521 by NAT_4:9;
5521 = 59*93 + 34; hence not 59 divides 5521 by NAT_4:9;
5521 = 61*90 + 31; hence not 61 divides 5521 by NAT_4:9;
5521 = 67*82 + 27; hence not 67 divides 5521 by NAT_4:9;
5521 = 71*77 + 54; hence not 71 divides 5521 by NAT_4:9;
5521 = 73*75 + 46; hence not 73 divides 5521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5521 & n is prime
holds not n divides 5521 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5527 is prime
proof
now
5527 = 2*2763 + 1; hence not 2 divides 5527 by NAT_4:9;
5527 = 3*1842 + 1; hence not 3 divides 5527 by NAT_4:9;
5527 = 5*1105 + 2; hence not 5 divides 5527 by NAT_4:9;
5527 = 7*789 + 4; hence not 7 divides 5527 by NAT_4:9;
5527 = 11*502 + 5; hence not 11 divides 5527 by NAT_4:9;
5527 = 13*425 + 2; hence not 13 divides 5527 by NAT_4:9;
5527 = 17*325 + 2; hence not 17 divides 5527 by NAT_4:9;
5527 = 19*290 + 17; hence not 19 divides 5527 by NAT_4:9;
5527 = 23*240 + 7; hence not 23 divides 5527 by NAT_4:9;
5527 = 29*190 + 17; hence not 29 divides 5527 by NAT_4:9;
5527 = 31*178 + 9; hence not 31 divides 5527 by NAT_4:9;
5527 = 37*149 + 14; hence not 37 divides 5527 by NAT_4:9;
5527 = 41*134 + 33; hence not 41 divides 5527 by NAT_4:9;
5527 = 43*128 + 23; hence not 43 divides 5527 by NAT_4:9;
5527 = 47*117 + 28; hence not 47 divides 5527 by NAT_4:9;
5527 = 53*104 + 15; hence not 53 divides 5527 by NAT_4:9;
5527 = 59*93 + 40; hence not 59 divides 5527 by NAT_4:9;
5527 = 61*90 + 37; hence not 61 divides 5527 by NAT_4:9;
5527 = 67*82 + 33; hence not 67 divides 5527 by NAT_4:9;
5527 = 71*77 + 60; hence not 71 divides 5527 by NAT_4:9;
5527 = 73*75 + 52; hence not 73 divides 5527 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5527 & n is prime
holds not n divides 5527 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5531 is prime
proof
now
5531 = 2*2765 + 1; hence not 2 divides 5531 by NAT_4:9;
5531 = 3*1843 + 2; hence not 3 divides 5531 by NAT_4:9;
5531 = 5*1106 + 1; hence not 5 divides 5531 by NAT_4:9;
5531 = 7*790 + 1; hence not 7 divides 5531 by NAT_4:9;
5531 = 11*502 + 9; hence not 11 divides 5531 by NAT_4:9;
5531 = 13*425 + 6; hence not 13 divides 5531 by NAT_4:9;
5531 = 17*325 + 6; hence not 17 divides 5531 by NAT_4:9;
5531 = 19*291 + 2; hence not 19 divides 5531 by NAT_4:9;
5531 = 23*240 + 11; hence not 23 divides 5531 by NAT_4:9;
5531 = 29*190 + 21; hence not 29 divides 5531 by NAT_4:9;
5531 = 31*178 + 13; hence not 31 divides 5531 by NAT_4:9;
5531 = 37*149 + 18; hence not 37 divides 5531 by NAT_4:9;
5531 = 41*134 + 37; hence not 41 divides 5531 by NAT_4:9;
5531 = 43*128 + 27; hence not 43 divides 5531 by NAT_4:9;
5531 = 47*117 + 32; hence not 47 divides 5531 by NAT_4:9;
5531 = 53*104 + 19; hence not 53 divides 5531 by NAT_4:9;
5531 = 59*93 + 44; hence not 59 divides 5531 by NAT_4:9;
5531 = 61*90 + 41; hence not 61 divides 5531 by NAT_4:9;
5531 = 67*82 + 37; hence not 67 divides 5531 by NAT_4:9;
5531 = 71*77 + 64; hence not 71 divides 5531 by NAT_4:9;
5531 = 73*75 + 56; hence not 73 divides 5531 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5531 & n is prime
holds not n divides 5531 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 25
theorem
5557 is prime
proof
now
5557 = 2*2778 + 1; hence not 2 divides 5557 by NAT_4:9;
5557 = 3*1852 + 1; hence not 3 divides 5557 by NAT_4:9;
5557 = 5*1111 + 2; hence not 5 divides 5557 by NAT_4:9;
5557 = 7*793 + 6; hence not 7 divides 5557 by NAT_4:9;
5557 = 11*505 + 2; hence not 11 divides 5557 by NAT_4:9;
5557 = 13*427 + 6; hence not 13 divides 5557 by NAT_4:9;
5557 = 17*326 + 15; hence not 17 divides 5557 by NAT_4:9;
5557 = 19*292 + 9; hence not 19 divides 5557 by NAT_4:9;
5557 = 23*241 + 14; hence not 23 divides 5557 by NAT_4:9;
5557 = 29*191 + 18; hence not 29 divides 5557 by NAT_4:9;
5557 = 31*179 + 8; hence not 31 divides 5557 by NAT_4:9;
5557 = 37*150 + 7; hence not 37 divides 5557 by NAT_4:9;
5557 = 41*135 + 22; hence not 41 divides 5557 by NAT_4:9;
5557 = 43*129 + 10; hence not 43 divides 5557 by NAT_4:9;
5557 = 47*118 + 11; hence not 47 divides 5557 by NAT_4:9;
5557 = 53*104 + 45; hence not 53 divides 5557 by NAT_4:9;
5557 = 59*94 + 11; hence not 59 divides 5557 by NAT_4:9;
5557 = 61*91 + 6; hence not 61 divides 5557 by NAT_4:9;
5557 = 67*82 + 63; hence not 67 divides 5557 by NAT_4:9;
5557 = 71*78 + 19; hence not 71 divides 5557 by NAT_4:9;
5557 = 73*76 + 9; hence not 73 divides 5557 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5557 & n is prime
holds not n divides 5557 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5563 is prime
proof
now
5563 = 2*2781 + 1; hence not 2 divides 5563 by NAT_4:9;
5563 = 3*1854 + 1; hence not 3 divides 5563 by NAT_4:9;
5563 = 5*1112 + 3; hence not 5 divides 5563 by NAT_4:9;
5563 = 7*794 + 5; hence not 7 divides 5563 by NAT_4:9;
5563 = 11*505 + 8; hence not 11 divides 5563 by NAT_4:9;
5563 = 13*427 + 12; hence not 13 divides 5563 by NAT_4:9;
5563 = 17*327 + 4; hence not 17 divides 5563 by NAT_4:9;
5563 = 19*292 + 15; hence not 19 divides 5563 by NAT_4:9;
5563 = 23*241 + 20; hence not 23 divides 5563 by NAT_4:9;
5563 = 29*191 + 24; hence not 29 divides 5563 by NAT_4:9;
5563 = 31*179 + 14; hence not 31 divides 5563 by NAT_4:9;
5563 = 37*150 + 13; hence not 37 divides 5563 by NAT_4:9;
5563 = 41*135 + 28; hence not 41 divides 5563 by NAT_4:9;
5563 = 43*129 + 16; hence not 43 divides 5563 by NAT_4:9;
5563 = 47*118 + 17; hence not 47 divides 5563 by NAT_4:9;
5563 = 53*104 + 51; hence not 53 divides 5563 by NAT_4:9;
5563 = 59*94 + 17; hence not 59 divides 5563 by NAT_4:9;
5563 = 61*91 + 12; hence not 61 divides 5563 by NAT_4:9;
5563 = 67*83 + 2; hence not 67 divides 5563 by NAT_4:9;
5563 = 71*78 + 25; hence not 71 divides 5563 by NAT_4:9;
5563 = 73*76 + 15; hence not 73 divides 5563 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5563 & n is prime
holds not n divides 5563 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5569 is prime
proof
now
5569 = 2*2784 + 1; hence not 2 divides 5569 by NAT_4:9;
5569 = 3*1856 + 1; hence not 3 divides 5569 by NAT_4:9;
5569 = 5*1113 + 4; hence not 5 divides 5569 by NAT_4:9;
5569 = 7*795 + 4; hence not 7 divides 5569 by NAT_4:9;
5569 = 11*506 + 3; hence not 11 divides 5569 by NAT_4:9;
5569 = 13*428 + 5; hence not 13 divides 5569 by NAT_4:9;
5569 = 17*327 + 10; hence not 17 divides 5569 by NAT_4:9;
5569 = 19*293 + 2; hence not 19 divides 5569 by NAT_4:9;
5569 = 23*242 + 3; hence not 23 divides 5569 by NAT_4:9;
5569 = 29*192 + 1; hence not 29 divides 5569 by NAT_4:9;
5569 = 31*179 + 20; hence not 31 divides 5569 by NAT_4:9;
5569 = 37*150 + 19; hence not 37 divides 5569 by NAT_4:9;
5569 = 41*135 + 34; hence not 41 divides 5569 by NAT_4:9;
5569 = 43*129 + 22; hence not 43 divides 5569 by NAT_4:9;
5569 = 47*118 + 23; hence not 47 divides 5569 by NAT_4:9;
5569 = 53*105 + 4; hence not 53 divides 5569 by NAT_4:9;
5569 = 59*94 + 23; hence not 59 divides 5569 by NAT_4:9;
5569 = 61*91 + 18; hence not 61 divides 5569 by NAT_4:9;
5569 = 67*83 + 8; hence not 67 divides 5569 by NAT_4:9;
5569 = 71*78 + 31; hence not 71 divides 5569 by NAT_4:9;
5569 = 73*76 + 21; hence not 73 divides 5569 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5569 & n is prime
holds not n divides 5569 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5573 is prime
proof
now
5573 = 2*2786 + 1; hence not 2 divides 5573 by NAT_4:9;
5573 = 3*1857 + 2; hence not 3 divides 5573 by NAT_4:9;
5573 = 5*1114 + 3; hence not 5 divides 5573 by NAT_4:9;
5573 = 7*796 + 1; hence not 7 divides 5573 by NAT_4:9;
5573 = 11*506 + 7; hence not 11 divides 5573 by NAT_4:9;
5573 = 13*428 + 9; hence not 13 divides 5573 by NAT_4:9;
5573 = 17*327 + 14; hence not 17 divides 5573 by NAT_4:9;
5573 = 19*293 + 6; hence not 19 divides 5573 by NAT_4:9;
5573 = 23*242 + 7; hence not 23 divides 5573 by NAT_4:9;
5573 = 29*192 + 5; hence not 29 divides 5573 by NAT_4:9;
5573 = 31*179 + 24; hence not 31 divides 5573 by NAT_4:9;
5573 = 37*150 + 23; hence not 37 divides 5573 by NAT_4:9;
5573 = 41*135 + 38; hence not 41 divides 5573 by NAT_4:9;
5573 = 43*129 + 26; hence not 43 divides 5573 by NAT_4:9;
5573 = 47*118 + 27; hence not 47 divides 5573 by NAT_4:9;
5573 = 53*105 + 8; hence not 53 divides 5573 by NAT_4:9;
5573 = 59*94 + 27; hence not 59 divides 5573 by NAT_4:9;
5573 = 61*91 + 22; hence not 61 divides 5573 by NAT_4:9;
5573 = 67*83 + 12; hence not 67 divides 5573 by NAT_4:9;
5573 = 71*78 + 35; hence not 71 divides 5573 by NAT_4:9;
5573 = 73*76 + 25; hence not 73 divides 5573 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5573 & n is prime
holds not n divides 5573 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5581 is prime
proof
now
5581 = 2*2790 + 1; hence not 2 divides 5581 by NAT_4:9;
5581 = 3*1860 + 1; hence not 3 divides 5581 by NAT_4:9;
5581 = 5*1116 + 1; hence not 5 divides 5581 by NAT_4:9;
5581 = 7*797 + 2; hence not 7 divides 5581 by NAT_4:9;
5581 = 11*507 + 4; hence not 11 divides 5581 by NAT_4:9;
5581 = 13*429 + 4; hence not 13 divides 5581 by NAT_4:9;
5581 = 17*328 + 5; hence not 17 divides 5581 by NAT_4:9;
5581 = 19*293 + 14; hence not 19 divides 5581 by NAT_4:9;
5581 = 23*242 + 15; hence not 23 divides 5581 by NAT_4:9;
5581 = 29*192 + 13; hence not 29 divides 5581 by NAT_4:9;
5581 = 31*180 + 1; hence not 31 divides 5581 by NAT_4:9;
5581 = 37*150 + 31; hence not 37 divides 5581 by NAT_4:9;
5581 = 41*136 + 5; hence not 41 divides 5581 by NAT_4:9;
5581 = 43*129 + 34; hence not 43 divides 5581 by NAT_4:9;
5581 = 47*118 + 35; hence not 47 divides 5581 by NAT_4:9;
5581 = 53*105 + 16; hence not 53 divides 5581 by NAT_4:9;
5581 = 59*94 + 35; hence not 59 divides 5581 by NAT_4:9;
5581 = 61*91 + 30; hence not 61 divides 5581 by NAT_4:9;
5581 = 67*83 + 20; hence not 67 divides 5581 by NAT_4:9;
5581 = 71*78 + 43; hence not 71 divides 5581 by NAT_4:9;
5581 = 73*76 + 33; hence not 73 divides 5581 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5581 & n is prime
holds not n divides 5581 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5591 is prime
proof
now
5591 = 2*2795 + 1; hence not 2 divides 5591 by NAT_4:9;
5591 = 3*1863 + 2; hence not 3 divides 5591 by NAT_4:9;
5591 = 5*1118 + 1; hence not 5 divides 5591 by NAT_4:9;
5591 = 7*798 + 5; hence not 7 divides 5591 by NAT_4:9;
5591 = 11*508 + 3; hence not 11 divides 5591 by NAT_4:9;
5591 = 13*430 + 1; hence not 13 divides 5591 by NAT_4:9;
5591 = 17*328 + 15; hence not 17 divides 5591 by NAT_4:9;
5591 = 19*294 + 5; hence not 19 divides 5591 by NAT_4:9;
5591 = 23*243 + 2; hence not 23 divides 5591 by NAT_4:9;
5591 = 29*192 + 23; hence not 29 divides 5591 by NAT_4:9;
5591 = 31*180 + 11; hence not 31 divides 5591 by NAT_4:9;
5591 = 37*151 + 4; hence not 37 divides 5591 by NAT_4:9;
5591 = 41*136 + 15; hence not 41 divides 5591 by NAT_4:9;
5591 = 43*130 + 1; hence not 43 divides 5591 by NAT_4:9;
5591 = 47*118 + 45; hence not 47 divides 5591 by NAT_4:9;
5591 = 53*105 + 26; hence not 53 divides 5591 by NAT_4:9;
5591 = 59*94 + 45; hence not 59 divides 5591 by NAT_4:9;
5591 = 61*91 + 40; hence not 61 divides 5591 by NAT_4:9;
5591 = 67*83 + 30; hence not 67 divides 5591 by NAT_4:9;
5591 = 71*78 + 53; hence not 71 divides 5591 by NAT_4:9;
5591 = 73*76 + 43; hence not 73 divides 5591 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5591 & n is prime
holds not n divides 5591 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 31
theorem
5623 is prime
proof
now
5623 = 2*2811 + 1; hence not 2 divides 5623 by NAT_4:9;
5623 = 3*1874 + 1; hence not 3 divides 5623 by NAT_4:9;
5623 = 5*1124 + 3; hence not 5 divides 5623 by NAT_4:9;
5623 = 7*803 + 2; hence not 7 divides 5623 by NAT_4:9;
5623 = 11*511 + 2; hence not 11 divides 5623 by NAT_4:9;
5623 = 13*432 + 7; hence not 13 divides 5623 by NAT_4:9;
5623 = 17*330 + 13; hence not 17 divides 5623 by NAT_4:9;
5623 = 19*295 + 18; hence not 19 divides 5623 by NAT_4:9;
5623 = 23*244 + 11; hence not 23 divides 5623 by NAT_4:9;
5623 = 29*193 + 26; hence not 29 divides 5623 by NAT_4:9;
5623 = 31*181 + 12; hence not 31 divides 5623 by NAT_4:9;
5623 = 37*151 + 36; hence not 37 divides 5623 by NAT_4:9;
5623 = 41*137 + 6; hence not 41 divides 5623 by NAT_4:9;
5623 = 43*130 + 33; hence not 43 divides 5623 by NAT_4:9;
5623 = 47*119 + 30; hence not 47 divides 5623 by NAT_4:9;
5623 = 53*106 + 5; hence not 53 divides 5623 by NAT_4:9;
5623 = 59*95 + 18; hence not 59 divides 5623 by NAT_4:9;
5623 = 61*92 + 11; hence not 61 divides 5623 by NAT_4:9;
5623 = 67*83 + 62; hence not 67 divides 5623 by NAT_4:9;
5623 = 71*79 + 14; hence not 71 divides 5623 by NAT_4:9;
5623 = 73*77 + 2; hence not 73 divides 5623 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5623 & n is prime
holds not n divides 5623 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
5639 is prime
proof
now
5639 = 2*2819 + 1; hence not 2 divides 5639 by NAT_4:9;
5639 = 3*1879 + 2; hence not 3 divides 5639 by NAT_4:9;
5639 = 5*1127 + 4; hence not 5 divides 5639 by NAT_4:9;
5639 = 7*805 + 4; hence not 7 divides 5639 by NAT_4:9;
5639 = 11*512 + 7; hence not 11 divides 5639 by NAT_4:9;
5639 = 13*433 + 10; hence not 13 divides 5639 by NAT_4:9;
5639 = 17*331 + 12; hence not 17 divides 5639 by NAT_4:9;
5639 = 19*296 + 15; hence not 19 divides 5639 by NAT_4:9;
5639 = 23*245 + 4; hence not 23 divides 5639 by NAT_4:9;
5639 = 29*194 + 13; hence not 29 divides 5639 by NAT_4:9;
5639 = 31*181 + 28; hence not 31 divides 5639 by NAT_4:9;
5639 = 37*152 + 15; hence not 37 divides 5639 by NAT_4:9;
5639 = 41*137 + 22; hence not 41 divides 5639 by NAT_4:9;
5639 = 43*131 + 6; hence not 43 divides 5639 by NAT_4:9;
5639 = 47*119 + 46; hence not 47 divides 5639 by NAT_4:9;
5639 = 53*106 + 21; hence not 53 divides 5639 by NAT_4:9;
5639 = 59*95 + 34; hence not 59 divides 5639 by NAT_4:9;
5639 = 61*92 + 27; hence not 61 divides 5639 by NAT_4:9;
5639 = 67*84 + 11; hence not 67 divides 5639 by NAT_4:9;
5639 = 71*79 + 30; hence not 71 divides 5639 by NAT_4:9;
5639 = 73*77 + 18; hence not 73 divides 5639 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5639 & n is prime
holds not n divides 5639 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5641 is prime
proof
now
5641 = 2*2820 + 1; hence not 2 divides 5641 by NAT_4:9;
5641 = 3*1880 + 1; hence not 3 divides 5641 by NAT_4:9;
5641 = 5*1128 + 1; hence not 5 divides 5641 by NAT_4:9;
5641 = 7*805 + 6; hence not 7 divides 5641 by NAT_4:9;
5641 = 11*512 + 9; hence not 11 divides 5641 by NAT_4:9;
5641 = 13*433 + 12; hence not 13 divides 5641 by NAT_4:9;
5641 = 17*331 + 14; hence not 17 divides 5641 by NAT_4:9;
5641 = 19*296 + 17; hence not 19 divides 5641 by NAT_4:9;
5641 = 23*245 + 6; hence not 23 divides 5641 by NAT_4:9;
5641 = 29*194 + 15; hence not 29 divides 5641 by NAT_4:9;
5641 = 31*181 + 30; hence not 31 divides 5641 by NAT_4:9;
5641 = 37*152 + 17; hence not 37 divides 5641 by NAT_4:9;
5641 = 41*137 + 24; hence not 41 divides 5641 by NAT_4:9;
5641 = 43*131 + 8; hence not 43 divides 5641 by NAT_4:9;
5641 = 47*120 + 1; hence not 47 divides 5641 by NAT_4:9;
5641 = 53*106 + 23; hence not 53 divides 5641 by NAT_4:9;
5641 = 59*95 + 36; hence not 59 divides 5641 by NAT_4:9;
5641 = 61*92 + 29; hence not 61 divides 5641 by NAT_4:9;
5641 = 67*84 + 13; hence not 67 divides 5641 by NAT_4:9;
5641 = 71*79 + 32; hence not 71 divides 5641 by NAT_4:9;
5641 = 73*77 + 20; hence not 73 divides 5641 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5641 & n is prime
holds not n divides 5641 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5647 is prime
proof
now
5647 = 2*2823 + 1; hence not 2 divides 5647 by NAT_4:9;
5647 = 3*1882 + 1; hence not 3 divides 5647 by NAT_4:9;
5647 = 5*1129 + 2; hence not 5 divides 5647 by NAT_4:9;
5647 = 7*806 + 5; hence not 7 divides 5647 by NAT_4:9;
5647 = 11*513 + 4; hence not 11 divides 5647 by NAT_4:9;
5647 = 13*434 + 5; hence not 13 divides 5647 by NAT_4:9;
5647 = 17*332 + 3; hence not 17 divides 5647 by NAT_4:9;
5647 = 19*297 + 4; hence not 19 divides 5647 by NAT_4:9;
5647 = 23*245 + 12; hence not 23 divides 5647 by NAT_4:9;
5647 = 29*194 + 21; hence not 29 divides 5647 by NAT_4:9;
5647 = 31*182 + 5; hence not 31 divides 5647 by NAT_4:9;
5647 = 37*152 + 23; hence not 37 divides 5647 by NAT_4:9;
5647 = 41*137 + 30; hence not 41 divides 5647 by NAT_4:9;
5647 = 43*131 + 14; hence not 43 divides 5647 by NAT_4:9;
5647 = 47*120 + 7; hence not 47 divides 5647 by NAT_4:9;
5647 = 53*106 + 29; hence not 53 divides 5647 by NAT_4:9;
5647 = 59*95 + 42; hence not 59 divides 5647 by NAT_4:9;
5647 = 61*92 + 35; hence not 61 divides 5647 by NAT_4:9;
5647 = 67*84 + 19; hence not 67 divides 5647 by NAT_4:9;
5647 = 71*79 + 38; hence not 71 divides 5647 by NAT_4:9;
5647 = 73*77 + 26; hence not 73 divides 5647 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5647 & n is prime
holds not n divides 5647 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5651 is prime
proof
now
5651 = 2*2825 + 1; hence not 2 divides 5651 by NAT_4:9;
5651 = 3*1883 + 2; hence not 3 divides 5651 by NAT_4:9;
5651 = 5*1130 + 1; hence not 5 divides 5651 by NAT_4:9;
5651 = 7*807 + 2; hence not 7 divides 5651 by NAT_4:9;
5651 = 11*513 + 8; hence not 11 divides 5651 by NAT_4:9;
5651 = 13*434 + 9; hence not 13 divides 5651 by NAT_4:9;
5651 = 17*332 + 7; hence not 17 divides 5651 by NAT_4:9;
5651 = 19*297 + 8; hence not 19 divides 5651 by NAT_4:9;
5651 = 23*245 + 16; hence not 23 divides 5651 by NAT_4:9;
5651 = 29*194 + 25; hence not 29 divides 5651 by NAT_4:9;
5651 = 31*182 + 9; hence not 31 divides 5651 by NAT_4:9;
5651 = 37*152 + 27; hence not 37 divides 5651 by NAT_4:9;
5651 = 41*137 + 34; hence not 41 divides 5651 by NAT_4:9;
5651 = 43*131 + 18; hence not 43 divides 5651 by NAT_4:9;
5651 = 47*120 + 11; hence not 47 divides 5651 by NAT_4:9;
5651 = 53*106 + 33; hence not 53 divides 5651 by NAT_4:9;
5651 = 59*95 + 46; hence not 59 divides 5651 by NAT_4:9;
5651 = 61*92 + 39; hence not 61 divides 5651 by NAT_4:9;
5651 = 67*84 + 23; hence not 67 divides 5651 by NAT_4:9;
5651 = 71*79 + 42; hence not 71 divides 5651 by NAT_4:9;
5651 = 73*77 + 30; hence not 73 divides 5651 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5651 & n is prime
holds not n divides 5651 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5653 is prime
proof
now
5653 = 2*2826 + 1; hence not 2 divides 5653 by NAT_4:9;
5653 = 3*1884 + 1; hence not 3 divides 5653 by NAT_4:9;
5653 = 5*1130 + 3; hence not 5 divides 5653 by NAT_4:9;
5653 = 7*807 + 4; hence not 7 divides 5653 by NAT_4:9;
5653 = 11*513 + 10; hence not 11 divides 5653 by NAT_4:9;
5653 = 13*434 + 11; hence not 13 divides 5653 by NAT_4:9;
5653 = 17*332 + 9; hence not 17 divides 5653 by NAT_4:9;
5653 = 19*297 + 10; hence not 19 divides 5653 by NAT_4:9;
5653 = 23*245 + 18; hence not 23 divides 5653 by NAT_4:9;
5653 = 29*194 + 27; hence not 29 divides 5653 by NAT_4:9;
5653 = 31*182 + 11; hence not 31 divides 5653 by NAT_4:9;
5653 = 37*152 + 29; hence not 37 divides 5653 by NAT_4:9;
5653 = 41*137 + 36; hence not 41 divides 5653 by NAT_4:9;
5653 = 43*131 + 20; hence not 43 divides 5653 by NAT_4:9;
5653 = 47*120 + 13; hence not 47 divides 5653 by NAT_4:9;
5653 = 53*106 + 35; hence not 53 divides 5653 by NAT_4:9;
5653 = 59*95 + 48; hence not 59 divides 5653 by NAT_4:9;
5653 = 61*92 + 41; hence not 61 divides 5653 by NAT_4:9;
5653 = 67*84 + 25; hence not 67 divides 5653 by NAT_4:9;
5653 = 71*79 + 44; hence not 71 divides 5653 by NAT_4:9;
5653 = 73*77 + 32; hence not 73 divides 5653 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5653 & n is prime
holds not n divides 5653 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5657 is prime
proof
now
5657 = 2*2828 + 1; hence not 2 divides 5657 by NAT_4:9;
5657 = 3*1885 + 2; hence not 3 divides 5657 by NAT_4:9;
5657 = 5*1131 + 2; hence not 5 divides 5657 by NAT_4:9;
5657 = 7*808 + 1; hence not 7 divides 5657 by NAT_4:9;
5657 = 11*514 + 3; hence not 11 divides 5657 by NAT_4:9;
5657 = 13*435 + 2; hence not 13 divides 5657 by NAT_4:9;
5657 = 17*332 + 13; hence not 17 divides 5657 by NAT_4:9;
5657 = 19*297 + 14; hence not 19 divides 5657 by NAT_4:9;
5657 = 23*245 + 22; hence not 23 divides 5657 by NAT_4:9;
5657 = 29*195 + 2; hence not 29 divides 5657 by NAT_4:9;
5657 = 31*182 + 15; hence not 31 divides 5657 by NAT_4:9;
5657 = 37*152 + 33; hence not 37 divides 5657 by NAT_4:9;
5657 = 41*137 + 40; hence not 41 divides 5657 by NAT_4:9;
5657 = 43*131 + 24; hence not 43 divides 5657 by NAT_4:9;
5657 = 47*120 + 17; hence not 47 divides 5657 by NAT_4:9;
5657 = 53*106 + 39; hence not 53 divides 5657 by NAT_4:9;
5657 = 59*95 + 52; hence not 59 divides 5657 by NAT_4:9;
5657 = 61*92 + 45; hence not 61 divides 5657 by NAT_4:9;
5657 = 67*84 + 29; hence not 67 divides 5657 by NAT_4:9;
5657 = 71*79 + 48; hence not 71 divides 5657 by NAT_4:9;
5657 = 73*77 + 36; hence not 73 divides 5657 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5657 & n is prime
holds not n divides 5657 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5659 is prime
proof
now
5659 = 2*2829 + 1; hence not 2 divides 5659 by NAT_4:9;
5659 = 3*1886 + 1; hence not 3 divides 5659 by NAT_4:9;
5659 = 5*1131 + 4; hence not 5 divides 5659 by NAT_4:9;
5659 = 7*808 + 3; hence not 7 divides 5659 by NAT_4:9;
5659 = 11*514 + 5; hence not 11 divides 5659 by NAT_4:9;
5659 = 13*435 + 4; hence not 13 divides 5659 by NAT_4:9;
5659 = 17*332 + 15; hence not 17 divides 5659 by NAT_4:9;
5659 = 19*297 + 16; hence not 19 divides 5659 by NAT_4:9;
5659 = 23*246 + 1; hence not 23 divides 5659 by NAT_4:9;
5659 = 29*195 + 4; hence not 29 divides 5659 by NAT_4:9;
5659 = 31*182 + 17; hence not 31 divides 5659 by NAT_4:9;
5659 = 37*152 + 35; hence not 37 divides 5659 by NAT_4:9;
5659 = 41*138 + 1; hence not 41 divides 5659 by NAT_4:9;
5659 = 43*131 + 26; hence not 43 divides 5659 by NAT_4:9;
5659 = 47*120 + 19; hence not 47 divides 5659 by NAT_4:9;
5659 = 53*106 + 41; hence not 53 divides 5659 by NAT_4:9;
5659 = 59*95 + 54; hence not 59 divides 5659 by NAT_4:9;
5659 = 61*92 + 47; hence not 61 divides 5659 by NAT_4:9;
5659 = 67*84 + 31; hence not 67 divides 5659 by NAT_4:9;
5659 = 71*79 + 50; hence not 71 divides 5659 by NAT_4:9;
5659 = 73*77 + 38; hence not 73 divides 5659 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5659 & n is prime
holds not n divides 5659 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5669 is prime
proof
now
5669 = 2*2834 + 1; hence not 2 divides 5669 by NAT_4:9;
5669 = 3*1889 + 2; hence not 3 divides 5669 by NAT_4:9;
5669 = 5*1133 + 4; hence not 5 divides 5669 by NAT_4:9;
5669 = 7*809 + 6; hence not 7 divides 5669 by NAT_4:9;
5669 = 11*515 + 4; hence not 11 divides 5669 by NAT_4:9;
5669 = 13*436 + 1; hence not 13 divides 5669 by NAT_4:9;
5669 = 17*333 + 8; hence not 17 divides 5669 by NAT_4:9;
5669 = 19*298 + 7; hence not 19 divides 5669 by NAT_4:9;
5669 = 23*246 + 11; hence not 23 divides 5669 by NAT_4:9;
5669 = 29*195 + 14; hence not 29 divides 5669 by NAT_4:9;
5669 = 31*182 + 27; hence not 31 divides 5669 by NAT_4:9;
5669 = 37*153 + 8; hence not 37 divides 5669 by NAT_4:9;
5669 = 41*138 + 11; hence not 41 divides 5669 by NAT_4:9;
5669 = 43*131 + 36; hence not 43 divides 5669 by NAT_4:9;
5669 = 47*120 + 29; hence not 47 divides 5669 by NAT_4:9;
5669 = 53*106 + 51; hence not 53 divides 5669 by NAT_4:9;
5669 = 59*96 + 5; hence not 59 divides 5669 by NAT_4:9;
5669 = 61*92 + 57; hence not 61 divides 5669 by NAT_4:9;
5669 = 67*84 + 41; hence not 67 divides 5669 by NAT_4:9;
5669 = 71*79 + 60; hence not 71 divides 5669 by NAT_4:9;
5669 = 73*77 + 48; hence not 73 divides 5669 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5669 & n is prime
holds not n divides 5669 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
5683 is prime
proof
now
5683 = 2*2841 + 1; hence not 2 divides 5683 by NAT_4:9;
5683 = 3*1894 + 1; hence not 3 divides 5683 by NAT_4:9;
5683 = 5*1136 + 3; hence not 5 divides 5683 by NAT_4:9;
5683 = 7*811 + 6; hence not 7 divides 5683 by NAT_4:9;
5683 = 11*516 + 7; hence not 11 divides 5683 by NAT_4:9;
5683 = 13*437 + 2; hence not 13 divides 5683 by NAT_4:9;
5683 = 17*334 + 5; hence not 17 divides 5683 by NAT_4:9;
5683 = 19*299 + 2; hence not 19 divides 5683 by NAT_4:9;
5683 = 23*247 + 2; hence not 23 divides 5683 by NAT_4:9;
5683 = 29*195 + 28; hence not 29 divides 5683 by NAT_4:9;
5683 = 31*183 + 10; hence not 31 divides 5683 by NAT_4:9;
5683 = 37*153 + 22; hence not 37 divides 5683 by NAT_4:9;
5683 = 41*138 + 25; hence not 41 divides 5683 by NAT_4:9;
5683 = 43*132 + 7; hence not 43 divides 5683 by NAT_4:9;
5683 = 47*120 + 43; hence not 47 divides 5683 by NAT_4:9;
5683 = 53*107 + 12; hence not 53 divides 5683 by NAT_4:9;
5683 = 59*96 + 19; hence not 59 divides 5683 by NAT_4:9;
5683 = 61*93 + 10; hence not 61 divides 5683 by NAT_4:9;
5683 = 67*84 + 55; hence not 67 divides 5683 by NAT_4:9;
5683 = 71*80 + 3; hence not 71 divides 5683 by NAT_4:9;
5683 = 73*77 + 62; hence not 73 divides 5683 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5683 & n is prime
holds not n divides 5683 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5689 is prime
proof
now
5689 = 2*2844 + 1; hence not 2 divides 5689 by NAT_4:9;
5689 = 3*1896 + 1; hence not 3 divides 5689 by NAT_4:9;
5689 = 5*1137 + 4; hence not 5 divides 5689 by NAT_4:9;
5689 = 7*812 + 5; hence not 7 divides 5689 by NAT_4:9;
5689 = 11*517 + 2; hence not 11 divides 5689 by NAT_4:9;
5689 = 13*437 + 8; hence not 13 divides 5689 by NAT_4:9;
5689 = 17*334 + 11; hence not 17 divides 5689 by NAT_4:9;
5689 = 19*299 + 8; hence not 19 divides 5689 by NAT_4:9;
5689 = 23*247 + 8; hence not 23 divides 5689 by NAT_4:9;
5689 = 29*196 + 5; hence not 29 divides 5689 by NAT_4:9;
5689 = 31*183 + 16; hence not 31 divides 5689 by NAT_4:9;
5689 = 37*153 + 28; hence not 37 divides 5689 by NAT_4:9;
5689 = 41*138 + 31; hence not 41 divides 5689 by NAT_4:9;
5689 = 43*132 + 13; hence not 43 divides 5689 by NAT_4:9;
5689 = 47*121 + 2; hence not 47 divides 5689 by NAT_4:9;
5689 = 53*107 + 18; hence not 53 divides 5689 by NAT_4:9;
5689 = 59*96 + 25; hence not 59 divides 5689 by NAT_4:9;
5689 = 61*93 + 16; hence not 61 divides 5689 by NAT_4:9;
5689 = 67*84 + 61; hence not 67 divides 5689 by NAT_4:9;
5689 = 71*80 + 9; hence not 71 divides 5689 by NAT_4:9;
5689 = 73*77 + 68; hence not 73 divides 5689 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5689 & n is prime
holds not n divides 5689 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5693 is prime
proof
now
5693 = 2*2846 + 1; hence not 2 divides 5693 by NAT_4:9;
5693 = 3*1897 + 2; hence not 3 divides 5693 by NAT_4:9;
5693 = 5*1138 + 3; hence not 5 divides 5693 by NAT_4:9;
5693 = 7*813 + 2; hence not 7 divides 5693 by NAT_4:9;
5693 = 11*517 + 6; hence not 11 divides 5693 by NAT_4:9;
5693 = 13*437 + 12; hence not 13 divides 5693 by NAT_4:9;
5693 = 17*334 + 15; hence not 17 divides 5693 by NAT_4:9;
5693 = 19*299 + 12; hence not 19 divides 5693 by NAT_4:9;
5693 = 23*247 + 12; hence not 23 divides 5693 by NAT_4:9;
5693 = 29*196 + 9; hence not 29 divides 5693 by NAT_4:9;
5693 = 31*183 + 20; hence not 31 divides 5693 by NAT_4:9;
5693 = 37*153 + 32; hence not 37 divides 5693 by NAT_4:9;
5693 = 41*138 + 35; hence not 41 divides 5693 by NAT_4:9;
5693 = 43*132 + 17; hence not 43 divides 5693 by NAT_4:9;
5693 = 47*121 + 6; hence not 47 divides 5693 by NAT_4:9;
5693 = 53*107 + 22; hence not 53 divides 5693 by NAT_4:9;
5693 = 59*96 + 29; hence not 59 divides 5693 by NAT_4:9;
5693 = 61*93 + 20; hence not 61 divides 5693 by NAT_4:9;
5693 = 67*84 + 65; hence not 67 divides 5693 by NAT_4:9;
5693 = 71*80 + 13; hence not 71 divides 5693 by NAT_4:9;
5693 = 73*77 + 72; hence not 73 divides 5693 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5693 & n is prime
holds not n divides 5693 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5701 is prime
proof
now
5701 = 2*2850 + 1; hence not 2 divides 5701 by NAT_4:9;
5701 = 3*1900 + 1; hence not 3 divides 5701 by NAT_4:9;
5701 = 5*1140 + 1; hence not 5 divides 5701 by NAT_4:9;
5701 = 7*814 + 3; hence not 7 divides 5701 by NAT_4:9;
5701 = 11*518 + 3; hence not 11 divides 5701 by NAT_4:9;
5701 = 13*438 + 7; hence not 13 divides 5701 by NAT_4:9;
5701 = 17*335 + 6; hence not 17 divides 5701 by NAT_4:9;
5701 = 19*300 + 1; hence not 19 divides 5701 by NAT_4:9;
5701 = 23*247 + 20; hence not 23 divides 5701 by NAT_4:9;
5701 = 29*196 + 17; hence not 29 divides 5701 by NAT_4:9;
5701 = 31*183 + 28; hence not 31 divides 5701 by NAT_4:9;
5701 = 37*154 + 3; hence not 37 divides 5701 by NAT_4:9;
5701 = 41*139 + 2; hence not 41 divides 5701 by NAT_4:9;
5701 = 43*132 + 25; hence not 43 divides 5701 by NAT_4:9;
5701 = 47*121 + 14; hence not 47 divides 5701 by NAT_4:9;
5701 = 53*107 + 30; hence not 53 divides 5701 by NAT_4:9;
5701 = 59*96 + 37; hence not 59 divides 5701 by NAT_4:9;
5701 = 61*93 + 28; hence not 61 divides 5701 by NAT_4:9;
5701 = 67*85 + 6; hence not 67 divides 5701 by NAT_4:9;
5701 = 71*80 + 21; hence not 71 divides 5701 by NAT_4:9;
5701 = 73*78 + 7; hence not 73 divides 5701 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5701 & n is prime
holds not n divides 5701 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5711 is prime
proof
now
5711 = 2*2855 + 1; hence not 2 divides 5711 by NAT_4:9;
5711 = 3*1903 + 2; hence not 3 divides 5711 by NAT_4:9;
5711 = 5*1142 + 1; hence not 5 divides 5711 by NAT_4:9;
5711 = 7*815 + 6; hence not 7 divides 5711 by NAT_4:9;
5711 = 11*519 + 2; hence not 11 divides 5711 by NAT_4:9;
5711 = 13*439 + 4; hence not 13 divides 5711 by NAT_4:9;
5711 = 17*335 + 16; hence not 17 divides 5711 by NAT_4:9;
5711 = 19*300 + 11; hence not 19 divides 5711 by NAT_4:9;
5711 = 23*248 + 7; hence not 23 divides 5711 by NAT_4:9;
5711 = 29*196 + 27; hence not 29 divides 5711 by NAT_4:9;
5711 = 31*184 + 7; hence not 31 divides 5711 by NAT_4:9;
5711 = 37*154 + 13; hence not 37 divides 5711 by NAT_4:9;
5711 = 41*139 + 12; hence not 41 divides 5711 by NAT_4:9;
5711 = 43*132 + 35; hence not 43 divides 5711 by NAT_4:9;
5711 = 47*121 + 24; hence not 47 divides 5711 by NAT_4:9;
5711 = 53*107 + 40; hence not 53 divides 5711 by NAT_4:9;
5711 = 59*96 + 47; hence not 59 divides 5711 by NAT_4:9;
5711 = 61*93 + 38; hence not 61 divides 5711 by NAT_4:9;
5711 = 67*85 + 16; hence not 67 divides 5711 by NAT_4:9;
5711 = 71*80 + 31; hence not 71 divides 5711 by NAT_4:9;
5711 = 73*78 + 17; hence not 73 divides 5711 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5711 & n is prime
holds not n divides 5711 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5717 is prime
proof
now
5717 = 2*2858 + 1; hence not 2 divides 5717 by NAT_4:9;
5717 = 3*1905 + 2; hence not 3 divides 5717 by NAT_4:9;
5717 = 5*1143 + 2; hence not 5 divides 5717 by NAT_4:9;
5717 = 7*816 + 5; hence not 7 divides 5717 by NAT_4:9;
5717 = 11*519 + 8; hence not 11 divides 5717 by NAT_4:9;
5717 = 13*439 + 10; hence not 13 divides 5717 by NAT_4:9;
5717 = 17*336 + 5; hence not 17 divides 5717 by NAT_4:9;
5717 = 19*300 + 17; hence not 19 divides 5717 by NAT_4:9;
5717 = 23*248 + 13; hence not 23 divides 5717 by NAT_4:9;
5717 = 29*197 + 4; hence not 29 divides 5717 by NAT_4:9;
5717 = 31*184 + 13; hence not 31 divides 5717 by NAT_4:9;
5717 = 37*154 + 19; hence not 37 divides 5717 by NAT_4:9;
5717 = 41*139 + 18; hence not 41 divides 5717 by NAT_4:9;
5717 = 43*132 + 41; hence not 43 divides 5717 by NAT_4:9;
5717 = 47*121 + 30; hence not 47 divides 5717 by NAT_4:9;
5717 = 53*107 + 46; hence not 53 divides 5717 by NAT_4:9;
5717 = 59*96 + 53; hence not 59 divides 5717 by NAT_4:9;
5717 = 61*93 + 44; hence not 61 divides 5717 by NAT_4:9;
5717 = 67*85 + 22; hence not 67 divides 5717 by NAT_4:9;
5717 = 71*80 + 37; hence not 71 divides 5717 by NAT_4:9;
5717 = 73*78 + 23; hence not 73 divides 5717 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5717 & n is prime
holds not n divides 5717 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
5737 is prime
proof
now
5737 = 2*2868 + 1; hence not 2 divides 5737 by NAT_4:9;
5737 = 3*1912 + 1; hence not 3 divides 5737 by NAT_4:9;
5737 = 5*1147 + 2; hence not 5 divides 5737 by NAT_4:9;
5737 = 7*819 + 4; hence not 7 divides 5737 by NAT_4:9;
5737 = 11*521 + 6; hence not 11 divides 5737 by NAT_4:9;
5737 = 13*441 + 4; hence not 13 divides 5737 by NAT_4:9;
5737 = 17*337 + 8; hence not 17 divides 5737 by NAT_4:9;
5737 = 19*301 + 18; hence not 19 divides 5737 by NAT_4:9;
5737 = 23*249 + 10; hence not 23 divides 5737 by NAT_4:9;
5737 = 29*197 + 24; hence not 29 divides 5737 by NAT_4:9;
5737 = 31*185 + 2; hence not 31 divides 5737 by NAT_4:9;
5737 = 37*155 + 2; hence not 37 divides 5737 by NAT_4:9;
5737 = 41*139 + 38; hence not 41 divides 5737 by NAT_4:9;
5737 = 43*133 + 18; hence not 43 divides 5737 by NAT_4:9;
5737 = 47*122 + 3; hence not 47 divides 5737 by NAT_4:9;
5737 = 53*108 + 13; hence not 53 divides 5737 by NAT_4:9;
5737 = 59*97 + 14; hence not 59 divides 5737 by NAT_4:9;
5737 = 61*94 + 3; hence not 61 divides 5737 by NAT_4:9;
5737 = 67*85 + 42; hence not 67 divides 5737 by NAT_4:9;
5737 = 71*80 + 57; hence not 71 divides 5737 by NAT_4:9;
5737 = 73*78 + 43; hence not 73 divides 5737 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5737 & n is prime
holds not n divides 5737 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5741 is prime
proof
now
5741 = 2*2870 + 1; hence not 2 divides 5741 by NAT_4:9;
5741 = 3*1913 + 2; hence not 3 divides 5741 by NAT_4:9;
5741 = 5*1148 + 1; hence not 5 divides 5741 by NAT_4:9;
5741 = 7*820 + 1; hence not 7 divides 5741 by NAT_4:9;
5741 = 11*521 + 10; hence not 11 divides 5741 by NAT_4:9;
5741 = 13*441 + 8; hence not 13 divides 5741 by NAT_4:9;
5741 = 17*337 + 12; hence not 17 divides 5741 by NAT_4:9;
5741 = 19*302 + 3; hence not 19 divides 5741 by NAT_4:9;
5741 = 23*249 + 14; hence not 23 divides 5741 by NAT_4:9;
5741 = 29*197 + 28; hence not 29 divides 5741 by NAT_4:9;
5741 = 31*185 + 6; hence not 31 divides 5741 by NAT_4:9;
5741 = 37*155 + 6; hence not 37 divides 5741 by NAT_4:9;
5741 = 41*140 + 1; hence not 41 divides 5741 by NAT_4:9;
5741 = 43*133 + 22; hence not 43 divides 5741 by NAT_4:9;
5741 = 47*122 + 7; hence not 47 divides 5741 by NAT_4:9;
5741 = 53*108 + 17; hence not 53 divides 5741 by NAT_4:9;
5741 = 59*97 + 18; hence not 59 divides 5741 by NAT_4:9;
5741 = 61*94 + 7; hence not 61 divides 5741 by NAT_4:9;
5741 = 67*85 + 46; hence not 67 divides 5741 by NAT_4:9;
5741 = 71*80 + 61; hence not 71 divides 5741 by NAT_4:9;
5741 = 73*78 + 47; hence not 73 divides 5741 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5741 & n is prime
holds not n divides 5741 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5743 is prime
proof
now
5743 = 2*2871 + 1; hence not 2 divides 5743 by NAT_4:9;
5743 = 3*1914 + 1; hence not 3 divides 5743 by NAT_4:9;
5743 = 5*1148 + 3; hence not 5 divides 5743 by NAT_4:9;
5743 = 7*820 + 3; hence not 7 divides 5743 by NAT_4:9;
5743 = 11*522 + 1; hence not 11 divides 5743 by NAT_4:9;
5743 = 13*441 + 10; hence not 13 divides 5743 by NAT_4:9;
5743 = 17*337 + 14; hence not 17 divides 5743 by NAT_4:9;
5743 = 19*302 + 5; hence not 19 divides 5743 by NAT_4:9;
5743 = 23*249 + 16; hence not 23 divides 5743 by NAT_4:9;
5743 = 29*198 + 1; hence not 29 divides 5743 by NAT_4:9;
5743 = 31*185 + 8; hence not 31 divides 5743 by NAT_4:9;
5743 = 37*155 + 8; hence not 37 divides 5743 by NAT_4:9;
5743 = 41*140 + 3; hence not 41 divides 5743 by NAT_4:9;
5743 = 43*133 + 24; hence not 43 divides 5743 by NAT_4:9;
5743 = 47*122 + 9; hence not 47 divides 5743 by NAT_4:9;
5743 = 53*108 + 19; hence not 53 divides 5743 by NAT_4:9;
5743 = 59*97 + 20; hence not 59 divides 5743 by NAT_4:9;
5743 = 61*94 + 9; hence not 61 divides 5743 by NAT_4:9;
5743 = 67*85 + 48; hence not 67 divides 5743 by NAT_4:9;
5743 = 71*80 + 63; hence not 71 divides 5743 by NAT_4:9;
5743 = 73*78 + 49; hence not 73 divides 5743 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5743 & n is prime
holds not n divides 5743 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5749 is prime
proof
now
5749 = 2*2874 + 1; hence not 2 divides 5749 by NAT_4:9;
5749 = 3*1916 + 1; hence not 3 divides 5749 by NAT_4:9;
5749 = 5*1149 + 4; hence not 5 divides 5749 by NAT_4:9;
5749 = 7*821 + 2; hence not 7 divides 5749 by NAT_4:9;
5749 = 11*522 + 7; hence not 11 divides 5749 by NAT_4:9;
5749 = 13*442 + 3; hence not 13 divides 5749 by NAT_4:9;
5749 = 17*338 + 3; hence not 17 divides 5749 by NAT_4:9;
5749 = 19*302 + 11; hence not 19 divides 5749 by NAT_4:9;
5749 = 23*249 + 22; hence not 23 divides 5749 by NAT_4:9;
5749 = 29*198 + 7; hence not 29 divides 5749 by NAT_4:9;
5749 = 31*185 + 14; hence not 31 divides 5749 by NAT_4:9;
5749 = 37*155 + 14; hence not 37 divides 5749 by NAT_4:9;
5749 = 41*140 + 9; hence not 41 divides 5749 by NAT_4:9;
5749 = 43*133 + 30; hence not 43 divides 5749 by NAT_4:9;
5749 = 47*122 + 15; hence not 47 divides 5749 by NAT_4:9;
5749 = 53*108 + 25; hence not 53 divides 5749 by NAT_4:9;
5749 = 59*97 + 26; hence not 59 divides 5749 by NAT_4:9;
5749 = 61*94 + 15; hence not 61 divides 5749 by NAT_4:9;
5749 = 67*85 + 54; hence not 67 divides 5749 by NAT_4:9;
5749 = 71*80 + 69; hence not 71 divides 5749 by NAT_4:9;
5749 = 73*78 + 55; hence not 73 divides 5749 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5749 & n is prime
holds not n divides 5749 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
5779 is prime
proof
now
5779 = 2*2889 + 1; hence not 2 divides 5779 by NAT_4:9;
5779 = 3*1926 + 1; hence not 3 divides 5779 by NAT_4:9;
5779 = 5*1155 + 4; hence not 5 divides 5779 by NAT_4:9;
5779 = 7*825 + 4; hence not 7 divides 5779 by NAT_4:9;
5779 = 11*525 + 4; hence not 11 divides 5779 by NAT_4:9;
5779 = 13*444 + 7; hence not 13 divides 5779 by NAT_4:9;
5779 = 17*339 + 16; hence not 17 divides 5779 by NAT_4:9;
5779 = 19*304 + 3; hence not 19 divides 5779 by NAT_4:9;
5779 = 23*251 + 6; hence not 23 divides 5779 by NAT_4:9;
5779 = 29*199 + 8; hence not 29 divides 5779 by NAT_4:9;
5779 = 31*186 + 13; hence not 31 divides 5779 by NAT_4:9;
5779 = 37*156 + 7; hence not 37 divides 5779 by NAT_4:9;
5779 = 41*140 + 39; hence not 41 divides 5779 by NAT_4:9;
5779 = 43*134 + 17; hence not 43 divides 5779 by NAT_4:9;
5779 = 47*122 + 45; hence not 47 divides 5779 by NAT_4:9;
5779 = 53*109 + 2; hence not 53 divides 5779 by NAT_4:9;
5779 = 59*97 + 56; hence not 59 divides 5779 by NAT_4:9;
5779 = 61*94 + 45; hence not 61 divides 5779 by NAT_4:9;
5779 = 67*86 + 17; hence not 67 divides 5779 by NAT_4:9;
5779 = 71*81 + 28; hence not 71 divides 5779 by NAT_4:9;
5779 = 73*79 + 12; hence not 73 divides 5779 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5779 & n is prime
holds not n divides 5779 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5783 is prime
proof
now
5783 = 2*2891 + 1; hence not 2 divides 5783 by NAT_4:9;
5783 = 3*1927 + 2; hence not 3 divides 5783 by NAT_4:9;
5783 = 5*1156 + 3; hence not 5 divides 5783 by NAT_4:9;
5783 = 7*826 + 1; hence not 7 divides 5783 by NAT_4:9;
5783 = 11*525 + 8; hence not 11 divides 5783 by NAT_4:9;
5783 = 13*444 + 11; hence not 13 divides 5783 by NAT_4:9;
5783 = 17*340 + 3; hence not 17 divides 5783 by NAT_4:9;
5783 = 19*304 + 7; hence not 19 divides 5783 by NAT_4:9;
5783 = 23*251 + 10; hence not 23 divides 5783 by NAT_4:9;
5783 = 29*199 + 12; hence not 29 divides 5783 by NAT_4:9;
5783 = 31*186 + 17; hence not 31 divides 5783 by NAT_4:9;
5783 = 37*156 + 11; hence not 37 divides 5783 by NAT_4:9;
5783 = 41*141 + 2; hence not 41 divides 5783 by NAT_4:9;
5783 = 43*134 + 21; hence not 43 divides 5783 by NAT_4:9;
5783 = 47*123 + 2; hence not 47 divides 5783 by NAT_4:9;
5783 = 53*109 + 6; hence not 53 divides 5783 by NAT_4:9;
5783 = 59*98 + 1; hence not 59 divides 5783 by NAT_4:9;
5783 = 61*94 + 49; hence not 61 divides 5783 by NAT_4:9;
5783 = 67*86 + 21; hence not 67 divides 5783 by NAT_4:9;
5783 = 71*81 + 32; hence not 71 divides 5783 by NAT_4:9;
5783 = 73*79 + 16; hence not 73 divides 5783 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5783 & n is prime
holds not n divides 5783 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5791 is prime
proof
now
5791 = 2*2895 + 1; hence not 2 divides 5791 by NAT_4:9;
5791 = 3*1930 + 1; hence not 3 divides 5791 by NAT_4:9;
5791 = 5*1158 + 1; hence not 5 divides 5791 by NAT_4:9;
5791 = 7*827 + 2; hence not 7 divides 5791 by NAT_4:9;
5791 = 11*526 + 5; hence not 11 divides 5791 by NAT_4:9;
5791 = 13*445 + 6; hence not 13 divides 5791 by NAT_4:9;
5791 = 17*340 + 11; hence not 17 divides 5791 by NAT_4:9;
5791 = 19*304 + 15; hence not 19 divides 5791 by NAT_4:9;
5791 = 23*251 + 18; hence not 23 divides 5791 by NAT_4:9;
5791 = 29*199 + 20; hence not 29 divides 5791 by NAT_4:9;
5791 = 31*186 + 25; hence not 31 divides 5791 by NAT_4:9;
5791 = 37*156 + 19; hence not 37 divides 5791 by NAT_4:9;
5791 = 41*141 + 10; hence not 41 divides 5791 by NAT_4:9;
5791 = 43*134 + 29; hence not 43 divides 5791 by NAT_4:9;
5791 = 47*123 + 10; hence not 47 divides 5791 by NAT_4:9;
5791 = 53*109 + 14; hence not 53 divides 5791 by NAT_4:9;
5791 = 59*98 + 9; hence not 59 divides 5791 by NAT_4:9;
5791 = 61*94 + 57; hence not 61 divides 5791 by NAT_4:9;
5791 = 67*86 + 29; hence not 67 divides 5791 by NAT_4:9;
5791 = 71*81 + 40; hence not 71 divides 5791 by NAT_4:9;
5791 = 73*79 + 24; hence not 73 divides 5791 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5791 & n is prime
holds not n divides 5791 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5801 is prime
proof
now
5801 = 2*2900 + 1; hence not 2 divides 5801 by NAT_4:9;
5801 = 3*1933 + 2; hence not 3 divides 5801 by NAT_4:9;
5801 = 5*1160 + 1; hence not 5 divides 5801 by NAT_4:9;
5801 = 7*828 + 5; hence not 7 divides 5801 by NAT_4:9;
5801 = 11*527 + 4; hence not 11 divides 5801 by NAT_4:9;
5801 = 13*446 + 3; hence not 13 divides 5801 by NAT_4:9;
5801 = 17*341 + 4; hence not 17 divides 5801 by NAT_4:9;
5801 = 19*305 + 6; hence not 19 divides 5801 by NAT_4:9;
5801 = 23*252 + 5; hence not 23 divides 5801 by NAT_4:9;
5801 = 29*200 + 1; hence not 29 divides 5801 by NAT_4:9;
5801 = 31*187 + 4; hence not 31 divides 5801 by NAT_4:9;
5801 = 37*156 + 29; hence not 37 divides 5801 by NAT_4:9;
5801 = 41*141 + 20; hence not 41 divides 5801 by NAT_4:9;
5801 = 43*134 + 39; hence not 43 divides 5801 by NAT_4:9;
5801 = 47*123 + 20; hence not 47 divides 5801 by NAT_4:9;
5801 = 53*109 + 24; hence not 53 divides 5801 by NAT_4:9;
5801 = 59*98 + 19; hence not 59 divides 5801 by NAT_4:9;
5801 = 61*95 + 6; hence not 61 divides 5801 by NAT_4:9;
5801 = 67*86 + 39; hence not 67 divides 5801 by NAT_4:9;
5801 = 71*81 + 50; hence not 71 divides 5801 by NAT_4:9;
5801 = 73*79 + 34; hence not 73 divides 5801 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5801 & n is prime
holds not n divides 5801 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5807 is prime
proof
now
5807 = 2*2903 + 1; hence not 2 divides 5807 by NAT_4:9;
5807 = 3*1935 + 2; hence not 3 divides 5807 by NAT_4:9;
5807 = 5*1161 + 2; hence not 5 divides 5807 by NAT_4:9;
5807 = 7*829 + 4; hence not 7 divides 5807 by NAT_4:9;
5807 = 11*527 + 10; hence not 11 divides 5807 by NAT_4:9;
5807 = 13*446 + 9; hence not 13 divides 5807 by NAT_4:9;
5807 = 17*341 + 10; hence not 17 divides 5807 by NAT_4:9;
5807 = 19*305 + 12; hence not 19 divides 5807 by NAT_4:9;
5807 = 23*252 + 11; hence not 23 divides 5807 by NAT_4:9;
5807 = 29*200 + 7; hence not 29 divides 5807 by NAT_4:9;
5807 = 31*187 + 10; hence not 31 divides 5807 by NAT_4:9;
5807 = 37*156 + 35; hence not 37 divides 5807 by NAT_4:9;
5807 = 41*141 + 26; hence not 41 divides 5807 by NAT_4:9;
5807 = 43*135 + 2; hence not 43 divides 5807 by NAT_4:9;
5807 = 47*123 + 26; hence not 47 divides 5807 by NAT_4:9;
5807 = 53*109 + 30; hence not 53 divides 5807 by NAT_4:9;
5807 = 59*98 + 25; hence not 59 divides 5807 by NAT_4:9;
5807 = 61*95 + 12; hence not 61 divides 5807 by NAT_4:9;
5807 = 67*86 + 45; hence not 67 divides 5807 by NAT_4:9;
5807 = 71*81 + 56; hence not 71 divides 5807 by NAT_4:9;
5807 = 73*79 + 40; hence not 73 divides 5807 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5807 & n is prime
holds not n divides 5807 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5813 is prime
proof
now
5813 = 2*2906 + 1; hence not 2 divides 5813 by NAT_4:9;
5813 = 3*1937 + 2; hence not 3 divides 5813 by NAT_4:9;
5813 = 5*1162 + 3; hence not 5 divides 5813 by NAT_4:9;
5813 = 7*830 + 3; hence not 7 divides 5813 by NAT_4:9;
5813 = 11*528 + 5; hence not 11 divides 5813 by NAT_4:9;
5813 = 13*447 + 2; hence not 13 divides 5813 by NAT_4:9;
5813 = 17*341 + 16; hence not 17 divides 5813 by NAT_4:9;
5813 = 19*305 + 18; hence not 19 divides 5813 by NAT_4:9;
5813 = 23*252 + 17; hence not 23 divides 5813 by NAT_4:9;
5813 = 29*200 + 13; hence not 29 divides 5813 by NAT_4:9;
5813 = 31*187 + 16; hence not 31 divides 5813 by NAT_4:9;
5813 = 37*157 + 4; hence not 37 divides 5813 by NAT_4:9;
5813 = 41*141 + 32; hence not 41 divides 5813 by NAT_4:9;
5813 = 43*135 + 8; hence not 43 divides 5813 by NAT_4:9;
5813 = 47*123 + 32; hence not 47 divides 5813 by NAT_4:9;
5813 = 53*109 + 36; hence not 53 divides 5813 by NAT_4:9;
5813 = 59*98 + 31; hence not 59 divides 5813 by NAT_4:9;
5813 = 61*95 + 18; hence not 61 divides 5813 by NAT_4:9;
5813 = 67*86 + 51; hence not 67 divides 5813 by NAT_4:9;
5813 = 71*81 + 62; hence not 71 divides 5813 by NAT_4:9;
5813 = 73*79 + 46; hence not 73 divides 5813 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5813 & n is prime
holds not n divides 5813 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
5821 is prime
proof
now
5821 = 2*2910 + 1; hence not 2 divides 5821 by NAT_4:9;
5821 = 3*1940 + 1; hence not 3 divides 5821 by NAT_4:9;
5821 = 5*1164 + 1; hence not 5 divides 5821 by NAT_4:9;
5821 = 7*831 + 4; hence not 7 divides 5821 by NAT_4:9;
5821 = 11*529 + 2; hence not 11 divides 5821 by NAT_4:9;
5821 = 13*447 + 10; hence not 13 divides 5821 by NAT_4:9;
5821 = 17*342 + 7; hence not 17 divides 5821 by NAT_4:9;
5821 = 19*306 + 7; hence not 19 divides 5821 by NAT_4:9;
5821 = 23*253 + 2; hence not 23 divides 5821 by NAT_4:9;
5821 = 29*200 + 21; hence not 29 divides 5821 by NAT_4:9;
5821 = 31*187 + 24; hence not 31 divides 5821 by NAT_4:9;
5821 = 37*157 + 12; hence not 37 divides 5821 by NAT_4:9;
5821 = 41*141 + 40; hence not 41 divides 5821 by NAT_4:9;
5821 = 43*135 + 16; hence not 43 divides 5821 by NAT_4:9;
5821 = 47*123 + 40; hence not 47 divides 5821 by NAT_4:9;
5821 = 53*109 + 44; hence not 53 divides 5821 by NAT_4:9;
5821 = 59*98 + 39; hence not 59 divides 5821 by NAT_4:9;
5821 = 61*95 + 26; hence not 61 divides 5821 by NAT_4:9;
5821 = 67*86 + 59; hence not 67 divides 5821 by NAT_4:9;
5821 = 71*81 + 70; hence not 71 divides 5821 by NAT_4:9;
5821 = 73*79 + 54; hence not 73 divides 5821 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5821 & n is prime
holds not n divides 5821 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5827 is prime
proof
now
5827 = 2*2913 + 1; hence not 2 divides 5827 by NAT_4:9;
5827 = 3*1942 + 1; hence not 3 divides 5827 by NAT_4:9;
5827 = 5*1165 + 2; hence not 5 divides 5827 by NAT_4:9;
5827 = 7*832 + 3; hence not 7 divides 5827 by NAT_4:9;
5827 = 11*529 + 8; hence not 11 divides 5827 by NAT_4:9;
5827 = 13*448 + 3; hence not 13 divides 5827 by NAT_4:9;
5827 = 17*342 + 13; hence not 17 divides 5827 by NAT_4:9;
5827 = 19*306 + 13; hence not 19 divides 5827 by NAT_4:9;
5827 = 23*253 + 8; hence not 23 divides 5827 by NAT_4:9;
5827 = 29*200 + 27; hence not 29 divides 5827 by NAT_4:9;
5827 = 31*187 + 30; hence not 31 divides 5827 by NAT_4:9;
5827 = 37*157 + 18; hence not 37 divides 5827 by NAT_4:9;
5827 = 41*142 + 5; hence not 41 divides 5827 by NAT_4:9;
5827 = 43*135 + 22; hence not 43 divides 5827 by NAT_4:9;
5827 = 47*123 + 46; hence not 47 divides 5827 by NAT_4:9;
5827 = 53*109 + 50; hence not 53 divides 5827 by NAT_4:9;
5827 = 59*98 + 45; hence not 59 divides 5827 by NAT_4:9;
5827 = 61*95 + 32; hence not 61 divides 5827 by NAT_4:9;
5827 = 67*86 + 65; hence not 67 divides 5827 by NAT_4:9;
5827 = 71*82 + 5; hence not 71 divides 5827 by NAT_4:9;
5827 = 73*79 + 60; hence not 73 divides 5827 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5827 & n is prime
holds not n divides 5827 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5839 is prime
proof
now
5839 = 2*2919 + 1; hence not 2 divides 5839 by NAT_4:9;
5839 = 3*1946 + 1; hence not 3 divides 5839 by NAT_4:9;
5839 = 5*1167 + 4; hence not 5 divides 5839 by NAT_4:9;
5839 = 7*834 + 1; hence not 7 divides 5839 by NAT_4:9;
5839 = 11*530 + 9; hence not 11 divides 5839 by NAT_4:9;
5839 = 13*449 + 2; hence not 13 divides 5839 by NAT_4:9;
5839 = 17*343 + 8; hence not 17 divides 5839 by NAT_4:9;
5839 = 19*307 + 6; hence not 19 divides 5839 by NAT_4:9;
5839 = 23*253 + 20; hence not 23 divides 5839 by NAT_4:9;
5839 = 29*201 + 10; hence not 29 divides 5839 by NAT_4:9;
5839 = 31*188 + 11; hence not 31 divides 5839 by NAT_4:9;
5839 = 37*157 + 30; hence not 37 divides 5839 by NAT_4:9;
5839 = 41*142 + 17; hence not 41 divides 5839 by NAT_4:9;
5839 = 43*135 + 34; hence not 43 divides 5839 by NAT_4:9;
5839 = 47*124 + 11; hence not 47 divides 5839 by NAT_4:9;
5839 = 53*110 + 9; hence not 53 divides 5839 by NAT_4:9;
5839 = 59*98 + 57; hence not 59 divides 5839 by NAT_4:9;
5839 = 61*95 + 44; hence not 61 divides 5839 by NAT_4:9;
5839 = 67*87 + 10; hence not 67 divides 5839 by NAT_4:9;
5839 = 71*82 + 17; hence not 71 divides 5839 by NAT_4:9;
5839 = 73*79 + 72; hence not 73 divides 5839 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5839 & n is prime
holds not n divides 5839 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5843 is prime
proof
now
5843 = 2*2921 + 1; hence not 2 divides 5843 by NAT_4:9;
5843 = 3*1947 + 2; hence not 3 divides 5843 by NAT_4:9;
5843 = 5*1168 + 3; hence not 5 divides 5843 by NAT_4:9;
5843 = 7*834 + 5; hence not 7 divides 5843 by NAT_4:9;
5843 = 11*531 + 2; hence not 11 divides 5843 by NAT_4:9;
5843 = 13*449 + 6; hence not 13 divides 5843 by NAT_4:9;
5843 = 17*343 + 12; hence not 17 divides 5843 by NAT_4:9;
5843 = 19*307 + 10; hence not 19 divides 5843 by NAT_4:9;
5843 = 23*254 + 1; hence not 23 divides 5843 by NAT_4:9;
5843 = 29*201 + 14; hence not 29 divides 5843 by NAT_4:9;
5843 = 31*188 + 15; hence not 31 divides 5843 by NAT_4:9;
5843 = 37*157 + 34; hence not 37 divides 5843 by NAT_4:9;
5843 = 41*142 + 21; hence not 41 divides 5843 by NAT_4:9;
5843 = 43*135 + 38; hence not 43 divides 5843 by NAT_4:9;
5843 = 47*124 + 15; hence not 47 divides 5843 by NAT_4:9;
5843 = 53*110 + 13; hence not 53 divides 5843 by NAT_4:9;
5843 = 59*99 + 2; hence not 59 divides 5843 by NAT_4:9;
5843 = 61*95 + 48; hence not 61 divides 5843 by NAT_4:9;
5843 = 67*87 + 14; hence not 67 divides 5843 by NAT_4:9;
5843 = 71*82 + 21; hence not 71 divides 5843 by NAT_4:9;
5843 = 73*80 + 3; hence not 73 divides 5843 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5843 & n is prime
holds not n divides 5843 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5849 is prime
proof
now
5849 = 2*2924 + 1; hence not 2 divides 5849 by NAT_4:9;
5849 = 3*1949 + 2; hence not 3 divides 5849 by NAT_4:9;
5849 = 5*1169 + 4; hence not 5 divides 5849 by NAT_4:9;
5849 = 7*835 + 4; hence not 7 divides 5849 by NAT_4:9;
5849 = 11*531 + 8; hence not 11 divides 5849 by NAT_4:9;
5849 = 13*449 + 12; hence not 13 divides 5849 by NAT_4:9;
5849 = 17*344 + 1; hence not 17 divides 5849 by NAT_4:9;
5849 = 19*307 + 16; hence not 19 divides 5849 by NAT_4:9;
5849 = 23*254 + 7; hence not 23 divides 5849 by NAT_4:9;
5849 = 29*201 + 20; hence not 29 divides 5849 by NAT_4:9;
5849 = 31*188 + 21; hence not 31 divides 5849 by NAT_4:9;
5849 = 37*158 + 3; hence not 37 divides 5849 by NAT_4:9;
5849 = 41*142 + 27; hence not 41 divides 5849 by NAT_4:9;
5849 = 43*136 + 1; hence not 43 divides 5849 by NAT_4:9;
5849 = 47*124 + 21; hence not 47 divides 5849 by NAT_4:9;
5849 = 53*110 + 19; hence not 53 divides 5849 by NAT_4:9;
5849 = 59*99 + 8; hence not 59 divides 5849 by NAT_4:9;
5849 = 61*95 + 54; hence not 61 divides 5849 by NAT_4:9;
5849 = 67*87 + 20; hence not 67 divides 5849 by NAT_4:9;
5849 = 71*82 + 27; hence not 71 divides 5849 by NAT_4:9;
5849 = 73*80 + 9; hence not 73 divides 5849 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5849 & n is prime
holds not n divides 5849 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5851 is prime
proof
now
5851 = 2*2925 + 1; hence not 2 divides 5851 by NAT_4:9;
5851 = 3*1950 + 1; hence not 3 divides 5851 by NAT_4:9;
5851 = 5*1170 + 1; hence not 5 divides 5851 by NAT_4:9;
5851 = 7*835 + 6; hence not 7 divides 5851 by NAT_4:9;
5851 = 11*531 + 10; hence not 11 divides 5851 by NAT_4:9;
5851 = 13*450 + 1; hence not 13 divides 5851 by NAT_4:9;
5851 = 17*344 + 3; hence not 17 divides 5851 by NAT_4:9;
5851 = 19*307 + 18; hence not 19 divides 5851 by NAT_4:9;
5851 = 23*254 + 9; hence not 23 divides 5851 by NAT_4:9;
5851 = 29*201 + 22; hence not 29 divides 5851 by NAT_4:9;
5851 = 31*188 + 23; hence not 31 divides 5851 by NAT_4:9;
5851 = 37*158 + 5; hence not 37 divides 5851 by NAT_4:9;
5851 = 41*142 + 29; hence not 41 divides 5851 by NAT_4:9;
5851 = 43*136 + 3; hence not 43 divides 5851 by NAT_4:9;
5851 = 47*124 + 23; hence not 47 divides 5851 by NAT_4:9;
5851 = 53*110 + 21; hence not 53 divides 5851 by NAT_4:9;
5851 = 59*99 + 10; hence not 59 divides 5851 by NAT_4:9;
5851 = 61*95 + 56; hence not 61 divides 5851 by NAT_4:9;
5851 = 67*87 + 22; hence not 67 divides 5851 by NAT_4:9;
5851 = 71*82 + 29; hence not 71 divides 5851 by NAT_4:9;
5851 = 73*80 + 11; hence not 73 divides 5851 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5851 & n is prime
holds not n divides 5851 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5857 is prime
proof
now
5857 = 2*2928 + 1; hence not 2 divides 5857 by NAT_4:9;
5857 = 3*1952 + 1; hence not 3 divides 5857 by NAT_4:9;
5857 = 5*1171 + 2; hence not 5 divides 5857 by NAT_4:9;
5857 = 7*836 + 5; hence not 7 divides 5857 by NAT_4:9;
5857 = 11*532 + 5; hence not 11 divides 5857 by NAT_4:9;
5857 = 13*450 + 7; hence not 13 divides 5857 by NAT_4:9;
5857 = 17*344 + 9; hence not 17 divides 5857 by NAT_4:9;
5857 = 19*308 + 5; hence not 19 divides 5857 by NAT_4:9;
5857 = 23*254 + 15; hence not 23 divides 5857 by NAT_4:9;
5857 = 29*201 + 28; hence not 29 divides 5857 by NAT_4:9;
5857 = 31*188 + 29; hence not 31 divides 5857 by NAT_4:9;
5857 = 37*158 + 11; hence not 37 divides 5857 by NAT_4:9;
5857 = 41*142 + 35; hence not 41 divides 5857 by NAT_4:9;
5857 = 43*136 + 9; hence not 43 divides 5857 by NAT_4:9;
5857 = 47*124 + 29; hence not 47 divides 5857 by NAT_4:9;
5857 = 53*110 + 27; hence not 53 divides 5857 by NAT_4:9;
5857 = 59*99 + 16; hence not 59 divides 5857 by NAT_4:9;
5857 = 61*96 + 1; hence not 61 divides 5857 by NAT_4:9;
5857 = 67*87 + 28; hence not 67 divides 5857 by NAT_4:9;
5857 = 71*82 + 35; hence not 71 divides 5857 by NAT_4:9;
5857 = 73*80 + 17; hence not 73 divides 5857 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5857 & n is prime
holds not n divides 5857 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5861 is prime
proof
now
5861 = 2*2930 + 1; hence not 2 divides 5861 by NAT_4:9;
5861 = 3*1953 + 2; hence not 3 divides 5861 by NAT_4:9;
5861 = 5*1172 + 1; hence not 5 divides 5861 by NAT_4:9;
5861 = 7*837 + 2; hence not 7 divides 5861 by NAT_4:9;
5861 = 11*532 + 9; hence not 11 divides 5861 by NAT_4:9;
5861 = 13*450 + 11; hence not 13 divides 5861 by NAT_4:9;
5861 = 17*344 + 13; hence not 17 divides 5861 by NAT_4:9;
5861 = 19*308 + 9; hence not 19 divides 5861 by NAT_4:9;
5861 = 23*254 + 19; hence not 23 divides 5861 by NAT_4:9;
5861 = 29*202 + 3; hence not 29 divides 5861 by NAT_4:9;
5861 = 31*189 + 2; hence not 31 divides 5861 by NAT_4:9;
5861 = 37*158 + 15; hence not 37 divides 5861 by NAT_4:9;
5861 = 41*142 + 39; hence not 41 divides 5861 by NAT_4:9;
5861 = 43*136 + 13; hence not 43 divides 5861 by NAT_4:9;
5861 = 47*124 + 33; hence not 47 divides 5861 by NAT_4:9;
5861 = 53*110 + 31; hence not 53 divides 5861 by NAT_4:9;
5861 = 59*99 + 20; hence not 59 divides 5861 by NAT_4:9;
5861 = 61*96 + 5; hence not 61 divides 5861 by NAT_4:9;
5861 = 67*87 + 32; hence not 67 divides 5861 by NAT_4:9;
5861 = 71*82 + 39; hence not 71 divides 5861 by NAT_4:9;
5861 = 73*80 + 21; hence not 73 divides 5861 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5861 & n is prime
holds not n divides 5861 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5867 is prime
proof
now
5867 = 2*2933 + 1; hence not 2 divides 5867 by NAT_4:9;
5867 = 3*1955 + 2; hence not 3 divides 5867 by NAT_4:9;
5867 = 5*1173 + 2; hence not 5 divides 5867 by NAT_4:9;
5867 = 7*838 + 1; hence not 7 divides 5867 by NAT_4:9;
5867 = 11*533 + 4; hence not 11 divides 5867 by NAT_4:9;
5867 = 13*451 + 4; hence not 13 divides 5867 by NAT_4:9;
5867 = 17*345 + 2; hence not 17 divides 5867 by NAT_4:9;
5867 = 19*308 + 15; hence not 19 divides 5867 by NAT_4:9;
5867 = 23*255 + 2; hence not 23 divides 5867 by NAT_4:9;
5867 = 29*202 + 9; hence not 29 divides 5867 by NAT_4:9;
5867 = 31*189 + 8; hence not 31 divides 5867 by NAT_4:9;
5867 = 37*158 + 21; hence not 37 divides 5867 by NAT_4:9;
5867 = 41*143 + 4; hence not 41 divides 5867 by NAT_4:9;
5867 = 43*136 + 19; hence not 43 divides 5867 by NAT_4:9;
5867 = 47*124 + 39; hence not 47 divides 5867 by NAT_4:9;
5867 = 53*110 + 37; hence not 53 divides 5867 by NAT_4:9;
5867 = 59*99 + 26; hence not 59 divides 5867 by NAT_4:9;
5867 = 61*96 + 11; hence not 61 divides 5867 by NAT_4:9;
5867 = 67*87 + 38; hence not 67 divides 5867 by NAT_4:9;
5867 = 71*82 + 45; hence not 71 divides 5867 by NAT_4:9;
5867 = 73*80 + 27; hence not 73 divides 5867 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5867 & n is prime
holds not n divides 5867 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5869 is prime
proof
now
5869 = 2*2934 + 1; hence not 2 divides 5869 by NAT_4:9;
5869 = 3*1956 + 1; hence not 3 divides 5869 by NAT_4:9;
5869 = 5*1173 + 4; hence not 5 divides 5869 by NAT_4:9;
5869 = 7*838 + 3; hence not 7 divides 5869 by NAT_4:9;
5869 = 11*533 + 6; hence not 11 divides 5869 by NAT_4:9;
5869 = 13*451 + 6; hence not 13 divides 5869 by NAT_4:9;
5869 = 17*345 + 4; hence not 17 divides 5869 by NAT_4:9;
5869 = 19*308 + 17; hence not 19 divides 5869 by NAT_4:9;
5869 = 23*255 + 4; hence not 23 divides 5869 by NAT_4:9;
5869 = 29*202 + 11; hence not 29 divides 5869 by NAT_4:9;
5869 = 31*189 + 10; hence not 31 divides 5869 by NAT_4:9;
5869 = 37*158 + 23; hence not 37 divides 5869 by NAT_4:9;
5869 = 41*143 + 6; hence not 41 divides 5869 by NAT_4:9;
5869 = 43*136 + 21; hence not 43 divides 5869 by NAT_4:9;
5869 = 47*124 + 41; hence not 47 divides 5869 by NAT_4:9;
5869 = 53*110 + 39; hence not 53 divides 5869 by NAT_4:9;
5869 = 59*99 + 28; hence not 59 divides 5869 by NAT_4:9;
5869 = 61*96 + 13; hence not 61 divides 5869 by NAT_4:9;
5869 = 67*87 + 40; hence not 67 divides 5869 by NAT_4:9;
5869 = 71*82 + 47; hence not 71 divides 5869 by NAT_4:9;
5869 = 73*80 + 29; hence not 73 divides 5869 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5869 & n is prime
holds not n divides 5869 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
5879 is prime
proof
now
5879 = 2*2939 + 1; hence not 2 divides 5879 by NAT_4:9;
5879 = 3*1959 + 2; hence not 3 divides 5879 by NAT_4:9;
5879 = 5*1175 + 4; hence not 5 divides 5879 by NAT_4:9;
5879 = 7*839 + 6; hence not 7 divides 5879 by NAT_4:9;
5879 = 11*534 + 5; hence not 11 divides 5879 by NAT_4:9;
5879 = 13*452 + 3; hence not 13 divides 5879 by NAT_4:9;
5879 = 17*345 + 14; hence not 17 divides 5879 by NAT_4:9;
5879 = 19*309 + 8; hence not 19 divides 5879 by NAT_4:9;
5879 = 23*255 + 14; hence not 23 divides 5879 by NAT_4:9;
5879 = 29*202 + 21; hence not 29 divides 5879 by NAT_4:9;
5879 = 31*189 + 20; hence not 31 divides 5879 by NAT_4:9;
5879 = 37*158 + 33; hence not 37 divides 5879 by NAT_4:9;
5879 = 41*143 + 16; hence not 41 divides 5879 by NAT_4:9;
5879 = 43*136 + 31; hence not 43 divides 5879 by NAT_4:9;
5879 = 47*125 + 4; hence not 47 divides 5879 by NAT_4:9;
5879 = 53*110 + 49; hence not 53 divides 5879 by NAT_4:9;
5879 = 59*99 + 38; hence not 59 divides 5879 by NAT_4:9;
5879 = 61*96 + 23; hence not 61 divides 5879 by NAT_4:9;
5879 = 67*87 + 50; hence not 67 divides 5879 by NAT_4:9;
5879 = 71*82 + 57; hence not 71 divides 5879 by NAT_4:9;
5879 = 73*80 + 39; hence not 73 divides 5879 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5879 & n is prime
holds not n divides 5879 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
5881 is prime
proof
now
5881 = 2*2940 + 1; hence not 2 divides 5881 by NAT_4:9;
5881 = 3*1960 + 1; hence not 3 divides 5881 by NAT_4:9;
5881 = 5*1176 + 1; hence not 5 divides 5881 by NAT_4:9;
5881 = 7*840 + 1; hence not 7 divides 5881 by NAT_4:9;
5881 = 11*534 + 7; hence not 11 divides 5881 by NAT_4:9;
5881 = 13*452 + 5; hence not 13 divides 5881 by NAT_4:9;
5881 = 17*345 + 16; hence not 17 divides 5881 by NAT_4:9;
5881 = 19*309 + 10; hence not 19 divides 5881 by NAT_4:9;
5881 = 23*255 + 16; hence not 23 divides 5881 by NAT_4:9;
5881 = 29*202 + 23; hence not 29 divides 5881 by NAT_4:9;
5881 = 31*189 + 22; hence not 31 divides 5881 by NAT_4:9;
5881 = 37*158 + 35; hence not 37 divides 5881 by NAT_4:9;
5881 = 41*143 + 18; hence not 41 divides 5881 by NAT_4:9;
5881 = 43*136 + 33; hence not 43 divides 5881 by NAT_4:9;
5881 = 47*125 + 6; hence not 47 divides 5881 by NAT_4:9;
5881 = 53*110 + 51; hence not 53 divides 5881 by NAT_4:9;
5881 = 59*99 + 40; hence not 59 divides 5881 by NAT_4:9;
5881 = 61*96 + 25; hence not 61 divides 5881 by NAT_4:9;
5881 = 67*87 + 52; hence not 67 divides 5881 by NAT_4:9;
5881 = 71*82 + 59; hence not 71 divides 5881 by NAT_4:9;
5881 = 73*80 + 41; hence not 73 divides 5881 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5881 & n is prime
holds not n divides 5881 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
5897 is prime
proof
now
5897 = 2*2948 + 1; hence not 2 divides 5897 by NAT_4:9;
5897 = 3*1965 + 2; hence not 3 divides 5897 by NAT_4:9;
5897 = 5*1179 + 2; hence not 5 divides 5897 by NAT_4:9;
5897 = 7*842 + 3; hence not 7 divides 5897 by NAT_4:9;
5897 = 11*536 + 1; hence not 11 divides 5897 by NAT_4:9;
5897 = 13*453 + 8; hence not 13 divides 5897 by NAT_4:9;
5897 = 17*346 + 15; hence not 17 divides 5897 by NAT_4:9;
5897 = 19*310 + 7; hence not 19 divides 5897 by NAT_4:9;
5897 = 23*256 + 9; hence not 23 divides 5897 by NAT_4:9;
5897 = 29*203 + 10; hence not 29 divides 5897 by NAT_4:9;
5897 = 31*190 + 7; hence not 31 divides 5897 by NAT_4:9;
5897 = 37*159 + 14; hence not 37 divides 5897 by NAT_4:9;
5897 = 41*143 + 34; hence not 41 divides 5897 by NAT_4:9;
5897 = 43*137 + 6; hence not 43 divides 5897 by NAT_4:9;
5897 = 47*125 + 22; hence not 47 divides 5897 by NAT_4:9;
5897 = 53*111 + 14; hence not 53 divides 5897 by NAT_4:9;
5897 = 59*99 + 56; hence not 59 divides 5897 by NAT_4:9;
5897 = 61*96 + 41; hence not 61 divides 5897 by NAT_4:9;
5897 = 67*88 + 1; hence not 67 divides 5897 by NAT_4:9;
5897 = 71*83 + 4; hence not 71 divides 5897 by NAT_4:9;
5897 = 73*80 + 57; hence not 73 divides 5897 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5897 & n is prime
holds not n divides 5897 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5903 is prime
proof
now
5903 = 2*2951 + 1; hence not 2 divides 5903 by NAT_4:9;
5903 = 3*1967 + 2; hence not 3 divides 5903 by NAT_4:9;
5903 = 5*1180 + 3; hence not 5 divides 5903 by NAT_4:9;
5903 = 7*843 + 2; hence not 7 divides 5903 by NAT_4:9;
5903 = 11*536 + 7; hence not 11 divides 5903 by NAT_4:9;
5903 = 13*454 + 1; hence not 13 divides 5903 by NAT_4:9;
5903 = 17*347 + 4; hence not 17 divides 5903 by NAT_4:9;
5903 = 19*310 + 13; hence not 19 divides 5903 by NAT_4:9;
5903 = 23*256 + 15; hence not 23 divides 5903 by NAT_4:9;
5903 = 29*203 + 16; hence not 29 divides 5903 by NAT_4:9;
5903 = 31*190 + 13; hence not 31 divides 5903 by NAT_4:9;
5903 = 37*159 + 20; hence not 37 divides 5903 by NAT_4:9;
5903 = 41*143 + 40; hence not 41 divides 5903 by NAT_4:9;
5903 = 43*137 + 12; hence not 43 divides 5903 by NAT_4:9;
5903 = 47*125 + 28; hence not 47 divides 5903 by NAT_4:9;
5903 = 53*111 + 20; hence not 53 divides 5903 by NAT_4:9;
5903 = 59*100 + 3; hence not 59 divides 5903 by NAT_4:9;
5903 = 61*96 + 47; hence not 61 divides 5903 by NAT_4:9;
5903 = 67*88 + 7; hence not 67 divides 5903 by NAT_4:9;
5903 = 71*83 + 10; hence not 71 divides 5903 by NAT_4:9;
5903 = 73*80 + 63; hence not 73 divides 5903 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5903 & n is prime
holds not n divides 5903 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
5923 is prime
proof
now
5923 = 2*2961 + 1; hence not 2 divides 5923 by NAT_4:9;
5923 = 3*1974 + 1; hence not 3 divides 5923 by NAT_4:9;
5923 = 5*1184 + 3; hence not 5 divides 5923 by NAT_4:9;
5923 = 7*846 + 1; hence not 7 divides 5923 by NAT_4:9;
5923 = 11*538 + 5; hence not 11 divides 5923 by NAT_4:9;
5923 = 13*455 + 8; hence not 13 divides 5923 by NAT_4:9;
5923 = 17*348 + 7; hence not 17 divides 5923 by NAT_4:9;
5923 = 19*311 + 14; hence not 19 divides 5923 by NAT_4:9;
5923 = 23*257 + 12; hence not 23 divides 5923 by NAT_4:9;
5923 = 29*204 + 7; hence not 29 divides 5923 by NAT_4:9;
5923 = 31*191 + 2; hence not 31 divides 5923 by NAT_4:9;
5923 = 37*160 + 3; hence not 37 divides 5923 by NAT_4:9;
5923 = 41*144 + 19; hence not 41 divides 5923 by NAT_4:9;
5923 = 43*137 + 32; hence not 43 divides 5923 by NAT_4:9;
5923 = 47*126 + 1; hence not 47 divides 5923 by NAT_4:9;
5923 = 53*111 + 40; hence not 53 divides 5923 by NAT_4:9;
5923 = 59*100 + 23; hence not 59 divides 5923 by NAT_4:9;
5923 = 61*97 + 6; hence not 61 divides 5923 by NAT_4:9;
5923 = 67*88 + 27; hence not 67 divides 5923 by NAT_4:9;
5923 = 71*83 + 30; hence not 71 divides 5923 by NAT_4:9;
5923 = 73*81 + 10; hence not 73 divides 5923 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5923 & n is prime
holds not n divides 5923 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
5927 is prime
proof
now
5927 = 2*2963 + 1; hence not 2 divides 5927 by NAT_4:9;
5927 = 3*1975 + 2; hence not 3 divides 5927 by NAT_4:9;
5927 = 5*1185 + 2; hence not 5 divides 5927 by NAT_4:9;
5927 = 7*846 + 5; hence not 7 divides 5927 by NAT_4:9;
5927 = 11*538 + 9; hence not 11 divides 5927 by NAT_4:9;
5927 = 13*455 + 12; hence not 13 divides 5927 by NAT_4:9;
5927 = 17*348 + 11; hence not 17 divides 5927 by NAT_4:9;
5927 = 19*311 + 18; hence not 19 divides 5927 by NAT_4:9;
5927 = 23*257 + 16; hence not 23 divides 5927 by NAT_4:9;
5927 = 29*204 + 11; hence not 29 divides 5927 by NAT_4:9;
5927 = 31*191 + 6; hence not 31 divides 5927 by NAT_4:9;
5927 = 37*160 + 7; hence not 37 divides 5927 by NAT_4:9;
5927 = 41*144 + 23; hence not 41 divides 5927 by NAT_4:9;
5927 = 43*137 + 36; hence not 43 divides 5927 by NAT_4:9;
5927 = 47*126 + 5; hence not 47 divides 5927 by NAT_4:9;
5927 = 53*111 + 44; hence not 53 divides 5927 by NAT_4:9;
5927 = 59*100 + 27; hence not 59 divides 5927 by NAT_4:9;
5927 = 61*97 + 10; hence not 61 divides 5927 by NAT_4:9;
5927 = 67*88 + 31; hence not 67 divides 5927 by NAT_4:9;
5927 = 71*83 + 34; hence not 71 divides 5927 by NAT_4:9;
5927 = 73*81 + 14; hence not 73 divides 5927 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5927 & n is prime
holds not n divides 5927 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
5939 is prime
proof
now
5939 = 2*2969 + 1; hence not 2 divides 5939 by NAT_4:9;
5939 = 3*1979 + 2; hence not 3 divides 5939 by NAT_4:9;
5939 = 5*1187 + 4; hence not 5 divides 5939 by NAT_4:9;
5939 = 7*848 + 3; hence not 7 divides 5939 by NAT_4:9;
5939 = 11*539 + 10; hence not 11 divides 5939 by NAT_4:9;
5939 = 13*456 + 11; hence not 13 divides 5939 by NAT_4:9;
5939 = 17*349 + 6; hence not 17 divides 5939 by NAT_4:9;
5939 = 19*312 + 11; hence not 19 divides 5939 by NAT_4:9;
5939 = 23*258 + 5; hence not 23 divides 5939 by NAT_4:9;
5939 = 29*204 + 23; hence not 29 divides 5939 by NAT_4:9;
5939 = 31*191 + 18; hence not 31 divides 5939 by NAT_4:9;
5939 = 37*160 + 19; hence not 37 divides 5939 by NAT_4:9;
5939 = 41*144 + 35; hence not 41 divides 5939 by NAT_4:9;
5939 = 43*138 + 5; hence not 43 divides 5939 by NAT_4:9;
5939 = 47*126 + 17; hence not 47 divides 5939 by NAT_4:9;
5939 = 53*112 + 3; hence not 53 divides 5939 by NAT_4:9;
5939 = 59*100 + 39; hence not 59 divides 5939 by NAT_4:9;
5939 = 61*97 + 22; hence not 61 divides 5939 by NAT_4:9;
5939 = 67*88 + 43; hence not 67 divides 5939 by NAT_4:9;
5939 = 71*83 + 46; hence not 71 divides 5939 by NAT_4:9;
5939 = 73*81 + 26; hence not 73 divides 5939 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5939 & n is prime
holds not n divides 5939 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
5953 is prime
proof
now
5953 = 2*2976 + 1; hence not 2 divides 5953 by NAT_4:9;
5953 = 3*1984 + 1; hence not 3 divides 5953 by NAT_4:9;
5953 = 5*1190 + 3; hence not 5 divides 5953 by NAT_4:9;
5953 = 7*850 + 3; hence not 7 divides 5953 by NAT_4:9;
5953 = 11*541 + 2; hence not 11 divides 5953 by NAT_4:9;
5953 = 13*457 + 12; hence not 13 divides 5953 by NAT_4:9;
5953 = 17*350 + 3; hence not 17 divides 5953 by NAT_4:9;
5953 = 19*313 + 6; hence not 19 divides 5953 by NAT_4:9;
5953 = 23*258 + 19; hence not 23 divides 5953 by NAT_4:9;
5953 = 29*205 + 8; hence not 29 divides 5953 by NAT_4:9;
5953 = 31*192 + 1; hence not 31 divides 5953 by NAT_4:9;
5953 = 37*160 + 33; hence not 37 divides 5953 by NAT_4:9;
5953 = 41*145 + 8; hence not 41 divides 5953 by NAT_4:9;
5953 = 43*138 + 19; hence not 43 divides 5953 by NAT_4:9;
5953 = 47*126 + 31; hence not 47 divides 5953 by NAT_4:9;
5953 = 53*112 + 17; hence not 53 divides 5953 by NAT_4:9;
5953 = 59*100 + 53; hence not 59 divides 5953 by NAT_4:9;
5953 = 61*97 + 36; hence not 61 divides 5953 by NAT_4:9;
5953 = 67*88 + 57; hence not 67 divides 5953 by NAT_4:9;
5953 = 71*83 + 60; hence not 71 divides 5953 by NAT_4:9;
5953 = 73*81 + 40; hence not 73 divides 5953 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5953 & n is prime
holds not n divides 5953 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 27
theorem
5981 is prime
proof
now
5981 = 2*2990 + 1; hence not 2 divides 5981 by NAT_4:9;
5981 = 3*1993 + 2; hence not 3 divides 5981 by NAT_4:9;
5981 = 5*1196 + 1; hence not 5 divides 5981 by NAT_4:9;
5981 = 7*854 + 3; hence not 7 divides 5981 by NAT_4:9;
5981 = 11*543 + 8; hence not 11 divides 5981 by NAT_4:9;
5981 = 13*460 + 1; hence not 13 divides 5981 by NAT_4:9;
5981 = 17*351 + 14; hence not 17 divides 5981 by NAT_4:9;
5981 = 19*314 + 15; hence not 19 divides 5981 by NAT_4:9;
5981 = 23*260 + 1; hence not 23 divides 5981 by NAT_4:9;
5981 = 29*206 + 7; hence not 29 divides 5981 by NAT_4:9;
5981 = 31*192 + 29; hence not 31 divides 5981 by NAT_4:9;
5981 = 37*161 + 24; hence not 37 divides 5981 by NAT_4:9;
5981 = 41*145 + 36; hence not 41 divides 5981 by NAT_4:9;
5981 = 43*139 + 4; hence not 43 divides 5981 by NAT_4:9;
5981 = 47*127 + 12; hence not 47 divides 5981 by NAT_4:9;
5981 = 53*112 + 45; hence not 53 divides 5981 by NAT_4:9;
5981 = 59*101 + 22; hence not 59 divides 5981 by NAT_4:9;
5981 = 61*98 + 3; hence not 61 divides 5981 by NAT_4:9;
5981 = 67*89 + 18; hence not 67 divides 5981 by NAT_4:9;
5981 = 71*84 + 17; hence not 71 divides 5981 by NAT_4:9;
5981 = 73*81 + 68; hence not 73 divides 5981 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5981 & n is prime
holds not n divides 5981 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
5987 is prime
proof
now
5987 = 2*2993 + 1; hence not 2 divides 5987 by NAT_4:9;
5987 = 3*1995 + 2; hence not 3 divides 5987 by NAT_4:9;
5987 = 5*1197 + 2; hence not 5 divides 5987 by NAT_4:9;
5987 = 7*855 + 2; hence not 7 divides 5987 by NAT_4:9;
5987 = 11*544 + 3; hence not 11 divides 5987 by NAT_4:9;
5987 = 13*460 + 7; hence not 13 divides 5987 by NAT_4:9;
5987 = 17*352 + 3; hence not 17 divides 5987 by NAT_4:9;
5987 = 19*315 + 2; hence not 19 divides 5987 by NAT_4:9;
5987 = 23*260 + 7; hence not 23 divides 5987 by NAT_4:9;
5987 = 29*206 + 13; hence not 29 divides 5987 by NAT_4:9;
5987 = 31*193 + 4; hence not 31 divides 5987 by NAT_4:9;
5987 = 37*161 + 30; hence not 37 divides 5987 by NAT_4:9;
5987 = 41*146 + 1; hence not 41 divides 5987 by NAT_4:9;
5987 = 43*139 + 10; hence not 43 divides 5987 by NAT_4:9;
5987 = 47*127 + 18; hence not 47 divides 5987 by NAT_4:9;
5987 = 53*112 + 51; hence not 53 divides 5987 by NAT_4:9;
5987 = 59*101 + 28; hence not 59 divides 5987 by NAT_4:9;
5987 = 61*98 + 9; hence not 61 divides 5987 by NAT_4:9;
5987 = 67*89 + 24; hence not 67 divides 5987 by NAT_4:9;
5987 = 71*84 + 23; hence not 71 divides 5987 by NAT_4:9;
5987 = 73*82 + 1; hence not 73 divides 5987 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 5987 & n is prime
holds not n divides 5987 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;