:: A List of Prime Numbers - Part II
:: 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
::$CT 6006
theorem
6007 is prime
proof
now
6007 = 2*3003 + 1; hence not 2 divides 6007 by NAT_4:9;
6007 = 3*2002 + 1; hence not 3 divides 6007 by NAT_4:9;
6007 = 5*1201 + 2; hence not 5 divides 6007 by NAT_4:9;
6007 = 7*858 + 1; hence not 7 divides 6007 by NAT_4:9;
6007 = 11*546 + 1; hence not 11 divides 6007 by NAT_4:9;
6007 = 13*462 + 1; hence not 13 divides 6007 by NAT_4:9;
6007 = 17*353 + 6; hence not 17 divides 6007 by NAT_4:9;
6007 = 19*316 + 3; hence not 19 divides 6007 by NAT_4:9;
6007 = 23*261 + 4; hence not 23 divides 6007 by NAT_4:9;
6007 = 29*207 + 4; hence not 29 divides 6007 by NAT_4:9;
6007 = 31*193 + 24; hence not 31 divides 6007 by NAT_4:9;
6007 = 37*162 + 13; hence not 37 divides 6007 by NAT_4:9;
6007 = 41*146 + 21; hence not 41 divides 6007 by NAT_4:9;
6007 = 43*139 + 30; hence not 43 divides 6007 by NAT_4:9;
6007 = 47*127 + 38; hence not 47 divides 6007 by NAT_4:9;
6007 = 53*113 + 18; hence not 53 divides 6007 by NAT_4:9;
6007 = 59*101 + 48; hence not 59 divides 6007 by NAT_4:9;
6007 = 61*98 + 29; hence not 61 divides 6007 by NAT_4:9;
6007 = 67*89 + 44; hence not 67 divides 6007 by NAT_4:9;
6007 = 71*84 + 43; hence not 71 divides 6007 by NAT_4:9;
6007 = 73*82 + 21; hence not 73 divides 6007 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6007 & n is prime
holds not n divides 6007 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6011 is prime
proof
now
6011 = 2*3005 + 1; hence not 2 divides 6011 by NAT_4:9;
6011 = 3*2003 + 2; hence not 3 divides 6011 by NAT_4:9;
6011 = 5*1202 + 1; hence not 5 divides 6011 by NAT_4:9;
6011 = 7*858 + 5; hence not 7 divides 6011 by NAT_4:9;
6011 = 11*546 + 5; hence not 11 divides 6011 by NAT_4:9;
6011 = 13*462 + 5; hence not 13 divides 6011 by NAT_4:9;
6011 = 17*353 + 10; hence not 17 divides 6011 by NAT_4:9;
6011 = 19*316 + 7; hence not 19 divides 6011 by NAT_4:9;
6011 = 23*261 + 8; hence not 23 divides 6011 by NAT_4:9;
6011 = 29*207 + 8; hence not 29 divides 6011 by NAT_4:9;
6011 = 31*193 + 28; hence not 31 divides 6011 by NAT_4:9;
6011 = 37*162 + 17; hence not 37 divides 6011 by NAT_4:9;
6011 = 41*146 + 25; hence not 41 divides 6011 by NAT_4:9;
6011 = 43*139 + 34; hence not 43 divides 6011 by NAT_4:9;
6011 = 47*127 + 42; hence not 47 divides 6011 by NAT_4:9;
6011 = 53*113 + 22; hence not 53 divides 6011 by NAT_4:9;
6011 = 59*101 + 52; hence not 59 divides 6011 by NAT_4:9;
6011 = 61*98 + 33; hence not 61 divides 6011 by NAT_4:9;
6011 = 67*89 + 48; hence not 67 divides 6011 by NAT_4:9;
6011 = 71*84 + 47; hence not 71 divides 6011 by NAT_4:9;
6011 = 73*82 + 25; hence not 73 divides 6011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6011 & n is prime
holds not n divides 6011 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6029 is prime
proof
now
6029 = 2*3014 + 1; hence not 2 divides 6029 by NAT_4:9;
6029 = 3*2009 + 2; hence not 3 divides 6029 by NAT_4:9;
6029 = 5*1205 + 4; hence not 5 divides 6029 by NAT_4:9;
6029 = 7*861 + 2; hence not 7 divides 6029 by NAT_4:9;
6029 = 11*548 + 1; hence not 11 divides 6029 by NAT_4:9;
6029 = 13*463 + 10; hence not 13 divides 6029 by NAT_4:9;
6029 = 17*354 + 11; hence not 17 divides 6029 by NAT_4:9;
6029 = 19*317 + 6; hence not 19 divides 6029 by NAT_4:9;
6029 = 23*262 + 3; hence not 23 divides 6029 by NAT_4:9;
6029 = 29*207 + 26; hence not 29 divides 6029 by NAT_4:9;
6029 = 31*194 + 15; hence not 31 divides 6029 by NAT_4:9;
6029 = 37*162 + 35; hence not 37 divides 6029 by NAT_4:9;
6029 = 41*147 + 2; hence not 41 divides 6029 by NAT_4:9;
6029 = 43*140 + 9; hence not 43 divides 6029 by NAT_4:9;
6029 = 47*128 + 13; hence not 47 divides 6029 by NAT_4:9;
6029 = 53*113 + 40; hence not 53 divides 6029 by NAT_4:9;
6029 = 59*102 + 11; hence not 59 divides 6029 by NAT_4:9;
6029 = 61*98 + 51; hence not 61 divides 6029 by NAT_4:9;
6029 = 67*89 + 66; hence not 67 divides 6029 by NAT_4:9;
6029 = 71*84 + 65; hence not 71 divides 6029 by NAT_4:9;
6029 = 73*82 + 43; hence not 73 divides 6029 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6029 & n is prime
holds not n divides 6029 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6037 is prime
proof
now
6037 = 2*3018 + 1; hence not 2 divides 6037 by NAT_4:9;
6037 = 3*2012 + 1; hence not 3 divides 6037 by NAT_4:9;
6037 = 5*1207 + 2; hence not 5 divides 6037 by NAT_4:9;
6037 = 7*862 + 3; hence not 7 divides 6037 by NAT_4:9;
6037 = 11*548 + 9; hence not 11 divides 6037 by NAT_4:9;
6037 = 13*464 + 5; hence not 13 divides 6037 by NAT_4:9;
6037 = 17*355 + 2; hence not 17 divides 6037 by NAT_4:9;
6037 = 19*317 + 14; hence not 19 divides 6037 by NAT_4:9;
6037 = 23*262 + 11; hence not 23 divides 6037 by NAT_4:9;
6037 = 29*208 + 5; hence not 29 divides 6037 by NAT_4:9;
6037 = 31*194 + 23; hence not 31 divides 6037 by NAT_4:9;
6037 = 37*163 + 6; hence not 37 divides 6037 by NAT_4:9;
6037 = 41*147 + 10; hence not 41 divides 6037 by NAT_4:9;
6037 = 43*140 + 17; hence not 43 divides 6037 by NAT_4:9;
6037 = 47*128 + 21; hence not 47 divides 6037 by NAT_4:9;
6037 = 53*113 + 48; hence not 53 divides 6037 by NAT_4:9;
6037 = 59*102 + 19; hence not 59 divides 6037 by NAT_4:9;
6037 = 61*98 + 59; hence not 61 divides 6037 by NAT_4:9;
6037 = 67*90 + 7; hence not 67 divides 6037 by NAT_4:9;
6037 = 71*85 + 2; hence not 71 divides 6037 by NAT_4:9;
6037 = 73*82 + 51; hence not 73 divides 6037 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6037 & n is prime
holds not n divides 6037 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6043 is prime
proof
now
6043 = 2*3021 + 1; hence not 2 divides 6043 by NAT_4:9;
6043 = 3*2014 + 1; hence not 3 divides 6043 by NAT_4:9;
6043 = 5*1208 + 3; hence not 5 divides 6043 by NAT_4:9;
6043 = 7*863 + 2; hence not 7 divides 6043 by NAT_4:9;
6043 = 11*549 + 4; hence not 11 divides 6043 by NAT_4:9;
6043 = 13*464 + 11; hence not 13 divides 6043 by NAT_4:9;
6043 = 17*355 + 8; hence not 17 divides 6043 by NAT_4:9;
6043 = 19*318 + 1; hence not 19 divides 6043 by NAT_4:9;
6043 = 23*262 + 17; hence not 23 divides 6043 by NAT_4:9;
6043 = 29*208 + 11; hence not 29 divides 6043 by NAT_4:9;
6043 = 31*194 + 29; hence not 31 divides 6043 by NAT_4:9;
6043 = 37*163 + 12; hence not 37 divides 6043 by NAT_4:9;
6043 = 41*147 + 16; hence not 41 divides 6043 by NAT_4:9;
6043 = 43*140 + 23; hence not 43 divides 6043 by NAT_4:9;
6043 = 47*128 + 27; hence not 47 divides 6043 by NAT_4:9;
6043 = 53*114 + 1; hence not 53 divides 6043 by NAT_4:9;
6043 = 59*102 + 25; hence not 59 divides 6043 by NAT_4:9;
6043 = 61*99 + 4; hence not 61 divides 6043 by NAT_4:9;
6043 = 67*90 + 13; hence not 67 divides 6043 by NAT_4:9;
6043 = 71*85 + 8; hence not 71 divides 6043 by NAT_4:9;
6043 = 73*82 + 57; hence not 73 divides 6043 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6043 & n is prime
holds not n divides 6043 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6047 is prime
proof
now
6047 = 2*3023 + 1; hence not 2 divides 6047 by NAT_4:9;
6047 = 3*2015 + 2; hence not 3 divides 6047 by NAT_4:9;
6047 = 5*1209 + 2; hence not 5 divides 6047 by NAT_4:9;
6047 = 7*863 + 6; hence not 7 divides 6047 by NAT_4:9;
6047 = 11*549 + 8; hence not 11 divides 6047 by NAT_4:9;
6047 = 13*465 + 2; hence not 13 divides 6047 by NAT_4:9;
6047 = 17*355 + 12; hence not 17 divides 6047 by NAT_4:9;
6047 = 19*318 + 5; hence not 19 divides 6047 by NAT_4:9;
6047 = 23*262 + 21; hence not 23 divides 6047 by NAT_4:9;
6047 = 29*208 + 15; hence not 29 divides 6047 by NAT_4:9;
6047 = 31*195 + 2; hence not 31 divides 6047 by NAT_4:9;
6047 = 37*163 + 16; hence not 37 divides 6047 by NAT_4:9;
6047 = 41*147 + 20; hence not 41 divides 6047 by NAT_4:9;
6047 = 43*140 + 27; hence not 43 divides 6047 by NAT_4:9;
6047 = 47*128 + 31; hence not 47 divides 6047 by NAT_4:9;
6047 = 53*114 + 5; hence not 53 divides 6047 by NAT_4:9;
6047 = 59*102 + 29; hence not 59 divides 6047 by NAT_4:9;
6047 = 61*99 + 8; hence not 61 divides 6047 by NAT_4:9;
6047 = 67*90 + 17; hence not 67 divides 6047 by NAT_4:9;
6047 = 71*85 + 12; hence not 71 divides 6047 by NAT_4:9;
6047 = 73*82 + 61; hence not 73 divides 6047 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6047 & n is prime
holds not n divides 6047 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6053 is prime
proof
now
6053 = 2*3026 + 1; hence not 2 divides 6053 by NAT_4:9;
6053 = 3*2017 + 2; hence not 3 divides 6053 by NAT_4:9;
6053 = 5*1210 + 3; hence not 5 divides 6053 by NAT_4:9;
6053 = 7*864 + 5; hence not 7 divides 6053 by NAT_4:9;
6053 = 11*550 + 3; hence not 11 divides 6053 by NAT_4:9;
6053 = 13*465 + 8; hence not 13 divides 6053 by NAT_4:9;
6053 = 17*356 + 1; hence not 17 divides 6053 by NAT_4:9;
6053 = 19*318 + 11; hence not 19 divides 6053 by NAT_4:9;
6053 = 23*263 + 4; hence not 23 divides 6053 by NAT_4:9;
6053 = 29*208 + 21; hence not 29 divides 6053 by NAT_4:9;
6053 = 31*195 + 8; hence not 31 divides 6053 by NAT_4:9;
6053 = 37*163 + 22; hence not 37 divides 6053 by NAT_4:9;
6053 = 41*147 + 26; hence not 41 divides 6053 by NAT_4:9;
6053 = 43*140 + 33; hence not 43 divides 6053 by NAT_4:9;
6053 = 47*128 + 37; hence not 47 divides 6053 by NAT_4:9;
6053 = 53*114 + 11; hence not 53 divides 6053 by NAT_4:9;
6053 = 59*102 + 35; hence not 59 divides 6053 by NAT_4:9;
6053 = 61*99 + 14; hence not 61 divides 6053 by NAT_4:9;
6053 = 67*90 + 23; hence not 67 divides 6053 by NAT_4:9;
6053 = 71*85 + 18; hence not 71 divides 6053 by NAT_4:9;
6053 = 73*82 + 67; hence not 73 divides 6053 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6053 & n is prime
holds not n divides 6053 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
6067 is prime
proof
now
6067 = 2*3033 + 1; hence not 2 divides 6067 by NAT_4:9;
6067 = 3*2022 + 1; hence not 3 divides 6067 by NAT_4:9;
6067 = 5*1213 + 2; hence not 5 divides 6067 by NAT_4:9;
6067 = 7*866 + 5; hence not 7 divides 6067 by NAT_4:9;
6067 = 11*551 + 6; hence not 11 divides 6067 by NAT_4:9;
6067 = 13*466 + 9; hence not 13 divides 6067 by NAT_4:9;
6067 = 17*356 + 15; hence not 17 divides 6067 by NAT_4:9;
6067 = 19*319 + 6; hence not 19 divides 6067 by NAT_4:9;
6067 = 23*263 + 18; hence not 23 divides 6067 by NAT_4:9;
6067 = 29*209 + 6; hence not 29 divides 6067 by NAT_4:9;
6067 = 31*195 + 22; hence not 31 divides 6067 by NAT_4:9;
6067 = 37*163 + 36; hence not 37 divides 6067 by NAT_4:9;
6067 = 41*147 + 40; hence not 41 divides 6067 by NAT_4:9;
6067 = 43*141 + 4; hence not 43 divides 6067 by NAT_4:9;
6067 = 47*129 + 4; hence not 47 divides 6067 by NAT_4:9;
6067 = 53*114 + 25; hence not 53 divides 6067 by NAT_4:9;
6067 = 59*102 + 49; hence not 59 divides 6067 by NAT_4:9;
6067 = 61*99 + 28; hence not 61 divides 6067 by NAT_4:9;
6067 = 67*90 + 37; hence not 67 divides 6067 by NAT_4:9;
6067 = 71*85 + 32; hence not 71 divides 6067 by NAT_4:9;
6067 = 73*83 + 8; hence not 73 divides 6067 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6067 & n is prime
holds not n divides 6067 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6073 is prime
proof
now
6073 = 2*3036 + 1; hence not 2 divides 6073 by NAT_4:9;
6073 = 3*2024 + 1; hence not 3 divides 6073 by NAT_4:9;
6073 = 5*1214 + 3; hence not 5 divides 6073 by NAT_4:9;
6073 = 7*867 + 4; hence not 7 divides 6073 by NAT_4:9;
6073 = 11*552 + 1; hence not 11 divides 6073 by NAT_4:9;
6073 = 13*467 + 2; hence not 13 divides 6073 by NAT_4:9;
6073 = 17*357 + 4; hence not 17 divides 6073 by NAT_4:9;
6073 = 19*319 + 12; hence not 19 divides 6073 by NAT_4:9;
6073 = 23*264 + 1; hence not 23 divides 6073 by NAT_4:9;
6073 = 29*209 + 12; hence not 29 divides 6073 by NAT_4:9;
6073 = 31*195 + 28; hence not 31 divides 6073 by NAT_4:9;
6073 = 37*164 + 5; hence not 37 divides 6073 by NAT_4:9;
6073 = 41*148 + 5; hence not 41 divides 6073 by NAT_4:9;
6073 = 43*141 + 10; hence not 43 divides 6073 by NAT_4:9;
6073 = 47*129 + 10; hence not 47 divides 6073 by NAT_4:9;
6073 = 53*114 + 31; hence not 53 divides 6073 by NAT_4:9;
6073 = 59*102 + 55; hence not 59 divides 6073 by NAT_4:9;
6073 = 61*99 + 34; hence not 61 divides 6073 by NAT_4:9;
6073 = 67*90 + 43; hence not 67 divides 6073 by NAT_4:9;
6073 = 71*85 + 38; hence not 71 divides 6073 by NAT_4:9;
6073 = 73*83 + 14; hence not 73 divides 6073 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6073 & n is prime
holds not n divides 6073 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6079 is prime
proof
now
6079 = 2*3039 + 1; hence not 2 divides 6079 by NAT_4:9;
6079 = 3*2026 + 1; hence not 3 divides 6079 by NAT_4:9;
6079 = 5*1215 + 4; hence not 5 divides 6079 by NAT_4:9;
6079 = 7*868 + 3; hence not 7 divides 6079 by NAT_4:9;
6079 = 11*552 + 7; hence not 11 divides 6079 by NAT_4:9;
6079 = 13*467 + 8; hence not 13 divides 6079 by NAT_4:9;
6079 = 17*357 + 10; hence not 17 divides 6079 by NAT_4:9;
6079 = 19*319 + 18; hence not 19 divides 6079 by NAT_4:9;
6079 = 23*264 + 7; hence not 23 divides 6079 by NAT_4:9;
6079 = 29*209 + 18; hence not 29 divides 6079 by NAT_4:9;
6079 = 31*196 + 3; hence not 31 divides 6079 by NAT_4:9;
6079 = 37*164 + 11; hence not 37 divides 6079 by NAT_4:9;
6079 = 41*148 + 11; hence not 41 divides 6079 by NAT_4:9;
6079 = 43*141 + 16; hence not 43 divides 6079 by NAT_4:9;
6079 = 47*129 + 16; hence not 47 divides 6079 by NAT_4:9;
6079 = 53*114 + 37; hence not 53 divides 6079 by NAT_4:9;
6079 = 59*103 + 2; hence not 59 divides 6079 by NAT_4:9;
6079 = 61*99 + 40; hence not 61 divides 6079 by NAT_4:9;
6079 = 67*90 + 49; hence not 67 divides 6079 by NAT_4:9;
6079 = 71*85 + 44; hence not 71 divides 6079 by NAT_4:9;
6079 = 73*83 + 20; hence not 73 divides 6079 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6079 & n is prime
holds not n divides 6079 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6089 is prime
proof
now
6089 = 2*3044 + 1; hence not 2 divides 6089 by NAT_4:9;
6089 = 3*2029 + 2; hence not 3 divides 6089 by NAT_4:9;
6089 = 5*1217 + 4; hence not 5 divides 6089 by NAT_4:9;
6089 = 7*869 + 6; hence not 7 divides 6089 by NAT_4:9;
6089 = 11*553 + 6; hence not 11 divides 6089 by NAT_4:9;
6089 = 13*468 + 5; hence not 13 divides 6089 by NAT_4:9;
6089 = 17*358 + 3; hence not 17 divides 6089 by NAT_4:9;
6089 = 19*320 + 9; hence not 19 divides 6089 by NAT_4:9;
6089 = 23*264 + 17; hence not 23 divides 6089 by NAT_4:9;
6089 = 29*209 + 28; hence not 29 divides 6089 by NAT_4:9;
6089 = 31*196 + 13; hence not 31 divides 6089 by NAT_4:9;
6089 = 37*164 + 21; hence not 37 divides 6089 by NAT_4:9;
6089 = 41*148 + 21; hence not 41 divides 6089 by NAT_4:9;
6089 = 43*141 + 26; hence not 43 divides 6089 by NAT_4:9;
6089 = 47*129 + 26; hence not 47 divides 6089 by NAT_4:9;
6089 = 53*114 + 47; hence not 53 divides 6089 by NAT_4:9;
6089 = 59*103 + 12; hence not 59 divides 6089 by NAT_4:9;
6089 = 61*99 + 50; hence not 61 divides 6089 by NAT_4:9;
6089 = 67*90 + 59; hence not 67 divides 6089 by NAT_4:9;
6089 = 71*85 + 54; hence not 71 divides 6089 by NAT_4:9;
6089 = 73*83 + 30; hence not 73 divides 6089 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6089 & n is prime
holds not n divides 6089 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6091 is prime
proof
now
6091 = 2*3045 + 1; hence not 2 divides 6091 by NAT_4:9;
6091 = 3*2030 + 1; hence not 3 divides 6091 by NAT_4:9;
6091 = 5*1218 + 1; hence not 5 divides 6091 by NAT_4:9;
6091 = 7*870 + 1; hence not 7 divides 6091 by NAT_4:9;
6091 = 11*553 + 8; hence not 11 divides 6091 by NAT_4:9;
6091 = 13*468 + 7; hence not 13 divides 6091 by NAT_4:9;
6091 = 17*358 + 5; hence not 17 divides 6091 by NAT_4:9;
6091 = 19*320 + 11; hence not 19 divides 6091 by NAT_4:9;
6091 = 23*264 + 19; hence not 23 divides 6091 by NAT_4:9;
6091 = 29*210 + 1; hence not 29 divides 6091 by NAT_4:9;
6091 = 31*196 + 15; hence not 31 divides 6091 by NAT_4:9;
6091 = 37*164 + 23; hence not 37 divides 6091 by NAT_4:9;
6091 = 41*148 + 23; hence not 41 divides 6091 by NAT_4:9;
6091 = 43*141 + 28; hence not 43 divides 6091 by NAT_4:9;
6091 = 47*129 + 28; hence not 47 divides 6091 by NAT_4:9;
6091 = 53*114 + 49; hence not 53 divides 6091 by NAT_4:9;
6091 = 59*103 + 14; hence not 59 divides 6091 by NAT_4:9;
6091 = 61*99 + 52; hence not 61 divides 6091 by NAT_4:9;
6091 = 67*90 + 61; hence not 67 divides 6091 by NAT_4:9;
6091 = 71*85 + 56; hence not 71 divides 6091 by NAT_4:9;
6091 = 73*83 + 32; hence not 73 divides 6091 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6091 & n is prime
holds not n divides 6091 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6101 is prime
proof
now
6101 = 2*3050 + 1; hence not 2 divides 6101 by NAT_4:9;
6101 = 3*2033 + 2; hence not 3 divides 6101 by NAT_4:9;
6101 = 5*1220 + 1; hence not 5 divides 6101 by NAT_4:9;
6101 = 7*871 + 4; hence not 7 divides 6101 by NAT_4:9;
6101 = 11*554 + 7; hence not 11 divides 6101 by NAT_4:9;
6101 = 13*469 + 4; hence not 13 divides 6101 by NAT_4:9;
6101 = 17*358 + 15; hence not 17 divides 6101 by NAT_4:9;
6101 = 19*321 + 2; hence not 19 divides 6101 by NAT_4:9;
6101 = 23*265 + 6; hence not 23 divides 6101 by NAT_4:9;
6101 = 29*210 + 11; hence not 29 divides 6101 by NAT_4:9;
6101 = 31*196 + 25; hence not 31 divides 6101 by NAT_4:9;
6101 = 37*164 + 33; hence not 37 divides 6101 by NAT_4:9;
6101 = 41*148 + 33; hence not 41 divides 6101 by NAT_4:9;
6101 = 43*141 + 38; hence not 43 divides 6101 by NAT_4:9;
6101 = 47*129 + 38; hence not 47 divides 6101 by NAT_4:9;
6101 = 53*115 + 6; hence not 53 divides 6101 by NAT_4:9;
6101 = 59*103 + 24; hence not 59 divides 6101 by NAT_4:9;
6101 = 61*100 + 1; hence not 61 divides 6101 by NAT_4:9;
6101 = 67*91 + 4; hence not 67 divides 6101 by NAT_4:9;
6101 = 71*85 + 66; hence not 71 divides 6101 by NAT_4:9;
6101 = 73*83 + 42; hence not 73 divides 6101 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6101 & n is prime
holds not n divides 6101 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6113 is prime
proof
now
6113 = 2*3056 + 1; hence not 2 divides 6113 by NAT_4:9;
6113 = 3*2037 + 2; hence not 3 divides 6113 by NAT_4:9;
6113 = 5*1222 + 3; hence not 5 divides 6113 by NAT_4:9;
6113 = 7*873 + 2; hence not 7 divides 6113 by NAT_4:9;
6113 = 11*555 + 8; hence not 11 divides 6113 by NAT_4:9;
6113 = 13*470 + 3; hence not 13 divides 6113 by NAT_4:9;
6113 = 17*359 + 10; hence not 17 divides 6113 by NAT_4:9;
6113 = 19*321 + 14; hence not 19 divides 6113 by NAT_4:9;
6113 = 23*265 + 18; hence not 23 divides 6113 by NAT_4:9;
6113 = 29*210 + 23; hence not 29 divides 6113 by NAT_4:9;
6113 = 31*197 + 6; hence not 31 divides 6113 by NAT_4:9;
6113 = 37*165 + 8; hence not 37 divides 6113 by NAT_4:9;
6113 = 41*149 + 4; hence not 41 divides 6113 by NAT_4:9;
6113 = 43*142 + 7; hence not 43 divides 6113 by NAT_4:9;
6113 = 47*130 + 3; hence not 47 divides 6113 by NAT_4:9;
6113 = 53*115 + 18; hence not 53 divides 6113 by NAT_4:9;
6113 = 59*103 + 36; hence not 59 divides 6113 by NAT_4:9;
6113 = 61*100 + 13; hence not 61 divides 6113 by NAT_4:9;
6113 = 67*91 + 16; hence not 67 divides 6113 by NAT_4:9;
6113 = 71*86 + 7; hence not 71 divides 6113 by NAT_4:9;
6113 = 73*83 + 54; hence not 73 divides 6113 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6113 & n is prime
holds not n divides 6113 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6121 is prime
proof
now
6121 = 2*3060 + 1; hence not 2 divides 6121 by NAT_4:9;
6121 = 3*2040 + 1; hence not 3 divides 6121 by NAT_4:9;
6121 = 5*1224 + 1; hence not 5 divides 6121 by NAT_4:9;
6121 = 7*874 + 3; hence not 7 divides 6121 by NAT_4:9;
6121 = 11*556 + 5; hence not 11 divides 6121 by NAT_4:9;
6121 = 13*470 + 11; hence not 13 divides 6121 by NAT_4:9;
6121 = 17*360 + 1; hence not 17 divides 6121 by NAT_4:9;
6121 = 19*322 + 3; hence not 19 divides 6121 by NAT_4:9;
6121 = 23*266 + 3; hence not 23 divides 6121 by NAT_4:9;
6121 = 29*211 + 2; hence not 29 divides 6121 by NAT_4:9;
6121 = 31*197 + 14; hence not 31 divides 6121 by NAT_4:9;
6121 = 37*165 + 16; hence not 37 divides 6121 by NAT_4:9;
6121 = 41*149 + 12; hence not 41 divides 6121 by NAT_4:9;
6121 = 43*142 + 15; hence not 43 divides 6121 by NAT_4:9;
6121 = 47*130 + 11; hence not 47 divides 6121 by NAT_4:9;
6121 = 53*115 + 26; hence not 53 divides 6121 by NAT_4:9;
6121 = 59*103 + 44; hence not 59 divides 6121 by NAT_4:9;
6121 = 61*100 + 21; hence not 61 divides 6121 by NAT_4:9;
6121 = 67*91 + 24; hence not 67 divides 6121 by NAT_4:9;
6121 = 71*86 + 15; hence not 71 divides 6121 by NAT_4:9;
6121 = 73*83 + 62; hence not 73 divides 6121 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6121 & n is prime
holds not n divides 6121 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6131 is prime
proof
now
6131 = 2*3065 + 1; hence not 2 divides 6131 by NAT_4:9;
6131 = 3*2043 + 2; hence not 3 divides 6131 by NAT_4:9;
6131 = 5*1226 + 1; hence not 5 divides 6131 by NAT_4:9;
6131 = 7*875 + 6; hence not 7 divides 6131 by NAT_4:9;
6131 = 11*557 + 4; hence not 11 divides 6131 by NAT_4:9;
6131 = 13*471 + 8; hence not 13 divides 6131 by NAT_4:9;
6131 = 17*360 + 11; hence not 17 divides 6131 by NAT_4:9;
6131 = 19*322 + 13; hence not 19 divides 6131 by NAT_4:9;
6131 = 23*266 + 13; hence not 23 divides 6131 by NAT_4:9;
6131 = 29*211 + 12; hence not 29 divides 6131 by NAT_4:9;
6131 = 31*197 + 24; hence not 31 divides 6131 by NAT_4:9;
6131 = 37*165 + 26; hence not 37 divides 6131 by NAT_4:9;
6131 = 41*149 + 22; hence not 41 divides 6131 by NAT_4:9;
6131 = 43*142 + 25; hence not 43 divides 6131 by NAT_4:9;
6131 = 47*130 + 21; hence not 47 divides 6131 by NAT_4:9;
6131 = 53*115 + 36; hence not 53 divides 6131 by NAT_4:9;
6131 = 59*103 + 54; hence not 59 divides 6131 by NAT_4:9;
6131 = 61*100 + 31; hence not 61 divides 6131 by NAT_4:9;
6131 = 67*91 + 34; hence not 67 divides 6131 by NAT_4:9;
6131 = 71*86 + 25; hence not 71 divides 6131 by NAT_4:9;
6131 = 73*83 + 72; hence not 73 divides 6131 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6131 & n is prime
holds not n divides 6131 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6133 is prime
proof
now
6133 = 2*3066 + 1; hence not 2 divides 6133 by NAT_4:9;
6133 = 3*2044 + 1; hence not 3 divides 6133 by NAT_4:9;
6133 = 5*1226 + 3; hence not 5 divides 6133 by NAT_4:9;
6133 = 7*876 + 1; hence not 7 divides 6133 by NAT_4:9;
6133 = 11*557 + 6; hence not 11 divides 6133 by NAT_4:9;
6133 = 13*471 + 10; hence not 13 divides 6133 by NAT_4:9;
6133 = 17*360 + 13; hence not 17 divides 6133 by NAT_4:9;
6133 = 19*322 + 15; hence not 19 divides 6133 by NAT_4:9;
6133 = 23*266 + 15; hence not 23 divides 6133 by NAT_4:9;
6133 = 29*211 + 14; hence not 29 divides 6133 by NAT_4:9;
6133 = 31*197 + 26; hence not 31 divides 6133 by NAT_4:9;
6133 = 37*165 + 28; hence not 37 divides 6133 by NAT_4:9;
6133 = 41*149 + 24; hence not 41 divides 6133 by NAT_4:9;
6133 = 43*142 + 27; hence not 43 divides 6133 by NAT_4:9;
6133 = 47*130 + 23; hence not 47 divides 6133 by NAT_4:9;
6133 = 53*115 + 38; hence not 53 divides 6133 by NAT_4:9;
6133 = 59*103 + 56; hence not 59 divides 6133 by NAT_4:9;
6133 = 61*100 + 33; hence not 61 divides 6133 by NAT_4:9;
6133 = 67*91 + 36; hence not 67 divides 6133 by NAT_4:9;
6133 = 71*86 + 27; hence not 71 divides 6133 by NAT_4:9;
6133 = 73*84 + 1; hence not 73 divides 6133 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6133 & n is prime
holds not n divides 6133 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6143 is prime
proof
now
6143 = 2*3071 + 1; hence not 2 divides 6143 by NAT_4:9;
6143 = 3*2047 + 2; hence not 3 divides 6143 by NAT_4:9;
6143 = 5*1228 + 3; hence not 5 divides 6143 by NAT_4:9;
6143 = 7*877 + 4; hence not 7 divides 6143 by NAT_4:9;
6143 = 11*558 + 5; hence not 11 divides 6143 by NAT_4:9;
6143 = 13*472 + 7; hence not 13 divides 6143 by NAT_4:9;
6143 = 17*361 + 6; hence not 17 divides 6143 by NAT_4:9;
6143 = 19*323 + 6; hence not 19 divides 6143 by NAT_4:9;
6143 = 23*267 + 2; hence not 23 divides 6143 by NAT_4:9;
6143 = 29*211 + 24; hence not 29 divides 6143 by NAT_4:9;
6143 = 31*198 + 5; hence not 31 divides 6143 by NAT_4:9;
6143 = 37*166 + 1; hence not 37 divides 6143 by NAT_4:9;
6143 = 41*149 + 34; hence not 41 divides 6143 by NAT_4:9;
6143 = 43*142 + 37; hence not 43 divides 6143 by NAT_4:9;
6143 = 47*130 + 33; hence not 47 divides 6143 by NAT_4:9;
6143 = 53*115 + 48; hence not 53 divides 6143 by NAT_4:9;
6143 = 59*104 + 7; hence not 59 divides 6143 by NAT_4:9;
6143 = 61*100 + 43; hence not 61 divides 6143 by NAT_4:9;
6143 = 67*91 + 46; hence not 67 divides 6143 by NAT_4:9;
6143 = 71*86 + 37; hence not 71 divides 6143 by NAT_4:9;
6143 = 73*84 + 11; hence not 73 divides 6143 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6143 & n is prime
holds not n divides 6143 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6151 is prime
proof
now
6151 = 2*3075 + 1; hence not 2 divides 6151 by NAT_4:9;
6151 = 3*2050 + 1; hence not 3 divides 6151 by NAT_4:9;
6151 = 5*1230 + 1; hence not 5 divides 6151 by NAT_4:9;
6151 = 7*878 + 5; hence not 7 divides 6151 by NAT_4:9;
6151 = 11*559 + 2; hence not 11 divides 6151 by NAT_4:9;
6151 = 13*473 + 2; hence not 13 divides 6151 by NAT_4:9;
6151 = 17*361 + 14; hence not 17 divides 6151 by NAT_4:9;
6151 = 19*323 + 14; hence not 19 divides 6151 by NAT_4:9;
6151 = 23*267 + 10; hence not 23 divides 6151 by NAT_4:9;
6151 = 29*212 + 3; hence not 29 divides 6151 by NAT_4:9;
6151 = 31*198 + 13; hence not 31 divides 6151 by NAT_4:9;
6151 = 37*166 + 9; hence not 37 divides 6151 by NAT_4:9;
6151 = 41*150 + 1; hence not 41 divides 6151 by NAT_4:9;
6151 = 43*143 + 2; hence not 43 divides 6151 by NAT_4:9;
6151 = 47*130 + 41; hence not 47 divides 6151 by NAT_4:9;
6151 = 53*116 + 3; hence not 53 divides 6151 by NAT_4:9;
6151 = 59*104 + 15; hence not 59 divides 6151 by NAT_4:9;
6151 = 61*100 + 51; hence not 61 divides 6151 by NAT_4:9;
6151 = 67*91 + 54; hence not 67 divides 6151 by NAT_4:9;
6151 = 71*86 + 45; hence not 71 divides 6151 by NAT_4:9;
6151 = 73*84 + 19; hence not 73 divides 6151 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6151 & n is prime
holds not n divides 6151 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6163 is prime
proof
now
6163 = 2*3081 + 1; hence not 2 divides 6163 by NAT_4:9;
6163 = 3*2054 + 1; hence not 3 divides 6163 by NAT_4:9;
6163 = 5*1232 + 3; hence not 5 divides 6163 by NAT_4:9;
6163 = 7*880 + 3; hence not 7 divides 6163 by NAT_4:9;
6163 = 11*560 + 3; hence not 11 divides 6163 by NAT_4:9;
6163 = 13*474 + 1; hence not 13 divides 6163 by NAT_4:9;
6163 = 17*362 + 9; hence not 17 divides 6163 by NAT_4:9;
6163 = 19*324 + 7; hence not 19 divides 6163 by NAT_4:9;
6163 = 23*267 + 22; hence not 23 divides 6163 by NAT_4:9;
6163 = 29*212 + 15; hence not 29 divides 6163 by NAT_4:9;
6163 = 31*198 + 25; hence not 31 divides 6163 by NAT_4:9;
6163 = 37*166 + 21; hence not 37 divides 6163 by NAT_4:9;
6163 = 41*150 + 13; hence not 41 divides 6163 by NAT_4:9;
6163 = 43*143 + 14; hence not 43 divides 6163 by NAT_4:9;
6163 = 47*131 + 6; hence not 47 divides 6163 by NAT_4:9;
6163 = 53*116 + 15; hence not 53 divides 6163 by NAT_4:9;
6163 = 59*104 + 27; hence not 59 divides 6163 by NAT_4:9;
6163 = 61*101 + 2; hence not 61 divides 6163 by NAT_4:9;
6163 = 67*91 + 66; hence not 67 divides 6163 by NAT_4:9;
6163 = 71*86 + 57; hence not 71 divides 6163 by NAT_4:9;
6163 = 73*84 + 31; hence not 73 divides 6163 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6163 & n is prime
holds not n divides 6163 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6173 is prime
proof
now
6173 = 2*3086 + 1; hence not 2 divides 6173 by NAT_4:9;
6173 = 3*2057 + 2; hence not 3 divides 6173 by NAT_4:9;
6173 = 5*1234 + 3; hence not 5 divides 6173 by NAT_4:9;
6173 = 7*881 + 6; hence not 7 divides 6173 by NAT_4:9;
6173 = 11*561 + 2; hence not 11 divides 6173 by NAT_4:9;
6173 = 13*474 + 11; hence not 13 divides 6173 by NAT_4:9;
6173 = 17*363 + 2; hence not 17 divides 6173 by NAT_4:9;
6173 = 19*324 + 17; hence not 19 divides 6173 by NAT_4:9;
6173 = 23*268 + 9; hence not 23 divides 6173 by NAT_4:9;
6173 = 29*212 + 25; hence not 29 divides 6173 by NAT_4:9;
6173 = 31*199 + 4; hence not 31 divides 6173 by NAT_4:9;
6173 = 37*166 + 31; hence not 37 divides 6173 by NAT_4:9;
6173 = 41*150 + 23; hence not 41 divides 6173 by NAT_4:9;
6173 = 43*143 + 24; hence not 43 divides 6173 by NAT_4:9;
6173 = 47*131 + 16; hence not 47 divides 6173 by NAT_4:9;
6173 = 53*116 + 25; hence not 53 divides 6173 by NAT_4:9;
6173 = 59*104 + 37; hence not 59 divides 6173 by NAT_4:9;
6173 = 61*101 + 12; hence not 61 divides 6173 by NAT_4:9;
6173 = 67*92 + 9; hence not 67 divides 6173 by NAT_4:9;
6173 = 71*86 + 67; hence not 71 divides 6173 by NAT_4:9;
6173 = 73*84 + 41; hence not 73 divides 6173 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6173 & n is prime
holds not n divides 6173 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
6197 is prime
proof
now
6197 = 2*3098 + 1; hence not 2 divides 6197 by NAT_4:9;
6197 = 3*2065 + 2; hence not 3 divides 6197 by NAT_4:9;
6197 = 5*1239 + 2; hence not 5 divides 6197 by NAT_4:9;
6197 = 7*885 + 2; hence not 7 divides 6197 by NAT_4:9;
6197 = 11*563 + 4; hence not 11 divides 6197 by NAT_4:9;
6197 = 13*476 + 9; hence not 13 divides 6197 by NAT_4:9;
6197 = 17*364 + 9; hence not 17 divides 6197 by NAT_4:9;
6197 = 19*326 + 3; hence not 19 divides 6197 by NAT_4:9;
6197 = 23*269 + 10; hence not 23 divides 6197 by NAT_4:9;
6197 = 29*213 + 20; hence not 29 divides 6197 by NAT_4:9;
6197 = 31*199 + 28; hence not 31 divides 6197 by NAT_4:9;
6197 = 37*167 + 18; hence not 37 divides 6197 by NAT_4:9;
6197 = 41*151 + 6; hence not 41 divides 6197 by NAT_4:9;
6197 = 43*144 + 5; hence not 43 divides 6197 by NAT_4:9;
6197 = 47*131 + 40; hence not 47 divides 6197 by NAT_4:9;
6197 = 53*116 + 49; hence not 53 divides 6197 by NAT_4:9;
6197 = 59*105 + 2; hence not 59 divides 6197 by NAT_4:9;
6197 = 61*101 + 36; hence not 61 divides 6197 by NAT_4:9;
6197 = 67*92 + 33; hence not 67 divides 6197 by NAT_4:9;
6197 = 71*87 + 20; hence not 71 divides 6197 by NAT_4:9;
6197 = 73*84 + 65; hence not 73 divides 6197 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6197 & n is prime
holds not n divides 6197 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6199 is prime
proof
now
6199 = 2*3099 + 1; hence not 2 divides 6199 by NAT_4:9;
6199 = 3*2066 + 1; hence not 3 divides 6199 by NAT_4:9;
6199 = 5*1239 + 4; hence not 5 divides 6199 by NAT_4:9;
6199 = 7*885 + 4; hence not 7 divides 6199 by NAT_4:9;
6199 = 11*563 + 6; hence not 11 divides 6199 by NAT_4:9;
6199 = 13*476 + 11; hence not 13 divides 6199 by NAT_4:9;
6199 = 17*364 + 11; hence not 17 divides 6199 by NAT_4:9;
6199 = 19*326 + 5; hence not 19 divides 6199 by NAT_4:9;
6199 = 23*269 + 12; hence not 23 divides 6199 by NAT_4:9;
6199 = 29*213 + 22; hence not 29 divides 6199 by NAT_4:9;
6199 = 31*199 + 30; hence not 31 divides 6199 by NAT_4:9;
6199 = 37*167 + 20; hence not 37 divides 6199 by NAT_4:9;
6199 = 41*151 + 8; hence not 41 divides 6199 by NAT_4:9;
6199 = 43*144 + 7; hence not 43 divides 6199 by NAT_4:9;
6199 = 47*131 + 42; hence not 47 divides 6199 by NAT_4:9;
6199 = 53*116 + 51; hence not 53 divides 6199 by NAT_4:9;
6199 = 59*105 + 4; hence not 59 divides 6199 by NAT_4:9;
6199 = 61*101 + 38; hence not 61 divides 6199 by NAT_4:9;
6199 = 67*92 + 35; hence not 67 divides 6199 by NAT_4:9;
6199 = 71*87 + 22; hence not 71 divides 6199 by NAT_4:9;
6199 = 73*84 + 67; hence not 73 divides 6199 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6199 & n is prime
holds not n divides 6199 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6203 is prime
proof
now
6203 = 2*3101 + 1; hence not 2 divides 6203 by NAT_4:9;
6203 = 3*2067 + 2; hence not 3 divides 6203 by NAT_4:9;
6203 = 5*1240 + 3; hence not 5 divides 6203 by NAT_4:9;
6203 = 7*886 + 1; hence not 7 divides 6203 by NAT_4:9;
6203 = 11*563 + 10; hence not 11 divides 6203 by NAT_4:9;
6203 = 13*477 + 2; hence not 13 divides 6203 by NAT_4:9;
6203 = 17*364 + 15; hence not 17 divides 6203 by NAT_4:9;
6203 = 19*326 + 9; hence not 19 divides 6203 by NAT_4:9;
6203 = 23*269 + 16; hence not 23 divides 6203 by NAT_4:9;
6203 = 29*213 + 26; hence not 29 divides 6203 by NAT_4:9;
6203 = 31*200 + 3; hence not 31 divides 6203 by NAT_4:9;
6203 = 37*167 + 24; hence not 37 divides 6203 by NAT_4:9;
6203 = 41*151 + 12; hence not 41 divides 6203 by NAT_4:9;
6203 = 43*144 + 11; hence not 43 divides 6203 by NAT_4:9;
6203 = 47*131 + 46; hence not 47 divides 6203 by NAT_4:9;
6203 = 53*117 + 2; hence not 53 divides 6203 by NAT_4:9;
6203 = 59*105 + 8; hence not 59 divides 6203 by NAT_4:9;
6203 = 61*101 + 42; hence not 61 divides 6203 by NAT_4:9;
6203 = 67*92 + 39; hence not 67 divides 6203 by NAT_4:9;
6203 = 71*87 + 26; hence not 71 divides 6203 by NAT_4:9;
6203 = 73*84 + 71; hence not 73 divides 6203 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6203 & n is prime
holds not n divides 6203 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6211 is prime
proof
now
6211 = 2*3105 + 1; hence not 2 divides 6211 by NAT_4:9;
6211 = 3*2070 + 1; hence not 3 divides 6211 by NAT_4:9;
6211 = 5*1242 + 1; hence not 5 divides 6211 by NAT_4:9;
6211 = 7*887 + 2; hence not 7 divides 6211 by NAT_4:9;
6211 = 11*564 + 7; hence not 11 divides 6211 by NAT_4:9;
6211 = 13*477 + 10; hence not 13 divides 6211 by NAT_4:9;
6211 = 17*365 + 6; hence not 17 divides 6211 by NAT_4:9;
6211 = 19*326 + 17; hence not 19 divides 6211 by NAT_4:9;
6211 = 23*270 + 1; hence not 23 divides 6211 by NAT_4:9;
6211 = 29*214 + 5; hence not 29 divides 6211 by NAT_4:9;
6211 = 31*200 + 11; hence not 31 divides 6211 by NAT_4:9;
6211 = 37*167 + 32; hence not 37 divides 6211 by NAT_4:9;
6211 = 41*151 + 20; hence not 41 divides 6211 by NAT_4:9;
6211 = 43*144 + 19; hence not 43 divides 6211 by NAT_4:9;
6211 = 47*132 + 7; hence not 47 divides 6211 by NAT_4:9;
6211 = 53*117 + 10; hence not 53 divides 6211 by NAT_4:9;
6211 = 59*105 + 16; hence not 59 divides 6211 by NAT_4:9;
6211 = 61*101 + 50; hence not 61 divides 6211 by NAT_4:9;
6211 = 67*92 + 47; hence not 67 divides 6211 by NAT_4:9;
6211 = 71*87 + 34; hence not 71 divides 6211 by NAT_4:9;
6211 = 73*85 + 6; hence not 73 divides 6211 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6211 & n is prime
holds not n divides 6211 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6217 is prime
proof
now
6217 = 2*3108 + 1; hence not 2 divides 6217 by NAT_4:9;
6217 = 3*2072 + 1; hence not 3 divides 6217 by NAT_4:9;
6217 = 5*1243 + 2; hence not 5 divides 6217 by NAT_4:9;
6217 = 7*888 + 1; hence not 7 divides 6217 by NAT_4:9;
6217 = 11*565 + 2; hence not 11 divides 6217 by NAT_4:9;
6217 = 13*478 + 3; hence not 13 divides 6217 by NAT_4:9;
6217 = 17*365 + 12; hence not 17 divides 6217 by NAT_4:9;
6217 = 19*327 + 4; hence not 19 divides 6217 by NAT_4:9;
6217 = 23*270 + 7; hence not 23 divides 6217 by NAT_4:9;
6217 = 29*214 + 11; hence not 29 divides 6217 by NAT_4:9;
6217 = 31*200 + 17; hence not 31 divides 6217 by NAT_4:9;
6217 = 37*168 + 1; hence not 37 divides 6217 by NAT_4:9;
6217 = 41*151 + 26; hence not 41 divides 6217 by NAT_4:9;
6217 = 43*144 + 25; hence not 43 divides 6217 by NAT_4:9;
6217 = 47*132 + 13; hence not 47 divides 6217 by NAT_4:9;
6217 = 53*117 + 16; hence not 53 divides 6217 by NAT_4:9;
6217 = 59*105 + 22; hence not 59 divides 6217 by NAT_4:9;
6217 = 61*101 + 56; hence not 61 divides 6217 by NAT_4:9;
6217 = 67*92 + 53; hence not 67 divides 6217 by NAT_4:9;
6217 = 71*87 + 40; hence not 71 divides 6217 by NAT_4:9;
6217 = 73*85 + 12; hence not 73 divides 6217 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6217 & n is prime
holds not n divides 6217 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6221 is prime
proof
now
6221 = 2*3110 + 1; hence not 2 divides 6221 by NAT_4:9;
6221 = 3*2073 + 2; hence not 3 divides 6221 by NAT_4:9;
6221 = 5*1244 + 1; hence not 5 divides 6221 by NAT_4:9;
6221 = 7*888 + 5; hence not 7 divides 6221 by NAT_4:9;
6221 = 11*565 + 6; hence not 11 divides 6221 by NAT_4:9;
6221 = 13*478 + 7; hence not 13 divides 6221 by NAT_4:9;
6221 = 17*365 + 16; hence not 17 divides 6221 by NAT_4:9;
6221 = 19*327 + 8; hence not 19 divides 6221 by NAT_4:9;
6221 = 23*270 + 11; hence not 23 divides 6221 by NAT_4:9;
6221 = 29*214 + 15; hence not 29 divides 6221 by NAT_4:9;
6221 = 31*200 + 21; hence not 31 divides 6221 by NAT_4:9;
6221 = 37*168 + 5; hence not 37 divides 6221 by NAT_4:9;
6221 = 41*151 + 30; hence not 41 divides 6221 by NAT_4:9;
6221 = 43*144 + 29; hence not 43 divides 6221 by NAT_4:9;
6221 = 47*132 + 17; hence not 47 divides 6221 by NAT_4:9;
6221 = 53*117 + 20; hence not 53 divides 6221 by NAT_4:9;
6221 = 59*105 + 26; hence not 59 divides 6221 by NAT_4:9;
6221 = 61*101 + 60; hence not 61 divides 6221 by NAT_4:9;
6221 = 67*92 + 57; hence not 67 divides 6221 by NAT_4:9;
6221 = 71*87 + 44; hence not 71 divides 6221 by NAT_4:9;
6221 = 73*85 + 16; hence not 73 divides 6221 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6221 & n is prime
holds not n divides 6221 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6229 is prime
proof
now
6229 = 2*3114 + 1; hence not 2 divides 6229 by NAT_4:9;
6229 = 3*2076 + 1; hence not 3 divides 6229 by NAT_4:9;
6229 = 5*1245 + 4; hence not 5 divides 6229 by NAT_4:9;
6229 = 7*889 + 6; hence not 7 divides 6229 by NAT_4:9;
6229 = 11*566 + 3; hence not 11 divides 6229 by NAT_4:9;
6229 = 13*479 + 2; hence not 13 divides 6229 by NAT_4:9;
6229 = 17*366 + 7; hence not 17 divides 6229 by NAT_4:9;
6229 = 19*327 + 16; hence not 19 divides 6229 by NAT_4:9;
6229 = 23*270 + 19; hence not 23 divides 6229 by NAT_4:9;
6229 = 29*214 + 23; hence not 29 divides 6229 by NAT_4:9;
6229 = 31*200 + 29; hence not 31 divides 6229 by NAT_4:9;
6229 = 37*168 + 13; hence not 37 divides 6229 by NAT_4:9;
6229 = 41*151 + 38; hence not 41 divides 6229 by NAT_4:9;
6229 = 43*144 + 37; hence not 43 divides 6229 by NAT_4:9;
6229 = 47*132 + 25; hence not 47 divides 6229 by NAT_4:9;
6229 = 53*117 + 28; hence not 53 divides 6229 by NAT_4:9;
6229 = 59*105 + 34; hence not 59 divides 6229 by NAT_4:9;
6229 = 61*102 + 7; hence not 61 divides 6229 by NAT_4:9;
6229 = 67*92 + 65; hence not 67 divides 6229 by NAT_4:9;
6229 = 71*87 + 52; hence not 71 divides 6229 by NAT_4:9;
6229 = 73*85 + 24; hence not 73 divides 6229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6229 & n is prime
holds not n divides 6229 by XPRIMET1:42;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6247 is prime
proof
now
6247 = 2*3123 + 1; hence not 2 divides 6247 by NAT_4:9;
6247 = 3*2082 + 1; hence not 3 divides 6247 by NAT_4:9;
6247 = 5*1249 + 2; hence not 5 divides 6247 by NAT_4:9;
6247 = 7*892 + 3; hence not 7 divides 6247 by NAT_4:9;
6247 = 11*567 + 10; hence not 11 divides 6247 by NAT_4:9;
6247 = 13*480 + 7; hence not 13 divides 6247 by NAT_4:9;
6247 = 17*367 + 8; hence not 17 divides 6247 by NAT_4:9;
6247 = 19*328 + 15; hence not 19 divides 6247 by NAT_4:9;
6247 = 23*271 + 14; hence not 23 divides 6247 by NAT_4:9;
6247 = 29*215 + 12; hence not 29 divides 6247 by NAT_4:9;
6247 = 31*201 + 16; hence not 31 divides 6247 by NAT_4:9;
6247 = 37*168 + 31; hence not 37 divides 6247 by NAT_4:9;
6247 = 41*152 + 15; hence not 41 divides 6247 by NAT_4:9;
6247 = 43*145 + 12; hence not 43 divides 6247 by NAT_4:9;
6247 = 47*132 + 43; hence not 47 divides 6247 by NAT_4:9;
6247 = 53*117 + 46; hence not 53 divides 6247 by NAT_4:9;
6247 = 59*105 + 52; hence not 59 divides 6247 by NAT_4:9;
6247 = 61*102 + 25; hence not 61 divides 6247 by NAT_4:9;
6247 = 67*93 + 16; hence not 67 divides 6247 by NAT_4:9;
6247 = 71*87 + 70; hence not 71 divides 6247 by NAT_4:9;
6247 = 73*85 + 42; hence not 73 divides 6247 by NAT_4:9;
6247 = 79*79 + 6; hence not 79 divides 6247 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6247 & n is prime
holds not n divides 6247 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6257 is prime
proof
now
6257 = 2*3128 + 1; hence not 2 divides 6257 by NAT_4:9;
6257 = 3*2085 + 2; hence not 3 divides 6257 by NAT_4:9;
6257 = 5*1251 + 2; hence not 5 divides 6257 by NAT_4:9;
6257 = 7*893 + 6; hence not 7 divides 6257 by NAT_4:9;
6257 = 11*568 + 9; hence not 11 divides 6257 by NAT_4:9;
6257 = 13*481 + 4; hence not 13 divides 6257 by NAT_4:9;
6257 = 17*368 + 1; hence not 17 divides 6257 by NAT_4:9;
6257 = 19*329 + 6; hence not 19 divides 6257 by NAT_4:9;
6257 = 23*272 + 1; hence not 23 divides 6257 by NAT_4:9;
6257 = 29*215 + 22; hence not 29 divides 6257 by NAT_4:9;
6257 = 31*201 + 26; hence not 31 divides 6257 by NAT_4:9;
6257 = 37*169 + 4; hence not 37 divides 6257 by NAT_4:9;
6257 = 41*152 + 25; hence not 41 divides 6257 by NAT_4:9;
6257 = 43*145 + 22; hence not 43 divides 6257 by NAT_4:9;
6257 = 47*133 + 6; hence not 47 divides 6257 by NAT_4:9;
6257 = 53*118 + 3; hence not 53 divides 6257 by NAT_4:9;
6257 = 59*106 + 3; hence not 59 divides 6257 by NAT_4:9;
6257 = 61*102 + 35; hence not 61 divides 6257 by NAT_4:9;
6257 = 67*93 + 26; hence not 67 divides 6257 by NAT_4:9;
6257 = 71*88 + 9; hence not 71 divides 6257 by NAT_4:9;
6257 = 73*85 + 52; hence not 73 divides 6257 by NAT_4:9;
6257 = 79*79 + 16; hence not 79 divides 6257 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6257 & n is prime
holds not n divides 6257 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6263 is prime
proof
now
6263 = 2*3131 + 1; hence not 2 divides 6263 by NAT_4:9;
6263 = 3*2087 + 2; hence not 3 divides 6263 by NAT_4:9;
6263 = 5*1252 + 3; hence not 5 divides 6263 by NAT_4:9;
6263 = 7*894 + 5; hence not 7 divides 6263 by NAT_4:9;
6263 = 11*569 + 4; hence not 11 divides 6263 by NAT_4:9;
6263 = 13*481 + 10; hence not 13 divides 6263 by NAT_4:9;
6263 = 17*368 + 7; hence not 17 divides 6263 by NAT_4:9;
6263 = 19*329 + 12; hence not 19 divides 6263 by NAT_4:9;
6263 = 23*272 + 7; hence not 23 divides 6263 by NAT_4:9;
6263 = 29*215 + 28; hence not 29 divides 6263 by NAT_4:9;
6263 = 31*202 + 1; hence not 31 divides 6263 by NAT_4:9;
6263 = 37*169 + 10; hence not 37 divides 6263 by NAT_4:9;
6263 = 41*152 + 31; hence not 41 divides 6263 by NAT_4:9;
6263 = 43*145 + 28; hence not 43 divides 6263 by NAT_4:9;
6263 = 47*133 + 12; hence not 47 divides 6263 by NAT_4:9;
6263 = 53*118 + 9; hence not 53 divides 6263 by NAT_4:9;
6263 = 59*106 + 9; hence not 59 divides 6263 by NAT_4:9;
6263 = 61*102 + 41; hence not 61 divides 6263 by NAT_4:9;
6263 = 67*93 + 32; hence not 67 divides 6263 by NAT_4:9;
6263 = 71*88 + 15; hence not 71 divides 6263 by NAT_4:9;
6263 = 73*85 + 58; hence not 73 divides 6263 by NAT_4:9;
6263 = 79*79 + 22; hence not 79 divides 6263 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6263 & n is prime
holds not n divides 6263 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6269 is prime
proof
now
6269 = 2*3134 + 1; hence not 2 divides 6269 by NAT_4:9;
6269 = 3*2089 + 2; hence not 3 divides 6269 by NAT_4:9;
6269 = 5*1253 + 4; hence not 5 divides 6269 by NAT_4:9;
6269 = 7*895 + 4; hence not 7 divides 6269 by NAT_4:9;
6269 = 11*569 + 10; hence not 11 divides 6269 by NAT_4:9;
6269 = 13*482 + 3; hence not 13 divides 6269 by NAT_4:9;
6269 = 17*368 + 13; hence not 17 divides 6269 by NAT_4:9;
6269 = 19*329 + 18; hence not 19 divides 6269 by NAT_4:9;
6269 = 23*272 + 13; hence not 23 divides 6269 by NAT_4:9;
6269 = 29*216 + 5; hence not 29 divides 6269 by NAT_4:9;
6269 = 31*202 + 7; hence not 31 divides 6269 by NAT_4:9;
6269 = 37*169 + 16; hence not 37 divides 6269 by NAT_4:9;
6269 = 41*152 + 37; hence not 41 divides 6269 by NAT_4:9;
6269 = 43*145 + 34; hence not 43 divides 6269 by NAT_4:9;
6269 = 47*133 + 18; hence not 47 divides 6269 by NAT_4:9;
6269 = 53*118 + 15; hence not 53 divides 6269 by NAT_4:9;
6269 = 59*106 + 15; hence not 59 divides 6269 by NAT_4:9;
6269 = 61*102 + 47; hence not 61 divides 6269 by NAT_4:9;
6269 = 67*93 + 38; hence not 67 divides 6269 by NAT_4:9;
6269 = 71*88 + 21; hence not 71 divides 6269 by NAT_4:9;
6269 = 73*85 + 64; hence not 73 divides 6269 by NAT_4:9;
6269 = 79*79 + 28; hence not 79 divides 6269 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6269 & n is prime
holds not n divides 6269 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6271 is prime
proof
now
6271 = 2*3135 + 1; hence not 2 divides 6271 by NAT_4:9;
6271 = 3*2090 + 1; hence not 3 divides 6271 by NAT_4:9;
6271 = 5*1254 + 1; hence not 5 divides 6271 by NAT_4:9;
6271 = 7*895 + 6; hence not 7 divides 6271 by NAT_4:9;
6271 = 11*570 + 1; hence not 11 divides 6271 by NAT_4:9;
6271 = 13*482 + 5; hence not 13 divides 6271 by NAT_4:9;
6271 = 17*368 + 15; hence not 17 divides 6271 by NAT_4:9;
6271 = 19*330 + 1; hence not 19 divides 6271 by NAT_4:9;
6271 = 23*272 + 15; hence not 23 divides 6271 by NAT_4:9;
6271 = 29*216 + 7; hence not 29 divides 6271 by NAT_4:9;
6271 = 31*202 + 9; hence not 31 divides 6271 by NAT_4:9;
6271 = 37*169 + 18; hence not 37 divides 6271 by NAT_4:9;
6271 = 41*152 + 39; hence not 41 divides 6271 by NAT_4:9;
6271 = 43*145 + 36; hence not 43 divides 6271 by NAT_4:9;
6271 = 47*133 + 20; hence not 47 divides 6271 by NAT_4:9;
6271 = 53*118 + 17; hence not 53 divides 6271 by NAT_4:9;
6271 = 59*106 + 17; hence not 59 divides 6271 by NAT_4:9;
6271 = 61*102 + 49; hence not 61 divides 6271 by NAT_4:9;
6271 = 67*93 + 40; hence not 67 divides 6271 by NAT_4:9;
6271 = 71*88 + 23; hence not 71 divides 6271 by NAT_4:9;
6271 = 73*85 + 66; hence not 73 divides 6271 by NAT_4:9;
6271 = 79*79 + 30; hence not 79 divides 6271 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6271 & n is prime
holds not n divides 6271 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6277 is prime
proof
now
6277 = 2*3138 + 1; hence not 2 divides 6277 by NAT_4:9;
6277 = 3*2092 + 1; hence not 3 divides 6277 by NAT_4:9;
6277 = 5*1255 + 2; hence not 5 divides 6277 by NAT_4:9;
6277 = 7*896 + 5; hence not 7 divides 6277 by NAT_4:9;
6277 = 11*570 + 7; hence not 11 divides 6277 by NAT_4:9;
6277 = 13*482 + 11; hence not 13 divides 6277 by NAT_4:9;
6277 = 17*369 + 4; hence not 17 divides 6277 by NAT_4:9;
6277 = 19*330 + 7; hence not 19 divides 6277 by NAT_4:9;
6277 = 23*272 + 21; hence not 23 divides 6277 by NAT_4:9;
6277 = 29*216 + 13; hence not 29 divides 6277 by NAT_4:9;
6277 = 31*202 + 15; hence not 31 divides 6277 by NAT_4:9;
6277 = 37*169 + 24; hence not 37 divides 6277 by NAT_4:9;
6277 = 41*153 + 4; hence not 41 divides 6277 by NAT_4:9;
6277 = 43*145 + 42; hence not 43 divides 6277 by NAT_4:9;
6277 = 47*133 + 26; hence not 47 divides 6277 by NAT_4:9;
6277 = 53*118 + 23; hence not 53 divides 6277 by NAT_4:9;
6277 = 59*106 + 23; hence not 59 divides 6277 by NAT_4:9;
6277 = 61*102 + 55; hence not 61 divides 6277 by NAT_4:9;
6277 = 67*93 + 46; hence not 67 divides 6277 by NAT_4:9;
6277 = 71*88 + 29; hence not 71 divides 6277 by NAT_4:9;
6277 = 73*85 + 72; hence not 73 divides 6277 by NAT_4:9;
6277 = 79*79 + 36; hence not 79 divides 6277 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6277 & n is prime
holds not n divides 6277 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6287 is prime
proof
now
6287 = 2*3143 + 1; hence not 2 divides 6287 by NAT_4:9;
6287 = 3*2095 + 2; hence not 3 divides 6287 by NAT_4:9;
6287 = 5*1257 + 2; hence not 5 divides 6287 by NAT_4:9;
6287 = 7*898 + 1; hence not 7 divides 6287 by NAT_4:9;
6287 = 11*571 + 6; hence not 11 divides 6287 by NAT_4:9;
6287 = 13*483 + 8; hence not 13 divides 6287 by NAT_4:9;
6287 = 17*369 + 14; hence not 17 divides 6287 by NAT_4:9;
6287 = 19*330 + 17; hence not 19 divides 6287 by NAT_4:9;
6287 = 23*273 + 8; hence not 23 divides 6287 by NAT_4:9;
6287 = 29*216 + 23; hence not 29 divides 6287 by NAT_4:9;
6287 = 31*202 + 25; hence not 31 divides 6287 by NAT_4:9;
6287 = 37*169 + 34; hence not 37 divides 6287 by NAT_4:9;
6287 = 41*153 + 14; hence not 41 divides 6287 by NAT_4:9;
6287 = 43*146 + 9; hence not 43 divides 6287 by NAT_4:9;
6287 = 47*133 + 36; hence not 47 divides 6287 by NAT_4:9;
6287 = 53*118 + 33; hence not 53 divides 6287 by NAT_4:9;
6287 = 59*106 + 33; hence not 59 divides 6287 by NAT_4:9;
6287 = 61*103 + 4; hence not 61 divides 6287 by NAT_4:9;
6287 = 67*93 + 56; hence not 67 divides 6287 by NAT_4:9;
6287 = 71*88 + 39; hence not 71 divides 6287 by NAT_4:9;
6287 = 73*86 + 9; hence not 73 divides 6287 by NAT_4:9;
6287 = 79*79 + 46; hence not 79 divides 6287 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6287 & n is prime
holds not n divides 6287 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6299 is prime
proof
now
6299 = 2*3149 + 1; hence not 2 divides 6299 by NAT_4:9;
6299 = 3*2099 + 2; hence not 3 divides 6299 by NAT_4:9;
6299 = 5*1259 + 4; hence not 5 divides 6299 by NAT_4:9;
6299 = 7*899 + 6; hence not 7 divides 6299 by NAT_4:9;
6299 = 11*572 + 7; hence not 11 divides 6299 by NAT_4:9;
6299 = 13*484 + 7; hence not 13 divides 6299 by NAT_4:9;
6299 = 17*370 + 9; hence not 17 divides 6299 by NAT_4:9;
6299 = 19*331 + 10; hence not 19 divides 6299 by NAT_4:9;
6299 = 23*273 + 20; hence not 23 divides 6299 by NAT_4:9;
6299 = 29*217 + 6; hence not 29 divides 6299 by NAT_4:9;
6299 = 31*203 + 6; hence not 31 divides 6299 by NAT_4:9;
6299 = 37*170 + 9; hence not 37 divides 6299 by NAT_4:9;
6299 = 41*153 + 26; hence not 41 divides 6299 by NAT_4:9;
6299 = 43*146 + 21; hence not 43 divides 6299 by NAT_4:9;
6299 = 47*134 + 1; hence not 47 divides 6299 by NAT_4:9;
6299 = 53*118 + 45; hence not 53 divides 6299 by NAT_4:9;
6299 = 59*106 + 45; hence not 59 divides 6299 by NAT_4:9;
6299 = 61*103 + 16; hence not 61 divides 6299 by NAT_4:9;
6299 = 67*94 + 1; hence not 67 divides 6299 by NAT_4:9;
6299 = 71*88 + 51; hence not 71 divides 6299 by NAT_4:9;
6299 = 73*86 + 21; hence not 73 divides 6299 by NAT_4:9;
6299 = 79*79 + 58; hence not 79 divides 6299 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6299 & n is prime
holds not n divides 6299 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6301 is prime
proof
now
6301 = 2*3150 + 1; hence not 2 divides 6301 by NAT_4:9;
6301 = 3*2100 + 1; hence not 3 divides 6301 by NAT_4:9;
6301 = 5*1260 + 1; hence not 5 divides 6301 by NAT_4:9;
6301 = 7*900 + 1; hence not 7 divides 6301 by NAT_4:9;
6301 = 11*572 + 9; hence not 11 divides 6301 by NAT_4:9;
6301 = 13*484 + 9; hence not 13 divides 6301 by NAT_4:9;
6301 = 17*370 + 11; hence not 17 divides 6301 by NAT_4:9;
6301 = 19*331 + 12; hence not 19 divides 6301 by NAT_4:9;
6301 = 23*273 + 22; hence not 23 divides 6301 by NAT_4:9;
6301 = 29*217 + 8; hence not 29 divides 6301 by NAT_4:9;
6301 = 31*203 + 8; hence not 31 divides 6301 by NAT_4:9;
6301 = 37*170 + 11; hence not 37 divides 6301 by NAT_4:9;
6301 = 41*153 + 28; hence not 41 divides 6301 by NAT_4:9;
6301 = 43*146 + 23; hence not 43 divides 6301 by NAT_4:9;
6301 = 47*134 + 3; hence not 47 divides 6301 by NAT_4:9;
6301 = 53*118 + 47; hence not 53 divides 6301 by NAT_4:9;
6301 = 59*106 + 47; hence not 59 divides 6301 by NAT_4:9;
6301 = 61*103 + 18; hence not 61 divides 6301 by NAT_4:9;
6301 = 67*94 + 3; hence not 67 divides 6301 by NAT_4:9;
6301 = 71*88 + 53; hence not 71 divides 6301 by NAT_4:9;
6301 = 73*86 + 23; hence not 73 divides 6301 by NAT_4:9;
6301 = 79*79 + 60; hence not 79 divides 6301 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6301 & n is prime
holds not n divides 6301 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6311 is prime
proof
now
6311 = 2*3155 + 1; hence not 2 divides 6311 by NAT_4:9;
6311 = 3*2103 + 2; hence not 3 divides 6311 by NAT_4:9;
6311 = 5*1262 + 1; hence not 5 divides 6311 by NAT_4:9;
6311 = 7*901 + 4; hence not 7 divides 6311 by NAT_4:9;
6311 = 11*573 + 8; hence not 11 divides 6311 by NAT_4:9;
6311 = 13*485 + 6; hence not 13 divides 6311 by NAT_4:9;
6311 = 17*371 + 4; hence not 17 divides 6311 by NAT_4:9;
6311 = 19*332 + 3; hence not 19 divides 6311 by NAT_4:9;
6311 = 23*274 + 9; hence not 23 divides 6311 by NAT_4:9;
6311 = 29*217 + 18; hence not 29 divides 6311 by NAT_4:9;
6311 = 31*203 + 18; hence not 31 divides 6311 by NAT_4:9;
6311 = 37*170 + 21; hence not 37 divides 6311 by NAT_4:9;
6311 = 41*153 + 38; hence not 41 divides 6311 by NAT_4:9;
6311 = 43*146 + 33; hence not 43 divides 6311 by NAT_4:9;
6311 = 47*134 + 13; hence not 47 divides 6311 by NAT_4:9;
6311 = 53*119 + 4; hence not 53 divides 6311 by NAT_4:9;
6311 = 59*106 + 57; hence not 59 divides 6311 by NAT_4:9;
6311 = 61*103 + 28; hence not 61 divides 6311 by NAT_4:9;
6311 = 67*94 + 13; hence not 67 divides 6311 by NAT_4:9;
6311 = 71*88 + 63; hence not 71 divides 6311 by NAT_4:9;
6311 = 73*86 + 33; hence not 73 divides 6311 by NAT_4:9;
6311 = 79*79 + 70; hence not 79 divides 6311 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6311 & n is prime
holds not n divides 6311 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6317 is prime
proof
now
6317 = 2*3158 + 1; hence not 2 divides 6317 by NAT_4:9;
6317 = 3*2105 + 2; hence not 3 divides 6317 by NAT_4:9;
6317 = 5*1263 + 2; hence not 5 divides 6317 by NAT_4:9;
6317 = 7*902 + 3; hence not 7 divides 6317 by NAT_4:9;
6317 = 11*574 + 3; hence not 11 divides 6317 by NAT_4:9;
6317 = 13*485 + 12; hence not 13 divides 6317 by NAT_4:9;
6317 = 17*371 + 10; hence not 17 divides 6317 by NAT_4:9;
6317 = 19*332 + 9; hence not 19 divides 6317 by NAT_4:9;
6317 = 23*274 + 15; hence not 23 divides 6317 by NAT_4:9;
6317 = 29*217 + 24; hence not 29 divides 6317 by NAT_4:9;
6317 = 31*203 + 24; hence not 31 divides 6317 by NAT_4:9;
6317 = 37*170 + 27; hence not 37 divides 6317 by NAT_4:9;
6317 = 41*154 + 3; hence not 41 divides 6317 by NAT_4:9;
6317 = 43*146 + 39; hence not 43 divides 6317 by NAT_4:9;
6317 = 47*134 + 19; hence not 47 divides 6317 by NAT_4:9;
6317 = 53*119 + 10; hence not 53 divides 6317 by NAT_4:9;
6317 = 59*107 + 4; hence not 59 divides 6317 by NAT_4:9;
6317 = 61*103 + 34; hence not 61 divides 6317 by NAT_4:9;
6317 = 67*94 + 19; hence not 67 divides 6317 by NAT_4:9;
6317 = 71*88 + 69; hence not 71 divides 6317 by NAT_4:9;
6317 = 73*86 + 39; hence not 73 divides 6317 by NAT_4:9;
6317 = 79*79 + 76; hence not 79 divides 6317 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6317 & n is prime
holds not n divides 6317 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6323 is prime
proof
now
6323 = 2*3161 + 1; hence not 2 divides 6323 by NAT_4:9;
6323 = 3*2107 + 2; hence not 3 divides 6323 by NAT_4:9;
6323 = 5*1264 + 3; hence not 5 divides 6323 by NAT_4:9;
6323 = 7*903 + 2; hence not 7 divides 6323 by NAT_4:9;
6323 = 11*574 + 9; hence not 11 divides 6323 by NAT_4:9;
6323 = 13*486 + 5; hence not 13 divides 6323 by NAT_4:9;
6323 = 17*371 + 16; hence not 17 divides 6323 by NAT_4:9;
6323 = 19*332 + 15; hence not 19 divides 6323 by NAT_4:9;
6323 = 23*274 + 21; hence not 23 divides 6323 by NAT_4:9;
6323 = 29*218 + 1; hence not 29 divides 6323 by NAT_4:9;
6323 = 31*203 + 30; hence not 31 divides 6323 by NAT_4:9;
6323 = 37*170 + 33; hence not 37 divides 6323 by NAT_4:9;
6323 = 41*154 + 9; hence not 41 divides 6323 by NAT_4:9;
6323 = 43*147 + 2; hence not 43 divides 6323 by NAT_4:9;
6323 = 47*134 + 25; hence not 47 divides 6323 by NAT_4:9;
6323 = 53*119 + 16; hence not 53 divides 6323 by NAT_4:9;
6323 = 59*107 + 10; hence not 59 divides 6323 by NAT_4:9;
6323 = 61*103 + 40; hence not 61 divides 6323 by NAT_4:9;
6323 = 67*94 + 25; hence not 67 divides 6323 by NAT_4:9;
6323 = 71*89 + 4; hence not 71 divides 6323 by NAT_4:9;
6323 = 73*86 + 45; hence not 73 divides 6323 by NAT_4:9;
6323 = 79*80 + 3; hence not 79 divides 6323 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6323 & n is prime
holds not n divides 6323 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6329 is prime
proof
now
6329 = 2*3164 + 1; hence not 2 divides 6329 by NAT_4:9;
6329 = 3*2109 + 2; hence not 3 divides 6329 by NAT_4:9;
6329 = 5*1265 + 4; hence not 5 divides 6329 by NAT_4:9;
6329 = 7*904 + 1; hence not 7 divides 6329 by NAT_4:9;
6329 = 11*575 + 4; hence not 11 divides 6329 by NAT_4:9;
6329 = 13*486 + 11; hence not 13 divides 6329 by NAT_4:9;
6329 = 17*372 + 5; hence not 17 divides 6329 by NAT_4:9;
6329 = 19*333 + 2; hence not 19 divides 6329 by NAT_4:9;
6329 = 23*275 + 4; hence not 23 divides 6329 by NAT_4:9;
6329 = 29*218 + 7; hence not 29 divides 6329 by NAT_4:9;
6329 = 31*204 + 5; hence not 31 divides 6329 by NAT_4:9;
6329 = 37*171 + 2; hence not 37 divides 6329 by NAT_4:9;
6329 = 41*154 + 15; hence not 41 divides 6329 by NAT_4:9;
6329 = 43*147 + 8; hence not 43 divides 6329 by NAT_4:9;
6329 = 47*134 + 31; hence not 47 divides 6329 by NAT_4:9;
6329 = 53*119 + 22; hence not 53 divides 6329 by NAT_4:9;
6329 = 59*107 + 16; hence not 59 divides 6329 by NAT_4:9;
6329 = 61*103 + 46; hence not 61 divides 6329 by NAT_4:9;
6329 = 67*94 + 31; hence not 67 divides 6329 by NAT_4:9;
6329 = 71*89 + 10; hence not 71 divides 6329 by NAT_4:9;
6329 = 73*86 + 51; hence not 73 divides 6329 by NAT_4:9;
6329 = 79*80 + 9; hence not 79 divides 6329 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6329 & n is prime
holds not n divides 6329 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6337 is prime
proof
now
6337 = 2*3168 + 1; hence not 2 divides 6337 by NAT_4:9;
6337 = 3*2112 + 1; hence not 3 divides 6337 by NAT_4:9;
6337 = 5*1267 + 2; hence not 5 divides 6337 by NAT_4:9;
6337 = 7*905 + 2; hence not 7 divides 6337 by NAT_4:9;
6337 = 11*576 + 1; hence not 11 divides 6337 by NAT_4:9;
6337 = 13*487 + 6; hence not 13 divides 6337 by NAT_4:9;
6337 = 17*372 + 13; hence not 17 divides 6337 by NAT_4:9;
6337 = 19*333 + 10; hence not 19 divides 6337 by NAT_4:9;
6337 = 23*275 + 12; hence not 23 divides 6337 by NAT_4:9;
6337 = 29*218 + 15; hence not 29 divides 6337 by NAT_4:9;
6337 = 31*204 + 13; hence not 31 divides 6337 by NAT_4:9;
6337 = 37*171 + 10; hence not 37 divides 6337 by NAT_4:9;
6337 = 41*154 + 23; hence not 41 divides 6337 by NAT_4:9;
6337 = 43*147 + 16; hence not 43 divides 6337 by NAT_4:9;
6337 = 47*134 + 39; hence not 47 divides 6337 by NAT_4:9;
6337 = 53*119 + 30; hence not 53 divides 6337 by NAT_4:9;
6337 = 59*107 + 24; hence not 59 divides 6337 by NAT_4:9;
6337 = 61*103 + 54; hence not 61 divides 6337 by NAT_4:9;
6337 = 67*94 + 39; hence not 67 divides 6337 by NAT_4:9;
6337 = 71*89 + 18; hence not 71 divides 6337 by NAT_4:9;
6337 = 73*86 + 59; hence not 73 divides 6337 by NAT_4:9;
6337 = 79*80 + 17; hence not 79 divides 6337 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6337 & n is prime
holds not n divides 6337 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6343 is prime
proof
now
6343 = 2*3171 + 1; hence not 2 divides 6343 by NAT_4:9;
6343 = 3*2114 + 1; hence not 3 divides 6343 by NAT_4:9;
6343 = 5*1268 + 3; hence not 5 divides 6343 by NAT_4:9;
6343 = 7*906 + 1; hence not 7 divides 6343 by NAT_4:9;
6343 = 11*576 + 7; hence not 11 divides 6343 by NAT_4:9;
6343 = 13*487 + 12; hence not 13 divides 6343 by NAT_4:9;
6343 = 17*373 + 2; hence not 17 divides 6343 by NAT_4:9;
6343 = 19*333 + 16; hence not 19 divides 6343 by NAT_4:9;
6343 = 23*275 + 18; hence not 23 divides 6343 by NAT_4:9;
6343 = 29*218 + 21; hence not 29 divides 6343 by NAT_4:9;
6343 = 31*204 + 19; hence not 31 divides 6343 by NAT_4:9;
6343 = 37*171 + 16; hence not 37 divides 6343 by NAT_4:9;
6343 = 41*154 + 29; hence not 41 divides 6343 by NAT_4:9;
6343 = 43*147 + 22; hence not 43 divides 6343 by NAT_4:9;
6343 = 47*134 + 45; hence not 47 divides 6343 by NAT_4:9;
6343 = 53*119 + 36; hence not 53 divides 6343 by NAT_4:9;
6343 = 59*107 + 30; hence not 59 divides 6343 by NAT_4:9;
6343 = 61*103 + 60; hence not 61 divides 6343 by NAT_4:9;
6343 = 67*94 + 45; hence not 67 divides 6343 by NAT_4:9;
6343 = 71*89 + 24; hence not 71 divides 6343 by NAT_4:9;
6343 = 73*86 + 65; hence not 73 divides 6343 by NAT_4:9;
6343 = 79*80 + 23; hence not 79 divides 6343 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6343 & n is prime
holds not n divides 6343 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6353 is prime
proof
now
6353 = 2*3176 + 1; hence not 2 divides 6353 by NAT_4:9;
6353 = 3*2117 + 2; hence not 3 divides 6353 by NAT_4:9;
6353 = 5*1270 + 3; hence not 5 divides 6353 by NAT_4:9;
6353 = 7*907 + 4; hence not 7 divides 6353 by NAT_4:9;
6353 = 11*577 + 6; hence not 11 divides 6353 by NAT_4:9;
6353 = 13*488 + 9; hence not 13 divides 6353 by NAT_4:9;
6353 = 17*373 + 12; hence not 17 divides 6353 by NAT_4:9;
6353 = 19*334 + 7; hence not 19 divides 6353 by NAT_4:9;
6353 = 23*276 + 5; hence not 23 divides 6353 by NAT_4:9;
6353 = 29*219 + 2; hence not 29 divides 6353 by NAT_4:9;
6353 = 31*204 + 29; hence not 31 divides 6353 by NAT_4:9;
6353 = 37*171 + 26; hence not 37 divides 6353 by NAT_4:9;
6353 = 41*154 + 39; hence not 41 divides 6353 by NAT_4:9;
6353 = 43*147 + 32; hence not 43 divides 6353 by NAT_4:9;
6353 = 47*135 + 8; hence not 47 divides 6353 by NAT_4:9;
6353 = 53*119 + 46; hence not 53 divides 6353 by NAT_4:9;
6353 = 59*107 + 40; hence not 59 divides 6353 by NAT_4:9;
6353 = 61*104 + 9; hence not 61 divides 6353 by NAT_4:9;
6353 = 67*94 + 55; hence not 67 divides 6353 by NAT_4:9;
6353 = 71*89 + 34; hence not 71 divides 6353 by NAT_4:9;
6353 = 73*87 + 2; hence not 73 divides 6353 by NAT_4:9;
6353 = 79*80 + 33; hence not 79 divides 6353 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6353 & n is prime
holds not n divides 6353 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6359 is prime
proof
now
6359 = 2*3179 + 1; hence not 2 divides 6359 by NAT_4:9;
6359 = 3*2119 + 2; hence not 3 divides 6359 by NAT_4:9;
6359 = 5*1271 + 4; hence not 5 divides 6359 by NAT_4:9;
6359 = 7*908 + 3; hence not 7 divides 6359 by NAT_4:9;
6359 = 11*578 + 1; hence not 11 divides 6359 by NAT_4:9;
6359 = 13*489 + 2; hence not 13 divides 6359 by NAT_4:9;
6359 = 17*374 + 1; hence not 17 divides 6359 by NAT_4:9;
6359 = 19*334 + 13; hence not 19 divides 6359 by NAT_4:9;
6359 = 23*276 + 11; hence not 23 divides 6359 by NAT_4:9;
6359 = 29*219 + 8; hence not 29 divides 6359 by NAT_4:9;
6359 = 31*205 + 4; hence not 31 divides 6359 by NAT_4:9;
6359 = 37*171 + 32; hence not 37 divides 6359 by NAT_4:9;
6359 = 41*155 + 4; hence not 41 divides 6359 by NAT_4:9;
6359 = 43*147 + 38; hence not 43 divides 6359 by NAT_4:9;
6359 = 47*135 + 14; hence not 47 divides 6359 by NAT_4:9;
6359 = 53*119 + 52; hence not 53 divides 6359 by NAT_4:9;
6359 = 59*107 + 46; hence not 59 divides 6359 by NAT_4:9;
6359 = 61*104 + 15; hence not 61 divides 6359 by NAT_4:9;
6359 = 67*94 + 61; hence not 67 divides 6359 by NAT_4:9;
6359 = 71*89 + 40; hence not 71 divides 6359 by NAT_4:9;
6359 = 73*87 + 8; hence not 73 divides 6359 by NAT_4:9;
6359 = 79*80 + 39; hence not 79 divides 6359 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6359 & n is prime
holds not n divides 6359 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6361 is prime
proof
now
6361 = 2*3180 + 1; hence not 2 divides 6361 by NAT_4:9;
6361 = 3*2120 + 1; hence not 3 divides 6361 by NAT_4:9;
6361 = 5*1272 + 1; hence not 5 divides 6361 by NAT_4:9;
6361 = 7*908 + 5; hence not 7 divides 6361 by NAT_4:9;
6361 = 11*578 + 3; hence not 11 divides 6361 by NAT_4:9;
6361 = 13*489 + 4; hence not 13 divides 6361 by NAT_4:9;
6361 = 17*374 + 3; hence not 17 divides 6361 by NAT_4:9;
6361 = 19*334 + 15; hence not 19 divides 6361 by NAT_4:9;
6361 = 23*276 + 13; hence not 23 divides 6361 by NAT_4:9;
6361 = 29*219 + 10; hence not 29 divides 6361 by NAT_4:9;
6361 = 31*205 + 6; hence not 31 divides 6361 by NAT_4:9;
6361 = 37*171 + 34; hence not 37 divides 6361 by NAT_4:9;
6361 = 41*155 + 6; hence not 41 divides 6361 by NAT_4:9;
6361 = 43*147 + 40; hence not 43 divides 6361 by NAT_4:9;
6361 = 47*135 + 16; hence not 47 divides 6361 by NAT_4:9;
6361 = 53*120 + 1; hence not 53 divides 6361 by NAT_4:9;
6361 = 59*107 + 48; hence not 59 divides 6361 by NAT_4:9;
6361 = 61*104 + 17; hence not 61 divides 6361 by NAT_4:9;
6361 = 67*94 + 63; hence not 67 divides 6361 by NAT_4:9;
6361 = 71*89 + 42; hence not 71 divides 6361 by NAT_4:9;
6361 = 73*87 + 10; hence not 73 divides 6361 by NAT_4:9;
6361 = 79*80 + 41; hence not 79 divides 6361 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6361 & n is prime
holds not n divides 6361 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6367 is prime
proof
now
6367 = 2*3183 + 1; hence not 2 divides 6367 by NAT_4:9;
6367 = 3*2122 + 1; hence not 3 divides 6367 by NAT_4:9;
6367 = 5*1273 + 2; hence not 5 divides 6367 by NAT_4:9;
6367 = 7*909 + 4; hence not 7 divides 6367 by NAT_4:9;
6367 = 11*578 + 9; hence not 11 divides 6367 by NAT_4:9;
6367 = 13*489 + 10; hence not 13 divides 6367 by NAT_4:9;
6367 = 17*374 + 9; hence not 17 divides 6367 by NAT_4:9;
6367 = 19*335 + 2; hence not 19 divides 6367 by NAT_4:9;
6367 = 23*276 + 19; hence not 23 divides 6367 by NAT_4:9;
6367 = 29*219 + 16; hence not 29 divides 6367 by NAT_4:9;
6367 = 31*205 + 12; hence not 31 divides 6367 by NAT_4:9;
6367 = 37*172 + 3; hence not 37 divides 6367 by NAT_4:9;
6367 = 41*155 + 12; hence not 41 divides 6367 by NAT_4:9;
6367 = 43*148 + 3; hence not 43 divides 6367 by NAT_4:9;
6367 = 47*135 + 22; hence not 47 divides 6367 by NAT_4:9;
6367 = 53*120 + 7; hence not 53 divides 6367 by NAT_4:9;
6367 = 59*107 + 54; hence not 59 divides 6367 by NAT_4:9;
6367 = 61*104 + 23; hence not 61 divides 6367 by NAT_4:9;
6367 = 67*95 + 2; hence not 67 divides 6367 by NAT_4:9;
6367 = 71*89 + 48; hence not 71 divides 6367 by NAT_4:9;
6367 = 73*87 + 16; hence not 73 divides 6367 by NAT_4:9;
6367 = 79*80 + 47; hence not 79 divides 6367 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6367 & n is prime
holds not n divides 6367 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6373 is prime
proof
now
6373 = 2*3186 + 1; hence not 2 divides 6373 by NAT_4:9;
6373 = 3*2124 + 1; hence not 3 divides 6373 by NAT_4:9;
6373 = 5*1274 + 3; hence not 5 divides 6373 by NAT_4:9;
6373 = 7*910 + 3; hence not 7 divides 6373 by NAT_4:9;
6373 = 11*579 + 4; hence not 11 divides 6373 by NAT_4:9;
6373 = 13*490 + 3; hence not 13 divides 6373 by NAT_4:9;
6373 = 17*374 + 15; hence not 17 divides 6373 by NAT_4:9;
6373 = 19*335 + 8; hence not 19 divides 6373 by NAT_4:9;
6373 = 23*277 + 2; hence not 23 divides 6373 by NAT_4:9;
6373 = 29*219 + 22; hence not 29 divides 6373 by NAT_4:9;
6373 = 31*205 + 18; hence not 31 divides 6373 by NAT_4:9;
6373 = 37*172 + 9; hence not 37 divides 6373 by NAT_4:9;
6373 = 41*155 + 18; hence not 41 divides 6373 by NAT_4:9;
6373 = 43*148 + 9; hence not 43 divides 6373 by NAT_4:9;
6373 = 47*135 + 28; hence not 47 divides 6373 by NAT_4:9;
6373 = 53*120 + 13; hence not 53 divides 6373 by NAT_4:9;
6373 = 59*108 + 1; hence not 59 divides 6373 by NAT_4:9;
6373 = 61*104 + 29; hence not 61 divides 6373 by NAT_4:9;
6373 = 67*95 + 8; hence not 67 divides 6373 by NAT_4:9;
6373 = 71*89 + 54; hence not 71 divides 6373 by NAT_4:9;
6373 = 73*87 + 22; hence not 73 divides 6373 by NAT_4:9;
6373 = 79*80 + 53; hence not 79 divides 6373 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6373 & n is prime
holds not n divides 6373 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6379 is prime
proof
now
6379 = 2*3189 + 1; hence not 2 divides 6379 by NAT_4:9;
6379 = 3*2126 + 1; hence not 3 divides 6379 by NAT_4:9;
6379 = 5*1275 + 4; hence not 5 divides 6379 by NAT_4:9;
6379 = 7*911 + 2; hence not 7 divides 6379 by NAT_4:9;
6379 = 11*579 + 10; hence not 11 divides 6379 by NAT_4:9;
6379 = 13*490 + 9; hence not 13 divides 6379 by NAT_4:9;
6379 = 17*375 + 4; hence not 17 divides 6379 by NAT_4:9;
6379 = 19*335 + 14; hence not 19 divides 6379 by NAT_4:9;
6379 = 23*277 + 8; hence not 23 divides 6379 by NAT_4:9;
6379 = 29*219 + 28; hence not 29 divides 6379 by NAT_4:9;
6379 = 31*205 + 24; hence not 31 divides 6379 by NAT_4:9;
6379 = 37*172 + 15; hence not 37 divides 6379 by NAT_4:9;
6379 = 41*155 + 24; hence not 41 divides 6379 by NAT_4:9;
6379 = 43*148 + 15; hence not 43 divides 6379 by NAT_4:9;
6379 = 47*135 + 34; hence not 47 divides 6379 by NAT_4:9;
6379 = 53*120 + 19; hence not 53 divides 6379 by NAT_4:9;
6379 = 59*108 + 7; hence not 59 divides 6379 by NAT_4:9;
6379 = 61*104 + 35; hence not 61 divides 6379 by NAT_4:9;
6379 = 67*95 + 14; hence not 67 divides 6379 by NAT_4:9;
6379 = 71*89 + 60; hence not 71 divides 6379 by NAT_4:9;
6379 = 73*87 + 28; hence not 73 divides 6379 by NAT_4:9;
6379 = 79*80 + 59; hence not 79 divides 6379 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6379 & n is prime
holds not n divides 6379 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6389 is prime
proof
now
6389 = 2*3194 + 1; hence not 2 divides 6389 by NAT_4:9;
6389 = 3*2129 + 2; hence not 3 divides 6389 by NAT_4:9;
6389 = 5*1277 + 4; hence not 5 divides 6389 by NAT_4:9;
6389 = 7*912 + 5; hence not 7 divides 6389 by NAT_4:9;
6389 = 11*580 + 9; hence not 11 divides 6389 by NAT_4:9;
6389 = 13*491 + 6; hence not 13 divides 6389 by NAT_4:9;
6389 = 17*375 + 14; hence not 17 divides 6389 by NAT_4:9;
6389 = 19*336 + 5; hence not 19 divides 6389 by NAT_4:9;
6389 = 23*277 + 18; hence not 23 divides 6389 by NAT_4:9;
6389 = 29*220 + 9; hence not 29 divides 6389 by NAT_4:9;
6389 = 31*206 + 3; hence not 31 divides 6389 by NAT_4:9;
6389 = 37*172 + 25; hence not 37 divides 6389 by NAT_4:9;
6389 = 41*155 + 34; hence not 41 divides 6389 by NAT_4:9;
6389 = 43*148 + 25; hence not 43 divides 6389 by NAT_4:9;
6389 = 47*135 + 44; hence not 47 divides 6389 by NAT_4:9;
6389 = 53*120 + 29; hence not 53 divides 6389 by NAT_4:9;
6389 = 59*108 + 17; hence not 59 divides 6389 by NAT_4:9;
6389 = 61*104 + 45; hence not 61 divides 6389 by NAT_4:9;
6389 = 67*95 + 24; hence not 67 divides 6389 by NAT_4:9;
6389 = 71*89 + 70; hence not 71 divides 6389 by NAT_4:9;
6389 = 73*87 + 38; hence not 73 divides 6389 by NAT_4:9;
6389 = 79*80 + 69; hence not 79 divides 6389 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6389 & n is prime
holds not n divides 6389 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6397 is prime
proof
now
6397 = 2*3198 + 1; hence not 2 divides 6397 by NAT_4:9;
6397 = 3*2132 + 1; hence not 3 divides 6397 by NAT_4:9;
6397 = 5*1279 + 2; hence not 5 divides 6397 by NAT_4:9;
6397 = 7*913 + 6; hence not 7 divides 6397 by NAT_4:9;
6397 = 11*581 + 6; hence not 11 divides 6397 by NAT_4:9;
6397 = 13*492 + 1; hence not 13 divides 6397 by NAT_4:9;
6397 = 17*376 + 5; hence not 17 divides 6397 by NAT_4:9;
6397 = 19*336 + 13; hence not 19 divides 6397 by NAT_4:9;
6397 = 23*278 + 3; hence not 23 divides 6397 by NAT_4:9;
6397 = 29*220 + 17; hence not 29 divides 6397 by NAT_4:9;
6397 = 31*206 + 11; hence not 31 divides 6397 by NAT_4:9;
6397 = 37*172 + 33; hence not 37 divides 6397 by NAT_4:9;
6397 = 41*156 + 1; hence not 41 divides 6397 by NAT_4:9;
6397 = 43*148 + 33; hence not 43 divides 6397 by NAT_4:9;
6397 = 47*136 + 5; hence not 47 divides 6397 by NAT_4:9;
6397 = 53*120 + 37; hence not 53 divides 6397 by NAT_4:9;
6397 = 59*108 + 25; hence not 59 divides 6397 by NAT_4:9;
6397 = 61*104 + 53; hence not 61 divides 6397 by NAT_4:9;
6397 = 67*95 + 32; hence not 67 divides 6397 by NAT_4:9;
6397 = 71*90 + 7; hence not 71 divides 6397 by NAT_4:9;
6397 = 73*87 + 46; hence not 73 divides 6397 by NAT_4:9;
6397 = 79*80 + 77; hence not 79 divides 6397 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6397 & n is prime
holds not n divides 6397 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
6421 is prime
proof
now
6421 = 2*3210 + 1; hence not 2 divides 6421 by NAT_4:9;
6421 = 3*2140 + 1; hence not 3 divides 6421 by NAT_4:9;
6421 = 5*1284 + 1; hence not 5 divides 6421 by NAT_4:9;
6421 = 7*917 + 2; hence not 7 divides 6421 by NAT_4:9;
6421 = 11*583 + 8; hence not 11 divides 6421 by NAT_4:9;
6421 = 13*493 + 12; hence not 13 divides 6421 by NAT_4:9;
6421 = 17*377 + 12; hence not 17 divides 6421 by NAT_4:9;
6421 = 19*337 + 18; hence not 19 divides 6421 by NAT_4:9;
6421 = 23*279 + 4; hence not 23 divides 6421 by NAT_4:9;
6421 = 29*221 + 12; hence not 29 divides 6421 by NAT_4:9;
6421 = 31*207 + 4; hence not 31 divides 6421 by NAT_4:9;
6421 = 37*173 + 20; hence not 37 divides 6421 by NAT_4:9;
6421 = 41*156 + 25; hence not 41 divides 6421 by NAT_4:9;
6421 = 43*149 + 14; hence not 43 divides 6421 by NAT_4:9;
6421 = 47*136 + 29; hence not 47 divides 6421 by NAT_4:9;
6421 = 53*121 + 8; hence not 53 divides 6421 by NAT_4:9;
6421 = 59*108 + 49; hence not 59 divides 6421 by NAT_4:9;
6421 = 61*105 + 16; hence not 61 divides 6421 by NAT_4:9;
6421 = 67*95 + 56; hence not 67 divides 6421 by NAT_4:9;
6421 = 71*90 + 31; hence not 71 divides 6421 by NAT_4:9;
6421 = 73*87 + 70; hence not 73 divides 6421 by NAT_4:9;
6421 = 79*81 + 22; hence not 79 divides 6421 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6421 & n is prime
holds not n divides 6421 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6427 is prime
proof
now
6427 = 2*3213 + 1; hence not 2 divides 6427 by NAT_4:9;
6427 = 3*2142 + 1; hence not 3 divides 6427 by NAT_4:9;
6427 = 5*1285 + 2; hence not 5 divides 6427 by NAT_4:9;
6427 = 7*918 + 1; hence not 7 divides 6427 by NAT_4:9;
6427 = 11*584 + 3; hence not 11 divides 6427 by NAT_4:9;
6427 = 13*494 + 5; hence not 13 divides 6427 by NAT_4:9;
6427 = 17*378 + 1; hence not 17 divides 6427 by NAT_4:9;
6427 = 19*338 + 5; hence not 19 divides 6427 by NAT_4:9;
6427 = 23*279 + 10; hence not 23 divides 6427 by NAT_4:9;
6427 = 29*221 + 18; hence not 29 divides 6427 by NAT_4:9;
6427 = 31*207 + 10; hence not 31 divides 6427 by NAT_4:9;
6427 = 37*173 + 26; hence not 37 divides 6427 by NAT_4:9;
6427 = 41*156 + 31; hence not 41 divides 6427 by NAT_4:9;
6427 = 43*149 + 20; hence not 43 divides 6427 by NAT_4:9;
6427 = 47*136 + 35; hence not 47 divides 6427 by NAT_4:9;
6427 = 53*121 + 14; hence not 53 divides 6427 by NAT_4:9;
6427 = 59*108 + 55; hence not 59 divides 6427 by NAT_4:9;
6427 = 61*105 + 22; hence not 61 divides 6427 by NAT_4:9;
6427 = 67*95 + 62; hence not 67 divides 6427 by NAT_4:9;
6427 = 71*90 + 37; hence not 71 divides 6427 by NAT_4:9;
6427 = 73*88 + 3; hence not 73 divides 6427 by NAT_4:9;
6427 = 79*81 + 28; hence not 79 divides 6427 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6427 & n is prime
holds not n divides 6427 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
6449 is prime
proof
now
6449 = 2*3224 + 1; hence not 2 divides 6449 by NAT_4:9;
6449 = 3*2149 + 2; hence not 3 divides 6449 by NAT_4:9;
6449 = 5*1289 + 4; hence not 5 divides 6449 by NAT_4:9;
6449 = 7*921 + 2; hence not 7 divides 6449 by NAT_4:9;
6449 = 11*586 + 3; hence not 11 divides 6449 by NAT_4:9;
6449 = 13*496 + 1; hence not 13 divides 6449 by NAT_4:9;
6449 = 17*379 + 6; hence not 17 divides 6449 by NAT_4:9;
6449 = 19*339 + 8; hence not 19 divides 6449 by NAT_4:9;
6449 = 23*280 + 9; hence not 23 divides 6449 by NAT_4:9;
6449 = 29*222 + 11; hence not 29 divides 6449 by NAT_4:9;
6449 = 31*208 + 1; hence not 31 divides 6449 by NAT_4:9;
6449 = 37*174 + 11; hence not 37 divides 6449 by NAT_4:9;
6449 = 41*157 + 12; hence not 41 divides 6449 by NAT_4:9;
6449 = 43*149 + 42; hence not 43 divides 6449 by NAT_4:9;
6449 = 47*137 + 10; hence not 47 divides 6449 by NAT_4:9;
6449 = 53*121 + 36; hence not 53 divides 6449 by NAT_4:9;
6449 = 59*109 + 18; hence not 59 divides 6449 by NAT_4:9;
6449 = 61*105 + 44; hence not 61 divides 6449 by NAT_4:9;
6449 = 67*96 + 17; hence not 67 divides 6449 by NAT_4:9;
6449 = 71*90 + 59; hence not 71 divides 6449 by NAT_4:9;
6449 = 73*88 + 25; hence not 73 divides 6449 by NAT_4:9;
6449 = 79*81 + 50; hence not 79 divides 6449 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6449 & n is prime
holds not n divides 6449 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6451 is prime
proof
now
6451 = 2*3225 + 1; hence not 2 divides 6451 by NAT_4:9;
6451 = 3*2150 + 1; hence not 3 divides 6451 by NAT_4:9;
6451 = 5*1290 + 1; hence not 5 divides 6451 by NAT_4:9;
6451 = 7*921 + 4; hence not 7 divides 6451 by NAT_4:9;
6451 = 11*586 + 5; hence not 11 divides 6451 by NAT_4:9;
6451 = 13*496 + 3; hence not 13 divides 6451 by NAT_4:9;
6451 = 17*379 + 8; hence not 17 divides 6451 by NAT_4:9;
6451 = 19*339 + 10; hence not 19 divides 6451 by NAT_4:9;
6451 = 23*280 + 11; hence not 23 divides 6451 by NAT_4:9;
6451 = 29*222 + 13; hence not 29 divides 6451 by NAT_4:9;
6451 = 31*208 + 3; hence not 31 divides 6451 by NAT_4:9;
6451 = 37*174 + 13; hence not 37 divides 6451 by NAT_4:9;
6451 = 41*157 + 14; hence not 41 divides 6451 by NAT_4:9;
6451 = 43*150 + 1; hence not 43 divides 6451 by NAT_4:9;
6451 = 47*137 + 12; hence not 47 divides 6451 by NAT_4:9;
6451 = 53*121 + 38; hence not 53 divides 6451 by NAT_4:9;
6451 = 59*109 + 20; hence not 59 divides 6451 by NAT_4:9;
6451 = 61*105 + 46; hence not 61 divides 6451 by NAT_4:9;
6451 = 67*96 + 19; hence not 67 divides 6451 by NAT_4:9;
6451 = 71*90 + 61; hence not 71 divides 6451 by NAT_4:9;
6451 = 73*88 + 27; hence not 73 divides 6451 by NAT_4:9;
6451 = 79*81 + 52; hence not 79 divides 6451 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6451 & n is prime
holds not n divides 6451 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6469 is prime
proof
now
6469 = 2*3234 + 1; hence not 2 divides 6469 by NAT_4:9;
6469 = 3*2156 + 1; hence not 3 divides 6469 by NAT_4:9;
6469 = 5*1293 + 4; hence not 5 divides 6469 by NAT_4:9;
6469 = 7*924 + 1; hence not 7 divides 6469 by NAT_4:9;
6469 = 11*588 + 1; hence not 11 divides 6469 by NAT_4:9;
6469 = 13*497 + 8; hence not 13 divides 6469 by NAT_4:9;
6469 = 17*380 + 9; hence not 17 divides 6469 by NAT_4:9;
6469 = 19*340 + 9; hence not 19 divides 6469 by NAT_4:9;
6469 = 23*281 + 6; hence not 23 divides 6469 by NAT_4:9;
6469 = 29*223 + 2; hence not 29 divides 6469 by NAT_4:9;
6469 = 31*208 + 21; hence not 31 divides 6469 by NAT_4:9;
6469 = 37*174 + 31; hence not 37 divides 6469 by NAT_4:9;
6469 = 41*157 + 32; hence not 41 divides 6469 by NAT_4:9;
6469 = 43*150 + 19; hence not 43 divides 6469 by NAT_4:9;
6469 = 47*137 + 30; hence not 47 divides 6469 by NAT_4:9;
6469 = 53*122 + 3; hence not 53 divides 6469 by NAT_4:9;
6469 = 59*109 + 38; hence not 59 divides 6469 by NAT_4:9;
6469 = 61*106 + 3; hence not 61 divides 6469 by NAT_4:9;
6469 = 67*96 + 37; hence not 67 divides 6469 by NAT_4:9;
6469 = 71*91 + 8; hence not 71 divides 6469 by NAT_4:9;
6469 = 73*88 + 45; hence not 73 divides 6469 by NAT_4:9;
6469 = 79*81 + 70; hence not 79 divides 6469 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6469 & n is prime
holds not n divides 6469 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6473 is prime
proof
now
6473 = 2*3236 + 1; hence not 2 divides 6473 by NAT_4:9;
6473 = 3*2157 + 2; hence not 3 divides 6473 by NAT_4:9;
6473 = 5*1294 + 3; hence not 5 divides 6473 by NAT_4:9;
6473 = 7*924 + 5; hence not 7 divides 6473 by NAT_4:9;
6473 = 11*588 + 5; hence not 11 divides 6473 by NAT_4:9;
6473 = 13*497 + 12; hence not 13 divides 6473 by NAT_4:9;
6473 = 17*380 + 13; hence not 17 divides 6473 by NAT_4:9;
6473 = 19*340 + 13; hence not 19 divides 6473 by NAT_4:9;
6473 = 23*281 + 10; hence not 23 divides 6473 by NAT_4:9;
6473 = 29*223 + 6; hence not 29 divides 6473 by NAT_4:9;
6473 = 31*208 + 25; hence not 31 divides 6473 by NAT_4:9;
6473 = 37*174 + 35; hence not 37 divides 6473 by NAT_4:9;
6473 = 41*157 + 36; hence not 41 divides 6473 by NAT_4:9;
6473 = 43*150 + 23; hence not 43 divides 6473 by NAT_4:9;
6473 = 47*137 + 34; hence not 47 divides 6473 by NAT_4:9;
6473 = 53*122 + 7; hence not 53 divides 6473 by NAT_4:9;
6473 = 59*109 + 42; hence not 59 divides 6473 by NAT_4:9;
6473 = 61*106 + 7; hence not 61 divides 6473 by NAT_4:9;
6473 = 67*96 + 41; hence not 67 divides 6473 by NAT_4:9;
6473 = 71*91 + 12; hence not 71 divides 6473 by NAT_4:9;
6473 = 73*88 + 49; hence not 73 divides 6473 by NAT_4:9;
6473 = 79*81 + 74; hence not 79 divides 6473 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6473 & n is prime
holds not n divides 6473 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6481 is prime
proof
now
6481 = 2*3240 + 1; hence not 2 divides 6481 by NAT_4:9;
6481 = 3*2160 + 1; hence not 3 divides 6481 by NAT_4:9;
6481 = 5*1296 + 1; hence not 5 divides 6481 by NAT_4:9;
6481 = 7*925 + 6; hence not 7 divides 6481 by NAT_4:9;
6481 = 11*589 + 2; hence not 11 divides 6481 by NAT_4:9;
6481 = 13*498 + 7; hence not 13 divides 6481 by NAT_4:9;
6481 = 17*381 + 4; hence not 17 divides 6481 by NAT_4:9;
6481 = 19*341 + 2; hence not 19 divides 6481 by NAT_4:9;
6481 = 23*281 + 18; hence not 23 divides 6481 by NAT_4:9;
6481 = 29*223 + 14; hence not 29 divides 6481 by NAT_4:9;
6481 = 31*209 + 2; hence not 31 divides 6481 by NAT_4:9;
6481 = 37*175 + 6; hence not 37 divides 6481 by NAT_4:9;
6481 = 41*158 + 3; hence not 41 divides 6481 by NAT_4:9;
6481 = 43*150 + 31; hence not 43 divides 6481 by NAT_4:9;
6481 = 47*137 + 42; hence not 47 divides 6481 by NAT_4:9;
6481 = 53*122 + 15; hence not 53 divides 6481 by NAT_4:9;
6481 = 59*109 + 50; hence not 59 divides 6481 by NAT_4:9;
6481 = 61*106 + 15; hence not 61 divides 6481 by NAT_4:9;
6481 = 67*96 + 49; hence not 67 divides 6481 by NAT_4:9;
6481 = 71*91 + 20; hence not 71 divides 6481 by NAT_4:9;
6481 = 73*88 + 57; hence not 73 divides 6481 by NAT_4:9;
6481 = 79*82 + 3; hence not 79 divides 6481 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6481 & n is prime
holds not n divides 6481 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6491 is prime
proof
now
6491 = 2*3245 + 1; hence not 2 divides 6491 by NAT_4:9;
6491 = 3*2163 + 2; hence not 3 divides 6491 by NAT_4:9;
6491 = 5*1298 + 1; hence not 5 divides 6491 by NAT_4:9;
6491 = 7*927 + 2; hence not 7 divides 6491 by NAT_4:9;
6491 = 11*590 + 1; hence not 11 divides 6491 by NAT_4:9;
6491 = 13*499 + 4; hence not 13 divides 6491 by NAT_4:9;
6491 = 17*381 + 14; hence not 17 divides 6491 by NAT_4:9;
6491 = 19*341 + 12; hence not 19 divides 6491 by NAT_4:9;
6491 = 23*282 + 5; hence not 23 divides 6491 by NAT_4:9;
6491 = 29*223 + 24; hence not 29 divides 6491 by NAT_4:9;
6491 = 31*209 + 12; hence not 31 divides 6491 by NAT_4:9;
6491 = 37*175 + 16; hence not 37 divides 6491 by NAT_4:9;
6491 = 41*158 + 13; hence not 41 divides 6491 by NAT_4:9;
6491 = 43*150 + 41; hence not 43 divides 6491 by NAT_4:9;
6491 = 47*138 + 5; hence not 47 divides 6491 by NAT_4:9;
6491 = 53*122 + 25; hence not 53 divides 6491 by NAT_4:9;
6491 = 59*110 + 1; hence not 59 divides 6491 by NAT_4:9;
6491 = 61*106 + 25; hence not 61 divides 6491 by NAT_4:9;
6491 = 67*96 + 59; hence not 67 divides 6491 by NAT_4:9;
6491 = 71*91 + 30; hence not 71 divides 6491 by NAT_4:9;
6491 = 73*88 + 67; hence not 73 divides 6491 by NAT_4:9;
6491 = 79*82 + 13; hence not 79 divides 6491 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6491 & n is prime
holds not n divides 6491 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
6521 is prime
proof
now
6521 = 2*3260 + 1; hence not 2 divides 6521 by NAT_4:9;
6521 = 3*2173 + 2; hence not 3 divides 6521 by NAT_4:9;
6521 = 5*1304 + 1; hence not 5 divides 6521 by NAT_4:9;
6521 = 7*931 + 4; hence not 7 divides 6521 by NAT_4:9;
6521 = 11*592 + 9; hence not 11 divides 6521 by NAT_4:9;
6521 = 13*501 + 8; hence not 13 divides 6521 by NAT_4:9;
6521 = 17*383 + 10; hence not 17 divides 6521 by NAT_4:9;
6521 = 19*343 + 4; hence not 19 divides 6521 by NAT_4:9;
6521 = 23*283 + 12; hence not 23 divides 6521 by NAT_4:9;
6521 = 29*224 + 25; hence not 29 divides 6521 by NAT_4:9;
6521 = 31*210 + 11; hence not 31 divides 6521 by NAT_4:9;
6521 = 37*176 + 9; hence not 37 divides 6521 by NAT_4:9;
6521 = 41*159 + 2; hence not 41 divides 6521 by NAT_4:9;
6521 = 43*151 + 28; hence not 43 divides 6521 by NAT_4:9;
6521 = 47*138 + 35; hence not 47 divides 6521 by NAT_4:9;
6521 = 53*123 + 2; hence not 53 divides 6521 by NAT_4:9;
6521 = 59*110 + 31; hence not 59 divides 6521 by NAT_4:9;
6521 = 61*106 + 55; hence not 61 divides 6521 by NAT_4:9;
6521 = 67*97 + 22; hence not 67 divides 6521 by NAT_4:9;
6521 = 71*91 + 60; hence not 71 divides 6521 by NAT_4:9;
6521 = 73*89 + 24; hence not 73 divides 6521 by NAT_4:9;
6521 = 79*82 + 43; hence not 79 divides 6521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6521 & n is prime
holds not n divides 6521 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6529 is prime
proof
now
6529 = 2*3264 + 1; hence not 2 divides 6529 by NAT_4:9;
6529 = 3*2176 + 1; hence not 3 divides 6529 by NAT_4:9;
6529 = 5*1305 + 4; hence not 5 divides 6529 by NAT_4:9;
6529 = 7*932 + 5; hence not 7 divides 6529 by NAT_4:9;
6529 = 11*593 + 6; hence not 11 divides 6529 by NAT_4:9;
6529 = 13*502 + 3; hence not 13 divides 6529 by NAT_4:9;
6529 = 17*384 + 1; hence not 17 divides 6529 by NAT_4:9;
6529 = 19*343 + 12; hence not 19 divides 6529 by NAT_4:9;
6529 = 23*283 + 20; hence not 23 divides 6529 by NAT_4:9;
6529 = 29*225 + 4; hence not 29 divides 6529 by NAT_4:9;
6529 = 31*210 + 19; hence not 31 divides 6529 by NAT_4:9;
6529 = 37*176 + 17; hence not 37 divides 6529 by NAT_4:9;
6529 = 41*159 + 10; hence not 41 divides 6529 by NAT_4:9;
6529 = 43*151 + 36; hence not 43 divides 6529 by NAT_4:9;
6529 = 47*138 + 43; hence not 47 divides 6529 by NAT_4:9;
6529 = 53*123 + 10; hence not 53 divides 6529 by NAT_4:9;
6529 = 59*110 + 39; hence not 59 divides 6529 by NAT_4:9;
6529 = 61*107 + 2; hence not 61 divides 6529 by NAT_4:9;
6529 = 67*97 + 30; hence not 67 divides 6529 by NAT_4:9;
6529 = 71*91 + 68; hence not 71 divides 6529 by NAT_4:9;
6529 = 73*89 + 32; hence not 73 divides 6529 by NAT_4:9;
6529 = 79*82 + 51; hence not 79 divides 6529 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6529 & n is prime
holds not n divides 6529 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6547 is prime
proof
now
6547 = 2*3273 + 1; hence not 2 divides 6547 by NAT_4:9;
6547 = 3*2182 + 1; hence not 3 divides 6547 by NAT_4:9;
6547 = 5*1309 + 2; hence not 5 divides 6547 by NAT_4:9;
6547 = 7*935 + 2; hence not 7 divides 6547 by NAT_4:9;
6547 = 11*595 + 2; hence not 11 divides 6547 by NAT_4:9;
6547 = 13*503 + 8; hence not 13 divides 6547 by NAT_4:9;
6547 = 17*385 + 2; hence not 17 divides 6547 by NAT_4:9;
6547 = 19*344 + 11; hence not 19 divides 6547 by NAT_4:9;
6547 = 23*284 + 15; hence not 23 divides 6547 by NAT_4:9;
6547 = 29*225 + 22; hence not 29 divides 6547 by NAT_4:9;
6547 = 31*211 + 6; hence not 31 divides 6547 by NAT_4:9;
6547 = 37*176 + 35; hence not 37 divides 6547 by NAT_4:9;
6547 = 41*159 + 28; hence not 41 divides 6547 by NAT_4:9;
6547 = 43*152 + 11; hence not 43 divides 6547 by NAT_4:9;
6547 = 47*139 + 14; hence not 47 divides 6547 by NAT_4:9;
6547 = 53*123 + 28; hence not 53 divides 6547 by NAT_4:9;
6547 = 59*110 + 57; hence not 59 divides 6547 by NAT_4:9;
6547 = 61*107 + 20; hence not 61 divides 6547 by NAT_4:9;
6547 = 67*97 + 48; hence not 67 divides 6547 by NAT_4:9;
6547 = 71*92 + 15; hence not 71 divides 6547 by NAT_4:9;
6547 = 73*89 + 50; hence not 73 divides 6547 by NAT_4:9;
6547 = 79*82 + 69; hence not 79 divides 6547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6547 & n is prime
holds not n divides 6547 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6551 is prime
proof
now
6551 = 2*3275 + 1; hence not 2 divides 6551 by NAT_4:9;
6551 = 3*2183 + 2; hence not 3 divides 6551 by NAT_4:9;
6551 = 5*1310 + 1; hence not 5 divides 6551 by NAT_4:9;
6551 = 7*935 + 6; hence not 7 divides 6551 by NAT_4:9;
6551 = 11*595 + 6; hence not 11 divides 6551 by NAT_4:9;
6551 = 13*503 + 12; hence not 13 divides 6551 by NAT_4:9;
6551 = 17*385 + 6; hence not 17 divides 6551 by NAT_4:9;
6551 = 19*344 + 15; hence not 19 divides 6551 by NAT_4:9;
6551 = 23*284 + 19; hence not 23 divides 6551 by NAT_4:9;
6551 = 29*225 + 26; hence not 29 divides 6551 by NAT_4:9;
6551 = 31*211 + 10; hence not 31 divides 6551 by NAT_4:9;
6551 = 37*177 + 2; hence not 37 divides 6551 by NAT_4:9;
6551 = 41*159 + 32; hence not 41 divides 6551 by NAT_4:9;
6551 = 43*152 + 15; hence not 43 divides 6551 by NAT_4:9;
6551 = 47*139 + 18; hence not 47 divides 6551 by NAT_4:9;
6551 = 53*123 + 32; hence not 53 divides 6551 by NAT_4:9;
6551 = 59*111 + 2; hence not 59 divides 6551 by NAT_4:9;
6551 = 61*107 + 24; hence not 61 divides 6551 by NAT_4:9;
6551 = 67*97 + 52; hence not 67 divides 6551 by NAT_4:9;
6551 = 71*92 + 19; hence not 71 divides 6551 by NAT_4:9;
6551 = 73*89 + 54; hence not 73 divides 6551 by NAT_4:9;
6551 = 79*82 + 73; hence not 79 divides 6551 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6551 & n is prime
holds not n divides 6551 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6553 is prime
proof
now
6553 = 2*3276 + 1; hence not 2 divides 6553 by NAT_4:9;
6553 = 3*2184 + 1; hence not 3 divides 6553 by NAT_4:9;
6553 = 5*1310 + 3; hence not 5 divides 6553 by NAT_4:9;
6553 = 7*936 + 1; hence not 7 divides 6553 by NAT_4:9;
6553 = 11*595 + 8; hence not 11 divides 6553 by NAT_4:9;
6553 = 13*504 + 1; hence not 13 divides 6553 by NAT_4:9;
6553 = 17*385 + 8; hence not 17 divides 6553 by NAT_4:9;
6553 = 19*344 + 17; hence not 19 divides 6553 by NAT_4:9;
6553 = 23*284 + 21; hence not 23 divides 6553 by NAT_4:9;
6553 = 29*225 + 28; hence not 29 divides 6553 by NAT_4:9;
6553 = 31*211 + 12; hence not 31 divides 6553 by NAT_4:9;
6553 = 37*177 + 4; hence not 37 divides 6553 by NAT_4:9;
6553 = 41*159 + 34; hence not 41 divides 6553 by NAT_4:9;
6553 = 43*152 + 17; hence not 43 divides 6553 by NAT_4:9;
6553 = 47*139 + 20; hence not 47 divides 6553 by NAT_4:9;
6553 = 53*123 + 34; hence not 53 divides 6553 by NAT_4:9;
6553 = 59*111 + 4; hence not 59 divides 6553 by NAT_4:9;
6553 = 61*107 + 26; hence not 61 divides 6553 by NAT_4:9;
6553 = 67*97 + 54; hence not 67 divides 6553 by NAT_4:9;
6553 = 71*92 + 21; hence not 71 divides 6553 by NAT_4:9;
6553 = 73*89 + 56; hence not 73 divides 6553 by NAT_4:9;
6553 = 79*82 + 75; hence not 79 divides 6553 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6553 & n is prime
holds not n divides 6553 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6563 is prime
proof
now
6563 = 2*3281 + 1; hence not 2 divides 6563 by NAT_4:9;
6563 = 3*2187 + 2; hence not 3 divides 6563 by NAT_4:9;
6563 = 5*1312 + 3; hence not 5 divides 6563 by NAT_4:9;
6563 = 7*937 + 4; hence not 7 divides 6563 by NAT_4:9;
6563 = 11*596 + 7; hence not 11 divides 6563 by NAT_4:9;
6563 = 13*504 + 11; hence not 13 divides 6563 by NAT_4:9;
6563 = 17*386 + 1; hence not 17 divides 6563 by NAT_4:9;
6563 = 19*345 + 8; hence not 19 divides 6563 by NAT_4:9;
6563 = 23*285 + 8; hence not 23 divides 6563 by NAT_4:9;
6563 = 29*226 + 9; hence not 29 divides 6563 by NAT_4:9;
6563 = 31*211 + 22; hence not 31 divides 6563 by NAT_4:9;
6563 = 37*177 + 14; hence not 37 divides 6563 by NAT_4:9;
6563 = 41*160 + 3; hence not 41 divides 6563 by NAT_4:9;
6563 = 43*152 + 27; hence not 43 divides 6563 by NAT_4:9;
6563 = 47*139 + 30; hence not 47 divides 6563 by NAT_4:9;
6563 = 53*123 + 44; hence not 53 divides 6563 by NAT_4:9;
6563 = 59*111 + 14; hence not 59 divides 6563 by NAT_4:9;
6563 = 61*107 + 36; hence not 61 divides 6563 by NAT_4:9;
6563 = 67*97 + 64; hence not 67 divides 6563 by NAT_4:9;
6563 = 71*92 + 31; hence not 71 divides 6563 by NAT_4:9;
6563 = 73*89 + 66; hence not 73 divides 6563 by NAT_4:9;
6563 = 79*83 + 6; hence not 79 divides 6563 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6563 & n is prime
holds not n divides 6563 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6569 is prime
proof
now
6569 = 2*3284 + 1; hence not 2 divides 6569 by NAT_4:9;
6569 = 3*2189 + 2; hence not 3 divides 6569 by NAT_4:9;
6569 = 5*1313 + 4; hence not 5 divides 6569 by NAT_4:9;
6569 = 7*938 + 3; hence not 7 divides 6569 by NAT_4:9;
6569 = 11*597 + 2; hence not 11 divides 6569 by NAT_4:9;
6569 = 13*505 + 4; hence not 13 divides 6569 by NAT_4:9;
6569 = 17*386 + 7; hence not 17 divides 6569 by NAT_4:9;
6569 = 19*345 + 14; hence not 19 divides 6569 by NAT_4:9;
6569 = 23*285 + 14; hence not 23 divides 6569 by NAT_4:9;
6569 = 29*226 + 15; hence not 29 divides 6569 by NAT_4:9;
6569 = 31*211 + 28; hence not 31 divides 6569 by NAT_4:9;
6569 = 37*177 + 20; hence not 37 divides 6569 by NAT_4:9;
6569 = 41*160 + 9; hence not 41 divides 6569 by NAT_4:9;
6569 = 43*152 + 33; hence not 43 divides 6569 by NAT_4:9;
6569 = 47*139 + 36; hence not 47 divides 6569 by NAT_4:9;
6569 = 53*123 + 50; hence not 53 divides 6569 by NAT_4:9;
6569 = 59*111 + 20; hence not 59 divides 6569 by NAT_4:9;
6569 = 61*107 + 42; hence not 61 divides 6569 by NAT_4:9;
6569 = 67*98 + 3; hence not 67 divides 6569 by NAT_4:9;
6569 = 71*92 + 37; hence not 71 divides 6569 by NAT_4:9;
6569 = 73*89 + 72; hence not 73 divides 6569 by NAT_4:9;
6569 = 79*83 + 12; hence not 79 divides 6569 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6569 & n is prime
holds not n divides 6569 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6571 is prime
proof
now
6571 = 2*3285 + 1; hence not 2 divides 6571 by NAT_4:9;
6571 = 3*2190 + 1; hence not 3 divides 6571 by NAT_4:9;
6571 = 5*1314 + 1; hence not 5 divides 6571 by NAT_4:9;
6571 = 7*938 + 5; hence not 7 divides 6571 by NAT_4:9;
6571 = 11*597 + 4; hence not 11 divides 6571 by NAT_4:9;
6571 = 13*505 + 6; hence not 13 divides 6571 by NAT_4:9;
6571 = 17*386 + 9; hence not 17 divides 6571 by NAT_4:9;
6571 = 19*345 + 16; hence not 19 divides 6571 by NAT_4:9;
6571 = 23*285 + 16; hence not 23 divides 6571 by NAT_4:9;
6571 = 29*226 + 17; hence not 29 divides 6571 by NAT_4:9;
6571 = 31*211 + 30; hence not 31 divides 6571 by NAT_4:9;
6571 = 37*177 + 22; hence not 37 divides 6571 by NAT_4:9;
6571 = 41*160 + 11; hence not 41 divides 6571 by NAT_4:9;
6571 = 43*152 + 35; hence not 43 divides 6571 by NAT_4:9;
6571 = 47*139 + 38; hence not 47 divides 6571 by NAT_4:9;
6571 = 53*123 + 52; hence not 53 divides 6571 by NAT_4:9;
6571 = 59*111 + 22; hence not 59 divides 6571 by NAT_4:9;
6571 = 61*107 + 44; hence not 61 divides 6571 by NAT_4:9;
6571 = 67*98 + 5; hence not 67 divides 6571 by NAT_4:9;
6571 = 71*92 + 39; hence not 71 divides 6571 by NAT_4:9;
6571 = 73*90 + 1; hence not 73 divides 6571 by NAT_4:9;
6571 = 79*83 + 14; hence not 79 divides 6571 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6571 & n is prime
holds not n divides 6571 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6577 is prime
proof
now
6577 = 2*3288 + 1; hence not 2 divides 6577 by NAT_4:9;
6577 = 3*2192 + 1; hence not 3 divides 6577 by NAT_4:9;
6577 = 5*1315 + 2; hence not 5 divides 6577 by NAT_4:9;
6577 = 7*939 + 4; hence not 7 divides 6577 by NAT_4:9;
6577 = 11*597 + 10; hence not 11 divides 6577 by NAT_4:9;
6577 = 13*505 + 12; hence not 13 divides 6577 by NAT_4:9;
6577 = 17*386 + 15; hence not 17 divides 6577 by NAT_4:9;
6577 = 19*346 + 3; hence not 19 divides 6577 by NAT_4:9;
6577 = 23*285 + 22; hence not 23 divides 6577 by NAT_4:9;
6577 = 29*226 + 23; hence not 29 divides 6577 by NAT_4:9;
6577 = 31*212 + 5; hence not 31 divides 6577 by NAT_4:9;
6577 = 37*177 + 28; hence not 37 divides 6577 by NAT_4:9;
6577 = 41*160 + 17; hence not 41 divides 6577 by NAT_4:9;
6577 = 43*152 + 41; hence not 43 divides 6577 by NAT_4:9;
6577 = 47*139 + 44; hence not 47 divides 6577 by NAT_4:9;
6577 = 53*124 + 5; hence not 53 divides 6577 by NAT_4:9;
6577 = 59*111 + 28; hence not 59 divides 6577 by NAT_4:9;
6577 = 61*107 + 50; hence not 61 divides 6577 by NAT_4:9;
6577 = 67*98 + 11; hence not 67 divides 6577 by NAT_4:9;
6577 = 71*92 + 45; hence not 71 divides 6577 by NAT_4:9;
6577 = 73*90 + 7; hence not 73 divides 6577 by NAT_4:9;
6577 = 79*83 + 20; hence not 79 divides 6577 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6577 & n is prime
holds not n divides 6577 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6581 is prime
proof
now
6581 = 2*3290 + 1; hence not 2 divides 6581 by NAT_4:9;
6581 = 3*2193 + 2; hence not 3 divides 6581 by NAT_4:9;
6581 = 5*1316 + 1; hence not 5 divides 6581 by NAT_4:9;
6581 = 7*940 + 1; hence not 7 divides 6581 by NAT_4:9;
6581 = 11*598 + 3; hence not 11 divides 6581 by NAT_4:9;
6581 = 13*506 + 3; hence not 13 divides 6581 by NAT_4:9;
6581 = 17*387 + 2; hence not 17 divides 6581 by NAT_4:9;
6581 = 19*346 + 7; hence not 19 divides 6581 by NAT_4:9;
6581 = 23*286 + 3; hence not 23 divides 6581 by NAT_4:9;
6581 = 29*226 + 27; hence not 29 divides 6581 by NAT_4:9;
6581 = 31*212 + 9; hence not 31 divides 6581 by NAT_4:9;
6581 = 37*177 + 32; hence not 37 divides 6581 by NAT_4:9;
6581 = 41*160 + 21; hence not 41 divides 6581 by NAT_4:9;
6581 = 43*153 + 2; hence not 43 divides 6581 by NAT_4:9;
6581 = 47*140 + 1; hence not 47 divides 6581 by NAT_4:9;
6581 = 53*124 + 9; hence not 53 divides 6581 by NAT_4:9;
6581 = 59*111 + 32; hence not 59 divides 6581 by NAT_4:9;
6581 = 61*107 + 54; hence not 61 divides 6581 by NAT_4:9;
6581 = 67*98 + 15; hence not 67 divides 6581 by NAT_4:9;
6581 = 71*92 + 49; hence not 71 divides 6581 by NAT_4:9;
6581 = 73*90 + 11; hence not 73 divides 6581 by NAT_4:9;
6581 = 79*83 + 24; hence not 79 divides 6581 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6581 & n is prime
holds not n divides 6581 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6599 is prime
proof
now
6599 = 2*3299 + 1; hence not 2 divides 6599 by NAT_4:9;
6599 = 3*2199 + 2; hence not 3 divides 6599 by NAT_4:9;
6599 = 5*1319 + 4; hence not 5 divides 6599 by NAT_4:9;
6599 = 7*942 + 5; hence not 7 divides 6599 by NAT_4:9;
6599 = 11*599 + 10; hence not 11 divides 6599 by NAT_4:9;
6599 = 13*507 + 8; hence not 13 divides 6599 by NAT_4:9;
6599 = 17*388 + 3; hence not 17 divides 6599 by NAT_4:9;
6599 = 19*347 + 6; hence not 19 divides 6599 by NAT_4:9;
6599 = 23*286 + 21; hence not 23 divides 6599 by NAT_4:9;
6599 = 29*227 + 16; hence not 29 divides 6599 by NAT_4:9;
6599 = 31*212 + 27; hence not 31 divides 6599 by NAT_4:9;
6599 = 37*178 + 13; hence not 37 divides 6599 by NAT_4:9;
6599 = 41*160 + 39; hence not 41 divides 6599 by NAT_4:9;
6599 = 43*153 + 20; hence not 43 divides 6599 by NAT_4:9;
6599 = 47*140 + 19; hence not 47 divides 6599 by NAT_4:9;
6599 = 53*124 + 27; hence not 53 divides 6599 by NAT_4:9;
6599 = 59*111 + 50; hence not 59 divides 6599 by NAT_4:9;
6599 = 61*108 + 11; hence not 61 divides 6599 by NAT_4:9;
6599 = 67*98 + 33; hence not 67 divides 6599 by NAT_4:9;
6599 = 71*92 + 67; hence not 71 divides 6599 by NAT_4:9;
6599 = 73*90 + 29; hence not 73 divides 6599 by NAT_4:9;
6599 = 79*83 + 42; hence not 79 divides 6599 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6599 & n is prime
holds not n divides 6599 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6607 is prime
proof
now
6607 = 2*3303 + 1; hence not 2 divides 6607 by NAT_4:9;
6607 = 3*2202 + 1; hence not 3 divides 6607 by NAT_4:9;
6607 = 5*1321 + 2; hence not 5 divides 6607 by NAT_4:9;
6607 = 7*943 + 6; hence not 7 divides 6607 by NAT_4:9;
6607 = 11*600 + 7; hence not 11 divides 6607 by NAT_4:9;
6607 = 13*508 + 3; hence not 13 divides 6607 by NAT_4:9;
6607 = 17*388 + 11; hence not 17 divides 6607 by NAT_4:9;
6607 = 19*347 + 14; hence not 19 divides 6607 by NAT_4:9;
6607 = 23*287 + 6; hence not 23 divides 6607 by NAT_4:9;
6607 = 29*227 + 24; hence not 29 divides 6607 by NAT_4:9;
6607 = 31*213 + 4; hence not 31 divides 6607 by NAT_4:9;
6607 = 37*178 + 21; hence not 37 divides 6607 by NAT_4:9;
6607 = 41*161 + 6; hence not 41 divides 6607 by NAT_4:9;
6607 = 43*153 + 28; hence not 43 divides 6607 by NAT_4:9;
6607 = 47*140 + 27; hence not 47 divides 6607 by NAT_4:9;
6607 = 53*124 + 35; hence not 53 divides 6607 by NAT_4:9;
6607 = 59*111 + 58; hence not 59 divides 6607 by NAT_4:9;
6607 = 61*108 + 19; hence not 61 divides 6607 by NAT_4:9;
6607 = 67*98 + 41; hence not 67 divides 6607 by NAT_4:9;
6607 = 71*93 + 4; hence not 71 divides 6607 by NAT_4:9;
6607 = 73*90 + 37; hence not 73 divides 6607 by NAT_4:9;
6607 = 79*83 + 50; hence not 79 divides 6607 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6607 & n is prime
holds not n divides 6607 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6619 is prime
proof
now
6619 = 2*3309 + 1; hence not 2 divides 6619 by NAT_4:9;
6619 = 3*2206 + 1; hence not 3 divides 6619 by NAT_4:9;
6619 = 5*1323 + 4; hence not 5 divides 6619 by NAT_4:9;
6619 = 7*945 + 4; hence not 7 divides 6619 by NAT_4:9;
6619 = 11*601 + 8; hence not 11 divides 6619 by NAT_4:9;
6619 = 13*509 + 2; hence not 13 divides 6619 by NAT_4:9;
6619 = 17*389 + 6; hence not 17 divides 6619 by NAT_4:9;
6619 = 19*348 + 7; hence not 19 divides 6619 by NAT_4:9;
6619 = 23*287 + 18; hence not 23 divides 6619 by NAT_4:9;
6619 = 29*228 + 7; hence not 29 divides 6619 by NAT_4:9;
6619 = 31*213 + 16; hence not 31 divides 6619 by NAT_4:9;
6619 = 37*178 + 33; hence not 37 divides 6619 by NAT_4:9;
6619 = 41*161 + 18; hence not 41 divides 6619 by NAT_4:9;
6619 = 43*153 + 40; hence not 43 divides 6619 by NAT_4:9;
6619 = 47*140 + 39; hence not 47 divides 6619 by NAT_4:9;
6619 = 53*124 + 47; hence not 53 divides 6619 by NAT_4:9;
6619 = 59*112 + 11; hence not 59 divides 6619 by NAT_4:9;
6619 = 61*108 + 31; hence not 61 divides 6619 by NAT_4:9;
6619 = 67*98 + 53; hence not 67 divides 6619 by NAT_4:9;
6619 = 71*93 + 16; hence not 71 divides 6619 by NAT_4:9;
6619 = 73*90 + 49; hence not 73 divides 6619 by NAT_4:9;
6619 = 79*83 + 62; hence not 79 divides 6619 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6619 & n is prime
holds not n divides 6619 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
6637 is prime
proof
now
6637 = 2*3318 + 1; hence not 2 divides 6637 by NAT_4:9;
6637 = 3*2212 + 1; hence not 3 divides 6637 by NAT_4:9;
6637 = 5*1327 + 2; hence not 5 divides 6637 by NAT_4:9;
6637 = 7*948 + 1; hence not 7 divides 6637 by NAT_4:9;
6637 = 11*603 + 4; hence not 11 divides 6637 by NAT_4:9;
6637 = 13*510 + 7; hence not 13 divides 6637 by NAT_4:9;
6637 = 17*390 + 7; hence not 17 divides 6637 by NAT_4:9;
6637 = 19*349 + 6; hence not 19 divides 6637 by NAT_4:9;
6637 = 23*288 + 13; hence not 23 divides 6637 by NAT_4:9;
6637 = 29*228 + 25; hence not 29 divides 6637 by NAT_4:9;
6637 = 31*214 + 3; hence not 31 divides 6637 by NAT_4:9;
6637 = 37*179 + 14; hence not 37 divides 6637 by NAT_4:9;
6637 = 41*161 + 36; hence not 41 divides 6637 by NAT_4:9;
6637 = 43*154 + 15; hence not 43 divides 6637 by NAT_4:9;
6637 = 47*141 + 10; hence not 47 divides 6637 by NAT_4:9;
6637 = 53*125 + 12; hence not 53 divides 6637 by NAT_4:9;
6637 = 59*112 + 29; hence not 59 divides 6637 by NAT_4:9;
6637 = 61*108 + 49; hence not 61 divides 6637 by NAT_4:9;
6637 = 67*99 + 4; hence not 67 divides 6637 by NAT_4:9;
6637 = 71*93 + 34; hence not 71 divides 6637 by NAT_4:9;
6637 = 73*90 + 67; hence not 73 divides 6637 by NAT_4:9;
6637 = 79*84 + 1; hence not 79 divides 6637 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6637 & n is prime
holds not n divides 6637 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
6653 is prime
proof
now
6653 = 2*3326 + 1; hence not 2 divides 6653 by NAT_4:9;
6653 = 3*2217 + 2; hence not 3 divides 6653 by NAT_4:9;
6653 = 5*1330 + 3; hence not 5 divides 6653 by NAT_4:9;
6653 = 7*950 + 3; hence not 7 divides 6653 by NAT_4:9;
6653 = 11*604 + 9; hence not 11 divides 6653 by NAT_4:9;
6653 = 13*511 + 10; hence not 13 divides 6653 by NAT_4:9;
6653 = 17*391 + 6; hence not 17 divides 6653 by NAT_4:9;
6653 = 19*350 + 3; hence not 19 divides 6653 by NAT_4:9;
6653 = 23*289 + 6; hence not 23 divides 6653 by NAT_4:9;
6653 = 29*229 + 12; hence not 29 divides 6653 by NAT_4:9;
6653 = 31*214 + 19; hence not 31 divides 6653 by NAT_4:9;
6653 = 37*179 + 30; hence not 37 divides 6653 by NAT_4:9;
6653 = 41*162 + 11; hence not 41 divides 6653 by NAT_4:9;
6653 = 43*154 + 31; hence not 43 divides 6653 by NAT_4:9;
6653 = 47*141 + 26; hence not 47 divides 6653 by NAT_4:9;
6653 = 53*125 + 28; hence not 53 divides 6653 by NAT_4:9;
6653 = 59*112 + 45; hence not 59 divides 6653 by NAT_4:9;
6653 = 61*109 + 4; hence not 61 divides 6653 by NAT_4:9;
6653 = 67*99 + 20; hence not 67 divides 6653 by NAT_4:9;
6653 = 71*93 + 50; hence not 71 divides 6653 by NAT_4:9;
6653 = 73*91 + 10; hence not 73 divides 6653 by NAT_4:9;
6653 = 79*84 + 17; hence not 79 divides 6653 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6653 & n is prime
holds not n divides 6653 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6659 is prime
proof
now
6659 = 2*3329 + 1; hence not 2 divides 6659 by NAT_4:9;
6659 = 3*2219 + 2; hence not 3 divides 6659 by NAT_4:9;
6659 = 5*1331 + 4; hence not 5 divides 6659 by NAT_4:9;
6659 = 7*951 + 2; hence not 7 divides 6659 by NAT_4:9;
6659 = 11*605 + 4; hence not 11 divides 6659 by NAT_4:9;
6659 = 13*512 + 3; hence not 13 divides 6659 by NAT_4:9;
6659 = 17*391 + 12; hence not 17 divides 6659 by NAT_4:9;
6659 = 19*350 + 9; hence not 19 divides 6659 by NAT_4:9;
6659 = 23*289 + 12; hence not 23 divides 6659 by NAT_4:9;
6659 = 29*229 + 18; hence not 29 divides 6659 by NAT_4:9;
6659 = 31*214 + 25; hence not 31 divides 6659 by NAT_4:9;
6659 = 37*179 + 36; hence not 37 divides 6659 by NAT_4:9;
6659 = 41*162 + 17; hence not 41 divides 6659 by NAT_4:9;
6659 = 43*154 + 37; hence not 43 divides 6659 by NAT_4:9;
6659 = 47*141 + 32; hence not 47 divides 6659 by NAT_4:9;
6659 = 53*125 + 34; hence not 53 divides 6659 by NAT_4:9;
6659 = 59*112 + 51; hence not 59 divides 6659 by NAT_4:9;
6659 = 61*109 + 10; hence not 61 divides 6659 by NAT_4:9;
6659 = 67*99 + 26; hence not 67 divides 6659 by NAT_4:9;
6659 = 71*93 + 56; hence not 71 divides 6659 by NAT_4:9;
6659 = 73*91 + 16; hence not 73 divides 6659 by NAT_4:9;
6659 = 79*84 + 23; hence not 79 divides 6659 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6659 & n is prime
holds not n divides 6659 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6661 is prime
proof
now
6661 = 2*3330 + 1; hence not 2 divides 6661 by NAT_4:9;
6661 = 3*2220 + 1; hence not 3 divides 6661 by NAT_4:9;
6661 = 5*1332 + 1; hence not 5 divides 6661 by NAT_4:9;
6661 = 7*951 + 4; hence not 7 divides 6661 by NAT_4:9;
6661 = 11*605 + 6; hence not 11 divides 6661 by NAT_4:9;
6661 = 13*512 + 5; hence not 13 divides 6661 by NAT_4:9;
6661 = 17*391 + 14; hence not 17 divides 6661 by NAT_4:9;
6661 = 19*350 + 11; hence not 19 divides 6661 by NAT_4:9;
6661 = 23*289 + 14; hence not 23 divides 6661 by NAT_4:9;
6661 = 29*229 + 20; hence not 29 divides 6661 by NAT_4:9;
6661 = 31*214 + 27; hence not 31 divides 6661 by NAT_4:9;
6661 = 37*180 + 1; hence not 37 divides 6661 by NAT_4:9;
6661 = 41*162 + 19; hence not 41 divides 6661 by NAT_4:9;
6661 = 43*154 + 39; hence not 43 divides 6661 by NAT_4:9;
6661 = 47*141 + 34; hence not 47 divides 6661 by NAT_4:9;
6661 = 53*125 + 36; hence not 53 divides 6661 by NAT_4:9;
6661 = 59*112 + 53; hence not 59 divides 6661 by NAT_4:9;
6661 = 61*109 + 12; hence not 61 divides 6661 by NAT_4:9;
6661 = 67*99 + 28; hence not 67 divides 6661 by NAT_4:9;
6661 = 71*93 + 58; hence not 71 divides 6661 by NAT_4:9;
6661 = 73*91 + 18; hence not 73 divides 6661 by NAT_4:9;
6661 = 79*84 + 25; hence not 79 divides 6661 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6661 & n is prime
holds not n divides 6661 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6673 is prime
proof
now
6673 = 2*3336 + 1; hence not 2 divides 6673 by NAT_4:9;
6673 = 3*2224 + 1; hence not 3 divides 6673 by NAT_4:9;
6673 = 5*1334 + 3; hence not 5 divides 6673 by NAT_4:9;
6673 = 7*953 + 2; hence not 7 divides 6673 by NAT_4:9;
6673 = 11*606 + 7; hence not 11 divides 6673 by NAT_4:9;
6673 = 13*513 + 4; hence not 13 divides 6673 by NAT_4:9;
6673 = 17*392 + 9; hence not 17 divides 6673 by NAT_4:9;
6673 = 19*351 + 4; hence not 19 divides 6673 by NAT_4:9;
6673 = 23*290 + 3; hence not 23 divides 6673 by NAT_4:9;
6673 = 29*230 + 3; hence not 29 divides 6673 by NAT_4:9;
6673 = 31*215 + 8; hence not 31 divides 6673 by NAT_4:9;
6673 = 37*180 + 13; hence not 37 divides 6673 by NAT_4:9;
6673 = 41*162 + 31; hence not 41 divides 6673 by NAT_4:9;
6673 = 43*155 + 8; hence not 43 divides 6673 by NAT_4:9;
6673 = 47*141 + 46; hence not 47 divides 6673 by NAT_4:9;
6673 = 53*125 + 48; hence not 53 divides 6673 by NAT_4:9;
6673 = 59*113 + 6; hence not 59 divides 6673 by NAT_4:9;
6673 = 61*109 + 24; hence not 61 divides 6673 by NAT_4:9;
6673 = 67*99 + 40; hence not 67 divides 6673 by NAT_4:9;
6673 = 71*93 + 70; hence not 71 divides 6673 by NAT_4:9;
6673 = 73*91 + 30; hence not 73 divides 6673 by NAT_4:9;
6673 = 79*84 + 37; hence not 79 divides 6673 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6673 & n is prime
holds not n divides 6673 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6679 is prime
proof
now
6679 = 2*3339 + 1; hence not 2 divides 6679 by NAT_4:9;
6679 = 3*2226 + 1; hence not 3 divides 6679 by NAT_4:9;
6679 = 5*1335 + 4; hence not 5 divides 6679 by NAT_4:9;
6679 = 7*954 + 1; hence not 7 divides 6679 by NAT_4:9;
6679 = 11*607 + 2; hence not 11 divides 6679 by NAT_4:9;
6679 = 13*513 + 10; hence not 13 divides 6679 by NAT_4:9;
6679 = 17*392 + 15; hence not 17 divides 6679 by NAT_4:9;
6679 = 19*351 + 10; hence not 19 divides 6679 by NAT_4:9;
6679 = 23*290 + 9; hence not 23 divides 6679 by NAT_4:9;
6679 = 29*230 + 9; hence not 29 divides 6679 by NAT_4:9;
6679 = 31*215 + 14; hence not 31 divides 6679 by NAT_4:9;
6679 = 37*180 + 19; hence not 37 divides 6679 by NAT_4:9;
6679 = 41*162 + 37; hence not 41 divides 6679 by NAT_4:9;
6679 = 43*155 + 14; hence not 43 divides 6679 by NAT_4:9;
6679 = 47*142 + 5; hence not 47 divides 6679 by NAT_4:9;
6679 = 53*126 + 1; hence not 53 divides 6679 by NAT_4:9;
6679 = 59*113 + 12; hence not 59 divides 6679 by NAT_4:9;
6679 = 61*109 + 30; hence not 61 divides 6679 by NAT_4:9;
6679 = 67*99 + 46; hence not 67 divides 6679 by NAT_4:9;
6679 = 71*94 + 5; hence not 71 divides 6679 by NAT_4:9;
6679 = 73*91 + 36; hence not 73 divides 6679 by NAT_4:9;
6679 = 79*84 + 43; hence not 79 divides 6679 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6679 & n is prime
holds not n divides 6679 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6689 is prime
proof
now
6689 = 2*3344 + 1; hence not 2 divides 6689 by NAT_4:9;
6689 = 3*2229 + 2; hence not 3 divides 6689 by NAT_4:9;
6689 = 5*1337 + 4; hence not 5 divides 6689 by NAT_4:9;
6689 = 7*955 + 4; hence not 7 divides 6689 by NAT_4:9;
6689 = 11*608 + 1; hence not 11 divides 6689 by NAT_4:9;
6689 = 13*514 + 7; hence not 13 divides 6689 by NAT_4:9;
6689 = 17*393 + 8; hence not 17 divides 6689 by NAT_4:9;
6689 = 19*352 + 1; hence not 19 divides 6689 by NAT_4:9;
6689 = 23*290 + 19; hence not 23 divides 6689 by NAT_4:9;
6689 = 29*230 + 19; hence not 29 divides 6689 by NAT_4:9;
6689 = 31*215 + 24; hence not 31 divides 6689 by NAT_4:9;
6689 = 37*180 + 29; hence not 37 divides 6689 by NAT_4:9;
6689 = 41*163 + 6; hence not 41 divides 6689 by NAT_4:9;
6689 = 43*155 + 24; hence not 43 divides 6689 by NAT_4:9;
6689 = 47*142 + 15; hence not 47 divides 6689 by NAT_4:9;
6689 = 53*126 + 11; hence not 53 divides 6689 by NAT_4:9;
6689 = 59*113 + 22; hence not 59 divides 6689 by NAT_4:9;
6689 = 61*109 + 40; hence not 61 divides 6689 by NAT_4:9;
6689 = 67*99 + 56; hence not 67 divides 6689 by NAT_4:9;
6689 = 71*94 + 15; hence not 71 divides 6689 by NAT_4:9;
6689 = 73*91 + 46; hence not 73 divides 6689 by NAT_4:9;
6689 = 79*84 + 53; hence not 79 divides 6689 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6689 & n is prime
holds not n divides 6689 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6691 is prime
proof
now
6691 = 2*3345 + 1; hence not 2 divides 6691 by NAT_4:9;
6691 = 3*2230 + 1; hence not 3 divides 6691 by NAT_4:9;
6691 = 5*1338 + 1; hence not 5 divides 6691 by NAT_4:9;
6691 = 7*955 + 6; hence not 7 divides 6691 by NAT_4:9;
6691 = 11*608 + 3; hence not 11 divides 6691 by NAT_4:9;
6691 = 13*514 + 9; hence not 13 divides 6691 by NAT_4:9;
6691 = 17*393 + 10; hence not 17 divides 6691 by NAT_4:9;
6691 = 19*352 + 3; hence not 19 divides 6691 by NAT_4:9;
6691 = 23*290 + 21; hence not 23 divides 6691 by NAT_4:9;
6691 = 29*230 + 21; hence not 29 divides 6691 by NAT_4:9;
6691 = 31*215 + 26; hence not 31 divides 6691 by NAT_4:9;
6691 = 37*180 + 31; hence not 37 divides 6691 by NAT_4:9;
6691 = 41*163 + 8; hence not 41 divides 6691 by NAT_4:9;
6691 = 43*155 + 26; hence not 43 divides 6691 by NAT_4:9;
6691 = 47*142 + 17; hence not 47 divides 6691 by NAT_4:9;
6691 = 53*126 + 13; hence not 53 divides 6691 by NAT_4:9;
6691 = 59*113 + 24; hence not 59 divides 6691 by NAT_4:9;
6691 = 61*109 + 42; hence not 61 divides 6691 by NAT_4:9;
6691 = 67*99 + 58; hence not 67 divides 6691 by NAT_4:9;
6691 = 71*94 + 17; hence not 71 divides 6691 by NAT_4:9;
6691 = 73*91 + 48; hence not 73 divides 6691 by NAT_4:9;
6691 = 79*84 + 55; hence not 79 divides 6691 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6691 & n is prime
holds not n divides 6691 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6701 is prime
proof
now
6701 = 2*3350 + 1; hence not 2 divides 6701 by NAT_4:9;
6701 = 3*2233 + 2; hence not 3 divides 6701 by NAT_4:9;
6701 = 5*1340 + 1; hence not 5 divides 6701 by NAT_4:9;
6701 = 7*957 + 2; hence not 7 divides 6701 by NAT_4:9;
6701 = 11*609 + 2; hence not 11 divides 6701 by NAT_4:9;
6701 = 13*515 + 6; hence not 13 divides 6701 by NAT_4:9;
6701 = 17*394 + 3; hence not 17 divides 6701 by NAT_4:9;
6701 = 19*352 + 13; hence not 19 divides 6701 by NAT_4:9;
6701 = 23*291 + 8; hence not 23 divides 6701 by NAT_4:9;
6701 = 29*231 + 2; hence not 29 divides 6701 by NAT_4:9;
6701 = 31*216 + 5; hence not 31 divides 6701 by NAT_4:9;
6701 = 37*181 + 4; hence not 37 divides 6701 by NAT_4:9;
6701 = 41*163 + 18; hence not 41 divides 6701 by NAT_4:9;
6701 = 43*155 + 36; hence not 43 divides 6701 by NAT_4:9;
6701 = 47*142 + 27; hence not 47 divides 6701 by NAT_4:9;
6701 = 53*126 + 23; hence not 53 divides 6701 by NAT_4:9;
6701 = 59*113 + 34; hence not 59 divides 6701 by NAT_4:9;
6701 = 61*109 + 52; hence not 61 divides 6701 by NAT_4:9;
6701 = 67*100 + 1; hence not 67 divides 6701 by NAT_4:9;
6701 = 71*94 + 27; hence not 71 divides 6701 by NAT_4:9;
6701 = 73*91 + 58; hence not 73 divides 6701 by NAT_4:9;
6701 = 79*84 + 65; hence not 79 divides 6701 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6701 & n is prime
holds not n divides 6701 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6703 is prime
proof
now
6703 = 2*3351 + 1; hence not 2 divides 6703 by NAT_4:9;
6703 = 3*2234 + 1; hence not 3 divides 6703 by NAT_4:9;
6703 = 5*1340 + 3; hence not 5 divides 6703 by NAT_4:9;
6703 = 7*957 + 4; hence not 7 divides 6703 by NAT_4:9;
6703 = 11*609 + 4; hence not 11 divides 6703 by NAT_4:9;
6703 = 13*515 + 8; hence not 13 divides 6703 by NAT_4:9;
6703 = 17*394 + 5; hence not 17 divides 6703 by NAT_4:9;
6703 = 19*352 + 15; hence not 19 divides 6703 by NAT_4:9;
6703 = 23*291 + 10; hence not 23 divides 6703 by NAT_4:9;
6703 = 29*231 + 4; hence not 29 divides 6703 by NAT_4:9;
6703 = 31*216 + 7; hence not 31 divides 6703 by NAT_4:9;
6703 = 37*181 + 6; hence not 37 divides 6703 by NAT_4:9;
6703 = 41*163 + 20; hence not 41 divides 6703 by NAT_4:9;
6703 = 43*155 + 38; hence not 43 divides 6703 by NAT_4:9;
6703 = 47*142 + 29; hence not 47 divides 6703 by NAT_4:9;
6703 = 53*126 + 25; hence not 53 divides 6703 by NAT_4:9;
6703 = 59*113 + 36; hence not 59 divides 6703 by NAT_4:9;
6703 = 61*109 + 54; hence not 61 divides 6703 by NAT_4:9;
6703 = 67*100 + 3; hence not 67 divides 6703 by NAT_4:9;
6703 = 71*94 + 29; hence not 71 divides 6703 by NAT_4:9;
6703 = 73*91 + 60; hence not 73 divides 6703 by NAT_4:9;
6703 = 79*84 + 67; hence not 79 divides 6703 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6703 & n is prime
holds not n divides 6703 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6709 is prime
proof
now
6709 = 2*3354 + 1; hence not 2 divides 6709 by NAT_4:9;
6709 = 3*2236 + 1; hence not 3 divides 6709 by NAT_4:9;
6709 = 5*1341 + 4; hence not 5 divides 6709 by NAT_4:9;
6709 = 7*958 + 3; hence not 7 divides 6709 by NAT_4:9;
6709 = 11*609 + 10; hence not 11 divides 6709 by NAT_4:9;
6709 = 13*516 + 1; hence not 13 divides 6709 by NAT_4:9;
6709 = 17*394 + 11; hence not 17 divides 6709 by NAT_4:9;
6709 = 19*353 + 2; hence not 19 divides 6709 by NAT_4:9;
6709 = 23*291 + 16; hence not 23 divides 6709 by NAT_4:9;
6709 = 29*231 + 10; hence not 29 divides 6709 by NAT_4:9;
6709 = 31*216 + 13; hence not 31 divides 6709 by NAT_4:9;
6709 = 37*181 + 12; hence not 37 divides 6709 by NAT_4:9;
6709 = 41*163 + 26; hence not 41 divides 6709 by NAT_4:9;
6709 = 43*156 + 1; hence not 43 divides 6709 by NAT_4:9;
6709 = 47*142 + 35; hence not 47 divides 6709 by NAT_4:9;
6709 = 53*126 + 31; hence not 53 divides 6709 by NAT_4:9;
6709 = 59*113 + 42; hence not 59 divides 6709 by NAT_4:9;
6709 = 61*109 + 60; hence not 61 divides 6709 by NAT_4:9;
6709 = 67*100 + 9; hence not 67 divides 6709 by NAT_4:9;
6709 = 71*94 + 35; hence not 71 divides 6709 by NAT_4:9;
6709 = 73*91 + 66; hence not 73 divides 6709 by NAT_4:9;
6709 = 79*84 + 73; hence not 79 divides 6709 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6709 & n is prime
holds not n divides 6709 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6719 is prime
proof
now
6719 = 2*3359 + 1; hence not 2 divides 6719 by NAT_4:9;
6719 = 3*2239 + 2; hence not 3 divides 6719 by NAT_4:9;
6719 = 5*1343 + 4; hence not 5 divides 6719 by NAT_4:9;
6719 = 7*959 + 6; hence not 7 divides 6719 by NAT_4:9;
6719 = 11*610 + 9; hence not 11 divides 6719 by NAT_4:9;
6719 = 13*516 + 11; hence not 13 divides 6719 by NAT_4:9;
6719 = 17*395 + 4; hence not 17 divides 6719 by NAT_4:9;
6719 = 19*353 + 12; hence not 19 divides 6719 by NAT_4:9;
6719 = 23*292 + 3; hence not 23 divides 6719 by NAT_4:9;
6719 = 29*231 + 20; hence not 29 divides 6719 by NAT_4:9;
6719 = 31*216 + 23; hence not 31 divides 6719 by NAT_4:9;
6719 = 37*181 + 22; hence not 37 divides 6719 by NAT_4:9;
6719 = 41*163 + 36; hence not 41 divides 6719 by NAT_4:9;
6719 = 43*156 + 11; hence not 43 divides 6719 by NAT_4:9;
6719 = 47*142 + 45; hence not 47 divides 6719 by NAT_4:9;
6719 = 53*126 + 41; hence not 53 divides 6719 by NAT_4:9;
6719 = 59*113 + 52; hence not 59 divides 6719 by NAT_4:9;
6719 = 61*110 + 9; hence not 61 divides 6719 by NAT_4:9;
6719 = 67*100 + 19; hence not 67 divides 6719 by NAT_4:9;
6719 = 71*94 + 45; hence not 71 divides 6719 by NAT_4:9;
6719 = 73*92 + 3; hence not 73 divides 6719 by NAT_4:9;
6719 = 79*85 + 4; hence not 79 divides 6719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6719 & n is prime
holds not n divides 6719 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
6733 is prime
proof
now
6733 = 2*3366 + 1; hence not 2 divides 6733 by NAT_4:9;
6733 = 3*2244 + 1; hence not 3 divides 6733 by NAT_4:9;
6733 = 5*1346 + 3; hence not 5 divides 6733 by NAT_4:9;
6733 = 7*961 + 6; hence not 7 divides 6733 by NAT_4:9;
6733 = 11*612 + 1; hence not 11 divides 6733 by NAT_4:9;
6733 = 13*517 + 12; hence not 13 divides 6733 by NAT_4:9;
6733 = 17*396 + 1; hence not 17 divides 6733 by NAT_4:9;
6733 = 19*354 + 7; hence not 19 divides 6733 by NAT_4:9;
6733 = 23*292 + 17; hence not 23 divides 6733 by NAT_4:9;
6733 = 29*232 + 5; hence not 29 divides 6733 by NAT_4:9;
6733 = 31*217 + 6; hence not 31 divides 6733 by NAT_4:9;
6733 = 37*181 + 36; hence not 37 divides 6733 by NAT_4:9;
6733 = 41*164 + 9; hence not 41 divides 6733 by NAT_4:9;
6733 = 43*156 + 25; hence not 43 divides 6733 by NAT_4:9;
6733 = 47*143 + 12; hence not 47 divides 6733 by NAT_4:9;
6733 = 53*127 + 2; hence not 53 divides 6733 by NAT_4:9;
6733 = 59*114 + 7; hence not 59 divides 6733 by NAT_4:9;
6733 = 61*110 + 23; hence not 61 divides 6733 by NAT_4:9;
6733 = 67*100 + 33; hence not 67 divides 6733 by NAT_4:9;
6733 = 71*94 + 59; hence not 71 divides 6733 by NAT_4:9;
6733 = 73*92 + 17; hence not 73 divides 6733 by NAT_4:9;
6733 = 79*85 + 18; hence not 79 divides 6733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6733 & n is prime
holds not n divides 6733 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6737 is prime
proof
now
6737 = 2*3368 + 1; hence not 2 divides 6737 by NAT_4:9;
6737 = 3*2245 + 2; hence not 3 divides 6737 by NAT_4:9;
6737 = 5*1347 + 2; hence not 5 divides 6737 by NAT_4:9;
6737 = 7*962 + 3; hence not 7 divides 6737 by NAT_4:9;
6737 = 11*612 + 5; hence not 11 divides 6737 by NAT_4:9;
6737 = 13*518 + 3; hence not 13 divides 6737 by NAT_4:9;
6737 = 17*396 + 5; hence not 17 divides 6737 by NAT_4:9;
6737 = 19*354 + 11; hence not 19 divides 6737 by NAT_4:9;
6737 = 23*292 + 21; hence not 23 divides 6737 by NAT_4:9;
6737 = 29*232 + 9; hence not 29 divides 6737 by NAT_4:9;
6737 = 31*217 + 10; hence not 31 divides 6737 by NAT_4:9;
6737 = 37*182 + 3; hence not 37 divides 6737 by NAT_4:9;
6737 = 41*164 + 13; hence not 41 divides 6737 by NAT_4:9;
6737 = 43*156 + 29; hence not 43 divides 6737 by NAT_4:9;
6737 = 47*143 + 16; hence not 47 divides 6737 by NAT_4:9;
6737 = 53*127 + 6; hence not 53 divides 6737 by NAT_4:9;
6737 = 59*114 + 11; hence not 59 divides 6737 by NAT_4:9;
6737 = 61*110 + 27; hence not 61 divides 6737 by NAT_4:9;
6737 = 67*100 + 37; hence not 67 divides 6737 by NAT_4:9;
6737 = 71*94 + 63; hence not 71 divides 6737 by NAT_4:9;
6737 = 73*92 + 21; hence not 73 divides 6737 by NAT_4:9;
6737 = 79*85 + 22; hence not 79 divides 6737 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6737 & n is prime
holds not n divides 6737 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
6761 is prime
proof
now
6761 = 2*3380 + 1; hence not 2 divides 6761 by NAT_4:9;
6761 = 3*2253 + 2; hence not 3 divides 6761 by NAT_4:9;
6761 = 5*1352 + 1; hence not 5 divides 6761 by NAT_4:9;
6761 = 7*965 + 6; hence not 7 divides 6761 by NAT_4:9;
6761 = 11*614 + 7; hence not 11 divides 6761 by NAT_4:9;
6761 = 13*520 + 1; hence not 13 divides 6761 by NAT_4:9;
6761 = 17*397 + 12; hence not 17 divides 6761 by NAT_4:9;
6761 = 19*355 + 16; hence not 19 divides 6761 by NAT_4:9;
6761 = 23*293 + 22; hence not 23 divides 6761 by NAT_4:9;
6761 = 29*233 + 4; hence not 29 divides 6761 by NAT_4:9;
6761 = 31*218 + 3; hence not 31 divides 6761 by NAT_4:9;
6761 = 37*182 + 27; hence not 37 divides 6761 by NAT_4:9;
6761 = 41*164 + 37; hence not 41 divides 6761 by NAT_4:9;
6761 = 43*157 + 10; hence not 43 divides 6761 by NAT_4:9;
6761 = 47*143 + 40; hence not 47 divides 6761 by NAT_4:9;
6761 = 53*127 + 30; hence not 53 divides 6761 by NAT_4:9;
6761 = 59*114 + 35; hence not 59 divides 6761 by NAT_4:9;
6761 = 61*110 + 51; hence not 61 divides 6761 by NAT_4:9;
6761 = 67*100 + 61; hence not 67 divides 6761 by NAT_4:9;
6761 = 71*95 + 16; hence not 71 divides 6761 by NAT_4:9;
6761 = 73*92 + 45; hence not 73 divides 6761 by NAT_4:9;
6761 = 79*85 + 46; hence not 79 divides 6761 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6761 & n is prime
holds not n divides 6761 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6763 is prime
proof
now
6763 = 2*3381 + 1; hence not 2 divides 6763 by NAT_4:9;
6763 = 3*2254 + 1; hence not 3 divides 6763 by NAT_4:9;
6763 = 5*1352 + 3; hence not 5 divides 6763 by NAT_4:9;
6763 = 7*966 + 1; hence not 7 divides 6763 by NAT_4:9;
6763 = 11*614 + 9; hence not 11 divides 6763 by NAT_4:9;
6763 = 13*520 + 3; hence not 13 divides 6763 by NAT_4:9;
6763 = 17*397 + 14; hence not 17 divides 6763 by NAT_4:9;
6763 = 19*355 + 18; hence not 19 divides 6763 by NAT_4:9;
6763 = 23*294 + 1; hence not 23 divides 6763 by NAT_4:9;
6763 = 29*233 + 6; hence not 29 divides 6763 by NAT_4:9;
6763 = 31*218 + 5; hence not 31 divides 6763 by NAT_4:9;
6763 = 37*182 + 29; hence not 37 divides 6763 by NAT_4:9;
6763 = 41*164 + 39; hence not 41 divides 6763 by NAT_4:9;
6763 = 43*157 + 12; hence not 43 divides 6763 by NAT_4:9;
6763 = 47*143 + 42; hence not 47 divides 6763 by NAT_4:9;
6763 = 53*127 + 32; hence not 53 divides 6763 by NAT_4:9;
6763 = 59*114 + 37; hence not 59 divides 6763 by NAT_4:9;
6763 = 61*110 + 53; hence not 61 divides 6763 by NAT_4:9;
6763 = 67*100 + 63; hence not 67 divides 6763 by NAT_4:9;
6763 = 71*95 + 18; hence not 71 divides 6763 by NAT_4:9;
6763 = 73*92 + 47; hence not 73 divides 6763 by NAT_4:9;
6763 = 79*85 + 48; hence not 79 divides 6763 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6763 & n is prime
holds not n divides 6763 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
6779 is prime
proof
now
6779 = 2*3389 + 1; hence not 2 divides 6779 by NAT_4:9;
6779 = 3*2259 + 2; hence not 3 divides 6779 by NAT_4:9;
6779 = 5*1355 + 4; hence not 5 divides 6779 by NAT_4:9;
6779 = 7*968 + 3; hence not 7 divides 6779 by NAT_4:9;
6779 = 11*616 + 3; hence not 11 divides 6779 by NAT_4:9;
6779 = 13*521 + 6; hence not 13 divides 6779 by NAT_4:9;
6779 = 17*398 + 13; hence not 17 divides 6779 by NAT_4:9;
6779 = 19*356 + 15; hence not 19 divides 6779 by NAT_4:9;
6779 = 23*294 + 17; hence not 23 divides 6779 by NAT_4:9;
6779 = 29*233 + 22; hence not 29 divides 6779 by NAT_4:9;
6779 = 31*218 + 21; hence not 31 divides 6779 by NAT_4:9;
6779 = 37*183 + 8; hence not 37 divides 6779 by NAT_4:9;
6779 = 41*165 + 14; hence not 41 divides 6779 by NAT_4:9;
6779 = 43*157 + 28; hence not 43 divides 6779 by NAT_4:9;
6779 = 47*144 + 11; hence not 47 divides 6779 by NAT_4:9;
6779 = 53*127 + 48; hence not 53 divides 6779 by NAT_4:9;
6779 = 59*114 + 53; hence not 59 divides 6779 by NAT_4:9;
6779 = 61*111 + 8; hence not 61 divides 6779 by NAT_4:9;
6779 = 67*101 + 12; hence not 67 divides 6779 by NAT_4:9;
6779 = 71*95 + 34; hence not 71 divides 6779 by NAT_4:9;
6779 = 73*92 + 63; hence not 73 divides 6779 by NAT_4:9;
6779 = 79*85 + 64; hence not 79 divides 6779 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6779 & n is prime
holds not n divides 6779 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6781 is prime
proof
now
6781 = 2*3390 + 1; hence not 2 divides 6781 by NAT_4:9;
6781 = 3*2260 + 1; hence not 3 divides 6781 by NAT_4:9;
6781 = 5*1356 + 1; hence not 5 divides 6781 by NAT_4:9;
6781 = 7*968 + 5; hence not 7 divides 6781 by NAT_4:9;
6781 = 11*616 + 5; hence not 11 divides 6781 by NAT_4:9;
6781 = 13*521 + 8; hence not 13 divides 6781 by NAT_4:9;
6781 = 17*398 + 15; hence not 17 divides 6781 by NAT_4:9;
6781 = 19*356 + 17; hence not 19 divides 6781 by NAT_4:9;
6781 = 23*294 + 19; hence not 23 divides 6781 by NAT_4:9;
6781 = 29*233 + 24; hence not 29 divides 6781 by NAT_4:9;
6781 = 31*218 + 23; hence not 31 divides 6781 by NAT_4:9;
6781 = 37*183 + 10; hence not 37 divides 6781 by NAT_4:9;
6781 = 41*165 + 16; hence not 41 divides 6781 by NAT_4:9;
6781 = 43*157 + 30; hence not 43 divides 6781 by NAT_4:9;
6781 = 47*144 + 13; hence not 47 divides 6781 by NAT_4:9;
6781 = 53*127 + 50; hence not 53 divides 6781 by NAT_4:9;
6781 = 59*114 + 55; hence not 59 divides 6781 by NAT_4:9;
6781 = 61*111 + 10; hence not 61 divides 6781 by NAT_4:9;
6781 = 67*101 + 14; hence not 67 divides 6781 by NAT_4:9;
6781 = 71*95 + 36; hence not 71 divides 6781 by NAT_4:9;
6781 = 73*92 + 65; hence not 73 divides 6781 by NAT_4:9;
6781 = 79*85 + 66; hence not 79 divides 6781 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6781 & n is prime
holds not n divides 6781 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6791 is prime
proof
now
6791 = 2*3395 + 1; hence not 2 divides 6791 by NAT_4:9;
6791 = 3*2263 + 2; hence not 3 divides 6791 by NAT_4:9;
6791 = 5*1358 + 1; hence not 5 divides 6791 by NAT_4:9;
6791 = 7*970 + 1; hence not 7 divides 6791 by NAT_4:9;
6791 = 11*617 + 4; hence not 11 divides 6791 by NAT_4:9;
6791 = 13*522 + 5; hence not 13 divides 6791 by NAT_4:9;
6791 = 17*399 + 8; hence not 17 divides 6791 by NAT_4:9;
6791 = 19*357 + 8; hence not 19 divides 6791 by NAT_4:9;
6791 = 23*295 + 6; hence not 23 divides 6791 by NAT_4:9;
6791 = 29*234 + 5; hence not 29 divides 6791 by NAT_4:9;
6791 = 31*219 + 2; hence not 31 divides 6791 by NAT_4:9;
6791 = 37*183 + 20; hence not 37 divides 6791 by NAT_4:9;
6791 = 41*165 + 26; hence not 41 divides 6791 by NAT_4:9;
6791 = 43*157 + 40; hence not 43 divides 6791 by NAT_4:9;
6791 = 47*144 + 23; hence not 47 divides 6791 by NAT_4:9;
6791 = 53*128 + 7; hence not 53 divides 6791 by NAT_4:9;
6791 = 59*115 + 6; hence not 59 divides 6791 by NAT_4:9;
6791 = 61*111 + 20; hence not 61 divides 6791 by NAT_4:9;
6791 = 67*101 + 24; hence not 67 divides 6791 by NAT_4:9;
6791 = 71*95 + 46; hence not 71 divides 6791 by NAT_4:9;
6791 = 73*93 + 2; hence not 73 divides 6791 by NAT_4:9;
6791 = 79*85 + 76; hence not 79 divides 6791 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6791 & n is prime
holds not n divides 6791 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6793 is prime
proof
now
6793 = 2*3396 + 1; hence not 2 divides 6793 by NAT_4:9;
6793 = 3*2264 + 1; hence not 3 divides 6793 by NAT_4:9;
6793 = 5*1358 + 3; hence not 5 divides 6793 by NAT_4:9;
6793 = 7*970 + 3; hence not 7 divides 6793 by NAT_4:9;
6793 = 11*617 + 6; hence not 11 divides 6793 by NAT_4:9;
6793 = 13*522 + 7; hence not 13 divides 6793 by NAT_4:9;
6793 = 17*399 + 10; hence not 17 divides 6793 by NAT_4:9;
6793 = 19*357 + 10; hence not 19 divides 6793 by NAT_4:9;
6793 = 23*295 + 8; hence not 23 divides 6793 by NAT_4:9;
6793 = 29*234 + 7; hence not 29 divides 6793 by NAT_4:9;
6793 = 31*219 + 4; hence not 31 divides 6793 by NAT_4:9;
6793 = 37*183 + 22; hence not 37 divides 6793 by NAT_4:9;
6793 = 41*165 + 28; hence not 41 divides 6793 by NAT_4:9;
6793 = 43*157 + 42; hence not 43 divides 6793 by NAT_4:9;
6793 = 47*144 + 25; hence not 47 divides 6793 by NAT_4:9;
6793 = 53*128 + 9; hence not 53 divides 6793 by NAT_4:9;
6793 = 59*115 + 8; hence not 59 divides 6793 by NAT_4:9;
6793 = 61*111 + 22; hence not 61 divides 6793 by NAT_4:9;
6793 = 67*101 + 26; hence not 67 divides 6793 by NAT_4:9;
6793 = 71*95 + 48; hence not 71 divides 6793 by NAT_4:9;
6793 = 73*93 + 4; hence not 73 divides 6793 by NAT_4:9;
6793 = 79*85 + 78; hence not 79 divides 6793 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6793 & n is prime
holds not n divides 6793 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6803 is prime
proof
now
6803 = 2*3401 + 1; hence not 2 divides 6803 by NAT_4:9;
6803 = 3*2267 + 2; hence not 3 divides 6803 by NAT_4:9;
6803 = 5*1360 + 3; hence not 5 divides 6803 by NAT_4:9;
6803 = 7*971 + 6; hence not 7 divides 6803 by NAT_4:9;
6803 = 11*618 + 5; hence not 11 divides 6803 by NAT_4:9;
6803 = 13*523 + 4; hence not 13 divides 6803 by NAT_4:9;
6803 = 17*400 + 3; hence not 17 divides 6803 by NAT_4:9;
6803 = 19*358 + 1; hence not 19 divides 6803 by NAT_4:9;
6803 = 23*295 + 18; hence not 23 divides 6803 by NAT_4:9;
6803 = 29*234 + 17; hence not 29 divides 6803 by NAT_4:9;
6803 = 31*219 + 14; hence not 31 divides 6803 by NAT_4:9;
6803 = 37*183 + 32; hence not 37 divides 6803 by NAT_4:9;
6803 = 41*165 + 38; hence not 41 divides 6803 by NAT_4:9;
6803 = 43*158 + 9; hence not 43 divides 6803 by NAT_4:9;
6803 = 47*144 + 35; hence not 47 divides 6803 by NAT_4:9;
6803 = 53*128 + 19; hence not 53 divides 6803 by NAT_4:9;
6803 = 59*115 + 18; hence not 59 divides 6803 by NAT_4:9;
6803 = 61*111 + 32; hence not 61 divides 6803 by NAT_4:9;
6803 = 67*101 + 36; hence not 67 divides 6803 by NAT_4:9;
6803 = 71*95 + 58; hence not 71 divides 6803 by NAT_4:9;
6803 = 73*93 + 14; hence not 73 divides 6803 by NAT_4:9;
6803 = 79*86 + 9; hence not 79 divides 6803 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6803 & n is prime
holds not n divides 6803 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
6823 is prime
proof
now
6823 = 2*3411 + 1; hence not 2 divides 6823 by NAT_4:9;
6823 = 3*2274 + 1; hence not 3 divides 6823 by NAT_4:9;
6823 = 5*1364 + 3; hence not 5 divides 6823 by NAT_4:9;
6823 = 7*974 + 5; hence not 7 divides 6823 by NAT_4:9;
6823 = 11*620 + 3; hence not 11 divides 6823 by NAT_4:9;
6823 = 13*524 + 11; hence not 13 divides 6823 by NAT_4:9;
6823 = 17*401 + 6; hence not 17 divides 6823 by NAT_4:9;
6823 = 19*359 + 2; hence not 19 divides 6823 by NAT_4:9;
6823 = 23*296 + 15; hence not 23 divides 6823 by NAT_4:9;
6823 = 29*235 + 8; hence not 29 divides 6823 by NAT_4:9;
6823 = 31*220 + 3; hence not 31 divides 6823 by NAT_4:9;
6823 = 37*184 + 15; hence not 37 divides 6823 by NAT_4:9;
6823 = 41*166 + 17; hence not 41 divides 6823 by NAT_4:9;
6823 = 43*158 + 29; hence not 43 divides 6823 by NAT_4:9;
6823 = 47*145 + 8; hence not 47 divides 6823 by NAT_4:9;
6823 = 53*128 + 39; hence not 53 divides 6823 by NAT_4:9;
6823 = 59*115 + 38; hence not 59 divides 6823 by NAT_4:9;
6823 = 61*111 + 52; hence not 61 divides 6823 by NAT_4:9;
6823 = 67*101 + 56; hence not 67 divides 6823 by NAT_4:9;
6823 = 71*96 + 7; hence not 71 divides 6823 by NAT_4:9;
6823 = 73*93 + 34; hence not 73 divides 6823 by NAT_4:9;
6823 = 79*86 + 29; hence not 79 divides 6823 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6823 & n is prime
holds not n divides 6823 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6827 is prime
proof
now
6827 = 2*3413 + 1; hence not 2 divides 6827 by NAT_4:9;
6827 = 3*2275 + 2; hence not 3 divides 6827 by NAT_4:9;
6827 = 5*1365 + 2; hence not 5 divides 6827 by NAT_4:9;
6827 = 7*975 + 2; hence not 7 divides 6827 by NAT_4:9;
6827 = 11*620 + 7; hence not 11 divides 6827 by NAT_4:9;
6827 = 13*525 + 2; hence not 13 divides 6827 by NAT_4:9;
6827 = 17*401 + 10; hence not 17 divides 6827 by NAT_4:9;
6827 = 19*359 + 6; hence not 19 divides 6827 by NAT_4:9;
6827 = 23*296 + 19; hence not 23 divides 6827 by NAT_4:9;
6827 = 29*235 + 12; hence not 29 divides 6827 by NAT_4:9;
6827 = 31*220 + 7; hence not 31 divides 6827 by NAT_4:9;
6827 = 37*184 + 19; hence not 37 divides 6827 by NAT_4:9;
6827 = 41*166 + 21; hence not 41 divides 6827 by NAT_4:9;
6827 = 43*158 + 33; hence not 43 divides 6827 by NAT_4:9;
6827 = 47*145 + 12; hence not 47 divides 6827 by NAT_4:9;
6827 = 53*128 + 43; hence not 53 divides 6827 by NAT_4:9;
6827 = 59*115 + 42; hence not 59 divides 6827 by NAT_4:9;
6827 = 61*111 + 56; hence not 61 divides 6827 by NAT_4:9;
6827 = 67*101 + 60; hence not 67 divides 6827 by NAT_4:9;
6827 = 71*96 + 11; hence not 71 divides 6827 by NAT_4:9;
6827 = 73*93 + 38; hence not 73 divides 6827 by NAT_4:9;
6827 = 79*86 + 33; hence not 79 divides 6827 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6827 & n is prime
holds not n divides 6827 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6829 is prime
proof
now
6829 = 2*3414 + 1; hence not 2 divides 6829 by NAT_4:9;
6829 = 3*2276 + 1; hence not 3 divides 6829 by NAT_4:9;
6829 = 5*1365 + 4; hence not 5 divides 6829 by NAT_4:9;
6829 = 7*975 + 4; hence not 7 divides 6829 by NAT_4:9;
6829 = 11*620 + 9; hence not 11 divides 6829 by NAT_4:9;
6829 = 13*525 + 4; hence not 13 divides 6829 by NAT_4:9;
6829 = 17*401 + 12; hence not 17 divides 6829 by NAT_4:9;
6829 = 19*359 + 8; hence not 19 divides 6829 by NAT_4:9;
6829 = 23*296 + 21; hence not 23 divides 6829 by NAT_4:9;
6829 = 29*235 + 14; hence not 29 divides 6829 by NAT_4:9;
6829 = 31*220 + 9; hence not 31 divides 6829 by NAT_4:9;
6829 = 37*184 + 21; hence not 37 divides 6829 by NAT_4:9;
6829 = 41*166 + 23; hence not 41 divides 6829 by NAT_4:9;
6829 = 43*158 + 35; hence not 43 divides 6829 by NAT_4:9;
6829 = 47*145 + 14; hence not 47 divides 6829 by NAT_4:9;
6829 = 53*128 + 45; hence not 53 divides 6829 by NAT_4:9;
6829 = 59*115 + 44; hence not 59 divides 6829 by NAT_4:9;
6829 = 61*111 + 58; hence not 61 divides 6829 by NAT_4:9;
6829 = 67*101 + 62; hence not 67 divides 6829 by NAT_4:9;
6829 = 71*96 + 13; hence not 71 divides 6829 by NAT_4:9;
6829 = 73*93 + 40; hence not 73 divides 6829 by NAT_4:9;
6829 = 79*86 + 35; hence not 79 divides 6829 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6829 & n is prime
holds not n divides 6829 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6833 is prime
proof
now
6833 = 2*3416 + 1; hence not 2 divides 6833 by NAT_4:9;
6833 = 3*2277 + 2; hence not 3 divides 6833 by NAT_4:9;
6833 = 5*1366 + 3; hence not 5 divides 6833 by NAT_4:9;
6833 = 7*976 + 1; hence not 7 divides 6833 by NAT_4:9;
6833 = 11*621 + 2; hence not 11 divides 6833 by NAT_4:9;
6833 = 13*525 + 8; hence not 13 divides 6833 by NAT_4:9;
6833 = 17*401 + 16; hence not 17 divides 6833 by NAT_4:9;
6833 = 19*359 + 12; hence not 19 divides 6833 by NAT_4:9;
6833 = 23*297 + 2; hence not 23 divides 6833 by NAT_4:9;
6833 = 29*235 + 18; hence not 29 divides 6833 by NAT_4:9;
6833 = 31*220 + 13; hence not 31 divides 6833 by NAT_4:9;
6833 = 37*184 + 25; hence not 37 divides 6833 by NAT_4:9;
6833 = 41*166 + 27; hence not 41 divides 6833 by NAT_4:9;
6833 = 43*158 + 39; hence not 43 divides 6833 by NAT_4:9;
6833 = 47*145 + 18; hence not 47 divides 6833 by NAT_4:9;
6833 = 53*128 + 49; hence not 53 divides 6833 by NAT_4:9;
6833 = 59*115 + 48; hence not 59 divides 6833 by NAT_4:9;
6833 = 61*112 + 1; hence not 61 divides 6833 by NAT_4:9;
6833 = 67*101 + 66; hence not 67 divides 6833 by NAT_4:9;
6833 = 71*96 + 17; hence not 71 divides 6833 by NAT_4:9;
6833 = 73*93 + 44; hence not 73 divides 6833 by NAT_4:9;
6833 = 79*86 + 39; hence not 79 divides 6833 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6833 & n is prime
holds not n divides 6833 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6841 is prime
proof
now
6841 = 2*3420 + 1; hence not 2 divides 6841 by NAT_4:9;
6841 = 3*2280 + 1; hence not 3 divides 6841 by NAT_4:9;
6841 = 5*1368 + 1; hence not 5 divides 6841 by NAT_4:9;
6841 = 7*977 + 2; hence not 7 divides 6841 by NAT_4:9;
6841 = 11*621 + 10; hence not 11 divides 6841 by NAT_4:9;
6841 = 13*526 + 3; hence not 13 divides 6841 by NAT_4:9;
6841 = 17*402 + 7; hence not 17 divides 6841 by NAT_4:9;
6841 = 19*360 + 1; hence not 19 divides 6841 by NAT_4:9;
6841 = 23*297 + 10; hence not 23 divides 6841 by NAT_4:9;
6841 = 29*235 + 26; hence not 29 divides 6841 by NAT_4:9;
6841 = 31*220 + 21; hence not 31 divides 6841 by NAT_4:9;
6841 = 37*184 + 33; hence not 37 divides 6841 by NAT_4:9;
6841 = 41*166 + 35; hence not 41 divides 6841 by NAT_4:9;
6841 = 43*159 + 4; hence not 43 divides 6841 by NAT_4:9;
6841 = 47*145 + 26; hence not 47 divides 6841 by NAT_4:9;
6841 = 53*129 + 4; hence not 53 divides 6841 by NAT_4:9;
6841 = 59*115 + 56; hence not 59 divides 6841 by NAT_4:9;
6841 = 61*112 + 9; hence not 61 divides 6841 by NAT_4:9;
6841 = 67*102 + 7; hence not 67 divides 6841 by NAT_4:9;
6841 = 71*96 + 25; hence not 71 divides 6841 by NAT_4:9;
6841 = 73*93 + 52; hence not 73 divides 6841 by NAT_4:9;
6841 = 79*86 + 47; hence not 79 divides 6841 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6841 & n is prime
holds not n divides 6841 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
6857 is prime
proof
now
6857 = 2*3428 + 1; hence not 2 divides 6857 by NAT_4:9;
6857 = 3*2285 + 2; hence not 3 divides 6857 by NAT_4:9;
6857 = 5*1371 + 2; hence not 5 divides 6857 by NAT_4:9;
6857 = 7*979 + 4; hence not 7 divides 6857 by NAT_4:9;
6857 = 11*623 + 4; hence not 11 divides 6857 by NAT_4:9;
6857 = 13*527 + 6; hence not 13 divides 6857 by NAT_4:9;
6857 = 17*403 + 6; hence not 17 divides 6857 by NAT_4:9;
6857 = 19*360 + 17; hence not 19 divides 6857 by NAT_4:9;
6857 = 23*298 + 3; hence not 23 divides 6857 by NAT_4:9;
6857 = 29*236 + 13; hence not 29 divides 6857 by NAT_4:9;
6857 = 31*221 + 6; hence not 31 divides 6857 by NAT_4:9;
6857 = 37*185 + 12; hence not 37 divides 6857 by NAT_4:9;
6857 = 41*167 + 10; hence not 41 divides 6857 by NAT_4:9;
6857 = 43*159 + 20; hence not 43 divides 6857 by NAT_4:9;
6857 = 47*145 + 42; hence not 47 divides 6857 by NAT_4:9;
6857 = 53*129 + 20; hence not 53 divides 6857 by NAT_4:9;
6857 = 59*116 + 13; hence not 59 divides 6857 by NAT_4:9;
6857 = 61*112 + 25; hence not 61 divides 6857 by NAT_4:9;
6857 = 67*102 + 23; hence not 67 divides 6857 by NAT_4:9;
6857 = 71*96 + 41; hence not 71 divides 6857 by NAT_4:9;
6857 = 73*93 + 68; hence not 73 divides 6857 by NAT_4:9;
6857 = 79*86 + 63; hence not 79 divides 6857 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6857 & n is prime
holds not n divides 6857 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6863 is prime
proof
now
6863 = 2*3431 + 1; hence not 2 divides 6863 by NAT_4:9;
6863 = 3*2287 + 2; hence not 3 divides 6863 by NAT_4:9;
6863 = 5*1372 + 3; hence not 5 divides 6863 by NAT_4:9;
6863 = 7*980 + 3; hence not 7 divides 6863 by NAT_4:9;
6863 = 11*623 + 10; hence not 11 divides 6863 by NAT_4:9;
6863 = 13*527 + 12; hence not 13 divides 6863 by NAT_4:9;
6863 = 17*403 + 12; hence not 17 divides 6863 by NAT_4:9;
6863 = 19*361 + 4; hence not 19 divides 6863 by NAT_4:9;
6863 = 23*298 + 9; hence not 23 divides 6863 by NAT_4:9;
6863 = 29*236 + 19; hence not 29 divides 6863 by NAT_4:9;
6863 = 31*221 + 12; hence not 31 divides 6863 by NAT_4:9;
6863 = 37*185 + 18; hence not 37 divides 6863 by NAT_4:9;
6863 = 41*167 + 16; hence not 41 divides 6863 by NAT_4:9;
6863 = 43*159 + 26; hence not 43 divides 6863 by NAT_4:9;
6863 = 47*146 + 1; hence not 47 divides 6863 by NAT_4:9;
6863 = 53*129 + 26; hence not 53 divides 6863 by NAT_4:9;
6863 = 59*116 + 19; hence not 59 divides 6863 by NAT_4:9;
6863 = 61*112 + 31; hence not 61 divides 6863 by NAT_4:9;
6863 = 67*102 + 29; hence not 67 divides 6863 by NAT_4:9;
6863 = 71*96 + 47; hence not 71 divides 6863 by NAT_4:9;
6863 = 73*94 + 1; hence not 73 divides 6863 by NAT_4:9;
6863 = 79*86 + 69; hence not 79 divides 6863 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6863 & n is prime
holds not n divides 6863 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6869 is prime
proof
now
6869 = 2*3434 + 1; hence not 2 divides 6869 by NAT_4:9;
6869 = 3*2289 + 2; hence not 3 divides 6869 by NAT_4:9;
6869 = 5*1373 + 4; hence not 5 divides 6869 by NAT_4:9;
6869 = 7*981 + 2; hence not 7 divides 6869 by NAT_4:9;
6869 = 11*624 + 5; hence not 11 divides 6869 by NAT_4:9;
6869 = 13*528 + 5; hence not 13 divides 6869 by NAT_4:9;
6869 = 17*404 + 1; hence not 17 divides 6869 by NAT_4:9;
6869 = 19*361 + 10; hence not 19 divides 6869 by NAT_4:9;
6869 = 23*298 + 15; hence not 23 divides 6869 by NAT_4:9;
6869 = 29*236 + 25; hence not 29 divides 6869 by NAT_4:9;
6869 = 31*221 + 18; hence not 31 divides 6869 by NAT_4:9;
6869 = 37*185 + 24; hence not 37 divides 6869 by NAT_4:9;
6869 = 41*167 + 22; hence not 41 divides 6869 by NAT_4:9;
6869 = 43*159 + 32; hence not 43 divides 6869 by NAT_4:9;
6869 = 47*146 + 7; hence not 47 divides 6869 by NAT_4:9;
6869 = 53*129 + 32; hence not 53 divides 6869 by NAT_4:9;
6869 = 59*116 + 25; hence not 59 divides 6869 by NAT_4:9;
6869 = 61*112 + 37; hence not 61 divides 6869 by NAT_4:9;
6869 = 67*102 + 35; hence not 67 divides 6869 by NAT_4:9;
6869 = 71*96 + 53; hence not 71 divides 6869 by NAT_4:9;
6869 = 73*94 + 7; hence not 73 divides 6869 by NAT_4:9;
6869 = 79*86 + 75; hence not 79 divides 6869 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6869 & n is prime
holds not n divides 6869 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6871 is prime
proof
now
6871 = 2*3435 + 1; hence not 2 divides 6871 by NAT_4:9;
6871 = 3*2290 + 1; hence not 3 divides 6871 by NAT_4:9;
6871 = 5*1374 + 1; hence not 5 divides 6871 by NAT_4:9;
6871 = 7*981 + 4; hence not 7 divides 6871 by NAT_4:9;
6871 = 11*624 + 7; hence not 11 divides 6871 by NAT_4:9;
6871 = 13*528 + 7; hence not 13 divides 6871 by NAT_4:9;
6871 = 17*404 + 3; hence not 17 divides 6871 by NAT_4:9;
6871 = 19*361 + 12; hence not 19 divides 6871 by NAT_4:9;
6871 = 23*298 + 17; hence not 23 divides 6871 by NAT_4:9;
6871 = 29*236 + 27; hence not 29 divides 6871 by NAT_4:9;
6871 = 31*221 + 20; hence not 31 divides 6871 by NAT_4:9;
6871 = 37*185 + 26; hence not 37 divides 6871 by NAT_4:9;
6871 = 41*167 + 24; hence not 41 divides 6871 by NAT_4:9;
6871 = 43*159 + 34; hence not 43 divides 6871 by NAT_4:9;
6871 = 47*146 + 9; hence not 47 divides 6871 by NAT_4:9;
6871 = 53*129 + 34; hence not 53 divides 6871 by NAT_4:9;
6871 = 59*116 + 27; hence not 59 divides 6871 by NAT_4:9;
6871 = 61*112 + 39; hence not 61 divides 6871 by NAT_4:9;
6871 = 67*102 + 37; hence not 67 divides 6871 by NAT_4:9;
6871 = 71*96 + 55; hence not 71 divides 6871 by NAT_4:9;
6871 = 73*94 + 9; hence not 73 divides 6871 by NAT_4:9;
6871 = 79*86 + 77; hence not 79 divides 6871 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6871 & n is prime
holds not n divides 6871 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
6883 is prime
proof
now
6883 = 2*3441 + 1; hence not 2 divides 6883 by NAT_4:9;
6883 = 3*2294 + 1; hence not 3 divides 6883 by NAT_4:9;
6883 = 5*1376 + 3; hence not 5 divides 6883 by NAT_4:9;
6883 = 7*983 + 2; hence not 7 divides 6883 by NAT_4:9;
6883 = 11*625 + 8; hence not 11 divides 6883 by NAT_4:9;
6883 = 13*529 + 6; hence not 13 divides 6883 by NAT_4:9;
6883 = 17*404 + 15; hence not 17 divides 6883 by NAT_4:9;
6883 = 19*362 + 5; hence not 19 divides 6883 by NAT_4:9;
6883 = 23*299 + 6; hence not 23 divides 6883 by NAT_4:9;
6883 = 29*237 + 10; hence not 29 divides 6883 by NAT_4:9;
6883 = 31*222 + 1; hence not 31 divides 6883 by NAT_4:9;
6883 = 37*186 + 1; hence not 37 divides 6883 by NAT_4:9;
6883 = 41*167 + 36; hence not 41 divides 6883 by NAT_4:9;
6883 = 43*160 + 3; hence not 43 divides 6883 by NAT_4:9;
6883 = 47*146 + 21; hence not 47 divides 6883 by NAT_4:9;
6883 = 53*129 + 46; hence not 53 divides 6883 by NAT_4:9;
6883 = 59*116 + 39; hence not 59 divides 6883 by NAT_4:9;
6883 = 61*112 + 51; hence not 61 divides 6883 by NAT_4:9;
6883 = 67*102 + 49; hence not 67 divides 6883 by NAT_4:9;
6883 = 71*96 + 67; hence not 71 divides 6883 by NAT_4:9;
6883 = 73*94 + 21; hence not 73 divides 6883 by NAT_4:9;
6883 = 79*87 + 10; hence not 79 divides 6883 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6883 & n is prime
holds not n divides 6883 by XPRIMET1:44;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
6899 is prime
proof
now
6899 = 2*3449 + 1; hence not 2 divides 6899 by NAT_4:9;
6899 = 3*2299 + 2; hence not 3 divides 6899 by NAT_4:9;
6899 = 5*1379 + 4; hence not 5 divides 6899 by NAT_4:9;
6899 = 7*985 + 4; hence not 7 divides 6899 by NAT_4:9;
6899 = 11*627 + 2; hence not 11 divides 6899 by NAT_4:9;
6899 = 13*530 + 9; hence not 13 divides 6899 by NAT_4:9;
6899 = 17*405 + 14; hence not 17 divides 6899 by NAT_4:9;
6899 = 19*363 + 2; hence not 19 divides 6899 by NAT_4:9;
6899 = 23*299 + 22; hence not 23 divides 6899 by NAT_4:9;
6899 = 29*237 + 26; hence not 29 divides 6899 by NAT_4:9;
6899 = 31*222 + 17; hence not 31 divides 6899 by NAT_4:9;
6899 = 37*186 + 17; hence not 37 divides 6899 by NAT_4:9;
6899 = 41*168 + 11; hence not 41 divides 6899 by NAT_4:9;
6899 = 43*160 + 19; hence not 43 divides 6899 by NAT_4:9;
6899 = 47*146 + 37; hence not 47 divides 6899 by NAT_4:9;
6899 = 53*130 + 9; hence not 53 divides 6899 by NAT_4:9;
6899 = 59*116 + 55; hence not 59 divides 6899 by NAT_4:9;
6899 = 61*113 + 6; hence not 61 divides 6899 by NAT_4:9;
6899 = 67*102 + 65; hence not 67 divides 6899 by NAT_4:9;
6899 = 71*97 + 12; hence not 71 divides 6899 by NAT_4:9;
6899 = 73*94 + 37; hence not 73 divides 6899 by NAT_4:9;
6899 = 79*87 + 26; hence not 79 divides 6899 by NAT_4:9;
6899 = 83*83 + 10; hence not 83 divides 6899 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6899 & n is prime
holds not n divides 6899 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6907 is prime
proof
now
6907 = 2*3453 + 1; hence not 2 divides 6907 by NAT_4:9;
6907 = 3*2302 + 1; hence not 3 divides 6907 by NAT_4:9;
6907 = 5*1381 + 2; hence not 5 divides 6907 by NAT_4:9;
6907 = 7*986 + 5; hence not 7 divides 6907 by NAT_4:9;
6907 = 11*627 + 10; hence not 11 divides 6907 by NAT_4:9;
6907 = 13*531 + 4; hence not 13 divides 6907 by NAT_4:9;
6907 = 17*406 + 5; hence not 17 divides 6907 by NAT_4:9;
6907 = 19*363 + 10; hence not 19 divides 6907 by NAT_4:9;
6907 = 23*300 + 7; hence not 23 divides 6907 by NAT_4:9;
6907 = 29*238 + 5; hence not 29 divides 6907 by NAT_4:9;
6907 = 31*222 + 25; hence not 31 divides 6907 by NAT_4:9;
6907 = 37*186 + 25; hence not 37 divides 6907 by NAT_4:9;
6907 = 41*168 + 19; hence not 41 divides 6907 by NAT_4:9;
6907 = 43*160 + 27; hence not 43 divides 6907 by NAT_4:9;
6907 = 47*146 + 45; hence not 47 divides 6907 by NAT_4:9;
6907 = 53*130 + 17; hence not 53 divides 6907 by NAT_4:9;
6907 = 59*117 + 4; hence not 59 divides 6907 by NAT_4:9;
6907 = 61*113 + 14; hence not 61 divides 6907 by NAT_4:9;
6907 = 67*103 + 6; hence not 67 divides 6907 by NAT_4:9;
6907 = 71*97 + 20; hence not 71 divides 6907 by NAT_4:9;
6907 = 73*94 + 45; hence not 73 divides 6907 by NAT_4:9;
6907 = 79*87 + 34; hence not 79 divides 6907 by NAT_4:9;
6907 = 83*83 + 18; hence not 83 divides 6907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6907 & n is prime
holds not n divides 6907 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6911 is prime
proof
now
6911 = 2*3455 + 1; hence not 2 divides 6911 by NAT_4:9;
6911 = 3*2303 + 2; hence not 3 divides 6911 by NAT_4:9;
6911 = 5*1382 + 1; hence not 5 divides 6911 by NAT_4:9;
6911 = 7*987 + 2; hence not 7 divides 6911 by NAT_4:9;
6911 = 11*628 + 3; hence not 11 divides 6911 by NAT_4:9;
6911 = 13*531 + 8; hence not 13 divides 6911 by NAT_4:9;
6911 = 17*406 + 9; hence not 17 divides 6911 by NAT_4:9;
6911 = 19*363 + 14; hence not 19 divides 6911 by NAT_4:9;
6911 = 23*300 + 11; hence not 23 divides 6911 by NAT_4:9;
6911 = 29*238 + 9; hence not 29 divides 6911 by NAT_4:9;
6911 = 31*222 + 29; hence not 31 divides 6911 by NAT_4:9;
6911 = 37*186 + 29; hence not 37 divides 6911 by NAT_4:9;
6911 = 41*168 + 23; hence not 41 divides 6911 by NAT_4:9;
6911 = 43*160 + 31; hence not 43 divides 6911 by NAT_4:9;
6911 = 47*147 + 2; hence not 47 divides 6911 by NAT_4:9;
6911 = 53*130 + 21; hence not 53 divides 6911 by NAT_4:9;
6911 = 59*117 + 8; hence not 59 divides 6911 by NAT_4:9;
6911 = 61*113 + 18; hence not 61 divides 6911 by NAT_4:9;
6911 = 67*103 + 10; hence not 67 divides 6911 by NAT_4:9;
6911 = 71*97 + 24; hence not 71 divides 6911 by NAT_4:9;
6911 = 73*94 + 49; hence not 73 divides 6911 by NAT_4:9;
6911 = 79*87 + 38; hence not 79 divides 6911 by NAT_4:9;
6911 = 83*83 + 22; hence not 83 divides 6911 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6911 & n is prime
holds not n divides 6911 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6917 is prime
proof
now
6917 = 2*3458 + 1; hence not 2 divides 6917 by NAT_4:9;
6917 = 3*2305 + 2; hence not 3 divides 6917 by NAT_4:9;
6917 = 5*1383 + 2; hence not 5 divides 6917 by NAT_4:9;
6917 = 7*988 + 1; hence not 7 divides 6917 by NAT_4:9;
6917 = 11*628 + 9; hence not 11 divides 6917 by NAT_4:9;
6917 = 13*532 + 1; hence not 13 divides 6917 by NAT_4:9;
6917 = 17*406 + 15; hence not 17 divides 6917 by NAT_4:9;
6917 = 19*364 + 1; hence not 19 divides 6917 by NAT_4:9;
6917 = 23*300 + 17; hence not 23 divides 6917 by NAT_4:9;
6917 = 29*238 + 15; hence not 29 divides 6917 by NAT_4:9;
6917 = 31*223 + 4; hence not 31 divides 6917 by NAT_4:9;
6917 = 37*186 + 35; hence not 37 divides 6917 by NAT_4:9;
6917 = 41*168 + 29; hence not 41 divides 6917 by NAT_4:9;
6917 = 43*160 + 37; hence not 43 divides 6917 by NAT_4:9;
6917 = 47*147 + 8; hence not 47 divides 6917 by NAT_4:9;
6917 = 53*130 + 27; hence not 53 divides 6917 by NAT_4:9;
6917 = 59*117 + 14; hence not 59 divides 6917 by NAT_4:9;
6917 = 61*113 + 24; hence not 61 divides 6917 by NAT_4:9;
6917 = 67*103 + 16; hence not 67 divides 6917 by NAT_4:9;
6917 = 71*97 + 30; hence not 71 divides 6917 by NAT_4:9;
6917 = 73*94 + 55; hence not 73 divides 6917 by NAT_4:9;
6917 = 79*87 + 44; hence not 79 divides 6917 by NAT_4:9;
6917 = 83*83 + 28; hence not 83 divides 6917 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6917 & n is prime
holds not n divides 6917 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
6947 is prime
proof
now
6947 = 2*3473 + 1; hence not 2 divides 6947 by NAT_4:9;
6947 = 3*2315 + 2; hence not 3 divides 6947 by NAT_4:9;
6947 = 5*1389 + 2; hence not 5 divides 6947 by NAT_4:9;
6947 = 7*992 + 3; hence not 7 divides 6947 by NAT_4:9;
6947 = 11*631 + 6; hence not 11 divides 6947 by NAT_4:9;
6947 = 13*534 + 5; hence not 13 divides 6947 by NAT_4:9;
6947 = 17*408 + 11; hence not 17 divides 6947 by NAT_4:9;
6947 = 19*365 + 12; hence not 19 divides 6947 by NAT_4:9;
6947 = 23*302 + 1; hence not 23 divides 6947 by NAT_4:9;
6947 = 29*239 + 16; hence not 29 divides 6947 by NAT_4:9;
6947 = 31*224 + 3; hence not 31 divides 6947 by NAT_4:9;
6947 = 37*187 + 28; hence not 37 divides 6947 by NAT_4:9;
6947 = 41*169 + 18; hence not 41 divides 6947 by NAT_4:9;
6947 = 43*161 + 24; hence not 43 divides 6947 by NAT_4:9;
6947 = 47*147 + 38; hence not 47 divides 6947 by NAT_4:9;
6947 = 53*131 + 4; hence not 53 divides 6947 by NAT_4:9;
6947 = 59*117 + 44; hence not 59 divides 6947 by NAT_4:9;
6947 = 61*113 + 54; hence not 61 divides 6947 by NAT_4:9;
6947 = 67*103 + 46; hence not 67 divides 6947 by NAT_4:9;
6947 = 71*97 + 60; hence not 71 divides 6947 by NAT_4:9;
6947 = 73*95 + 12; hence not 73 divides 6947 by NAT_4:9;
6947 = 79*87 + 74; hence not 79 divides 6947 by NAT_4:9;
6947 = 83*83 + 58; hence not 83 divides 6947 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6947 & n is prime
holds not n divides 6947 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6949 is prime
proof
now
6949 = 2*3474 + 1; hence not 2 divides 6949 by NAT_4:9;
6949 = 3*2316 + 1; hence not 3 divides 6949 by NAT_4:9;
6949 = 5*1389 + 4; hence not 5 divides 6949 by NAT_4:9;
6949 = 7*992 + 5; hence not 7 divides 6949 by NAT_4:9;
6949 = 11*631 + 8; hence not 11 divides 6949 by NAT_4:9;
6949 = 13*534 + 7; hence not 13 divides 6949 by NAT_4:9;
6949 = 17*408 + 13; hence not 17 divides 6949 by NAT_4:9;
6949 = 19*365 + 14; hence not 19 divides 6949 by NAT_4:9;
6949 = 23*302 + 3; hence not 23 divides 6949 by NAT_4:9;
6949 = 29*239 + 18; hence not 29 divides 6949 by NAT_4:9;
6949 = 31*224 + 5; hence not 31 divides 6949 by NAT_4:9;
6949 = 37*187 + 30; hence not 37 divides 6949 by NAT_4:9;
6949 = 41*169 + 20; hence not 41 divides 6949 by NAT_4:9;
6949 = 43*161 + 26; hence not 43 divides 6949 by NAT_4:9;
6949 = 47*147 + 40; hence not 47 divides 6949 by NAT_4:9;
6949 = 53*131 + 6; hence not 53 divides 6949 by NAT_4:9;
6949 = 59*117 + 46; hence not 59 divides 6949 by NAT_4:9;
6949 = 61*113 + 56; hence not 61 divides 6949 by NAT_4:9;
6949 = 67*103 + 48; hence not 67 divides 6949 by NAT_4:9;
6949 = 71*97 + 62; hence not 71 divides 6949 by NAT_4:9;
6949 = 73*95 + 14; hence not 73 divides 6949 by NAT_4:9;
6949 = 79*87 + 76; hence not 79 divides 6949 by NAT_4:9;
6949 = 83*83 + 60; hence not 83 divides 6949 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6949 & n is prime
holds not n divides 6949 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
6959 is prime
proof
now
6959 = 2*3479 + 1; hence not 2 divides 6959 by NAT_4:9;
6959 = 3*2319 + 2; hence not 3 divides 6959 by NAT_4:9;
6959 = 5*1391 + 4; hence not 5 divides 6959 by NAT_4:9;
6959 = 7*994 + 1; hence not 7 divides 6959 by NAT_4:9;
6959 = 11*632 + 7; hence not 11 divides 6959 by NAT_4:9;
6959 = 13*535 + 4; hence not 13 divides 6959 by NAT_4:9;
6959 = 17*409 + 6; hence not 17 divides 6959 by NAT_4:9;
6959 = 19*366 + 5; hence not 19 divides 6959 by NAT_4:9;
6959 = 23*302 + 13; hence not 23 divides 6959 by NAT_4:9;
6959 = 29*239 + 28; hence not 29 divides 6959 by NAT_4:9;
6959 = 31*224 + 15; hence not 31 divides 6959 by NAT_4:9;
6959 = 37*188 + 3; hence not 37 divides 6959 by NAT_4:9;
6959 = 41*169 + 30; hence not 41 divides 6959 by NAT_4:9;
6959 = 43*161 + 36; hence not 43 divides 6959 by NAT_4:9;
6959 = 47*148 + 3; hence not 47 divides 6959 by NAT_4:9;
6959 = 53*131 + 16; hence not 53 divides 6959 by NAT_4:9;
6959 = 59*117 + 56; hence not 59 divides 6959 by NAT_4:9;
6959 = 61*114 + 5; hence not 61 divides 6959 by NAT_4:9;
6959 = 67*103 + 58; hence not 67 divides 6959 by NAT_4:9;
6959 = 71*98 + 1; hence not 71 divides 6959 by NAT_4:9;
6959 = 73*95 + 24; hence not 73 divides 6959 by NAT_4:9;
6959 = 79*88 + 7; hence not 79 divides 6959 by NAT_4:9;
6959 = 83*83 + 70; hence not 83 divides 6959 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6959 & n is prime
holds not n divides 6959 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
6961 is prime
proof
now
6961 = 2*3480 + 1; hence not 2 divides 6961 by NAT_4:9;
6961 = 3*2320 + 1; hence not 3 divides 6961 by NAT_4:9;
6961 = 5*1392 + 1; hence not 5 divides 6961 by NAT_4:9;
6961 = 7*994 + 3; hence not 7 divides 6961 by NAT_4:9;
6961 = 11*632 + 9; hence not 11 divides 6961 by NAT_4:9;
6961 = 13*535 + 6; hence not 13 divides 6961 by NAT_4:9;
6961 = 17*409 + 8; hence not 17 divides 6961 by NAT_4:9;
6961 = 19*366 + 7; hence not 19 divides 6961 by NAT_4:9;
6961 = 23*302 + 15; hence not 23 divides 6961 by NAT_4:9;
6961 = 29*240 + 1; hence not 29 divides 6961 by NAT_4:9;
6961 = 31*224 + 17; hence not 31 divides 6961 by NAT_4:9;
6961 = 37*188 + 5; hence not 37 divides 6961 by NAT_4:9;
6961 = 41*169 + 32; hence not 41 divides 6961 by NAT_4:9;
6961 = 43*161 + 38; hence not 43 divides 6961 by NAT_4:9;
6961 = 47*148 + 5; hence not 47 divides 6961 by NAT_4:9;
6961 = 53*131 + 18; hence not 53 divides 6961 by NAT_4:9;
6961 = 59*117 + 58; hence not 59 divides 6961 by NAT_4:9;
6961 = 61*114 + 7; hence not 61 divides 6961 by NAT_4:9;
6961 = 67*103 + 60; hence not 67 divides 6961 by NAT_4:9;
6961 = 71*98 + 3; hence not 71 divides 6961 by NAT_4:9;
6961 = 73*95 + 26; hence not 73 divides 6961 by NAT_4:9;
6961 = 79*88 + 9; hence not 79 divides 6961 by NAT_4:9;
6961 = 83*83 + 72; hence not 83 divides 6961 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6961 & n is prime
holds not n divides 6961 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6967 is prime
proof
now
6967 = 2*3483 + 1; hence not 2 divides 6967 by NAT_4:9;
6967 = 3*2322 + 1; hence not 3 divides 6967 by NAT_4:9;
6967 = 5*1393 + 2; hence not 5 divides 6967 by NAT_4:9;
6967 = 7*995 + 2; hence not 7 divides 6967 by NAT_4:9;
6967 = 11*633 + 4; hence not 11 divides 6967 by NAT_4:9;
6967 = 13*535 + 12; hence not 13 divides 6967 by NAT_4:9;
6967 = 17*409 + 14; hence not 17 divides 6967 by NAT_4:9;
6967 = 19*366 + 13; hence not 19 divides 6967 by NAT_4:9;
6967 = 23*302 + 21; hence not 23 divides 6967 by NAT_4:9;
6967 = 29*240 + 7; hence not 29 divides 6967 by NAT_4:9;
6967 = 31*224 + 23; hence not 31 divides 6967 by NAT_4:9;
6967 = 37*188 + 11; hence not 37 divides 6967 by NAT_4:9;
6967 = 41*169 + 38; hence not 41 divides 6967 by NAT_4:9;
6967 = 43*162 + 1; hence not 43 divides 6967 by NAT_4:9;
6967 = 47*148 + 11; hence not 47 divides 6967 by NAT_4:9;
6967 = 53*131 + 24; hence not 53 divides 6967 by NAT_4:9;
6967 = 59*118 + 5; hence not 59 divides 6967 by NAT_4:9;
6967 = 61*114 + 13; hence not 61 divides 6967 by NAT_4:9;
6967 = 67*103 + 66; hence not 67 divides 6967 by NAT_4:9;
6967 = 71*98 + 9; hence not 71 divides 6967 by NAT_4:9;
6967 = 73*95 + 32; hence not 73 divides 6967 by NAT_4:9;
6967 = 79*88 + 15; hence not 79 divides 6967 by NAT_4:9;
6967 = 83*83 + 78; hence not 83 divides 6967 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6967 & n is prime
holds not n divides 6967 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
6971 is prime
proof
now
6971 = 2*3485 + 1; hence not 2 divides 6971 by NAT_4:9;
6971 = 3*2323 + 2; hence not 3 divides 6971 by NAT_4:9;
6971 = 5*1394 + 1; hence not 5 divides 6971 by NAT_4:9;
6971 = 7*995 + 6; hence not 7 divides 6971 by NAT_4:9;
6971 = 11*633 + 8; hence not 11 divides 6971 by NAT_4:9;
6971 = 13*536 + 3; hence not 13 divides 6971 by NAT_4:9;
6971 = 17*410 + 1; hence not 17 divides 6971 by NAT_4:9;
6971 = 19*366 + 17; hence not 19 divides 6971 by NAT_4:9;
6971 = 23*303 + 2; hence not 23 divides 6971 by NAT_4:9;
6971 = 29*240 + 11; hence not 29 divides 6971 by NAT_4:9;
6971 = 31*224 + 27; hence not 31 divides 6971 by NAT_4:9;
6971 = 37*188 + 15; hence not 37 divides 6971 by NAT_4:9;
6971 = 41*170 + 1; hence not 41 divides 6971 by NAT_4:9;
6971 = 43*162 + 5; hence not 43 divides 6971 by NAT_4:9;
6971 = 47*148 + 15; hence not 47 divides 6971 by NAT_4:9;
6971 = 53*131 + 28; hence not 53 divides 6971 by NAT_4:9;
6971 = 59*118 + 9; hence not 59 divides 6971 by NAT_4:9;
6971 = 61*114 + 17; hence not 61 divides 6971 by NAT_4:9;
6971 = 67*104 + 3; hence not 67 divides 6971 by NAT_4:9;
6971 = 71*98 + 13; hence not 71 divides 6971 by NAT_4:9;
6971 = 73*95 + 36; hence not 73 divides 6971 by NAT_4:9;
6971 = 79*88 + 19; hence not 79 divides 6971 by NAT_4:9;
6971 = 83*83 + 82; hence not 83 divides 6971 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6971 & n is prime
holds not n divides 6971 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6977 is prime
proof
now
6977 = 2*3488 + 1; hence not 2 divides 6977 by NAT_4:9;
6977 = 3*2325 + 2; hence not 3 divides 6977 by NAT_4:9;
6977 = 5*1395 + 2; hence not 5 divides 6977 by NAT_4:9;
6977 = 7*996 + 5; hence not 7 divides 6977 by NAT_4:9;
6977 = 11*634 + 3; hence not 11 divides 6977 by NAT_4:9;
6977 = 13*536 + 9; hence not 13 divides 6977 by NAT_4:9;
6977 = 17*410 + 7; hence not 17 divides 6977 by NAT_4:9;
6977 = 19*367 + 4; hence not 19 divides 6977 by NAT_4:9;
6977 = 23*303 + 8; hence not 23 divides 6977 by NAT_4:9;
6977 = 29*240 + 17; hence not 29 divides 6977 by NAT_4:9;
6977 = 31*225 + 2; hence not 31 divides 6977 by NAT_4:9;
6977 = 37*188 + 21; hence not 37 divides 6977 by NAT_4:9;
6977 = 41*170 + 7; hence not 41 divides 6977 by NAT_4:9;
6977 = 43*162 + 11; hence not 43 divides 6977 by NAT_4:9;
6977 = 47*148 + 21; hence not 47 divides 6977 by NAT_4:9;
6977 = 53*131 + 34; hence not 53 divides 6977 by NAT_4:9;
6977 = 59*118 + 15; hence not 59 divides 6977 by NAT_4:9;
6977 = 61*114 + 23; hence not 61 divides 6977 by NAT_4:9;
6977 = 67*104 + 9; hence not 67 divides 6977 by NAT_4:9;
6977 = 71*98 + 19; hence not 71 divides 6977 by NAT_4:9;
6977 = 73*95 + 42; hence not 73 divides 6977 by NAT_4:9;
6977 = 79*88 + 25; hence not 79 divides 6977 by NAT_4:9;
6977 = 83*84 + 5; hence not 83 divides 6977 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6977 & n is prime
holds not n divides 6977 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6983 is prime
proof
now
6983 = 2*3491 + 1; hence not 2 divides 6983 by NAT_4:9;
6983 = 3*2327 + 2; hence not 3 divides 6983 by NAT_4:9;
6983 = 5*1396 + 3; hence not 5 divides 6983 by NAT_4:9;
6983 = 7*997 + 4; hence not 7 divides 6983 by NAT_4:9;
6983 = 11*634 + 9; hence not 11 divides 6983 by NAT_4:9;
6983 = 13*537 + 2; hence not 13 divides 6983 by NAT_4:9;
6983 = 17*410 + 13; hence not 17 divides 6983 by NAT_4:9;
6983 = 19*367 + 10; hence not 19 divides 6983 by NAT_4:9;
6983 = 23*303 + 14; hence not 23 divides 6983 by NAT_4:9;
6983 = 29*240 + 23; hence not 29 divides 6983 by NAT_4:9;
6983 = 31*225 + 8; hence not 31 divides 6983 by NAT_4:9;
6983 = 37*188 + 27; hence not 37 divides 6983 by NAT_4:9;
6983 = 41*170 + 13; hence not 41 divides 6983 by NAT_4:9;
6983 = 43*162 + 17; hence not 43 divides 6983 by NAT_4:9;
6983 = 47*148 + 27; hence not 47 divides 6983 by NAT_4:9;
6983 = 53*131 + 40; hence not 53 divides 6983 by NAT_4:9;
6983 = 59*118 + 21; hence not 59 divides 6983 by NAT_4:9;
6983 = 61*114 + 29; hence not 61 divides 6983 by NAT_4:9;
6983 = 67*104 + 15; hence not 67 divides 6983 by NAT_4:9;
6983 = 71*98 + 25; hence not 71 divides 6983 by NAT_4:9;
6983 = 73*95 + 48; hence not 73 divides 6983 by NAT_4:9;
6983 = 79*88 + 31; hence not 79 divides 6983 by NAT_4:9;
6983 = 83*84 + 11; hence not 83 divides 6983 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6983 & n is prime
holds not n divides 6983 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
6991 is prime
proof
now
6991 = 2*3495 + 1; hence not 2 divides 6991 by NAT_4:9;
6991 = 3*2330 + 1; hence not 3 divides 6991 by NAT_4:9;
6991 = 5*1398 + 1; hence not 5 divides 6991 by NAT_4:9;
6991 = 7*998 + 5; hence not 7 divides 6991 by NAT_4:9;
6991 = 11*635 + 6; hence not 11 divides 6991 by NAT_4:9;
6991 = 13*537 + 10; hence not 13 divides 6991 by NAT_4:9;
6991 = 17*411 + 4; hence not 17 divides 6991 by NAT_4:9;
6991 = 19*367 + 18; hence not 19 divides 6991 by NAT_4:9;
6991 = 23*303 + 22; hence not 23 divides 6991 by NAT_4:9;
6991 = 29*241 + 2; hence not 29 divides 6991 by NAT_4:9;
6991 = 31*225 + 16; hence not 31 divides 6991 by NAT_4:9;
6991 = 37*188 + 35; hence not 37 divides 6991 by NAT_4:9;
6991 = 41*170 + 21; hence not 41 divides 6991 by NAT_4:9;
6991 = 43*162 + 25; hence not 43 divides 6991 by NAT_4:9;
6991 = 47*148 + 35; hence not 47 divides 6991 by NAT_4:9;
6991 = 53*131 + 48; hence not 53 divides 6991 by NAT_4:9;
6991 = 59*118 + 29; hence not 59 divides 6991 by NAT_4:9;
6991 = 61*114 + 37; hence not 61 divides 6991 by NAT_4:9;
6991 = 67*104 + 23; hence not 67 divides 6991 by NAT_4:9;
6991 = 71*98 + 33; hence not 71 divides 6991 by NAT_4:9;
6991 = 73*95 + 56; hence not 73 divides 6991 by NAT_4:9;
6991 = 79*88 + 39; hence not 79 divides 6991 by NAT_4:9;
6991 = 83*84 + 19; hence not 83 divides 6991 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6991 & n is prime
holds not n divides 6991 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
6997 is prime
proof
now
6997 = 2*3498 + 1; hence not 2 divides 6997 by NAT_4:9;
6997 = 3*2332 + 1; hence not 3 divides 6997 by NAT_4:9;
6997 = 5*1399 + 2; hence not 5 divides 6997 by NAT_4:9;
6997 = 7*999 + 4; hence not 7 divides 6997 by NAT_4:9;
6997 = 11*636 + 1; hence not 11 divides 6997 by NAT_4:9;
6997 = 13*538 + 3; hence not 13 divides 6997 by NAT_4:9;
6997 = 17*411 + 10; hence not 17 divides 6997 by NAT_4:9;
6997 = 19*368 + 5; hence not 19 divides 6997 by NAT_4:9;
6997 = 23*304 + 5; hence not 23 divides 6997 by NAT_4:9;
6997 = 29*241 + 8; hence not 29 divides 6997 by NAT_4:9;
6997 = 31*225 + 22; hence not 31 divides 6997 by NAT_4:9;
6997 = 37*189 + 4; hence not 37 divides 6997 by NAT_4:9;
6997 = 41*170 + 27; hence not 41 divides 6997 by NAT_4:9;
6997 = 43*162 + 31; hence not 43 divides 6997 by NAT_4:9;
6997 = 47*148 + 41; hence not 47 divides 6997 by NAT_4:9;
6997 = 53*132 + 1; hence not 53 divides 6997 by NAT_4:9;
6997 = 59*118 + 35; hence not 59 divides 6997 by NAT_4:9;
6997 = 61*114 + 43; hence not 61 divides 6997 by NAT_4:9;
6997 = 67*104 + 29; hence not 67 divides 6997 by NAT_4:9;
6997 = 71*98 + 39; hence not 71 divides 6997 by NAT_4:9;
6997 = 73*95 + 62; hence not 73 divides 6997 by NAT_4:9;
6997 = 79*88 + 45; hence not 79 divides 6997 by NAT_4:9;
6997 = 83*84 + 25; hence not 83 divides 6997 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 6997 & n is prime
holds not n divides 6997 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7001 is prime
proof
now
7001 = 2*3500 + 1; hence not 2 divides 7001 by NAT_4:9;
7001 = 3*2333 + 2; hence not 3 divides 7001 by NAT_4:9;
7001 = 5*1400 + 1; hence not 5 divides 7001 by NAT_4:9;
7001 = 7*1000 + 1; hence not 7 divides 7001 by NAT_4:9;
7001 = 11*636 + 5; hence not 11 divides 7001 by NAT_4:9;
7001 = 13*538 + 7; hence not 13 divides 7001 by NAT_4:9;
7001 = 17*411 + 14; hence not 17 divides 7001 by NAT_4:9;
7001 = 19*368 + 9; hence not 19 divides 7001 by NAT_4:9;
7001 = 23*304 + 9; hence not 23 divides 7001 by NAT_4:9;
7001 = 29*241 + 12; hence not 29 divides 7001 by NAT_4:9;
7001 = 31*225 + 26; hence not 31 divides 7001 by NAT_4:9;
7001 = 37*189 + 8; hence not 37 divides 7001 by NAT_4:9;
7001 = 41*170 + 31; hence not 41 divides 7001 by NAT_4:9;
7001 = 43*162 + 35; hence not 43 divides 7001 by NAT_4:9;
7001 = 47*148 + 45; hence not 47 divides 7001 by NAT_4:9;
7001 = 53*132 + 5; hence not 53 divides 7001 by NAT_4:9;
7001 = 59*118 + 39; hence not 59 divides 7001 by NAT_4:9;
7001 = 61*114 + 47; hence not 61 divides 7001 by NAT_4:9;
7001 = 67*104 + 33; hence not 67 divides 7001 by NAT_4:9;
7001 = 71*98 + 43; hence not 71 divides 7001 by NAT_4:9;
7001 = 73*95 + 66; hence not 73 divides 7001 by NAT_4:9;
7001 = 79*88 + 49; hence not 79 divides 7001 by NAT_4:9;
7001 = 83*84 + 29; hence not 83 divides 7001 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7001 & n is prime
holds not n divides 7001 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7013 is prime
proof
now
7013 = 2*3506 + 1; hence not 2 divides 7013 by NAT_4:9;
7013 = 3*2337 + 2; hence not 3 divides 7013 by NAT_4:9;
7013 = 5*1402 + 3; hence not 5 divides 7013 by NAT_4:9;
7013 = 7*1001 + 6; hence not 7 divides 7013 by NAT_4:9;
7013 = 11*637 + 6; hence not 11 divides 7013 by NAT_4:9;
7013 = 13*539 + 6; hence not 13 divides 7013 by NAT_4:9;
7013 = 17*412 + 9; hence not 17 divides 7013 by NAT_4:9;
7013 = 19*369 + 2; hence not 19 divides 7013 by NAT_4:9;
7013 = 23*304 + 21; hence not 23 divides 7013 by NAT_4:9;
7013 = 29*241 + 24; hence not 29 divides 7013 by NAT_4:9;
7013 = 31*226 + 7; hence not 31 divides 7013 by NAT_4:9;
7013 = 37*189 + 20; hence not 37 divides 7013 by NAT_4:9;
7013 = 41*171 + 2; hence not 41 divides 7013 by NAT_4:9;
7013 = 43*163 + 4; hence not 43 divides 7013 by NAT_4:9;
7013 = 47*149 + 10; hence not 47 divides 7013 by NAT_4:9;
7013 = 53*132 + 17; hence not 53 divides 7013 by NAT_4:9;
7013 = 59*118 + 51; hence not 59 divides 7013 by NAT_4:9;
7013 = 61*114 + 59; hence not 61 divides 7013 by NAT_4:9;
7013 = 67*104 + 45; hence not 67 divides 7013 by NAT_4:9;
7013 = 71*98 + 55; hence not 71 divides 7013 by NAT_4:9;
7013 = 73*96 + 5; hence not 73 divides 7013 by NAT_4:9;
7013 = 79*88 + 61; hence not 79 divides 7013 by NAT_4:9;
7013 = 83*84 + 41; hence not 83 divides 7013 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7013 & n is prime
holds not n divides 7013 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7019 is prime
proof
now
7019 = 2*3509 + 1; hence not 2 divides 7019 by NAT_4:9;
7019 = 3*2339 + 2; hence not 3 divides 7019 by NAT_4:9;
7019 = 5*1403 + 4; hence not 5 divides 7019 by NAT_4:9;
7019 = 7*1002 + 5; hence not 7 divides 7019 by NAT_4:9;
7019 = 11*638 + 1; hence not 11 divides 7019 by NAT_4:9;
7019 = 13*539 + 12; hence not 13 divides 7019 by NAT_4:9;
7019 = 17*412 + 15; hence not 17 divides 7019 by NAT_4:9;
7019 = 19*369 + 8; hence not 19 divides 7019 by NAT_4:9;
7019 = 23*305 + 4; hence not 23 divides 7019 by NAT_4:9;
7019 = 29*242 + 1; hence not 29 divides 7019 by NAT_4:9;
7019 = 31*226 + 13; hence not 31 divides 7019 by NAT_4:9;
7019 = 37*189 + 26; hence not 37 divides 7019 by NAT_4:9;
7019 = 41*171 + 8; hence not 41 divides 7019 by NAT_4:9;
7019 = 43*163 + 10; hence not 43 divides 7019 by NAT_4:9;
7019 = 47*149 + 16; hence not 47 divides 7019 by NAT_4:9;
7019 = 53*132 + 23; hence not 53 divides 7019 by NAT_4:9;
7019 = 59*118 + 57; hence not 59 divides 7019 by NAT_4:9;
7019 = 61*115 + 4; hence not 61 divides 7019 by NAT_4:9;
7019 = 67*104 + 51; hence not 67 divides 7019 by NAT_4:9;
7019 = 71*98 + 61; hence not 71 divides 7019 by NAT_4:9;
7019 = 73*96 + 11; hence not 73 divides 7019 by NAT_4:9;
7019 = 79*88 + 67; hence not 79 divides 7019 by NAT_4:9;
7019 = 83*84 + 47; hence not 83 divides 7019 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7019 & n is prime
holds not n divides 7019 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7027 is prime
proof
now
7027 = 2*3513 + 1; hence not 2 divides 7027 by NAT_4:9;
7027 = 3*2342 + 1; hence not 3 divides 7027 by NAT_4:9;
7027 = 5*1405 + 2; hence not 5 divides 7027 by NAT_4:9;
7027 = 7*1003 + 6; hence not 7 divides 7027 by NAT_4:9;
7027 = 11*638 + 9; hence not 11 divides 7027 by NAT_4:9;
7027 = 13*540 + 7; hence not 13 divides 7027 by NAT_4:9;
7027 = 17*413 + 6; hence not 17 divides 7027 by NAT_4:9;
7027 = 19*369 + 16; hence not 19 divides 7027 by NAT_4:9;
7027 = 23*305 + 12; hence not 23 divides 7027 by NAT_4:9;
7027 = 29*242 + 9; hence not 29 divides 7027 by NAT_4:9;
7027 = 31*226 + 21; hence not 31 divides 7027 by NAT_4:9;
7027 = 37*189 + 34; hence not 37 divides 7027 by NAT_4:9;
7027 = 41*171 + 16; hence not 41 divides 7027 by NAT_4:9;
7027 = 43*163 + 18; hence not 43 divides 7027 by NAT_4:9;
7027 = 47*149 + 24; hence not 47 divides 7027 by NAT_4:9;
7027 = 53*132 + 31; hence not 53 divides 7027 by NAT_4:9;
7027 = 59*119 + 6; hence not 59 divides 7027 by NAT_4:9;
7027 = 61*115 + 12; hence not 61 divides 7027 by NAT_4:9;
7027 = 67*104 + 59; hence not 67 divides 7027 by NAT_4:9;
7027 = 71*98 + 69; hence not 71 divides 7027 by NAT_4:9;
7027 = 73*96 + 19; hence not 73 divides 7027 by NAT_4:9;
7027 = 79*88 + 75; hence not 79 divides 7027 by NAT_4:9;
7027 = 83*84 + 55; hence not 83 divides 7027 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7027 & n is prime
holds not n divides 7027 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7039 is prime
proof
now
7039 = 2*3519 + 1; hence not 2 divides 7039 by NAT_4:9;
7039 = 3*2346 + 1; hence not 3 divides 7039 by NAT_4:9;
7039 = 5*1407 + 4; hence not 5 divides 7039 by NAT_4:9;
7039 = 7*1005 + 4; hence not 7 divides 7039 by NAT_4:9;
7039 = 11*639 + 10; hence not 11 divides 7039 by NAT_4:9;
7039 = 13*541 + 6; hence not 13 divides 7039 by NAT_4:9;
7039 = 17*414 + 1; hence not 17 divides 7039 by NAT_4:9;
7039 = 19*370 + 9; hence not 19 divides 7039 by NAT_4:9;
7039 = 23*306 + 1; hence not 23 divides 7039 by NAT_4:9;
7039 = 29*242 + 21; hence not 29 divides 7039 by NAT_4:9;
7039 = 31*227 + 2; hence not 31 divides 7039 by NAT_4:9;
7039 = 37*190 + 9; hence not 37 divides 7039 by NAT_4:9;
7039 = 41*171 + 28; hence not 41 divides 7039 by NAT_4:9;
7039 = 43*163 + 30; hence not 43 divides 7039 by NAT_4:9;
7039 = 47*149 + 36; hence not 47 divides 7039 by NAT_4:9;
7039 = 53*132 + 43; hence not 53 divides 7039 by NAT_4:9;
7039 = 59*119 + 18; hence not 59 divides 7039 by NAT_4:9;
7039 = 61*115 + 24; hence not 61 divides 7039 by NAT_4:9;
7039 = 67*105 + 4; hence not 67 divides 7039 by NAT_4:9;
7039 = 71*99 + 10; hence not 71 divides 7039 by NAT_4:9;
7039 = 73*96 + 31; hence not 73 divides 7039 by NAT_4:9;
7039 = 79*89 + 8; hence not 79 divides 7039 by NAT_4:9;
7039 = 83*84 + 67; hence not 83 divides 7039 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7039 & n is prime
holds not n divides 7039 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7043 is prime
proof
now
7043 = 2*3521 + 1; hence not 2 divides 7043 by NAT_4:9;
7043 = 3*2347 + 2; hence not 3 divides 7043 by NAT_4:9;
7043 = 5*1408 + 3; hence not 5 divides 7043 by NAT_4:9;
7043 = 7*1006 + 1; hence not 7 divides 7043 by NAT_4:9;
7043 = 11*640 + 3; hence not 11 divides 7043 by NAT_4:9;
7043 = 13*541 + 10; hence not 13 divides 7043 by NAT_4:9;
7043 = 17*414 + 5; hence not 17 divides 7043 by NAT_4:9;
7043 = 19*370 + 13; hence not 19 divides 7043 by NAT_4:9;
7043 = 23*306 + 5; hence not 23 divides 7043 by NAT_4:9;
7043 = 29*242 + 25; hence not 29 divides 7043 by NAT_4:9;
7043 = 31*227 + 6; hence not 31 divides 7043 by NAT_4:9;
7043 = 37*190 + 13; hence not 37 divides 7043 by NAT_4:9;
7043 = 41*171 + 32; hence not 41 divides 7043 by NAT_4:9;
7043 = 43*163 + 34; hence not 43 divides 7043 by NAT_4:9;
7043 = 47*149 + 40; hence not 47 divides 7043 by NAT_4:9;
7043 = 53*132 + 47; hence not 53 divides 7043 by NAT_4:9;
7043 = 59*119 + 22; hence not 59 divides 7043 by NAT_4:9;
7043 = 61*115 + 28; hence not 61 divides 7043 by NAT_4:9;
7043 = 67*105 + 8; hence not 67 divides 7043 by NAT_4:9;
7043 = 71*99 + 14; hence not 71 divides 7043 by NAT_4:9;
7043 = 73*96 + 35; hence not 73 divides 7043 by NAT_4:9;
7043 = 79*89 + 12; hence not 79 divides 7043 by NAT_4:9;
7043 = 83*84 + 71; hence not 83 divides 7043 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7043 & n is prime
holds not n divides 7043 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7057 is prime
proof
now
7057 = 2*3528 + 1; hence not 2 divides 7057 by NAT_4:9;
7057 = 3*2352 + 1; hence not 3 divides 7057 by NAT_4:9;
7057 = 5*1411 + 2; hence not 5 divides 7057 by NAT_4:9;
7057 = 7*1008 + 1; hence not 7 divides 7057 by NAT_4:9;
7057 = 11*641 + 6; hence not 11 divides 7057 by NAT_4:9;
7057 = 13*542 + 11; hence not 13 divides 7057 by NAT_4:9;
7057 = 17*415 + 2; hence not 17 divides 7057 by NAT_4:9;
7057 = 19*371 + 8; hence not 19 divides 7057 by NAT_4:9;
7057 = 23*306 + 19; hence not 23 divides 7057 by NAT_4:9;
7057 = 29*243 + 10; hence not 29 divides 7057 by NAT_4:9;
7057 = 31*227 + 20; hence not 31 divides 7057 by NAT_4:9;
7057 = 37*190 + 27; hence not 37 divides 7057 by NAT_4:9;
7057 = 41*172 + 5; hence not 41 divides 7057 by NAT_4:9;
7057 = 43*164 + 5; hence not 43 divides 7057 by NAT_4:9;
7057 = 47*150 + 7; hence not 47 divides 7057 by NAT_4:9;
7057 = 53*133 + 8; hence not 53 divides 7057 by NAT_4:9;
7057 = 59*119 + 36; hence not 59 divides 7057 by NAT_4:9;
7057 = 61*115 + 42; hence not 61 divides 7057 by NAT_4:9;
7057 = 67*105 + 22; hence not 67 divides 7057 by NAT_4:9;
7057 = 71*99 + 28; hence not 71 divides 7057 by NAT_4:9;
7057 = 73*96 + 49; hence not 73 divides 7057 by NAT_4:9;
7057 = 79*89 + 26; hence not 79 divides 7057 by NAT_4:9;
7057 = 83*85 + 2; hence not 83 divides 7057 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7057 & n is prime
holds not n divides 7057 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7069 is prime
proof
now
7069 = 2*3534 + 1; hence not 2 divides 7069 by NAT_4:9;
7069 = 3*2356 + 1; hence not 3 divides 7069 by NAT_4:9;
7069 = 5*1413 + 4; hence not 5 divides 7069 by NAT_4:9;
7069 = 7*1009 + 6; hence not 7 divides 7069 by NAT_4:9;
7069 = 11*642 + 7; hence not 11 divides 7069 by NAT_4:9;
7069 = 13*543 + 10; hence not 13 divides 7069 by NAT_4:9;
7069 = 17*415 + 14; hence not 17 divides 7069 by NAT_4:9;
7069 = 19*372 + 1; hence not 19 divides 7069 by NAT_4:9;
7069 = 23*307 + 8; hence not 23 divides 7069 by NAT_4:9;
7069 = 29*243 + 22; hence not 29 divides 7069 by NAT_4:9;
7069 = 31*228 + 1; hence not 31 divides 7069 by NAT_4:9;
7069 = 37*191 + 2; hence not 37 divides 7069 by NAT_4:9;
7069 = 41*172 + 17; hence not 41 divides 7069 by NAT_4:9;
7069 = 43*164 + 17; hence not 43 divides 7069 by NAT_4:9;
7069 = 47*150 + 19; hence not 47 divides 7069 by NAT_4:9;
7069 = 53*133 + 20; hence not 53 divides 7069 by NAT_4:9;
7069 = 59*119 + 48; hence not 59 divides 7069 by NAT_4:9;
7069 = 61*115 + 54; hence not 61 divides 7069 by NAT_4:9;
7069 = 67*105 + 34; hence not 67 divides 7069 by NAT_4:9;
7069 = 71*99 + 40; hence not 71 divides 7069 by NAT_4:9;
7069 = 73*96 + 61; hence not 73 divides 7069 by NAT_4:9;
7069 = 79*89 + 38; hence not 79 divides 7069 by NAT_4:9;
7069 = 83*85 + 14; hence not 83 divides 7069 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7069 & n is prime
holds not n divides 7069 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7079 is prime
proof
now
7079 = 2*3539 + 1; hence not 2 divides 7079 by NAT_4:9;
7079 = 3*2359 + 2; hence not 3 divides 7079 by NAT_4:9;
7079 = 5*1415 + 4; hence not 5 divides 7079 by NAT_4:9;
7079 = 7*1011 + 2; hence not 7 divides 7079 by NAT_4:9;
7079 = 11*643 + 6; hence not 11 divides 7079 by NAT_4:9;
7079 = 13*544 + 7; hence not 13 divides 7079 by NAT_4:9;
7079 = 17*416 + 7; hence not 17 divides 7079 by NAT_4:9;
7079 = 19*372 + 11; hence not 19 divides 7079 by NAT_4:9;
7079 = 23*307 + 18; hence not 23 divides 7079 by NAT_4:9;
7079 = 29*244 + 3; hence not 29 divides 7079 by NAT_4:9;
7079 = 31*228 + 11; hence not 31 divides 7079 by NAT_4:9;
7079 = 37*191 + 12; hence not 37 divides 7079 by NAT_4:9;
7079 = 41*172 + 27; hence not 41 divides 7079 by NAT_4:9;
7079 = 43*164 + 27; hence not 43 divides 7079 by NAT_4:9;
7079 = 47*150 + 29; hence not 47 divides 7079 by NAT_4:9;
7079 = 53*133 + 30; hence not 53 divides 7079 by NAT_4:9;
7079 = 59*119 + 58; hence not 59 divides 7079 by NAT_4:9;
7079 = 61*116 + 3; hence not 61 divides 7079 by NAT_4:9;
7079 = 67*105 + 44; hence not 67 divides 7079 by NAT_4:9;
7079 = 71*99 + 50; hence not 71 divides 7079 by NAT_4:9;
7079 = 73*96 + 71; hence not 73 divides 7079 by NAT_4:9;
7079 = 79*89 + 48; hence not 79 divides 7079 by NAT_4:9;
7079 = 83*85 + 24; hence not 83 divides 7079 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7079 & n is prime
holds not n divides 7079 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
7103 is prime
proof
now
7103 = 2*3551 + 1; hence not 2 divides 7103 by NAT_4:9;
7103 = 3*2367 + 2; hence not 3 divides 7103 by NAT_4:9;
7103 = 5*1420 + 3; hence not 5 divides 7103 by NAT_4:9;
7103 = 7*1014 + 5; hence not 7 divides 7103 by NAT_4:9;
7103 = 11*645 + 8; hence not 11 divides 7103 by NAT_4:9;
7103 = 13*546 + 5; hence not 13 divides 7103 by NAT_4:9;
7103 = 17*417 + 14; hence not 17 divides 7103 by NAT_4:9;
7103 = 19*373 + 16; hence not 19 divides 7103 by NAT_4:9;
7103 = 23*308 + 19; hence not 23 divides 7103 by NAT_4:9;
7103 = 29*244 + 27; hence not 29 divides 7103 by NAT_4:9;
7103 = 31*229 + 4; hence not 31 divides 7103 by NAT_4:9;
7103 = 37*191 + 36; hence not 37 divides 7103 by NAT_4:9;
7103 = 41*173 + 10; hence not 41 divides 7103 by NAT_4:9;
7103 = 43*165 + 8; hence not 43 divides 7103 by NAT_4:9;
7103 = 47*151 + 6; hence not 47 divides 7103 by NAT_4:9;
7103 = 53*134 + 1; hence not 53 divides 7103 by NAT_4:9;
7103 = 59*120 + 23; hence not 59 divides 7103 by NAT_4:9;
7103 = 61*116 + 27; hence not 61 divides 7103 by NAT_4:9;
7103 = 67*106 + 1; hence not 67 divides 7103 by NAT_4:9;
7103 = 71*100 + 3; hence not 71 divides 7103 by NAT_4:9;
7103 = 73*97 + 22; hence not 73 divides 7103 by NAT_4:9;
7103 = 79*89 + 72; hence not 79 divides 7103 by NAT_4:9;
7103 = 83*85 + 48; hence not 83 divides 7103 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7103 & n is prime
holds not n divides 7103 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7109 is prime
proof
now
7109 = 2*3554 + 1; hence not 2 divides 7109 by NAT_4:9;
7109 = 3*2369 + 2; hence not 3 divides 7109 by NAT_4:9;
7109 = 5*1421 + 4; hence not 5 divides 7109 by NAT_4:9;
7109 = 7*1015 + 4; hence not 7 divides 7109 by NAT_4:9;
7109 = 11*646 + 3; hence not 11 divides 7109 by NAT_4:9;
7109 = 13*546 + 11; hence not 13 divides 7109 by NAT_4:9;
7109 = 17*418 + 3; hence not 17 divides 7109 by NAT_4:9;
7109 = 19*374 + 3; hence not 19 divides 7109 by NAT_4:9;
7109 = 23*309 + 2; hence not 23 divides 7109 by NAT_4:9;
7109 = 29*245 + 4; hence not 29 divides 7109 by NAT_4:9;
7109 = 31*229 + 10; hence not 31 divides 7109 by NAT_4:9;
7109 = 37*192 + 5; hence not 37 divides 7109 by NAT_4:9;
7109 = 41*173 + 16; hence not 41 divides 7109 by NAT_4:9;
7109 = 43*165 + 14; hence not 43 divides 7109 by NAT_4:9;
7109 = 47*151 + 12; hence not 47 divides 7109 by NAT_4:9;
7109 = 53*134 + 7; hence not 53 divides 7109 by NAT_4:9;
7109 = 59*120 + 29; hence not 59 divides 7109 by NAT_4:9;
7109 = 61*116 + 33; hence not 61 divides 7109 by NAT_4:9;
7109 = 67*106 + 7; hence not 67 divides 7109 by NAT_4:9;
7109 = 71*100 + 9; hence not 71 divides 7109 by NAT_4:9;
7109 = 73*97 + 28; hence not 73 divides 7109 by NAT_4:9;
7109 = 79*89 + 78; hence not 79 divides 7109 by NAT_4:9;
7109 = 83*85 + 54; hence not 83 divides 7109 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7109 & n is prime
holds not n divides 7109 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7121 is prime
proof
now
7121 = 2*3560 + 1; hence not 2 divides 7121 by NAT_4:9;
7121 = 3*2373 + 2; hence not 3 divides 7121 by NAT_4:9;
7121 = 5*1424 + 1; hence not 5 divides 7121 by NAT_4:9;
7121 = 7*1017 + 2; hence not 7 divides 7121 by NAT_4:9;
7121 = 11*647 + 4; hence not 11 divides 7121 by NAT_4:9;
7121 = 13*547 + 10; hence not 13 divides 7121 by NAT_4:9;
7121 = 17*418 + 15; hence not 17 divides 7121 by NAT_4:9;
7121 = 19*374 + 15; hence not 19 divides 7121 by NAT_4:9;
7121 = 23*309 + 14; hence not 23 divides 7121 by NAT_4:9;
7121 = 29*245 + 16; hence not 29 divides 7121 by NAT_4:9;
7121 = 31*229 + 22; hence not 31 divides 7121 by NAT_4:9;
7121 = 37*192 + 17; hence not 37 divides 7121 by NAT_4:9;
7121 = 41*173 + 28; hence not 41 divides 7121 by NAT_4:9;
7121 = 43*165 + 26; hence not 43 divides 7121 by NAT_4:9;
7121 = 47*151 + 24; hence not 47 divides 7121 by NAT_4:9;
7121 = 53*134 + 19; hence not 53 divides 7121 by NAT_4:9;
7121 = 59*120 + 41; hence not 59 divides 7121 by NAT_4:9;
7121 = 61*116 + 45; hence not 61 divides 7121 by NAT_4:9;
7121 = 67*106 + 19; hence not 67 divides 7121 by NAT_4:9;
7121 = 71*100 + 21; hence not 71 divides 7121 by NAT_4:9;
7121 = 73*97 + 40; hence not 73 divides 7121 by NAT_4:9;
7121 = 79*90 + 11; hence not 79 divides 7121 by NAT_4:9;
7121 = 83*85 + 66; hence not 83 divides 7121 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7121 & n is prime
holds not n divides 7121 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7127 is prime
proof
now
7127 = 2*3563 + 1; hence not 2 divides 7127 by NAT_4:9;
7127 = 3*2375 + 2; hence not 3 divides 7127 by NAT_4:9;
7127 = 5*1425 + 2; hence not 5 divides 7127 by NAT_4:9;
7127 = 7*1018 + 1; hence not 7 divides 7127 by NAT_4:9;
7127 = 11*647 + 10; hence not 11 divides 7127 by NAT_4:9;
7127 = 13*548 + 3; hence not 13 divides 7127 by NAT_4:9;
7127 = 17*419 + 4; hence not 17 divides 7127 by NAT_4:9;
7127 = 19*375 + 2; hence not 19 divides 7127 by NAT_4:9;
7127 = 23*309 + 20; hence not 23 divides 7127 by NAT_4:9;
7127 = 29*245 + 22; hence not 29 divides 7127 by NAT_4:9;
7127 = 31*229 + 28; hence not 31 divides 7127 by NAT_4:9;
7127 = 37*192 + 23; hence not 37 divides 7127 by NAT_4:9;
7127 = 41*173 + 34; hence not 41 divides 7127 by NAT_4:9;
7127 = 43*165 + 32; hence not 43 divides 7127 by NAT_4:9;
7127 = 47*151 + 30; hence not 47 divides 7127 by NAT_4:9;
7127 = 53*134 + 25; hence not 53 divides 7127 by NAT_4:9;
7127 = 59*120 + 47; hence not 59 divides 7127 by NAT_4:9;
7127 = 61*116 + 51; hence not 61 divides 7127 by NAT_4:9;
7127 = 67*106 + 25; hence not 67 divides 7127 by NAT_4:9;
7127 = 71*100 + 27; hence not 71 divides 7127 by NAT_4:9;
7127 = 73*97 + 46; hence not 73 divides 7127 by NAT_4:9;
7127 = 79*90 + 17; hence not 79 divides 7127 by NAT_4:9;
7127 = 83*85 + 72; hence not 83 divides 7127 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7127 & n is prime
holds not n divides 7127 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7129 is prime
proof
now
7129 = 2*3564 + 1; hence not 2 divides 7129 by NAT_4:9;
7129 = 3*2376 + 1; hence not 3 divides 7129 by NAT_4:9;
7129 = 5*1425 + 4; hence not 5 divides 7129 by NAT_4:9;
7129 = 7*1018 + 3; hence not 7 divides 7129 by NAT_4:9;
7129 = 11*648 + 1; hence not 11 divides 7129 by NAT_4:9;
7129 = 13*548 + 5; hence not 13 divides 7129 by NAT_4:9;
7129 = 17*419 + 6; hence not 17 divides 7129 by NAT_4:9;
7129 = 19*375 + 4; hence not 19 divides 7129 by NAT_4:9;
7129 = 23*309 + 22; hence not 23 divides 7129 by NAT_4:9;
7129 = 29*245 + 24; hence not 29 divides 7129 by NAT_4:9;
7129 = 31*229 + 30; hence not 31 divides 7129 by NAT_4:9;
7129 = 37*192 + 25; hence not 37 divides 7129 by NAT_4:9;
7129 = 41*173 + 36; hence not 41 divides 7129 by NAT_4:9;
7129 = 43*165 + 34; hence not 43 divides 7129 by NAT_4:9;
7129 = 47*151 + 32; hence not 47 divides 7129 by NAT_4:9;
7129 = 53*134 + 27; hence not 53 divides 7129 by NAT_4:9;
7129 = 59*120 + 49; hence not 59 divides 7129 by NAT_4:9;
7129 = 61*116 + 53; hence not 61 divides 7129 by NAT_4:9;
7129 = 67*106 + 27; hence not 67 divides 7129 by NAT_4:9;
7129 = 71*100 + 29; hence not 71 divides 7129 by NAT_4:9;
7129 = 73*97 + 48; hence not 73 divides 7129 by NAT_4:9;
7129 = 79*90 + 19; hence not 79 divides 7129 by NAT_4:9;
7129 = 83*85 + 74; hence not 83 divides 7129 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7129 & n is prime
holds not n divides 7129 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
7151 is prime
proof
now
7151 = 2*3575 + 1; hence not 2 divides 7151 by NAT_4:9;
7151 = 3*2383 + 2; hence not 3 divides 7151 by NAT_4:9;
7151 = 5*1430 + 1; hence not 5 divides 7151 by NAT_4:9;
7151 = 7*1021 + 4; hence not 7 divides 7151 by NAT_4:9;
7151 = 11*650 + 1; hence not 11 divides 7151 by NAT_4:9;
7151 = 13*550 + 1; hence not 13 divides 7151 by NAT_4:9;
7151 = 17*420 + 11; hence not 17 divides 7151 by NAT_4:9;
7151 = 19*376 + 7; hence not 19 divides 7151 by NAT_4:9;
7151 = 23*310 + 21; hence not 23 divides 7151 by NAT_4:9;
7151 = 29*246 + 17; hence not 29 divides 7151 by NAT_4:9;
7151 = 31*230 + 21; hence not 31 divides 7151 by NAT_4:9;
7151 = 37*193 + 10; hence not 37 divides 7151 by NAT_4:9;
7151 = 41*174 + 17; hence not 41 divides 7151 by NAT_4:9;
7151 = 43*166 + 13; hence not 43 divides 7151 by NAT_4:9;
7151 = 47*152 + 7; hence not 47 divides 7151 by NAT_4:9;
7151 = 53*134 + 49; hence not 53 divides 7151 by NAT_4:9;
7151 = 59*121 + 12; hence not 59 divides 7151 by NAT_4:9;
7151 = 61*117 + 14; hence not 61 divides 7151 by NAT_4:9;
7151 = 67*106 + 49; hence not 67 divides 7151 by NAT_4:9;
7151 = 71*100 + 51; hence not 71 divides 7151 by NAT_4:9;
7151 = 73*97 + 70; hence not 73 divides 7151 by NAT_4:9;
7151 = 79*90 + 41; hence not 79 divides 7151 by NAT_4:9;
7151 = 83*86 + 13; hence not 83 divides 7151 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7151 & n is prime
holds not n divides 7151 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7159 is prime
proof
now
7159 = 2*3579 + 1; hence not 2 divides 7159 by NAT_4:9;
7159 = 3*2386 + 1; hence not 3 divides 7159 by NAT_4:9;
7159 = 5*1431 + 4; hence not 5 divides 7159 by NAT_4:9;
7159 = 7*1022 + 5; hence not 7 divides 7159 by NAT_4:9;
7159 = 11*650 + 9; hence not 11 divides 7159 by NAT_4:9;
7159 = 13*550 + 9; hence not 13 divides 7159 by NAT_4:9;
7159 = 17*421 + 2; hence not 17 divides 7159 by NAT_4:9;
7159 = 19*376 + 15; hence not 19 divides 7159 by NAT_4:9;
7159 = 23*311 + 6; hence not 23 divides 7159 by NAT_4:9;
7159 = 29*246 + 25; hence not 29 divides 7159 by NAT_4:9;
7159 = 31*230 + 29; hence not 31 divides 7159 by NAT_4:9;
7159 = 37*193 + 18; hence not 37 divides 7159 by NAT_4:9;
7159 = 41*174 + 25; hence not 41 divides 7159 by NAT_4:9;
7159 = 43*166 + 21; hence not 43 divides 7159 by NAT_4:9;
7159 = 47*152 + 15; hence not 47 divides 7159 by NAT_4:9;
7159 = 53*135 + 4; hence not 53 divides 7159 by NAT_4:9;
7159 = 59*121 + 20; hence not 59 divides 7159 by NAT_4:9;
7159 = 61*117 + 22; hence not 61 divides 7159 by NAT_4:9;
7159 = 67*106 + 57; hence not 67 divides 7159 by NAT_4:9;
7159 = 71*100 + 59; hence not 71 divides 7159 by NAT_4:9;
7159 = 73*98 + 5; hence not 73 divides 7159 by NAT_4:9;
7159 = 79*90 + 49; hence not 79 divides 7159 by NAT_4:9;
7159 = 83*86 + 21; hence not 83 divides 7159 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7159 & n is prime
holds not n divides 7159 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7177 is prime
proof
now
7177 = 2*3588 + 1; hence not 2 divides 7177 by NAT_4:9;
7177 = 3*2392 + 1; hence not 3 divides 7177 by NAT_4:9;
7177 = 5*1435 + 2; hence not 5 divides 7177 by NAT_4:9;
7177 = 7*1025 + 2; hence not 7 divides 7177 by NAT_4:9;
7177 = 11*652 + 5; hence not 11 divides 7177 by NAT_4:9;
7177 = 13*552 + 1; hence not 13 divides 7177 by NAT_4:9;
7177 = 17*422 + 3; hence not 17 divides 7177 by NAT_4:9;
7177 = 19*377 + 14; hence not 19 divides 7177 by NAT_4:9;
7177 = 23*312 + 1; hence not 23 divides 7177 by NAT_4:9;
7177 = 29*247 + 14; hence not 29 divides 7177 by NAT_4:9;
7177 = 31*231 + 16; hence not 31 divides 7177 by NAT_4:9;
7177 = 37*193 + 36; hence not 37 divides 7177 by NAT_4:9;
7177 = 41*175 + 2; hence not 41 divides 7177 by NAT_4:9;
7177 = 43*166 + 39; hence not 43 divides 7177 by NAT_4:9;
7177 = 47*152 + 33; hence not 47 divides 7177 by NAT_4:9;
7177 = 53*135 + 22; hence not 53 divides 7177 by NAT_4:9;
7177 = 59*121 + 38; hence not 59 divides 7177 by NAT_4:9;
7177 = 61*117 + 40; hence not 61 divides 7177 by NAT_4:9;
7177 = 67*107 + 8; hence not 67 divides 7177 by NAT_4:9;
7177 = 71*101 + 6; hence not 71 divides 7177 by NAT_4:9;
7177 = 73*98 + 23; hence not 73 divides 7177 by NAT_4:9;
7177 = 79*90 + 67; hence not 79 divides 7177 by NAT_4:9;
7177 = 83*86 + 39; hence not 83 divides 7177 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7177 & n is prime
holds not n divides 7177 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7187 is prime
proof
now
7187 = 2*3593 + 1; hence not 2 divides 7187 by NAT_4:9;
7187 = 3*2395 + 2; hence not 3 divides 7187 by NAT_4:9;
7187 = 5*1437 + 2; hence not 5 divides 7187 by NAT_4:9;
7187 = 7*1026 + 5; hence not 7 divides 7187 by NAT_4:9;
7187 = 11*653 + 4; hence not 11 divides 7187 by NAT_4:9;
7187 = 13*552 + 11; hence not 13 divides 7187 by NAT_4:9;
7187 = 17*422 + 13; hence not 17 divides 7187 by NAT_4:9;
7187 = 19*378 + 5; hence not 19 divides 7187 by NAT_4:9;
7187 = 23*312 + 11; hence not 23 divides 7187 by NAT_4:9;
7187 = 29*247 + 24; hence not 29 divides 7187 by NAT_4:9;
7187 = 31*231 + 26; hence not 31 divides 7187 by NAT_4:9;
7187 = 37*194 + 9; hence not 37 divides 7187 by NAT_4:9;
7187 = 41*175 + 12; hence not 41 divides 7187 by NAT_4:9;
7187 = 43*167 + 6; hence not 43 divides 7187 by NAT_4:9;
7187 = 47*152 + 43; hence not 47 divides 7187 by NAT_4:9;
7187 = 53*135 + 32; hence not 53 divides 7187 by NAT_4:9;
7187 = 59*121 + 48; hence not 59 divides 7187 by NAT_4:9;
7187 = 61*117 + 50; hence not 61 divides 7187 by NAT_4:9;
7187 = 67*107 + 18; hence not 67 divides 7187 by NAT_4:9;
7187 = 71*101 + 16; hence not 71 divides 7187 by NAT_4:9;
7187 = 73*98 + 33; hence not 73 divides 7187 by NAT_4:9;
7187 = 79*90 + 77; hence not 79 divides 7187 by NAT_4:9;
7187 = 83*86 + 49; hence not 83 divides 7187 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7187 & n is prime
holds not n divides 7187 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7193 is prime
proof
now
7193 = 2*3596 + 1; hence not 2 divides 7193 by NAT_4:9;
7193 = 3*2397 + 2; hence not 3 divides 7193 by NAT_4:9;
7193 = 5*1438 + 3; hence not 5 divides 7193 by NAT_4:9;
7193 = 7*1027 + 4; hence not 7 divides 7193 by NAT_4:9;
7193 = 11*653 + 10; hence not 11 divides 7193 by NAT_4:9;
7193 = 13*553 + 4; hence not 13 divides 7193 by NAT_4:9;
7193 = 17*423 + 2; hence not 17 divides 7193 by NAT_4:9;
7193 = 19*378 + 11; hence not 19 divides 7193 by NAT_4:9;
7193 = 23*312 + 17; hence not 23 divides 7193 by NAT_4:9;
7193 = 29*248 + 1; hence not 29 divides 7193 by NAT_4:9;
7193 = 31*232 + 1; hence not 31 divides 7193 by NAT_4:9;
7193 = 37*194 + 15; hence not 37 divides 7193 by NAT_4:9;
7193 = 41*175 + 18; hence not 41 divides 7193 by NAT_4:9;
7193 = 43*167 + 12; hence not 43 divides 7193 by NAT_4:9;
7193 = 47*153 + 2; hence not 47 divides 7193 by NAT_4:9;
7193 = 53*135 + 38; hence not 53 divides 7193 by NAT_4:9;
7193 = 59*121 + 54; hence not 59 divides 7193 by NAT_4:9;
7193 = 61*117 + 56; hence not 61 divides 7193 by NAT_4:9;
7193 = 67*107 + 24; hence not 67 divides 7193 by NAT_4:9;
7193 = 71*101 + 22; hence not 71 divides 7193 by NAT_4:9;
7193 = 73*98 + 39; hence not 73 divides 7193 by NAT_4:9;
7193 = 79*91 + 4; hence not 79 divides 7193 by NAT_4:9;
7193 = 83*86 + 55; hence not 83 divides 7193 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7193 & n is prime
holds not n divides 7193 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7207 is prime
proof
now
7207 = 2*3603 + 1; hence not 2 divides 7207 by NAT_4:9;
7207 = 3*2402 + 1; hence not 3 divides 7207 by NAT_4:9;
7207 = 5*1441 + 2; hence not 5 divides 7207 by NAT_4:9;
7207 = 7*1029 + 4; hence not 7 divides 7207 by NAT_4:9;
7207 = 11*655 + 2; hence not 11 divides 7207 by NAT_4:9;
7207 = 13*554 + 5; hence not 13 divides 7207 by NAT_4:9;
7207 = 17*423 + 16; hence not 17 divides 7207 by NAT_4:9;
7207 = 19*379 + 6; hence not 19 divides 7207 by NAT_4:9;
7207 = 23*313 + 8; hence not 23 divides 7207 by NAT_4:9;
7207 = 29*248 + 15; hence not 29 divides 7207 by NAT_4:9;
7207 = 31*232 + 15; hence not 31 divides 7207 by NAT_4:9;
7207 = 37*194 + 29; hence not 37 divides 7207 by NAT_4:9;
7207 = 41*175 + 32; hence not 41 divides 7207 by NAT_4:9;
7207 = 43*167 + 26; hence not 43 divides 7207 by NAT_4:9;
7207 = 47*153 + 16; hence not 47 divides 7207 by NAT_4:9;
7207 = 53*135 + 52; hence not 53 divides 7207 by NAT_4:9;
7207 = 59*122 + 9; hence not 59 divides 7207 by NAT_4:9;
7207 = 61*118 + 9; hence not 61 divides 7207 by NAT_4:9;
7207 = 67*107 + 38; hence not 67 divides 7207 by NAT_4:9;
7207 = 71*101 + 36; hence not 71 divides 7207 by NAT_4:9;
7207 = 73*98 + 53; hence not 73 divides 7207 by NAT_4:9;
7207 = 79*91 + 18; hence not 79 divides 7207 by NAT_4:9;
7207 = 83*86 + 69; hence not 83 divides 7207 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7207 & n is prime
holds not n divides 7207 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7211 is prime
proof
now
7211 = 2*3605 + 1; hence not 2 divides 7211 by NAT_4:9;
7211 = 3*2403 + 2; hence not 3 divides 7211 by NAT_4:9;
7211 = 5*1442 + 1; hence not 5 divides 7211 by NAT_4:9;
7211 = 7*1030 + 1; hence not 7 divides 7211 by NAT_4:9;
7211 = 11*655 + 6; hence not 11 divides 7211 by NAT_4:9;
7211 = 13*554 + 9; hence not 13 divides 7211 by NAT_4:9;
7211 = 17*424 + 3; hence not 17 divides 7211 by NAT_4:9;
7211 = 19*379 + 10; hence not 19 divides 7211 by NAT_4:9;
7211 = 23*313 + 12; hence not 23 divides 7211 by NAT_4:9;
7211 = 29*248 + 19; hence not 29 divides 7211 by NAT_4:9;
7211 = 31*232 + 19; hence not 31 divides 7211 by NAT_4:9;
7211 = 37*194 + 33; hence not 37 divides 7211 by NAT_4:9;
7211 = 41*175 + 36; hence not 41 divides 7211 by NAT_4:9;
7211 = 43*167 + 30; hence not 43 divides 7211 by NAT_4:9;
7211 = 47*153 + 20; hence not 47 divides 7211 by NAT_4:9;
7211 = 53*136 + 3; hence not 53 divides 7211 by NAT_4:9;
7211 = 59*122 + 13; hence not 59 divides 7211 by NAT_4:9;
7211 = 61*118 + 13; hence not 61 divides 7211 by NAT_4:9;
7211 = 67*107 + 42; hence not 67 divides 7211 by NAT_4:9;
7211 = 71*101 + 40; hence not 71 divides 7211 by NAT_4:9;
7211 = 73*98 + 57; hence not 73 divides 7211 by NAT_4:9;
7211 = 79*91 + 22; hence not 79 divides 7211 by NAT_4:9;
7211 = 83*86 + 73; hence not 83 divides 7211 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7211 & n is prime
holds not n divides 7211 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7213 is prime
proof
now
7213 = 2*3606 + 1; hence not 2 divides 7213 by NAT_4:9;
7213 = 3*2404 + 1; hence not 3 divides 7213 by NAT_4:9;
7213 = 5*1442 + 3; hence not 5 divides 7213 by NAT_4:9;
7213 = 7*1030 + 3; hence not 7 divides 7213 by NAT_4:9;
7213 = 11*655 + 8; hence not 11 divides 7213 by NAT_4:9;
7213 = 13*554 + 11; hence not 13 divides 7213 by NAT_4:9;
7213 = 17*424 + 5; hence not 17 divides 7213 by NAT_4:9;
7213 = 19*379 + 12; hence not 19 divides 7213 by NAT_4:9;
7213 = 23*313 + 14; hence not 23 divides 7213 by NAT_4:9;
7213 = 29*248 + 21; hence not 29 divides 7213 by NAT_4:9;
7213 = 31*232 + 21; hence not 31 divides 7213 by NAT_4:9;
7213 = 37*194 + 35; hence not 37 divides 7213 by NAT_4:9;
7213 = 41*175 + 38; hence not 41 divides 7213 by NAT_4:9;
7213 = 43*167 + 32; hence not 43 divides 7213 by NAT_4:9;
7213 = 47*153 + 22; hence not 47 divides 7213 by NAT_4:9;
7213 = 53*136 + 5; hence not 53 divides 7213 by NAT_4:9;
7213 = 59*122 + 15; hence not 59 divides 7213 by NAT_4:9;
7213 = 61*118 + 15; hence not 61 divides 7213 by NAT_4:9;
7213 = 67*107 + 44; hence not 67 divides 7213 by NAT_4:9;
7213 = 71*101 + 42; hence not 71 divides 7213 by NAT_4:9;
7213 = 73*98 + 59; hence not 73 divides 7213 by NAT_4:9;
7213 = 79*91 + 24; hence not 79 divides 7213 by NAT_4:9;
7213 = 83*86 + 75; hence not 83 divides 7213 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7213 & n is prime
holds not n divides 7213 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7219 is prime
proof
now
7219 = 2*3609 + 1; hence not 2 divides 7219 by NAT_4:9;
7219 = 3*2406 + 1; hence not 3 divides 7219 by NAT_4:9;
7219 = 5*1443 + 4; hence not 5 divides 7219 by NAT_4:9;
7219 = 7*1031 + 2; hence not 7 divides 7219 by NAT_4:9;
7219 = 11*656 + 3; hence not 11 divides 7219 by NAT_4:9;
7219 = 13*555 + 4; hence not 13 divides 7219 by NAT_4:9;
7219 = 17*424 + 11; hence not 17 divides 7219 by NAT_4:9;
7219 = 19*379 + 18; hence not 19 divides 7219 by NAT_4:9;
7219 = 23*313 + 20; hence not 23 divides 7219 by NAT_4:9;
7219 = 29*248 + 27; hence not 29 divides 7219 by NAT_4:9;
7219 = 31*232 + 27; hence not 31 divides 7219 by NAT_4:9;
7219 = 37*195 + 4; hence not 37 divides 7219 by NAT_4:9;
7219 = 41*176 + 3; hence not 41 divides 7219 by NAT_4:9;
7219 = 43*167 + 38; hence not 43 divides 7219 by NAT_4:9;
7219 = 47*153 + 28; hence not 47 divides 7219 by NAT_4:9;
7219 = 53*136 + 11; hence not 53 divides 7219 by NAT_4:9;
7219 = 59*122 + 21; hence not 59 divides 7219 by NAT_4:9;
7219 = 61*118 + 21; hence not 61 divides 7219 by NAT_4:9;
7219 = 67*107 + 50; hence not 67 divides 7219 by NAT_4:9;
7219 = 71*101 + 48; hence not 71 divides 7219 by NAT_4:9;
7219 = 73*98 + 65; hence not 73 divides 7219 by NAT_4:9;
7219 = 79*91 + 30; hence not 79 divides 7219 by NAT_4:9;
7219 = 83*86 + 81; hence not 83 divides 7219 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7219 & n is prime
holds not n divides 7219 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7229 is prime
proof
now
7229 = 2*3614 + 1; hence not 2 divides 7229 by NAT_4:9;
7229 = 3*2409 + 2; hence not 3 divides 7229 by NAT_4:9;
7229 = 5*1445 + 4; hence not 5 divides 7229 by NAT_4:9;
7229 = 7*1032 + 5; hence not 7 divides 7229 by NAT_4:9;
7229 = 11*657 + 2; hence not 11 divides 7229 by NAT_4:9;
7229 = 13*556 + 1; hence not 13 divides 7229 by NAT_4:9;
7229 = 17*425 + 4; hence not 17 divides 7229 by NAT_4:9;
7229 = 19*380 + 9; hence not 19 divides 7229 by NAT_4:9;
7229 = 23*314 + 7; hence not 23 divides 7229 by NAT_4:9;
7229 = 29*249 + 8; hence not 29 divides 7229 by NAT_4:9;
7229 = 31*233 + 6; hence not 31 divides 7229 by NAT_4:9;
7229 = 37*195 + 14; hence not 37 divides 7229 by NAT_4:9;
7229 = 41*176 + 13; hence not 41 divides 7229 by NAT_4:9;
7229 = 43*168 + 5; hence not 43 divides 7229 by NAT_4:9;
7229 = 47*153 + 38; hence not 47 divides 7229 by NAT_4:9;
7229 = 53*136 + 21; hence not 53 divides 7229 by NAT_4:9;
7229 = 59*122 + 31; hence not 59 divides 7229 by NAT_4:9;
7229 = 61*118 + 31; hence not 61 divides 7229 by NAT_4:9;
7229 = 67*107 + 60; hence not 67 divides 7229 by NAT_4:9;
7229 = 71*101 + 58; hence not 71 divides 7229 by NAT_4:9;
7229 = 73*99 + 2; hence not 73 divides 7229 by NAT_4:9;
7229 = 79*91 + 40; hence not 79 divides 7229 by NAT_4:9;
7229 = 83*87 + 8; hence not 83 divides 7229 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7229 & n is prime
holds not n divides 7229 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7237 is prime
proof
now
7237 = 2*3618 + 1; hence not 2 divides 7237 by NAT_4:9;
7237 = 3*2412 + 1; hence not 3 divides 7237 by NAT_4:9;
7237 = 5*1447 + 2; hence not 5 divides 7237 by NAT_4:9;
7237 = 7*1033 + 6; hence not 7 divides 7237 by NAT_4:9;
7237 = 11*657 + 10; hence not 11 divides 7237 by NAT_4:9;
7237 = 13*556 + 9; hence not 13 divides 7237 by NAT_4:9;
7237 = 17*425 + 12; hence not 17 divides 7237 by NAT_4:9;
7237 = 19*380 + 17; hence not 19 divides 7237 by NAT_4:9;
7237 = 23*314 + 15; hence not 23 divides 7237 by NAT_4:9;
7237 = 29*249 + 16; hence not 29 divides 7237 by NAT_4:9;
7237 = 31*233 + 14; hence not 31 divides 7237 by NAT_4:9;
7237 = 37*195 + 22; hence not 37 divides 7237 by NAT_4:9;
7237 = 41*176 + 21; hence not 41 divides 7237 by NAT_4:9;
7237 = 43*168 + 13; hence not 43 divides 7237 by NAT_4:9;
7237 = 47*153 + 46; hence not 47 divides 7237 by NAT_4:9;
7237 = 53*136 + 29; hence not 53 divides 7237 by NAT_4:9;
7237 = 59*122 + 39; hence not 59 divides 7237 by NAT_4:9;
7237 = 61*118 + 39; hence not 61 divides 7237 by NAT_4:9;
7237 = 67*108 + 1; hence not 67 divides 7237 by NAT_4:9;
7237 = 71*101 + 66; hence not 71 divides 7237 by NAT_4:9;
7237 = 73*99 + 10; hence not 73 divides 7237 by NAT_4:9;
7237 = 79*91 + 48; hence not 79 divides 7237 by NAT_4:9;
7237 = 83*87 + 16; hence not 83 divides 7237 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7237 & n is prime
holds not n divides 7237 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7243 is prime
proof
now
7243 = 2*3621 + 1; hence not 2 divides 7243 by NAT_4:9;
7243 = 3*2414 + 1; hence not 3 divides 7243 by NAT_4:9;
7243 = 5*1448 + 3; hence not 5 divides 7243 by NAT_4:9;
7243 = 7*1034 + 5; hence not 7 divides 7243 by NAT_4:9;
7243 = 11*658 + 5; hence not 11 divides 7243 by NAT_4:9;
7243 = 13*557 + 2; hence not 13 divides 7243 by NAT_4:9;
7243 = 17*426 + 1; hence not 17 divides 7243 by NAT_4:9;
7243 = 19*381 + 4; hence not 19 divides 7243 by NAT_4:9;
7243 = 23*314 + 21; hence not 23 divides 7243 by NAT_4:9;
7243 = 29*249 + 22; hence not 29 divides 7243 by NAT_4:9;
7243 = 31*233 + 20; hence not 31 divides 7243 by NAT_4:9;
7243 = 37*195 + 28; hence not 37 divides 7243 by NAT_4:9;
7243 = 41*176 + 27; hence not 41 divides 7243 by NAT_4:9;
7243 = 43*168 + 19; hence not 43 divides 7243 by NAT_4:9;
7243 = 47*154 + 5; hence not 47 divides 7243 by NAT_4:9;
7243 = 53*136 + 35; hence not 53 divides 7243 by NAT_4:9;
7243 = 59*122 + 45; hence not 59 divides 7243 by NAT_4:9;
7243 = 61*118 + 45; hence not 61 divides 7243 by NAT_4:9;
7243 = 67*108 + 7; hence not 67 divides 7243 by NAT_4:9;
7243 = 71*102 + 1; hence not 71 divides 7243 by NAT_4:9;
7243 = 73*99 + 16; hence not 73 divides 7243 by NAT_4:9;
7243 = 79*91 + 54; hence not 79 divides 7243 by NAT_4:9;
7243 = 83*87 + 22; hence not 83 divides 7243 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7243 & n is prime
holds not n divides 7243 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7247 is prime
proof
now
7247 = 2*3623 + 1; hence not 2 divides 7247 by NAT_4:9;
7247 = 3*2415 + 2; hence not 3 divides 7247 by NAT_4:9;
7247 = 5*1449 + 2; hence not 5 divides 7247 by NAT_4:9;
7247 = 7*1035 + 2; hence not 7 divides 7247 by NAT_4:9;
7247 = 11*658 + 9; hence not 11 divides 7247 by NAT_4:9;
7247 = 13*557 + 6; hence not 13 divides 7247 by NAT_4:9;
7247 = 17*426 + 5; hence not 17 divides 7247 by NAT_4:9;
7247 = 19*381 + 8; hence not 19 divides 7247 by NAT_4:9;
7247 = 23*315 + 2; hence not 23 divides 7247 by NAT_4:9;
7247 = 29*249 + 26; hence not 29 divides 7247 by NAT_4:9;
7247 = 31*233 + 24; hence not 31 divides 7247 by NAT_4:9;
7247 = 37*195 + 32; hence not 37 divides 7247 by NAT_4:9;
7247 = 41*176 + 31; hence not 41 divides 7247 by NAT_4:9;
7247 = 43*168 + 23; hence not 43 divides 7247 by NAT_4:9;
7247 = 47*154 + 9; hence not 47 divides 7247 by NAT_4:9;
7247 = 53*136 + 39; hence not 53 divides 7247 by NAT_4:9;
7247 = 59*122 + 49; hence not 59 divides 7247 by NAT_4:9;
7247 = 61*118 + 49; hence not 61 divides 7247 by NAT_4:9;
7247 = 67*108 + 11; hence not 67 divides 7247 by NAT_4:9;
7247 = 71*102 + 5; hence not 71 divides 7247 by NAT_4:9;
7247 = 73*99 + 20; hence not 73 divides 7247 by NAT_4:9;
7247 = 79*91 + 58; hence not 79 divides 7247 by NAT_4:9;
7247 = 83*87 + 26; hence not 83 divides 7247 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7247 & n is prime
holds not n divides 7247 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7253 is prime
proof
now
7253 = 2*3626 + 1; hence not 2 divides 7253 by NAT_4:9;
7253 = 3*2417 + 2; hence not 3 divides 7253 by NAT_4:9;
7253 = 5*1450 + 3; hence not 5 divides 7253 by NAT_4:9;
7253 = 7*1036 + 1; hence not 7 divides 7253 by NAT_4:9;
7253 = 11*659 + 4; hence not 11 divides 7253 by NAT_4:9;
7253 = 13*557 + 12; hence not 13 divides 7253 by NAT_4:9;
7253 = 17*426 + 11; hence not 17 divides 7253 by NAT_4:9;
7253 = 19*381 + 14; hence not 19 divides 7253 by NAT_4:9;
7253 = 23*315 + 8; hence not 23 divides 7253 by NAT_4:9;
7253 = 29*250 + 3; hence not 29 divides 7253 by NAT_4:9;
7253 = 31*233 + 30; hence not 31 divides 7253 by NAT_4:9;
7253 = 37*196 + 1; hence not 37 divides 7253 by NAT_4:9;
7253 = 41*176 + 37; hence not 41 divides 7253 by NAT_4:9;
7253 = 43*168 + 29; hence not 43 divides 7253 by NAT_4:9;
7253 = 47*154 + 15; hence not 47 divides 7253 by NAT_4:9;
7253 = 53*136 + 45; hence not 53 divides 7253 by NAT_4:9;
7253 = 59*122 + 55; hence not 59 divides 7253 by NAT_4:9;
7253 = 61*118 + 55; hence not 61 divides 7253 by NAT_4:9;
7253 = 67*108 + 17; hence not 67 divides 7253 by NAT_4:9;
7253 = 71*102 + 11; hence not 71 divides 7253 by NAT_4:9;
7253 = 73*99 + 26; hence not 73 divides 7253 by NAT_4:9;
7253 = 79*91 + 64; hence not 79 divides 7253 by NAT_4:9;
7253 = 83*87 + 32; hence not 83 divides 7253 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7253 & n is prime
holds not n divides 7253 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
7283 is prime
proof
now
7283 = 2*3641 + 1; hence not 2 divides 7283 by NAT_4:9;
7283 = 3*2427 + 2; hence not 3 divides 7283 by NAT_4:9;
7283 = 5*1456 + 3; hence not 5 divides 7283 by NAT_4:9;
7283 = 7*1040 + 3; hence not 7 divides 7283 by NAT_4:9;
7283 = 11*662 + 1; hence not 11 divides 7283 by NAT_4:9;
7283 = 13*560 + 3; hence not 13 divides 7283 by NAT_4:9;
7283 = 17*428 + 7; hence not 17 divides 7283 by NAT_4:9;
7283 = 19*383 + 6; hence not 19 divides 7283 by NAT_4:9;
7283 = 23*316 + 15; hence not 23 divides 7283 by NAT_4:9;
7283 = 29*251 + 4; hence not 29 divides 7283 by NAT_4:9;
7283 = 31*234 + 29; hence not 31 divides 7283 by NAT_4:9;
7283 = 37*196 + 31; hence not 37 divides 7283 by NAT_4:9;
7283 = 41*177 + 26; hence not 41 divides 7283 by NAT_4:9;
7283 = 43*169 + 16; hence not 43 divides 7283 by NAT_4:9;
7283 = 47*154 + 45; hence not 47 divides 7283 by NAT_4:9;
7283 = 53*137 + 22; hence not 53 divides 7283 by NAT_4:9;
7283 = 59*123 + 26; hence not 59 divides 7283 by NAT_4:9;
7283 = 61*119 + 24; hence not 61 divides 7283 by NAT_4:9;
7283 = 67*108 + 47; hence not 67 divides 7283 by NAT_4:9;
7283 = 71*102 + 41; hence not 71 divides 7283 by NAT_4:9;
7283 = 73*99 + 56; hence not 73 divides 7283 by NAT_4:9;
7283 = 79*92 + 15; hence not 79 divides 7283 by NAT_4:9;
7283 = 83*87 + 62; hence not 83 divides 7283 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7283 & n is prime
holds not n divides 7283 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7297 is prime
proof
now
7297 = 2*3648 + 1; hence not 2 divides 7297 by NAT_4:9;
7297 = 3*2432 + 1; hence not 3 divides 7297 by NAT_4:9;
7297 = 5*1459 + 2; hence not 5 divides 7297 by NAT_4:9;
7297 = 7*1042 + 3; hence not 7 divides 7297 by NAT_4:9;
7297 = 11*663 + 4; hence not 11 divides 7297 by NAT_4:9;
7297 = 13*561 + 4; hence not 13 divides 7297 by NAT_4:9;
7297 = 17*429 + 4; hence not 17 divides 7297 by NAT_4:9;
7297 = 19*384 + 1; hence not 19 divides 7297 by NAT_4:9;
7297 = 23*317 + 6; hence not 23 divides 7297 by NAT_4:9;
7297 = 29*251 + 18; hence not 29 divides 7297 by NAT_4:9;
7297 = 31*235 + 12; hence not 31 divides 7297 by NAT_4:9;
7297 = 37*197 + 8; hence not 37 divides 7297 by NAT_4:9;
7297 = 41*177 + 40; hence not 41 divides 7297 by NAT_4:9;
7297 = 43*169 + 30; hence not 43 divides 7297 by NAT_4:9;
7297 = 47*155 + 12; hence not 47 divides 7297 by NAT_4:9;
7297 = 53*137 + 36; hence not 53 divides 7297 by NAT_4:9;
7297 = 59*123 + 40; hence not 59 divides 7297 by NAT_4:9;
7297 = 61*119 + 38; hence not 61 divides 7297 by NAT_4:9;
7297 = 67*108 + 61; hence not 67 divides 7297 by NAT_4:9;
7297 = 71*102 + 55; hence not 71 divides 7297 by NAT_4:9;
7297 = 73*99 + 70; hence not 73 divides 7297 by NAT_4:9;
7297 = 79*92 + 29; hence not 79 divides 7297 by NAT_4:9;
7297 = 83*87 + 76; hence not 83 divides 7297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7297 & n is prime
holds not n divides 7297 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7307 is prime
proof
now
7307 = 2*3653 + 1; hence not 2 divides 7307 by NAT_4:9;
7307 = 3*2435 + 2; hence not 3 divides 7307 by NAT_4:9;
7307 = 5*1461 + 2; hence not 5 divides 7307 by NAT_4:9;
7307 = 7*1043 + 6; hence not 7 divides 7307 by NAT_4:9;
7307 = 11*664 + 3; hence not 11 divides 7307 by NAT_4:9;
7307 = 13*562 + 1; hence not 13 divides 7307 by NAT_4:9;
7307 = 17*429 + 14; hence not 17 divides 7307 by NAT_4:9;
7307 = 19*384 + 11; hence not 19 divides 7307 by NAT_4:9;
7307 = 23*317 + 16; hence not 23 divides 7307 by NAT_4:9;
7307 = 29*251 + 28; hence not 29 divides 7307 by NAT_4:9;
7307 = 31*235 + 22; hence not 31 divides 7307 by NAT_4:9;
7307 = 37*197 + 18; hence not 37 divides 7307 by NAT_4:9;
7307 = 41*178 + 9; hence not 41 divides 7307 by NAT_4:9;
7307 = 43*169 + 40; hence not 43 divides 7307 by NAT_4:9;
7307 = 47*155 + 22; hence not 47 divides 7307 by NAT_4:9;
7307 = 53*137 + 46; hence not 53 divides 7307 by NAT_4:9;
7307 = 59*123 + 50; hence not 59 divides 7307 by NAT_4:9;
7307 = 61*119 + 48; hence not 61 divides 7307 by NAT_4:9;
7307 = 67*109 + 4; hence not 67 divides 7307 by NAT_4:9;
7307 = 71*102 + 65; hence not 71 divides 7307 by NAT_4:9;
7307 = 73*100 + 7; hence not 73 divides 7307 by NAT_4:9;
7307 = 79*92 + 39; hence not 79 divides 7307 by NAT_4:9;
7307 = 83*88 + 3; hence not 83 divides 7307 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7307 & n is prime
holds not n divides 7307 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7309 is prime
proof
now
7309 = 2*3654 + 1; hence not 2 divides 7309 by NAT_4:9;
7309 = 3*2436 + 1; hence not 3 divides 7309 by NAT_4:9;
7309 = 5*1461 + 4; hence not 5 divides 7309 by NAT_4:9;
7309 = 7*1044 + 1; hence not 7 divides 7309 by NAT_4:9;
7309 = 11*664 + 5; hence not 11 divides 7309 by NAT_4:9;
7309 = 13*562 + 3; hence not 13 divides 7309 by NAT_4:9;
7309 = 17*429 + 16; hence not 17 divides 7309 by NAT_4:9;
7309 = 19*384 + 13; hence not 19 divides 7309 by NAT_4:9;
7309 = 23*317 + 18; hence not 23 divides 7309 by NAT_4:9;
7309 = 29*252 + 1; hence not 29 divides 7309 by NAT_4:9;
7309 = 31*235 + 24; hence not 31 divides 7309 by NAT_4:9;
7309 = 37*197 + 20; hence not 37 divides 7309 by NAT_4:9;
7309 = 41*178 + 11; hence not 41 divides 7309 by NAT_4:9;
7309 = 43*169 + 42; hence not 43 divides 7309 by NAT_4:9;
7309 = 47*155 + 24; hence not 47 divides 7309 by NAT_4:9;
7309 = 53*137 + 48; hence not 53 divides 7309 by NAT_4:9;
7309 = 59*123 + 52; hence not 59 divides 7309 by NAT_4:9;
7309 = 61*119 + 50; hence not 61 divides 7309 by NAT_4:9;
7309 = 67*109 + 6; hence not 67 divides 7309 by NAT_4:9;
7309 = 71*102 + 67; hence not 71 divides 7309 by NAT_4:9;
7309 = 73*100 + 9; hence not 73 divides 7309 by NAT_4:9;
7309 = 79*92 + 41; hence not 79 divides 7309 by NAT_4:9;
7309 = 83*88 + 5; hence not 83 divides 7309 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7309 & n is prime
holds not n divides 7309 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7321 is prime
proof
now
7321 = 2*3660 + 1; hence not 2 divides 7321 by NAT_4:9;
7321 = 3*2440 + 1; hence not 3 divides 7321 by NAT_4:9;
7321 = 5*1464 + 1; hence not 5 divides 7321 by NAT_4:9;
7321 = 7*1045 + 6; hence not 7 divides 7321 by NAT_4:9;
7321 = 11*665 + 6; hence not 11 divides 7321 by NAT_4:9;
7321 = 13*563 + 2; hence not 13 divides 7321 by NAT_4:9;
7321 = 17*430 + 11; hence not 17 divides 7321 by NAT_4:9;
7321 = 19*385 + 6; hence not 19 divides 7321 by NAT_4:9;
7321 = 23*318 + 7; hence not 23 divides 7321 by NAT_4:9;
7321 = 29*252 + 13; hence not 29 divides 7321 by NAT_4:9;
7321 = 31*236 + 5; hence not 31 divides 7321 by NAT_4:9;
7321 = 37*197 + 32; hence not 37 divides 7321 by NAT_4:9;
7321 = 41*178 + 23; hence not 41 divides 7321 by NAT_4:9;
7321 = 43*170 + 11; hence not 43 divides 7321 by NAT_4:9;
7321 = 47*155 + 36; hence not 47 divides 7321 by NAT_4:9;
7321 = 53*138 + 7; hence not 53 divides 7321 by NAT_4:9;
7321 = 59*124 + 5; hence not 59 divides 7321 by NAT_4:9;
7321 = 61*120 + 1; hence not 61 divides 7321 by NAT_4:9;
7321 = 67*109 + 18; hence not 67 divides 7321 by NAT_4:9;
7321 = 71*103 + 8; hence not 71 divides 7321 by NAT_4:9;
7321 = 73*100 + 21; hence not 73 divides 7321 by NAT_4:9;
7321 = 79*92 + 53; hence not 79 divides 7321 by NAT_4:9;
7321 = 83*88 + 17; hence not 83 divides 7321 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7321 & n is prime
holds not n divides 7321 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7331 is prime
proof
now
7331 = 2*3665 + 1; hence not 2 divides 7331 by NAT_4:9;
7331 = 3*2443 + 2; hence not 3 divides 7331 by NAT_4:9;
7331 = 5*1466 + 1; hence not 5 divides 7331 by NAT_4:9;
7331 = 7*1047 + 2; hence not 7 divides 7331 by NAT_4:9;
7331 = 11*666 + 5; hence not 11 divides 7331 by NAT_4:9;
7331 = 13*563 + 12; hence not 13 divides 7331 by NAT_4:9;
7331 = 17*431 + 4; hence not 17 divides 7331 by NAT_4:9;
7331 = 19*385 + 16; hence not 19 divides 7331 by NAT_4:9;
7331 = 23*318 + 17; hence not 23 divides 7331 by NAT_4:9;
7331 = 29*252 + 23; hence not 29 divides 7331 by NAT_4:9;
7331 = 31*236 + 15; hence not 31 divides 7331 by NAT_4:9;
7331 = 37*198 + 5; hence not 37 divides 7331 by NAT_4:9;
7331 = 41*178 + 33; hence not 41 divides 7331 by NAT_4:9;
7331 = 43*170 + 21; hence not 43 divides 7331 by NAT_4:9;
7331 = 47*155 + 46; hence not 47 divides 7331 by NAT_4:9;
7331 = 53*138 + 17; hence not 53 divides 7331 by NAT_4:9;
7331 = 59*124 + 15; hence not 59 divides 7331 by NAT_4:9;
7331 = 61*120 + 11; hence not 61 divides 7331 by NAT_4:9;
7331 = 67*109 + 28; hence not 67 divides 7331 by NAT_4:9;
7331 = 71*103 + 18; hence not 71 divides 7331 by NAT_4:9;
7331 = 73*100 + 31; hence not 73 divides 7331 by NAT_4:9;
7331 = 79*92 + 63; hence not 79 divides 7331 by NAT_4:9;
7331 = 83*88 + 27; hence not 83 divides 7331 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7331 & n is prime
holds not n divides 7331 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7333 is prime
proof
now
7333 = 2*3666 + 1; hence not 2 divides 7333 by NAT_4:9;
7333 = 3*2444 + 1; hence not 3 divides 7333 by NAT_4:9;
7333 = 5*1466 + 3; hence not 5 divides 7333 by NAT_4:9;
7333 = 7*1047 + 4; hence not 7 divides 7333 by NAT_4:9;
7333 = 11*666 + 7; hence not 11 divides 7333 by NAT_4:9;
7333 = 13*564 + 1; hence not 13 divides 7333 by NAT_4:9;
7333 = 17*431 + 6; hence not 17 divides 7333 by NAT_4:9;
7333 = 19*385 + 18; hence not 19 divides 7333 by NAT_4:9;
7333 = 23*318 + 19; hence not 23 divides 7333 by NAT_4:9;
7333 = 29*252 + 25; hence not 29 divides 7333 by NAT_4:9;
7333 = 31*236 + 17; hence not 31 divides 7333 by NAT_4:9;
7333 = 37*198 + 7; hence not 37 divides 7333 by NAT_4:9;
7333 = 41*178 + 35; hence not 41 divides 7333 by NAT_4:9;
7333 = 43*170 + 23; hence not 43 divides 7333 by NAT_4:9;
7333 = 47*156 + 1; hence not 47 divides 7333 by NAT_4:9;
7333 = 53*138 + 19; hence not 53 divides 7333 by NAT_4:9;
7333 = 59*124 + 17; hence not 59 divides 7333 by NAT_4:9;
7333 = 61*120 + 13; hence not 61 divides 7333 by NAT_4:9;
7333 = 67*109 + 30; hence not 67 divides 7333 by NAT_4:9;
7333 = 71*103 + 20; hence not 71 divides 7333 by NAT_4:9;
7333 = 73*100 + 33; hence not 73 divides 7333 by NAT_4:9;
7333 = 79*92 + 65; hence not 79 divides 7333 by NAT_4:9;
7333 = 83*88 + 29; hence not 83 divides 7333 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7333 & n is prime
holds not n divides 7333 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
7349 is prime
proof
now
7349 = 2*3674 + 1; hence not 2 divides 7349 by NAT_4:9;
7349 = 3*2449 + 2; hence not 3 divides 7349 by NAT_4:9;
7349 = 5*1469 + 4; hence not 5 divides 7349 by NAT_4:9;
7349 = 7*1049 + 6; hence not 7 divides 7349 by NAT_4:9;
7349 = 11*668 + 1; hence not 11 divides 7349 by NAT_4:9;
7349 = 13*565 + 4; hence not 13 divides 7349 by NAT_4:9;
7349 = 17*432 + 5; hence not 17 divides 7349 by NAT_4:9;
7349 = 19*386 + 15; hence not 19 divides 7349 by NAT_4:9;
7349 = 23*319 + 12; hence not 23 divides 7349 by NAT_4:9;
7349 = 29*253 + 12; hence not 29 divides 7349 by NAT_4:9;
7349 = 31*237 + 2; hence not 31 divides 7349 by NAT_4:9;
7349 = 37*198 + 23; hence not 37 divides 7349 by NAT_4:9;
7349 = 41*179 + 10; hence not 41 divides 7349 by NAT_4:9;
7349 = 43*170 + 39; hence not 43 divides 7349 by NAT_4:9;
7349 = 47*156 + 17; hence not 47 divides 7349 by NAT_4:9;
7349 = 53*138 + 35; hence not 53 divides 7349 by NAT_4:9;
7349 = 59*124 + 33; hence not 59 divides 7349 by NAT_4:9;
7349 = 61*120 + 29; hence not 61 divides 7349 by NAT_4:9;
7349 = 67*109 + 46; hence not 67 divides 7349 by NAT_4:9;
7349 = 71*103 + 36; hence not 71 divides 7349 by NAT_4:9;
7349 = 73*100 + 49; hence not 73 divides 7349 by NAT_4:9;
7349 = 79*93 + 2; hence not 79 divides 7349 by NAT_4:9;
7349 = 83*88 + 45; hence not 83 divides 7349 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7349 & n is prime
holds not n divides 7349 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7351 is prime
proof
now
7351 = 2*3675 + 1; hence not 2 divides 7351 by NAT_4:9;
7351 = 3*2450 + 1; hence not 3 divides 7351 by NAT_4:9;
7351 = 5*1470 + 1; hence not 5 divides 7351 by NAT_4:9;
7351 = 7*1050 + 1; hence not 7 divides 7351 by NAT_4:9;
7351 = 11*668 + 3; hence not 11 divides 7351 by NAT_4:9;
7351 = 13*565 + 6; hence not 13 divides 7351 by NAT_4:9;
7351 = 17*432 + 7; hence not 17 divides 7351 by NAT_4:9;
7351 = 19*386 + 17; hence not 19 divides 7351 by NAT_4:9;
7351 = 23*319 + 14; hence not 23 divides 7351 by NAT_4:9;
7351 = 29*253 + 14; hence not 29 divides 7351 by NAT_4:9;
7351 = 31*237 + 4; hence not 31 divides 7351 by NAT_4:9;
7351 = 37*198 + 25; hence not 37 divides 7351 by NAT_4:9;
7351 = 41*179 + 12; hence not 41 divides 7351 by NAT_4:9;
7351 = 43*170 + 41; hence not 43 divides 7351 by NAT_4:9;
7351 = 47*156 + 19; hence not 47 divides 7351 by NAT_4:9;
7351 = 53*138 + 37; hence not 53 divides 7351 by NAT_4:9;
7351 = 59*124 + 35; hence not 59 divides 7351 by NAT_4:9;
7351 = 61*120 + 31; hence not 61 divides 7351 by NAT_4:9;
7351 = 67*109 + 48; hence not 67 divides 7351 by NAT_4:9;
7351 = 71*103 + 38; hence not 71 divides 7351 by NAT_4:9;
7351 = 73*100 + 51; hence not 73 divides 7351 by NAT_4:9;
7351 = 79*93 + 4; hence not 79 divides 7351 by NAT_4:9;
7351 = 83*88 + 47; hence not 83 divides 7351 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7351 & n is prime
holds not n divides 7351 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7369 is prime
proof
now
7369 = 2*3684 + 1; hence not 2 divides 7369 by NAT_4:9;
7369 = 3*2456 + 1; hence not 3 divides 7369 by NAT_4:9;
7369 = 5*1473 + 4; hence not 5 divides 7369 by NAT_4:9;
7369 = 7*1052 + 5; hence not 7 divides 7369 by NAT_4:9;
7369 = 11*669 + 10; hence not 11 divides 7369 by NAT_4:9;
7369 = 13*566 + 11; hence not 13 divides 7369 by NAT_4:9;
7369 = 17*433 + 8; hence not 17 divides 7369 by NAT_4:9;
7369 = 19*387 + 16; hence not 19 divides 7369 by NAT_4:9;
7369 = 23*320 + 9; hence not 23 divides 7369 by NAT_4:9;
7369 = 29*254 + 3; hence not 29 divides 7369 by NAT_4:9;
7369 = 31*237 + 22; hence not 31 divides 7369 by NAT_4:9;
7369 = 37*199 + 6; hence not 37 divides 7369 by NAT_4:9;
7369 = 41*179 + 30; hence not 41 divides 7369 by NAT_4:9;
7369 = 43*171 + 16; hence not 43 divides 7369 by NAT_4:9;
7369 = 47*156 + 37; hence not 47 divides 7369 by NAT_4:9;
7369 = 53*139 + 2; hence not 53 divides 7369 by NAT_4:9;
7369 = 59*124 + 53; hence not 59 divides 7369 by NAT_4:9;
7369 = 61*120 + 49; hence not 61 divides 7369 by NAT_4:9;
7369 = 67*109 + 66; hence not 67 divides 7369 by NAT_4:9;
7369 = 71*103 + 56; hence not 71 divides 7369 by NAT_4:9;
7369 = 73*100 + 69; hence not 73 divides 7369 by NAT_4:9;
7369 = 79*93 + 22; hence not 79 divides 7369 by NAT_4:9;
7369 = 83*88 + 65; hence not 83 divides 7369 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7369 & n is prime
holds not n divides 7369 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
7393 is prime
proof
now
7393 = 2*3696 + 1; hence not 2 divides 7393 by NAT_4:9;
7393 = 3*2464 + 1; hence not 3 divides 7393 by NAT_4:9;
7393 = 5*1478 + 3; hence not 5 divides 7393 by NAT_4:9;
7393 = 7*1056 + 1; hence not 7 divides 7393 by NAT_4:9;
7393 = 11*672 + 1; hence not 11 divides 7393 by NAT_4:9;
7393 = 13*568 + 9; hence not 13 divides 7393 by NAT_4:9;
7393 = 17*434 + 15; hence not 17 divides 7393 by NAT_4:9;
7393 = 19*389 + 2; hence not 19 divides 7393 by NAT_4:9;
7393 = 23*321 + 10; hence not 23 divides 7393 by NAT_4:9;
7393 = 29*254 + 27; hence not 29 divides 7393 by NAT_4:9;
7393 = 31*238 + 15; hence not 31 divides 7393 by NAT_4:9;
7393 = 37*199 + 30; hence not 37 divides 7393 by NAT_4:9;
7393 = 41*180 + 13; hence not 41 divides 7393 by NAT_4:9;
7393 = 43*171 + 40; hence not 43 divides 7393 by NAT_4:9;
7393 = 47*157 + 14; hence not 47 divides 7393 by NAT_4:9;
7393 = 53*139 + 26; hence not 53 divides 7393 by NAT_4:9;
7393 = 59*125 + 18; hence not 59 divides 7393 by NAT_4:9;
7393 = 61*121 + 12; hence not 61 divides 7393 by NAT_4:9;
7393 = 67*110 + 23; hence not 67 divides 7393 by NAT_4:9;
7393 = 71*104 + 9; hence not 71 divides 7393 by NAT_4:9;
7393 = 73*101 + 20; hence not 73 divides 7393 by NAT_4:9;
7393 = 79*93 + 46; hence not 79 divides 7393 by NAT_4:9;
7393 = 83*89 + 6; hence not 83 divides 7393 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7393 & n is prime
holds not n divides 7393 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7411 is prime
proof
now
7411 = 2*3705 + 1; hence not 2 divides 7411 by NAT_4:9;
7411 = 3*2470 + 1; hence not 3 divides 7411 by NAT_4:9;
7411 = 5*1482 + 1; hence not 5 divides 7411 by NAT_4:9;
7411 = 7*1058 + 5; hence not 7 divides 7411 by NAT_4:9;
7411 = 11*673 + 8; hence not 11 divides 7411 by NAT_4:9;
7411 = 13*570 + 1; hence not 13 divides 7411 by NAT_4:9;
7411 = 17*435 + 16; hence not 17 divides 7411 by NAT_4:9;
7411 = 19*390 + 1; hence not 19 divides 7411 by NAT_4:9;
7411 = 23*322 + 5; hence not 23 divides 7411 by NAT_4:9;
7411 = 29*255 + 16; hence not 29 divides 7411 by NAT_4:9;
7411 = 31*239 + 2; hence not 31 divides 7411 by NAT_4:9;
7411 = 37*200 + 11; hence not 37 divides 7411 by NAT_4:9;
7411 = 41*180 + 31; hence not 41 divides 7411 by NAT_4:9;
7411 = 43*172 + 15; hence not 43 divides 7411 by NAT_4:9;
7411 = 47*157 + 32; hence not 47 divides 7411 by NAT_4:9;
7411 = 53*139 + 44; hence not 53 divides 7411 by NAT_4:9;
7411 = 59*125 + 36; hence not 59 divides 7411 by NAT_4:9;
7411 = 61*121 + 30; hence not 61 divides 7411 by NAT_4:9;
7411 = 67*110 + 41; hence not 67 divides 7411 by NAT_4:9;
7411 = 71*104 + 27; hence not 71 divides 7411 by NAT_4:9;
7411 = 73*101 + 38; hence not 73 divides 7411 by NAT_4:9;
7411 = 79*93 + 64; hence not 79 divides 7411 by NAT_4:9;
7411 = 83*89 + 24; hence not 83 divides 7411 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7411 & n is prime
holds not n divides 7411 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7417 is prime
proof
now
7417 = 2*3708 + 1; hence not 2 divides 7417 by NAT_4:9;
7417 = 3*2472 + 1; hence not 3 divides 7417 by NAT_4:9;
7417 = 5*1483 + 2; hence not 5 divides 7417 by NAT_4:9;
7417 = 7*1059 + 4; hence not 7 divides 7417 by NAT_4:9;
7417 = 11*674 + 3; hence not 11 divides 7417 by NAT_4:9;
7417 = 13*570 + 7; hence not 13 divides 7417 by NAT_4:9;
7417 = 17*436 + 5; hence not 17 divides 7417 by NAT_4:9;
7417 = 19*390 + 7; hence not 19 divides 7417 by NAT_4:9;
7417 = 23*322 + 11; hence not 23 divides 7417 by NAT_4:9;
7417 = 29*255 + 22; hence not 29 divides 7417 by NAT_4:9;
7417 = 31*239 + 8; hence not 31 divides 7417 by NAT_4:9;
7417 = 37*200 + 17; hence not 37 divides 7417 by NAT_4:9;
7417 = 41*180 + 37; hence not 41 divides 7417 by NAT_4:9;
7417 = 43*172 + 21; hence not 43 divides 7417 by NAT_4:9;
7417 = 47*157 + 38; hence not 47 divides 7417 by NAT_4:9;
7417 = 53*139 + 50; hence not 53 divides 7417 by NAT_4:9;
7417 = 59*125 + 42; hence not 59 divides 7417 by NAT_4:9;
7417 = 61*121 + 36; hence not 61 divides 7417 by NAT_4:9;
7417 = 67*110 + 47; hence not 67 divides 7417 by NAT_4:9;
7417 = 71*104 + 33; hence not 71 divides 7417 by NAT_4:9;
7417 = 73*101 + 44; hence not 73 divides 7417 by NAT_4:9;
7417 = 79*93 + 70; hence not 79 divides 7417 by NAT_4:9;
7417 = 83*89 + 30; hence not 83 divides 7417 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7417 & n is prime
holds not n divides 7417 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
7433 is prime
proof
now
7433 = 2*3716 + 1; hence not 2 divides 7433 by NAT_4:9;
7433 = 3*2477 + 2; hence not 3 divides 7433 by NAT_4:9;
7433 = 5*1486 + 3; hence not 5 divides 7433 by NAT_4:9;
7433 = 7*1061 + 6; hence not 7 divides 7433 by NAT_4:9;
7433 = 11*675 + 8; hence not 11 divides 7433 by NAT_4:9;
7433 = 13*571 + 10; hence not 13 divides 7433 by NAT_4:9;
7433 = 17*437 + 4; hence not 17 divides 7433 by NAT_4:9;
7433 = 19*391 + 4; hence not 19 divides 7433 by NAT_4:9;
7433 = 23*323 + 4; hence not 23 divides 7433 by NAT_4:9;
7433 = 29*256 + 9; hence not 29 divides 7433 by NAT_4:9;
7433 = 31*239 + 24; hence not 31 divides 7433 by NAT_4:9;
7433 = 37*200 + 33; hence not 37 divides 7433 by NAT_4:9;
7433 = 41*181 + 12; hence not 41 divides 7433 by NAT_4:9;
7433 = 43*172 + 37; hence not 43 divides 7433 by NAT_4:9;
7433 = 47*158 + 7; hence not 47 divides 7433 by NAT_4:9;
7433 = 53*140 + 13; hence not 53 divides 7433 by NAT_4:9;
7433 = 59*125 + 58; hence not 59 divides 7433 by NAT_4:9;
7433 = 61*121 + 52; hence not 61 divides 7433 by NAT_4:9;
7433 = 67*110 + 63; hence not 67 divides 7433 by NAT_4:9;
7433 = 71*104 + 49; hence not 71 divides 7433 by NAT_4:9;
7433 = 73*101 + 60; hence not 73 divides 7433 by NAT_4:9;
7433 = 79*94 + 7; hence not 79 divides 7433 by NAT_4:9;
7433 = 83*89 + 46; hence not 83 divides 7433 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7433 & n is prime
holds not n divides 7433 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7451 is prime
proof
now
7451 = 2*3725 + 1; hence not 2 divides 7451 by NAT_4:9;
7451 = 3*2483 + 2; hence not 3 divides 7451 by NAT_4:9;
7451 = 5*1490 + 1; hence not 5 divides 7451 by NAT_4:9;
7451 = 7*1064 + 3; hence not 7 divides 7451 by NAT_4:9;
7451 = 11*677 + 4; hence not 11 divides 7451 by NAT_4:9;
7451 = 13*573 + 2; hence not 13 divides 7451 by NAT_4:9;
7451 = 17*438 + 5; hence not 17 divides 7451 by NAT_4:9;
7451 = 19*392 + 3; hence not 19 divides 7451 by NAT_4:9;
7451 = 23*323 + 22; hence not 23 divides 7451 by NAT_4:9;
7451 = 29*256 + 27; hence not 29 divides 7451 by NAT_4:9;
7451 = 31*240 + 11; hence not 31 divides 7451 by NAT_4:9;
7451 = 37*201 + 14; hence not 37 divides 7451 by NAT_4:9;
7451 = 41*181 + 30; hence not 41 divides 7451 by NAT_4:9;
7451 = 43*173 + 12; hence not 43 divides 7451 by NAT_4:9;
7451 = 47*158 + 25; hence not 47 divides 7451 by NAT_4:9;
7451 = 53*140 + 31; hence not 53 divides 7451 by NAT_4:9;
7451 = 59*126 + 17; hence not 59 divides 7451 by NAT_4:9;
7451 = 61*122 + 9; hence not 61 divides 7451 by NAT_4:9;
7451 = 67*111 + 14; hence not 67 divides 7451 by NAT_4:9;
7451 = 71*104 + 67; hence not 71 divides 7451 by NAT_4:9;
7451 = 73*102 + 5; hence not 73 divides 7451 by NAT_4:9;
7451 = 79*94 + 25; hence not 79 divides 7451 by NAT_4:9;
7451 = 83*89 + 64; hence not 83 divides 7451 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7451 & n is prime
holds not n divides 7451 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7457 is prime
proof
now
7457 = 2*3728 + 1; hence not 2 divides 7457 by NAT_4:9;
7457 = 3*2485 + 2; hence not 3 divides 7457 by NAT_4:9;
7457 = 5*1491 + 2; hence not 5 divides 7457 by NAT_4:9;
7457 = 7*1065 + 2; hence not 7 divides 7457 by NAT_4:9;
7457 = 11*677 + 10; hence not 11 divides 7457 by NAT_4:9;
7457 = 13*573 + 8; hence not 13 divides 7457 by NAT_4:9;
7457 = 17*438 + 11; hence not 17 divides 7457 by NAT_4:9;
7457 = 19*392 + 9; hence not 19 divides 7457 by NAT_4:9;
7457 = 23*324 + 5; hence not 23 divides 7457 by NAT_4:9;
7457 = 29*257 + 4; hence not 29 divides 7457 by NAT_4:9;
7457 = 31*240 + 17; hence not 31 divides 7457 by NAT_4:9;
7457 = 37*201 + 20; hence not 37 divides 7457 by NAT_4:9;
7457 = 41*181 + 36; hence not 41 divides 7457 by NAT_4:9;
7457 = 43*173 + 18; hence not 43 divides 7457 by NAT_4:9;
7457 = 47*158 + 31; hence not 47 divides 7457 by NAT_4:9;
7457 = 53*140 + 37; hence not 53 divides 7457 by NAT_4:9;
7457 = 59*126 + 23; hence not 59 divides 7457 by NAT_4:9;
7457 = 61*122 + 15; hence not 61 divides 7457 by NAT_4:9;
7457 = 67*111 + 20; hence not 67 divides 7457 by NAT_4:9;
7457 = 71*105 + 2; hence not 71 divides 7457 by NAT_4:9;
7457 = 73*102 + 11; hence not 73 divides 7457 by NAT_4:9;
7457 = 79*94 + 31; hence not 79 divides 7457 by NAT_4:9;
7457 = 83*89 + 70; hence not 83 divides 7457 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7457 & n is prime
holds not n divides 7457 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7459 is prime
proof
now
7459 = 2*3729 + 1; hence not 2 divides 7459 by NAT_4:9;
7459 = 3*2486 + 1; hence not 3 divides 7459 by NAT_4:9;
7459 = 5*1491 + 4; hence not 5 divides 7459 by NAT_4:9;
7459 = 7*1065 + 4; hence not 7 divides 7459 by NAT_4:9;
7459 = 11*678 + 1; hence not 11 divides 7459 by NAT_4:9;
7459 = 13*573 + 10; hence not 13 divides 7459 by NAT_4:9;
7459 = 17*438 + 13; hence not 17 divides 7459 by NAT_4:9;
7459 = 19*392 + 11; hence not 19 divides 7459 by NAT_4:9;
7459 = 23*324 + 7; hence not 23 divides 7459 by NAT_4:9;
7459 = 29*257 + 6; hence not 29 divides 7459 by NAT_4:9;
7459 = 31*240 + 19; hence not 31 divides 7459 by NAT_4:9;
7459 = 37*201 + 22; hence not 37 divides 7459 by NAT_4:9;
7459 = 41*181 + 38; hence not 41 divides 7459 by NAT_4:9;
7459 = 43*173 + 20; hence not 43 divides 7459 by NAT_4:9;
7459 = 47*158 + 33; hence not 47 divides 7459 by NAT_4:9;
7459 = 53*140 + 39; hence not 53 divides 7459 by NAT_4:9;
7459 = 59*126 + 25; hence not 59 divides 7459 by NAT_4:9;
7459 = 61*122 + 17; hence not 61 divides 7459 by NAT_4:9;
7459 = 67*111 + 22; hence not 67 divides 7459 by NAT_4:9;
7459 = 71*105 + 4; hence not 71 divides 7459 by NAT_4:9;
7459 = 73*102 + 13; hence not 73 divides 7459 by NAT_4:9;
7459 = 79*94 + 33; hence not 79 divides 7459 by NAT_4:9;
7459 = 83*89 + 72; hence not 83 divides 7459 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7459 & n is prime
holds not n divides 7459 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7477 is prime
proof
now
7477 = 2*3738 + 1; hence not 2 divides 7477 by NAT_4:9;
7477 = 3*2492 + 1; hence not 3 divides 7477 by NAT_4:9;
7477 = 5*1495 + 2; hence not 5 divides 7477 by NAT_4:9;
7477 = 7*1068 + 1; hence not 7 divides 7477 by NAT_4:9;
7477 = 11*679 + 8; hence not 11 divides 7477 by NAT_4:9;
7477 = 13*575 + 2; hence not 13 divides 7477 by NAT_4:9;
7477 = 17*439 + 14; hence not 17 divides 7477 by NAT_4:9;
7477 = 19*393 + 10; hence not 19 divides 7477 by NAT_4:9;
7477 = 23*325 + 2; hence not 23 divides 7477 by NAT_4:9;
7477 = 29*257 + 24; hence not 29 divides 7477 by NAT_4:9;
7477 = 31*241 + 6; hence not 31 divides 7477 by NAT_4:9;
7477 = 37*202 + 3; hence not 37 divides 7477 by NAT_4:9;
7477 = 41*182 + 15; hence not 41 divides 7477 by NAT_4:9;
7477 = 43*173 + 38; hence not 43 divides 7477 by NAT_4:9;
7477 = 47*159 + 4; hence not 47 divides 7477 by NAT_4:9;
7477 = 53*141 + 4; hence not 53 divides 7477 by NAT_4:9;
7477 = 59*126 + 43; hence not 59 divides 7477 by NAT_4:9;
7477 = 61*122 + 35; hence not 61 divides 7477 by NAT_4:9;
7477 = 67*111 + 40; hence not 67 divides 7477 by NAT_4:9;
7477 = 71*105 + 22; hence not 71 divides 7477 by NAT_4:9;
7477 = 73*102 + 31; hence not 73 divides 7477 by NAT_4:9;
7477 = 79*94 + 51; hence not 79 divides 7477 by NAT_4:9;
7477 = 83*90 + 7; hence not 83 divides 7477 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7477 & n is prime
holds not n divides 7477 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7481 is prime
proof
now
7481 = 2*3740 + 1; hence not 2 divides 7481 by NAT_4:9;
7481 = 3*2493 + 2; hence not 3 divides 7481 by NAT_4:9;
7481 = 5*1496 + 1; hence not 5 divides 7481 by NAT_4:9;
7481 = 7*1068 + 5; hence not 7 divides 7481 by NAT_4:9;
7481 = 11*680 + 1; hence not 11 divides 7481 by NAT_4:9;
7481 = 13*575 + 6; hence not 13 divides 7481 by NAT_4:9;
7481 = 17*440 + 1; hence not 17 divides 7481 by NAT_4:9;
7481 = 19*393 + 14; hence not 19 divides 7481 by NAT_4:9;
7481 = 23*325 + 6; hence not 23 divides 7481 by NAT_4:9;
7481 = 29*257 + 28; hence not 29 divides 7481 by NAT_4:9;
7481 = 31*241 + 10; hence not 31 divides 7481 by NAT_4:9;
7481 = 37*202 + 7; hence not 37 divides 7481 by NAT_4:9;
7481 = 41*182 + 19; hence not 41 divides 7481 by NAT_4:9;
7481 = 43*173 + 42; hence not 43 divides 7481 by NAT_4:9;
7481 = 47*159 + 8; hence not 47 divides 7481 by NAT_4:9;
7481 = 53*141 + 8; hence not 53 divides 7481 by NAT_4:9;
7481 = 59*126 + 47; hence not 59 divides 7481 by NAT_4:9;
7481 = 61*122 + 39; hence not 61 divides 7481 by NAT_4:9;
7481 = 67*111 + 44; hence not 67 divides 7481 by NAT_4:9;
7481 = 71*105 + 26; hence not 71 divides 7481 by NAT_4:9;
7481 = 73*102 + 35; hence not 73 divides 7481 by NAT_4:9;
7481 = 79*94 + 55; hence not 79 divides 7481 by NAT_4:9;
7481 = 83*90 + 11; hence not 83 divides 7481 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7481 & n is prime
holds not n divides 7481 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7487 is prime
proof
now
7487 = 2*3743 + 1; hence not 2 divides 7487 by NAT_4:9;
7487 = 3*2495 + 2; hence not 3 divides 7487 by NAT_4:9;
7487 = 5*1497 + 2; hence not 5 divides 7487 by NAT_4:9;
7487 = 7*1069 + 4; hence not 7 divides 7487 by NAT_4:9;
7487 = 11*680 + 7; hence not 11 divides 7487 by NAT_4:9;
7487 = 13*575 + 12; hence not 13 divides 7487 by NAT_4:9;
7487 = 17*440 + 7; hence not 17 divides 7487 by NAT_4:9;
7487 = 19*394 + 1; hence not 19 divides 7487 by NAT_4:9;
7487 = 23*325 + 12; hence not 23 divides 7487 by NAT_4:9;
7487 = 29*258 + 5; hence not 29 divides 7487 by NAT_4:9;
7487 = 31*241 + 16; hence not 31 divides 7487 by NAT_4:9;
7487 = 37*202 + 13; hence not 37 divides 7487 by NAT_4:9;
7487 = 41*182 + 25; hence not 41 divides 7487 by NAT_4:9;
7487 = 43*174 + 5; hence not 43 divides 7487 by NAT_4:9;
7487 = 47*159 + 14; hence not 47 divides 7487 by NAT_4:9;
7487 = 53*141 + 14; hence not 53 divides 7487 by NAT_4:9;
7487 = 59*126 + 53; hence not 59 divides 7487 by NAT_4:9;
7487 = 61*122 + 45; hence not 61 divides 7487 by NAT_4:9;
7487 = 67*111 + 50; hence not 67 divides 7487 by NAT_4:9;
7487 = 71*105 + 32; hence not 71 divides 7487 by NAT_4:9;
7487 = 73*102 + 41; hence not 73 divides 7487 by NAT_4:9;
7487 = 79*94 + 61; hence not 79 divides 7487 by NAT_4:9;
7487 = 83*90 + 17; hence not 83 divides 7487 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7487 & n is prime
holds not n divides 7487 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7489 is prime
proof
now
7489 = 2*3744 + 1; hence not 2 divides 7489 by NAT_4:9;
7489 = 3*2496 + 1; hence not 3 divides 7489 by NAT_4:9;
7489 = 5*1497 + 4; hence not 5 divides 7489 by NAT_4:9;
7489 = 7*1069 + 6; hence not 7 divides 7489 by NAT_4:9;
7489 = 11*680 + 9; hence not 11 divides 7489 by NAT_4:9;
7489 = 13*576 + 1; hence not 13 divides 7489 by NAT_4:9;
7489 = 17*440 + 9; hence not 17 divides 7489 by NAT_4:9;
7489 = 19*394 + 3; hence not 19 divides 7489 by NAT_4:9;
7489 = 23*325 + 14; hence not 23 divides 7489 by NAT_4:9;
7489 = 29*258 + 7; hence not 29 divides 7489 by NAT_4:9;
7489 = 31*241 + 18; hence not 31 divides 7489 by NAT_4:9;
7489 = 37*202 + 15; hence not 37 divides 7489 by NAT_4:9;
7489 = 41*182 + 27; hence not 41 divides 7489 by NAT_4:9;
7489 = 43*174 + 7; hence not 43 divides 7489 by NAT_4:9;
7489 = 47*159 + 16; hence not 47 divides 7489 by NAT_4:9;
7489 = 53*141 + 16; hence not 53 divides 7489 by NAT_4:9;
7489 = 59*126 + 55; hence not 59 divides 7489 by NAT_4:9;
7489 = 61*122 + 47; hence not 61 divides 7489 by NAT_4:9;
7489 = 67*111 + 52; hence not 67 divides 7489 by NAT_4:9;
7489 = 71*105 + 34; hence not 71 divides 7489 by NAT_4:9;
7489 = 73*102 + 43; hence not 73 divides 7489 by NAT_4:9;
7489 = 79*94 + 63; hence not 79 divides 7489 by NAT_4:9;
7489 = 83*90 + 19; hence not 83 divides 7489 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7489 & n is prime
holds not n divides 7489 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7499 is prime
proof
now
7499 = 2*3749 + 1; hence not 2 divides 7499 by NAT_4:9;
7499 = 3*2499 + 2; hence not 3 divides 7499 by NAT_4:9;
7499 = 5*1499 + 4; hence not 5 divides 7499 by NAT_4:9;
7499 = 7*1071 + 2; hence not 7 divides 7499 by NAT_4:9;
7499 = 11*681 + 8; hence not 11 divides 7499 by NAT_4:9;
7499 = 13*576 + 11; hence not 13 divides 7499 by NAT_4:9;
7499 = 17*441 + 2; hence not 17 divides 7499 by NAT_4:9;
7499 = 19*394 + 13; hence not 19 divides 7499 by NAT_4:9;
7499 = 23*326 + 1; hence not 23 divides 7499 by NAT_4:9;
7499 = 29*258 + 17; hence not 29 divides 7499 by NAT_4:9;
7499 = 31*241 + 28; hence not 31 divides 7499 by NAT_4:9;
7499 = 37*202 + 25; hence not 37 divides 7499 by NAT_4:9;
7499 = 41*182 + 37; hence not 41 divides 7499 by NAT_4:9;
7499 = 43*174 + 17; hence not 43 divides 7499 by NAT_4:9;
7499 = 47*159 + 26; hence not 47 divides 7499 by NAT_4:9;
7499 = 53*141 + 26; hence not 53 divides 7499 by NAT_4:9;
7499 = 59*127 + 6; hence not 59 divides 7499 by NAT_4:9;
7499 = 61*122 + 57; hence not 61 divides 7499 by NAT_4:9;
7499 = 67*111 + 62; hence not 67 divides 7499 by NAT_4:9;
7499 = 71*105 + 44; hence not 71 divides 7499 by NAT_4:9;
7499 = 73*102 + 53; hence not 73 divides 7499 by NAT_4:9;
7499 = 79*94 + 73; hence not 79 divides 7499 by NAT_4:9;
7499 = 83*90 + 29; hence not 83 divides 7499 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7499 & n is prime
holds not n divides 7499 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7507 is prime
proof
now
7507 = 2*3753 + 1; hence not 2 divides 7507 by NAT_4:9;
7507 = 3*2502 + 1; hence not 3 divides 7507 by NAT_4:9;
7507 = 5*1501 + 2; hence not 5 divides 7507 by NAT_4:9;
7507 = 7*1072 + 3; hence not 7 divides 7507 by NAT_4:9;
7507 = 11*682 + 5; hence not 11 divides 7507 by NAT_4:9;
7507 = 13*577 + 6; hence not 13 divides 7507 by NAT_4:9;
7507 = 17*441 + 10; hence not 17 divides 7507 by NAT_4:9;
7507 = 19*395 + 2; hence not 19 divides 7507 by NAT_4:9;
7507 = 23*326 + 9; hence not 23 divides 7507 by NAT_4:9;
7507 = 29*258 + 25; hence not 29 divides 7507 by NAT_4:9;
7507 = 31*242 + 5; hence not 31 divides 7507 by NAT_4:9;
7507 = 37*202 + 33; hence not 37 divides 7507 by NAT_4:9;
7507 = 41*183 + 4; hence not 41 divides 7507 by NAT_4:9;
7507 = 43*174 + 25; hence not 43 divides 7507 by NAT_4:9;
7507 = 47*159 + 34; hence not 47 divides 7507 by NAT_4:9;
7507 = 53*141 + 34; hence not 53 divides 7507 by NAT_4:9;
7507 = 59*127 + 14; hence not 59 divides 7507 by NAT_4:9;
7507 = 61*123 + 4; hence not 61 divides 7507 by NAT_4:9;
7507 = 67*112 + 3; hence not 67 divides 7507 by NAT_4:9;
7507 = 71*105 + 52; hence not 71 divides 7507 by NAT_4:9;
7507 = 73*102 + 61; hence not 73 divides 7507 by NAT_4:9;
7507 = 79*95 + 2; hence not 79 divides 7507 by NAT_4:9;
7507 = 83*90 + 37; hence not 83 divides 7507 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7507 & n is prime
holds not n divides 7507 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7517 is prime
proof
now
7517 = 2*3758 + 1; hence not 2 divides 7517 by NAT_4:9;
7517 = 3*2505 + 2; hence not 3 divides 7517 by NAT_4:9;
7517 = 5*1503 + 2; hence not 5 divides 7517 by NAT_4:9;
7517 = 7*1073 + 6; hence not 7 divides 7517 by NAT_4:9;
7517 = 11*683 + 4; hence not 11 divides 7517 by NAT_4:9;
7517 = 13*578 + 3; hence not 13 divides 7517 by NAT_4:9;
7517 = 17*442 + 3; hence not 17 divides 7517 by NAT_4:9;
7517 = 19*395 + 12; hence not 19 divides 7517 by NAT_4:9;
7517 = 23*326 + 19; hence not 23 divides 7517 by NAT_4:9;
7517 = 29*259 + 6; hence not 29 divides 7517 by NAT_4:9;
7517 = 31*242 + 15; hence not 31 divides 7517 by NAT_4:9;
7517 = 37*203 + 6; hence not 37 divides 7517 by NAT_4:9;
7517 = 41*183 + 14; hence not 41 divides 7517 by NAT_4:9;
7517 = 43*174 + 35; hence not 43 divides 7517 by NAT_4:9;
7517 = 47*159 + 44; hence not 47 divides 7517 by NAT_4:9;
7517 = 53*141 + 44; hence not 53 divides 7517 by NAT_4:9;
7517 = 59*127 + 24; hence not 59 divides 7517 by NAT_4:9;
7517 = 61*123 + 14; hence not 61 divides 7517 by NAT_4:9;
7517 = 67*112 + 13; hence not 67 divides 7517 by NAT_4:9;
7517 = 71*105 + 62; hence not 71 divides 7517 by NAT_4:9;
7517 = 73*102 + 71; hence not 73 divides 7517 by NAT_4:9;
7517 = 79*95 + 12; hence not 79 divides 7517 by NAT_4:9;
7517 = 83*90 + 47; hence not 83 divides 7517 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7517 & n is prime
holds not n divides 7517 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7523 is prime
proof
now
7523 = 2*3761 + 1; hence not 2 divides 7523 by NAT_4:9;
7523 = 3*2507 + 2; hence not 3 divides 7523 by NAT_4:9;
7523 = 5*1504 + 3; hence not 5 divides 7523 by NAT_4:9;
7523 = 7*1074 + 5; hence not 7 divides 7523 by NAT_4:9;
7523 = 11*683 + 10; hence not 11 divides 7523 by NAT_4:9;
7523 = 13*578 + 9; hence not 13 divides 7523 by NAT_4:9;
7523 = 17*442 + 9; hence not 17 divides 7523 by NAT_4:9;
7523 = 19*395 + 18; hence not 19 divides 7523 by NAT_4:9;
7523 = 23*327 + 2; hence not 23 divides 7523 by NAT_4:9;
7523 = 29*259 + 12; hence not 29 divides 7523 by NAT_4:9;
7523 = 31*242 + 21; hence not 31 divides 7523 by NAT_4:9;
7523 = 37*203 + 12; hence not 37 divides 7523 by NAT_4:9;
7523 = 41*183 + 20; hence not 41 divides 7523 by NAT_4:9;
7523 = 43*174 + 41; hence not 43 divides 7523 by NAT_4:9;
7523 = 47*160 + 3; hence not 47 divides 7523 by NAT_4:9;
7523 = 53*141 + 50; hence not 53 divides 7523 by NAT_4:9;
7523 = 59*127 + 30; hence not 59 divides 7523 by NAT_4:9;
7523 = 61*123 + 20; hence not 61 divides 7523 by NAT_4:9;
7523 = 67*112 + 19; hence not 67 divides 7523 by NAT_4:9;
7523 = 71*105 + 68; hence not 71 divides 7523 by NAT_4:9;
7523 = 73*103 + 4; hence not 73 divides 7523 by NAT_4:9;
7523 = 79*95 + 18; hence not 79 divides 7523 by NAT_4:9;
7523 = 83*90 + 53; hence not 83 divides 7523 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7523 & n is prime
holds not n divides 7523 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7529 is prime
proof
now
7529 = 2*3764 + 1; hence not 2 divides 7529 by NAT_4:9;
7529 = 3*2509 + 2; hence not 3 divides 7529 by NAT_4:9;
7529 = 5*1505 + 4; hence not 5 divides 7529 by NAT_4:9;
7529 = 7*1075 + 4; hence not 7 divides 7529 by NAT_4:9;
7529 = 11*684 + 5; hence not 11 divides 7529 by NAT_4:9;
7529 = 13*579 + 2; hence not 13 divides 7529 by NAT_4:9;
7529 = 17*442 + 15; hence not 17 divides 7529 by NAT_4:9;
7529 = 19*396 + 5; hence not 19 divides 7529 by NAT_4:9;
7529 = 23*327 + 8; hence not 23 divides 7529 by NAT_4:9;
7529 = 29*259 + 18; hence not 29 divides 7529 by NAT_4:9;
7529 = 31*242 + 27; hence not 31 divides 7529 by NAT_4:9;
7529 = 37*203 + 18; hence not 37 divides 7529 by NAT_4:9;
7529 = 41*183 + 26; hence not 41 divides 7529 by NAT_4:9;
7529 = 43*175 + 4; hence not 43 divides 7529 by NAT_4:9;
7529 = 47*160 + 9; hence not 47 divides 7529 by NAT_4:9;
7529 = 53*142 + 3; hence not 53 divides 7529 by NAT_4:9;
7529 = 59*127 + 36; hence not 59 divides 7529 by NAT_4:9;
7529 = 61*123 + 26; hence not 61 divides 7529 by NAT_4:9;
7529 = 67*112 + 25; hence not 67 divides 7529 by NAT_4:9;
7529 = 71*106 + 3; hence not 71 divides 7529 by NAT_4:9;
7529 = 73*103 + 10; hence not 73 divides 7529 by NAT_4:9;
7529 = 79*95 + 24; hence not 79 divides 7529 by NAT_4:9;
7529 = 83*90 + 59; hence not 83 divides 7529 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7529 & n is prime
holds not n divides 7529 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7537 is prime
proof
now
7537 = 2*3768 + 1; hence not 2 divides 7537 by NAT_4:9;
7537 = 3*2512 + 1; hence not 3 divides 7537 by NAT_4:9;
7537 = 5*1507 + 2; hence not 5 divides 7537 by NAT_4:9;
7537 = 7*1076 + 5; hence not 7 divides 7537 by NAT_4:9;
7537 = 11*685 + 2; hence not 11 divides 7537 by NAT_4:9;
7537 = 13*579 + 10; hence not 13 divides 7537 by NAT_4:9;
7537 = 17*443 + 6; hence not 17 divides 7537 by NAT_4:9;
7537 = 19*396 + 13; hence not 19 divides 7537 by NAT_4:9;
7537 = 23*327 + 16; hence not 23 divides 7537 by NAT_4:9;
7537 = 29*259 + 26; hence not 29 divides 7537 by NAT_4:9;
7537 = 31*243 + 4; hence not 31 divides 7537 by NAT_4:9;
7537 = 37*203 + 26; hence not 37 divides 7537 by NAT_4:9;
7537 = 41*183 + 34; hence not 41 divides 7537 by NAT_4:9;
7537 = 43*175 + 12; hence not 43 divides 7537 by NAT_4:9;
7537 = 47*160 + 17; hence not 47 divides 7537 by NAT_4:9;
7537 = 53*142 + 11; hence not 53 divides 7537 by NAT_4:9;
7537 = 59*127 + 44; hence not 59 divides 7537 by NAT_4:9;
7537 = 61*123 + 34; hence not 61 divides 7537 by NAT_4:9;
7537 = 67*112 + 33; hence not 67 divides 7537 by NAT_4:9;
7537 = 71*106 + 11; hence not 71 divides 7537 by NAT_4:9;
7537 = 73*103 + 18; hence not 73 divides 7537 by NAT_4:9;
7537 = 79*95 + 32; hence not 79 divides 7537 by NAT_4:9;
7537 = 83*90 + 67; hence not 83 divides 7537 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7537 & n is prime
holds not n divides 7537 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7541 is prime
proof
now
7541 = 2*3770 + 1; hence not 2 divides 7541 by NAT_4:9;
7541 = 3*2513 + 2; hence not 3 divides 7541 by NAT_4:9;
7541 = 5*1508 + 1; hence not 5 divides 7541 by NAT_4:9;
7541 = 7*1077 + 2; hence not 7 divides 7541 by NAT_4:9;
7541 = 11*685 + 6; hence not 11 divides 7541 by NAT_4:9;
7541 = 13*580 + 1; hence not 13 divides 7541 by NAT_4:9;
7541 = 17*443 + 10; hence not 17 divides 7541 by NAT_4:9;
7541 = 19*396 + 17; hence not 19 divides 7541 by NAT_4:9;
7541 = 23*327 + 20; hence not 23 divides 7541 by NAT_4:9;
7541 = 29*260 + 1; hence not 29 divides 7541 by NAT_4:9;
7541 = 31*243 + 8; hence not 31 divides 7541 by NAT_4:9;
7541 = 37*203 + 30; hence not 37 divides 7541 by NAT_4:9;
7541 = 41*183 + 38; hence not 41 divides 7541 by NAT_4:9;
7541 = 43*175 + 16; hence not 43 divides 7541 by NAT_4:9;
7541 = 47*160 + 21; hence not 47 divides 7541 by NAT_4:9;
7541 = 53*142 + 15; hence not 53 divides 7541 by NAT_4:9;
7541 = 59*127 + 48; hence not 59 divides 7541 by NAT_4:9;
7541 = 61*123 + 38; hence not 61 divides 7541 by NAT_4:9;
7541 = 67*112 + 37; hence not 67 divides 7541 by NAT_4:9;
7541 = 71*106 + 15; hence not 71 divides 7541 by NAT_4:9;
7541 = 73*103 + 22; hence not 73 divides 7541 by NAT_4:9;
7541 = 79*95 + 36; hence not 79 divides 7541 by NAT_4:9;
7541 = 83*90 + 71; hence not 83 divides 7541 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7541 & n is prime
holds not n divides 7541 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7547 is prime
proof
now
7547 = 2*3773 + 1; hence not 2 divides 7547 by NAT_4:9;
7547 = 3*2515 + 2; hence not 3 divides 7547 by NAT_4:9;
7547 = 5*1509 + 2; hence not 5 divides 7547 by NAT_4:9;
7547 = 7*1078 + 1; hence not 7 divides 7547 by NAT_4:9;
7547 = 11*686 + 1; hence not 11 divides 7547 by NAT_4:9;
7547 = 13*580 + 7; hence not 13 divides 7547 by NAT_4:9;
7547 = 17*443 + 16; hence not 17 divides 7547 by NAT_4:9;
7547 = 19*397 + 4; hence not 19 divides 7547 by NAT_4:9;
7547 = 23*328 + 3; hence not 23 divides 7547 by NAT_4:9;
7547 = 29*260 + 7; hence not 29 divides 7547 by NAT_4:9;
7547 = 31*243 + 14; hence not 31 divides 7547 by NAT_4:9;
7547 = 37*203 + 36; hence not 37 divides 7547 by NAT_4:9;
7547 = 41*184 + 3; hence not 41 divides 7547 by NAT_4:9;
7547 = 43*175 + 22; hence not 43 divides 7547 by NAT_4:9;
7547 = 47*160 + 27; hence not 47 divides 7547 by NAT_4:9;
7547 = 53*142 + 21; hence not 53 divides 7547 by NAT_4:9;
7547 = 59*127 + 54; hence not 59 divides 7547 by NAT_4:9;
7547 = 61*123 + 44; hence not 61 divides 7547 by NAT_4:9;
7547 = 67*112 + 43; hence not 67 divides 7547 by NAT_4:9;
7547 = 71*106 + 21; hence not 71 divides 7547 by NAT_4:9;
7547 = 73*103 + 28; hence not 73 divides 7547 by NAT_4:9;
7547 = 79*95 + 42; hence not 79 divides 7547 by NAT_4:9;
7547 = 83*90 + 77; hence not 83 divides 7547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7547 & n is prime
holds not n divides 7547 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7549 is prime
proof
now
7549 = 2*3774 + 1; hence not 2 divides 7549 by NAT_4:9;
7549 = 3*2516 + 1; hence not 3 divides 7549 by NAT_4:9;
7549 = 5*1509 + 4; hence not 5 divides 7549 by NAT_4:9;
7549 = 7*1078 + 3; hence not 7 divides 7549 by NAT_4:9;
7549 = 11*686 + 3; hence not 11 divides 7549 by NAT_4:9;
7549 = 13*580 + 9; hence not 13 divides 7549 by NAT_4:9;
7549 = 17*444 + 1; hence not 17 divides 7549 by NAT_4:9;
7549 = 19*397 + 6; hence not 19 divides 7549 by NAT_4:9;
7549 = 23*328 + 5; hence not 23 divides 7549 by NAT_4:9;
7549 = 29*260 + 9; hence not 29 divides 7549 by NAT_4:9;
7549 = 31*243 + 16; hence not 31 divides 7549 by NAT_4:9;
7549 = 37*204 + 1; hence not 37 divides 7549 by NAT_4:9;
7549 = 41*184 + 5; hence not 41 divides 7549 by NAT_4:9;
7549 = 43*175 + 24; hence not 43 divides 7549 by NAT_4:9;
7549 = 47*160 + 29; hence not 47 divides 7549 by NAT_4:9;
7549 = 53*142 + 23; hence not 53 divides 7549 by NAT_4:9;
7549 = 59*127 + 56; hence not 59 divides 7549 by NAT_4:9;
7549 = 61*123 + 46; hence not 61 divides 7549 by NAT_4:9;
7549 = 67*112 + 45; hence not 67 divides 7549 by NAT_4:9;
7549 = 71*106 + 23; hence not 71 divides 7549 by NAT_4:9;
7549 = 73*103 + 30; hence not 73 divides 7549 by NAT_4:9;
7549 = 79*95 + 44; hence not 79 divides 7549 by NAT_4:9;
7549 = 83*90 + 79; hence not 83 divides 7549 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7549 & n is prime
holds not n divides 7549 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
7559 is prime
proof
now
7559 = 2*3779 + 1; hence not 2 divides 7559 by NAT_4:9;
7559 = 3*2519 + 2; hence not 3 divides 7559 by NAT_4:9;
7559 = 5*1511 + 4; hence not 5 divides 7559 by NAT_4:9;
7559 = 7*1079 + 6; hence not 7 divides 7559 by NAT_4:9;
7559 = 11*687 + 2; hence not 11 divides 7559 by NAT_4:9;
7559 = 13*581 + 6; hence not 13 divides 7559 by NAT_4:9;
7559 = 17*444 + 11; hence not 17 divides 7559 by NAT_4:9;
7559 = 19*397 + 16; hence not 19 divides 7559 by NAT_4:9;
7559 = 23*328 + 15; hence not 23 divides 7559 by NAT_4:9;
7559 = 29*260 + 19; hence not 29 divides 7559 by NAT_4:9;
7559 = 31*243 + 26; hence not 31 divides 7559 by NAT_4:9;
7559 = 37*204 + 11; hence not 37 divides 7559 by NAT_4:9;
7559 = 41*184 + 15; hence not 41 divides 7559 by NAT_4:9;
7559 = 43*175 + 34; hence not 43 divides 7559 by NAT_4:9;
7559 = 47*160 + 39; hence not 47 divides 7559 by NAT_4:9;
7559 = 53*142 + 33; hence not 53 divides 7559 by NAT_4:9;
7559 = 59*128 + 7; hence not 59 divides 7559 by NAT_4:9;
7559 = 61*123 + 56; hence not 61 divides 7559 by NAT_4:9;
7559 = 67*112 + 55; hence not 67 divides 7559 by NAT_4:9;
7559 = 71*106 + 33; hence not 71 divides 7559 by NAT_4:9;
7559 = 73*103 + 40; hence not 73 divides 7559 by NAT_4:9;
7559 = 79*95 + 54; hence not 79 divides 7559 by NAT_4:9;
7559 = 83*91 + 6; hence not 83 divides 7559 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7559 & n is prime
holds not n divides 7559 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7561 is prime
proof
now
7561 = 2*3780 + 1; hence not 2 divides 7561 by NAT_4:9;
7561 = 3*2520 + 1; hence not 3 divides 7561 by NAT_4:9;
7561 = 5*1512 + 1; hence not 5 divides 7561 by NAT_4:9;
7561 = 7*1080 + 1; hence not 7 divides 7561 by NAT_4:9;
7561 = 11*687 + 4; hence not 11 divides 7561 by NAT_4:9;
7561 = 13*581 + 8; hence not 13 divides 7561 by NAT_4:9;
7561 = 17*444 + 13; hence not 17 divides 7561 by NAT_4:9;
7561 = 19*397 + 18; hence not 19 divides 7561 by NAT_4:9;
7561 = 23*328 + 17; hence not 23 divides 7561 by NAT_4:9;
7561 = 29*260 + 21; hence not 29 divides 7561 by NAT_4:9;
7561 = 31*243 + 28; hence not 31 divides 7561 by NAT_4:9;
7561 = 37*204 + 13; hence not 37 divides 7561 by NAT_4:9;
7561 = 41*184 + 17; hence not 41 divides 7561 by NAT_4:9;
7561 = 43*175 + 36; hence not 43 divides 7561 by NAT_4:9;
7561 = 47*160 + 41; hence not 47 divides 7561 by NAT_4:9;
7561 = 53*142 + 35; hence not 53 divides 7561 by NAT_4:9;
7561 = 59*128 + 9; hence not 59 divides 7561 by NAT_4:9;
7561 = 61*123 + 58; hence not 61 divides 7561 by NAT_4:9;
7561 = 67*112 + 57; hence not 67 divides 7561 by NAT_4:9;
7561 = 71*106 + 35; hence not 71 divides 7561 by NAT_4:9;
7561 = 73*103 + 42; hence not 73 divides 7561 by NAT_4:9;
7561 = 79*95 + 56; hence not 79 divides 7561 by NAT_4:9;
7561 = 83*91 + 8; hence not 83 divides 7561 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7561 & n is prime
holds not n divides 7561 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7573 is prime
proof
now
7573 = 2*3786 + 1; hence not 2 divides 7573 by NAT_4:9;
7573 = 3*2524 + 1; hence not 3 divides 7573 by NAT_4:9;
7573 = 5*1514 + 3; hence not 5 divides 7573 by NAT_4:9;
7573 = 7*1081 + 6; hence not 7 divides 7573 by NAT_4:9;
7573 = 11*688 + 5; hence not 11 divides 7573 by NAT_4:9;
7573 = 13*582 + 7; hence not 13 divides 7573 by NAT_4:9;
7573 = 17*445 + 8; hence not 17 divides 7573 by NAT_4:9;
7573 = 19*398 + 11; hence not 19 divides 7573 by NAT_4:9;
7573 = 23*329 + 6; hence not 23 divides 7573 by NAT_4:9;
7573 = 29*261 + 4; hence not 29 divides 7573 by NAT_4:9;
7573 = 31*244 + 9; hence not 31 divides 7573 by NAT_4:9;
7573 = 37*204 + 25; hence not 37 divides 7573 by NAT_4:9;
7573 = 41*184 + 29; hence not 41 divides 7573 by NAT_4:9;
7573 = 43*176 + 5; hence not 43 divides 7573 by NAT_4:9;
7573 = 47*161 + 6; hence not 47 divides 7573 by NAT_4:9;
7573 = 53*142 + 47; hence not 53 divides 7573 by NAT_4:9;
7573 = 59*128 + 21; hence not 59 divides 7573 by NAT_4:9;
7573 = 61*124 + 9; hence not 61 divides 7573 by NAT_4:9;
7573 = 67*113 + 2; hence not 67 divides 7573 by NAT_4:9;
7573 = 71*106 + 47; hence not 71 divides 7573 by NAT_4:9;
7573 = 73*103 + 54; hence not 73 divides 7573 by NAT_4:9;
7573 = 79*95 + 68; hence not 79 divides 7573 by NAT_4:9;
7573 = 83*91 + 20; hence not 83 divides 7573 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7573 & n is prime
holds not n divides 7573 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7577 is prime
proof
now
7577 = 2*3788 + 1; hence not 2 divides 7577 by NAT_4:9;
7577 = 3*2525 + 2; hence not 3 divides 7577 by NAT_4:9;
7577 = 5*1515 + 2; hence not 5 divides 7577 by NAT_4:9;
7577 = 7*1082 + 3; hence not 7 divides 7577 by NAT_4:9;
7577 = 11*688 + 9; hence not 11 divides 7577 by NAT_4:9;
7577 = 13*582 + 11; hence not 13 divides 7577 by NAT_4:9;
7577 = 17*445 + 12; hence not 17 divides 7577 by NAT_4:9;
7577 = 19*398 + 15; hence not 19 divides 7577 by NAT_4:9;
7577 = 23*329 + 10; hence not 23 divides 7577 by NAT_4:9;
7577 = 29*261 + 8; hence not 29 divides 7577 by NAT_4:9;
7577 = 31*244 + 13; hence not 31 divides 7577 by NAT_4:9;
7577 = 37*204 + 29; hence not 37 divides 7577 by NAT_4:9;
7577 = 41*184 + 33; hence not 41 divides 7577 by NAT_4:9;
7577 = 43*176 + 9; hence not 43 divides 7577 by NAT_4:9;
7577 = 47*161 + 10; hence not 47 divides 7577 by NAT_4:9;
7577 = 53*142 + 51; hence not 53 divides 7577 by NAT_4:9;
7577 = 59*128 + 25; hence not 59 divides 7577 by NAT_4:9;
7577 = 61*124 + 13; hence not 61 divides 7577 by NAT_4:9;
7577 = 67*113 + 6; hence not 67 divides 7577 by NAT_4:9;
7577 = 71*106 + 51; hence not 71 divides 7577 by NAT_4:9;
7577 = 73*103 + 58; hence not 73 divides 7577 by NAT_4:9;
7577 = 79*95 + 72; hence not 79 divides 7577 by NAT_4:9;
7577 = 83*91 + 24; hence not 83 divides 7577 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7577 & n is prime
holds not n divides 7577 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7583 is prime
proof
now
7583 = 2*3791 + 1; hence not 2 divides 7583 by NAT_4:9;
7583 = 3*2527 + 2; hence not 3 divides 7583 by NAT_4:9;
7583 = 5*1516 + 3; hence not 5 divides 7583 by NAT_4:9;
7583 = 7*1083 + 2; hence not 7 divides 7583 by NAT_4:9;
7583 = 11*689 + 4; hence not 11 divides 7583 by NAT_4:9;
7583 = 13*583 + 4; hence not 13 divides 7583 by NAT_4:9;
7583 = 17*446 + 1; hence not 17 divides 7583 by NAT_4:9;
7583 = 19*399 + 2; hence not 19 divides 7583 by NAT_4:9;
7583 = 23*329 + 16; hence not 23 divides 7583 by NAT_4:9;
7583 = 29*261 + 14; hence not 29 divides 7583 by NAT_4:9;
7583 = 31*244 + 19; hence not 31 divides 7583 by NAT_4:9;
7583 = 37*204 + 35; hence not 37 divides 7583 by NAT_4:9;
7583 = 41*184 + 39; hence not 41 divides 7583 by NAT_4:9;
7583 = 43*176 + 15; hence not 43 divides 7583 by NAT_4:9;
7583 = 47*161 + 16; hence not 47 divides 7583 by NAT_4:9;
7583 = 53*143 + 4; hence not 53 divides 7583 by NAT_4:9;
7583 = 59*128 + 31; hence not 59 divides 7583 by NAT_4:9;
7583 = 61*124 + 19; hence not 61 divides 7583 by NAT_4:9;
7583 = 67*113 + 12; hence not 67 divides 7583 by NAT_4:9;
7583 = 71*106 + 57; hence not 71 divides 7583 by NAT_4:9;
7583 = 73*103 + 64; hence not 73 divides 7583 by NAT_4:9;
7583 = 79*95 + 78; hence not 79 divides 7583 by NAT_4:9;
7583 = 83*91 + 30; hence not 83 divides 7583 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7583 & n is prime
holds not n divides 7583 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7589 is prime
proof
now
7589 = 2*3794 + 1; hence not 2 divides 7589 by NAT_4:9;
7589 = 3*2529 + 2; hence not 3 divides 7589 by NAT_4:9;
7589 = 5*1517 + 4; hence not 5 divides 7589 by NAT_4:9;
7589 = 7*1084 + 1; hence not 7 divides 7589 by NAT_4:9;
7589 = 11*689 + 10; hence not 11 divides 7589 by NAT_4:9;
7589 = 13*583 + 10; hence not 13 divides 7589 by NAT_4:9;
7589 = 17*446 + 7; hence not 17 divides 7589 by NAT_4:9;
7589 = 19*399 + 8; hence not 19 divides 7589 by NAT_4:9;
7589 = 23*329 + 22; hence not 23 divides 7589 by NAT_4:9;
7589 = 29*261 + 20; hence not 29 divides 7589 by NAT_4:9;
7589 = 31*244 + 25; hence not 31 divides 7589 by NAT_4:9;
7589 = 37*205 + 4; hence not 37 divides 7589 by NAT_4:9;
7589 = 41*185 + 4; hence not 41 divides 7589 by NAT_4:9;
7589 = 43*176 + 21; hence not 43 divides 7589 by NAT_4:9;
7589 = 47*161 + 22; hence not 47 divides 7589 by NAT_4:9;
7589 = 53*143 + 10; hence not 53 divides 7589 by NAT_4:9;
7589 = 59*128 + 37; hence not 59 divides 7589 by NAT_4:9;
7589 = 61*124 + 25; hence not 61 divides 7589 by NAT_4:9;
7589 = 67*113 + 18; hence not 67 divides 7589 by NAT_4:9;
7589 = 71*106 + 63; hence not 71 divides 7589 by NAT_4:9;
7589 = 73*103 + 70; hence not 73 divides 7589 by NAT_4:9;
7589 = 79*96 + 5; hence not 79 divides 7589 by NAT_4:9;
7589 = 83*91 + 36; hence not 83 divides 7589 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7589 & n is prime
holds not n divides 7589 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7591 is prime
proof
now
7591 = 2*3795 + 1; hence not 2 divides 7591 by NAT_4:9;
7591 = 3*2530 + 1; hence not 3 divides 7591 by NAT_4:9;
7591 = 5*1518 + 1; hence not 5 divides 7591 by NAT_4:9;
7591 = 7*1084 + 3; hence not 7 divides 7591 by NAT_4:9;
7591 = 11*690 + 1; hence not 11 divides 7591 by NAT_4:9;
7591 = 13*583 + 12; hence not 13 divides 7591 by NAT_4:9;
7591 = 17*446 + 9; hence not 17 divides 7591 by NAT_4:9;
7591 = 19*399 + 10; hence not 19 divides 7591 by NAT_4:9;
7591 = 23*330 + 1; hence not 23 divides 7591 by NAT_4:9;
7591 = 29*261 + 22; hence not 29 divides 7591 by NAT_4:9;
7591 = 31*244 + 27; hence not 31 divides 7591 by NAT_4:9;
7591 = 37*205 + 6; hence not 37 divides 7591 by NAT_4:9;
7591 = 41*185 + 6; hence not 41 divides 7591 by NAT_4:9;
7591 = 43*176 + 23; hence not 43 divides 7591 by NAT_4:9;
7591 = 47*161 + 24; hence not 47 divides 7591 by NAT_4:9;
7591 = 53*143 + 12; hence not 53 divides 7591 by NAT_4:9;
7591 = 59*128 + 39; hence not 59 divides 7591 by NAT_4:9;
7591 = 61*124 + 27; hence not 61 divides 7591 by NAT_4:9;
7591 = 67*113 + 20; hence not 67 divides 7591 by NAT_4:9;
7591 = 71*106 + 65; hence not 71 divides 7591 by NAT_4:9;
7591 = 73*103 + 72; hence not 73 divides 7591 by NAT_4:9;
7591 = 79*96 + 7; hence not 79 divides 7591 by NAT_4:9;
7591 = 83*91 + 38; hence not 83 divides 7591 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7591 & n is prime
holds not n divides 7591 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7603 is prime
proof
now
7603 = 2*3801 + 1; hence not 2 divides 7603 by NAT_4:9;
7603 = 3*2534 + 1; hence not 3 divides 7603 by NAT_4:9;
7603 = 5*1520 + 3; hence not 5 divides 7603 by NAT_4:9;
7603 = 7*1086 + 1; hence not 7 divides 7603 by NAT_4:9;
7603 = 11*691 + 2; hence not 11 divides 7603 by NAT_4:9;
7603 = 13*584 + 11; hence not 13 divides 7603 by NAT_4:9;
7603 = 17*447 + 4; hence not 17 divides 7603 by NAT_4:9;
7603 = 19*400 + 3; hence not 19 divides 7603 by NAT_4:9;
7603 = 23*330 + 13; hence not 23 divides 7603 by NAT_4:9;
7603 = 29*262 + 5; hence not 29 divides 7603 by NAT_4:9;
7603 = 31*245 + 8; hence not 31 divides 7603 by NAT_4:9;
7603 = 37*205 + 18; hence not 37 divides 7603 by NAT_4:9;
7603 = 41*185 + 18; hence not 41 divides 7603 by NAT_4:9;
7603 = 43*176 + 35; hence not 43 divides 7603 by NAT_4:9;
7603 = 47*161 + 36; hence not 47 divides 7603 by NAT_4:9;
7603 = 53*143 + 24; hence not 53 divides 7603 by NAT_4:9;
7603 = 59*128 + 51; hence not 59 divides 7603 by NAT_4:9;
7603 = 61*124 + 39; hence not 61 divides 7603 by NAT_4:9;
7603 = 67*113 + 32; hence not 67 divides 7603 by NAT_4:9;
7603 = 71*107 + 6; hence not 71 divides 7603 by NAT_4:9;
7603 = 73*104 + 11; hence not 73 divides 7603 by NAT_4:9;
7603 = 79*96 + 19; hence not 79 divides 7603 by NAT_4:9;
7603 = 83*91 + 50; hence not 83 divides 7603 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7603 & n is prime
holds not n divides 7603 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7607 is prime
proof
now
7607 = 2*3803 + 1; hence not 2 divides 7607 by NAT_4:9;
7607 = 3*2535 + 2; hence not 3 divides 7607 by NAT_4:9;
7607 = 5*1521 + 2; hence not 5 divides 7607 by NAT_4:9;
7607 = 7*1086 + 5; hence not 7 divides 7607 by NAT_4:9;
7607 = 11*691 + 6; hence not 11 divides 7607 by NAT_4:9;
7607 = 13*585 + 2; hence not 13 divides 7607 by NAT_4:9;
7607 = 17*447 + 8; hence not 17 divides 7607 by NAT_4:9;
7607 = 19*400 + 7; hence not 19 divides 7607 by NAT_4:9;
7607 = 23*330 + 17; hence not 23 divides 7607 by NAT_4:9;
7607 = 29*262 + 9; hence not 29 divides 7607 by NAT_4:9;
7607 = 31*245 + 12; hence not 31 divides 7607 by NAT_4:9;
7607 = 37*205 + 22; hence not 37 divides 7607 by NAT_4:9;
7607 = 41*185 + 22; hence not 41 divides 7607 by NAT_4:9;
7607 = 43*176 + 39; hence not 43 divides 7607 by NAT_4:9;
7607 = 47*161 + 40; hence not 47 divides 7607 by NAT_4:9;
7607 = 53*143 + 28; hence not 53 divides 7607 by NAT_4:9;
7607 = 59*128 + 55; hence not 59 divides 7607 by NAT_4:9;
7607 = 61*124 + 43; hence not 61 divides 7607 by NAT_4:9;
7607 = 67*113 + 36; hence not 67 divides 7607 by NAT_4:9;
7607 = 71*107 + 10; hence not 71 divides 7607 by NAT_4:9;
7607 = 73*104 + 15; hence not 73 divides 7607 by NAT_4:9;
7607 = 79*96 + 23; hence not 79 divides 7607 by NAT_4:9;
7607 = 83*91 + 54; hence not 83 divides 7607 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7607 & n is prime
holds not n divides 7607 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7621 is prime
proof
now
7621 = 2*3810 + 1; hence not 2 divides 7621 by NAT_4:9;
7621 = 3*2540 + 1; hence not 3 divides 7621 by NAT_4:9;
7621 = 5*1524 + 1; hence not 5 divides 7621 by NAT_4:9;
7621 = 7*1088 + 5; hence not 7 divides 7621 by NAT_4:9;
7621 = 11*692 + 9; hence not 11 divides 7621 by NAT_4:9;
7621 = 13*586 + 3; hence not 13 divides 7621 by NAT_4:9;
7621 = 17*448 + 5; hence not 17 divides 7621 by NAT_4:9;
7621 = 19*401 + 2; hence not 19 divides 7621 by NAT_4:9;
7621 = 23*331 + 8; hence not 23 divides 7621 by NAT_4:9;
7621 = 29*262 + 23; hence not 29 divides 7621 by NAT_4:9;
7621 = 31*245 + 26; hence not 31 divides 7621 by NAT_4:9;
7621 = 37*205 + 36; hence not 37 divides 7621 by NAT_4:9;
7621 = 41*185 + 36; hence not 41 divides 7621 by NAT_4:9;
7621 = 43*177 + 10; hence not 43 divides 7621 by NAT_4:9;
7621 = 47*162 + 7; hence not 47 divides 7621 by NAT_4:9;
7621 = 53*143 + 42; hence not 53 divides 7621 by NAT_4:9;
7621 = 59*129 + 10; hence not 59 divides 7621 by NAT_4:9;
7621 = 61*124 + 57; hence not 61 divides 7621 by NAT_4:9;
7621 = 67*113 + 50; hence not 67 divides 7621 by NAT_4:9;
7621 = 71*107 + 24; hence not 71 divides 7621 by NAT_4:9;
7621 = 73*104 + 29; hence not 73 divides 7621 by NAT_4:9;
7621 = 79*96 + 37; hence not 79 divides 7621 by NAT_4:9;
7621 = 83*91 + 68; hence not 83 divides 7621 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7621 & n is prime
holds not n divides 7621 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7639 is prime
proof
now
7639 = 2*3819 + 1; hence not 2 divides 7639 by NAT_4:9;
7639 = 3*2546 + 1; hence not 3 divides 7639 by NAT_4:9;
7639 = 5*1527 + 4; hence not 5 divides 7639 by NAT_4:9;
7639 = 7*1091 + 2; hence not 7 divides 7639 by NAT_4:9;
7639 = 11*694 + 5; hence not 11 divides 7639 by NAT_4:9;
7639 = 13*587 + 8; hence not 13 divides 7639 by NAT_4:9;
7639 = 17*449 + 6; hence not 17 divides 7639 by NAT_4:9;
7639 = 19*402 + 1; hence not 19 divides 7639 by NAT_4:9;
7639 = 23*332 + 3; hence not 23 divides 7639 by NAT_4:9;
7639 = 29*263 + 12; hence not 29 divides 7639 by NAT_4:9;
7639 = 31*246 + 13; hence not 31 divides 7639 by NAT_4:9;
7639 = 37*206 + 17; hence not 37 divides 7639 by NAT_4:9;
7639 = 41*186 + 13; hence not 41 divides 7639 by NAT_4:9;
7639 = 43*177 + 28; hence not 43 divides 7639 by NAT_4:9;
7639 = 47*162 + 25; hence not 47 divides 7639 by NAT_4:9;
7639 = 53*144 + 7; hence not 53 divides 7639 by NAT_4:9;
7639 = 59*129 + 28; hence not 59 divides 7639 by NAT_4:9;
7639 = 61*125 + 14; hence not 61 divides 7639 by NAT_4:9;
7639 = 67*114 + 1; hence not 67 divides 7639 by NAT_4:9;
7639 = 71*107 + 42; hence not 71 divides 7639 by NAT_4:9;
7639 = 73*104 + 47; hence not 73 divides 7639 by NAT_4:9;
7639 = 79*96 + 55; hence not 79 divides 7639 by NAT_4:9;
7639 = 83*92 + 3; hence not 83 divides 7639 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7639 & n is prime
holds not n divides 7639 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7643 is prime
proof
now
7643 = 2*3821 + 1; hence not 2 divides 7643 by NAT_4:9;
7643 = 3*2547 + 2; hence not 3 divides 7643 by NAT_4:9;
7643 = 5*1528 + 3; hence not 5 divides 7643 by NAT_4:9;
7643 = 7*1091 + 6; hence not 7 divides 7643 by NAT_4:9;
7643 = 11*694 + 9; hence not 11 divides 7643 by NAT_4:9;
7643 = 13*587 + 12; hence not 13 divides 7643 by NAT_4:9;
7643 = 17*449 + 10; hence not 17 divides 7643 by NAT_4:9;
7643 = 19*402 + 5; hence not 19 divides 7643 by NAT_4:9;
7643 = 23*332 + 7; hence not 23 divides 7643 by NAT_4:9;
7643 = 29*263 + 16; hence not 29 divides 7643 by NAT_4:9;
7643 = 31*246 + 17; hence not 31 divides 7643 by NAT_4:9;
7643 = 37*206 + 21; hence not 37 divides 7643 by NAT_4:9;
7643 = 41*186 + 17; hence not 41 divides 7643 by NAT_4:9;
7643 = 43*177 + 32; hence not 43 divides 7643 by NAT_4:9;
7643 = 47*162 + 29; hence not 47 divides 7643 by NAT_4:9;
7643 = 53*144 + 11; hence not 53 divides 7643 by NAT_4:9;
7643 = 59*129 + 32; hence not 59 divides 7643 by NAT_4:9;
7643 = 61*125 + 18; hence not 61 divides 7643 by NAT_4:9;
7643 = 67*114 + 5; hence not 67 divides 7643 by NAT_4:9;
7643 = 71*107 + 46; hence not 71 divides 7643 by NAT_4:9;
7643 = 73*104 + 51; hence not 73 divides 7643 by NAT_4:9;
7643 = 79*96 + 59; hence not 79 divides 7643 by NAT_4:9;
7643 = 83*92 + 7; hence not 83 divides 7643 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7643 & n is prime
holds not n divides 7643 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7649 is prime
proof
now
7649 = 2*3824 + 1; hence not 2 divides 7649 by NAT_4:9;
7649 = 3*2549 + 2; hence not 3 divides 7649 by NAT_4:9;
7649 = 5*1529 + 4; hence not 5 divides 7649 by NAT_4:9;
7649 = 7*1092 + 5; hence not 7 divides 7649 by NAT_4:9;
7649 = 11*695 + 4; hence not 11 divides 7649 by NAT_4:9;
7649 = 13*588 + 5; hence not 13 divides 7649 by NAT_4:9;
7649 = 17*449 + 16; hence not 17 divides 7649 by NAT_4:9;
7649 = 19*402 + 11; hence not 19 divides 7649 by NAT_4:9;
7649 = 23*332 + 13; hence not 23 divides 7649 by NAT_4:9;
7649 = 29*263 + 22; hence not 29 divides 7649 by NAT_4:9;
7649 = 31*246 + 23; hence not 31 divides 7649 by NAT_4:9;
7649 = 37*206 + 27; hence not 37 divides 7649 by NAT_4:9;
7649 = 41*186 + 23; hence not 41 divides 7649 by NAT_4:9;
7649 = 43*177 + 38; hence not 43 divides 7649 by NAT_4:9;
7649 = 47*162 + 35; hence not 47 divides 7649 by NAT_4:9;
7649 = 53*144 + 17; hence not 53 divides 7649 by NAT_4:9;
7649 = 59*129 + 38; hence not 59 divides 7649 by NAT_4:9;
7649 = 61*125 + 24; hence not 61 divides 7649 by NAT_4:9;
7649 = 67*114 + 11; hence not 67 divides 7649 by NAT_4:9;
7649 = 71*107 + 52; hence not 71 divides 7649 by NAT_4:9;
7649 = 73*104 + 57; hence not 73 divides 7649 by NAT_4:9;
7649 = 79*96 + 65; hence not 79 divides 7649 by NAT_4:9;
7649 = 83*92 + 13; hence not 83 divides 7649 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7649 & n is prime
holds not n divides 7649 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
7669 is prime
proof
now
7669 = 2*3834 + 1; hence not 2 divides 7669 by NAT_4:9;
7669 = 3*2556 + 1; hence not 3 divides 7669 by NAT_4:9;
7669 = 5*1533 + 4; hence not 5 divides 7669 by NAT_4:9;
7669 = 7*1095 + 4; hence not 7 divides 7669 by NAT_4:9;
7669 = 11*697 + 2; hence not 11 divides 7669 by NAT_4:9;
7669 = 13*589 + 12; hence not 13 divides 7669 by NAT_4:9;
7669 = 17*451 + 2; hence not 17 divides 7669 by NAT_4:9;
7669 = 19*403 + 12; hence not 19 divides 7669 by NAT_4:9;
7669 = 23*333 + 10; hence not 23 divides 7669 by NAT_4:9;
7669 = 29*264 + 13; hence not 29 divides 7669 by NAT_4:9;
7669 = 31*247 + 12; hence not 31 divides 7669 by NAT_4:9;
7669 = 37*207 + 10; hence not 37 divides 7669 by NAT_4:9;
7669 = 41*187 + 2; hence not 41 divides 7669 by NAT_4:9;
7669 = 43*178 + 15; hence not 43 divides 7669 by NAT_4:9;
7669 = 47*163 + 8; hence not 47 divides 7669 by NAT_4:9;
7669 = 53*144 + 37; hence not 53 divides 7669 by NAT_4:9;
7669 = 59*129 + 58; hence not 59 divides 7669 by NAT_4:9;
7669 = 61*125 + 44; hence not 61 divides 7669 by NAT_4:9;
7669 = 67*114 + 31; hence not 67 divides 7669 by NAT_4:9;
7669 = 71*108 + 1; hence not 71 divides 7669 by NAT_4:9;
7669 = 73*105 + 4; hence not 73 divides 7669 by NAT_4:9;
7669 = 79*97 + 6; hence not 79 divides 7669 by NAT_4:9;
7669 = 83*92 + 33; hence not 83 divides 7669 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7669 & n is prime
holds not n divides 7669 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7673 is prime
proof
now
7673 = 2*3836 + 1; hence not 2 divides 7673 by NAT_4:9;
7673 = 3*2557 + 2; hence not 3 divides 7673 by NAT_4:9;
7673 = 5*1534 + 3; hence not 5 divides 7673 by NAT_4:9;
7673 = 7*1096 + 1; hence not 7 divides 7673 by NAT_4:9;
7673 = 11*697 + 6; hence not 11 divides 7673 by NAT_4:9;
7673 = 13*590 + 3; hence not 13 divides 7673 by NAT_4:9;
7673 = 17*451 + 6; hence not 17 divides 7673 by NAT_4:9;
7673 = 19*403 + 16; hence not 19 divides 7673 by NAT_4:9;
7673 = 23*333 + 14; hence not 23 divides 7673 by NAT_4:9;
7673 = 29*264 + 17; hence not 29 divides 7673 by NAT_4:9;
7673 = 31*247 + 16; hence not 31 divides 7673 by NAT_4:9;
7673 = 37*207 + 14; hence not 37 divides 7673 by NAT_4:9;
7673 = 41*187 + 6; hence not 41 divides 7673 by NAT_4:9;
7673 = 43*178 + 19; hence not 43 divides 7673 by NAT_4:9;
7673 = 47*163 + 12; hence not 47 divides 7673 by NAT_4:9;
7673 = 53*144 + 41; hence not 53 divides 7673 by NAT_4:9;
7673 = 59*130 + 3; hence not 59 divides 7673 by NAT_4:9;
7673 = 61*125 + 48; hence not 61 divides 7673 by NAT_4:9;
7673 = 67*114 + 35; hence not 67 divides 7673 by NAT_4:9;
7673 = 71*108 + 5; hence not 71 divides 7673 by NAT_4:9;
7673 = 73*105 + 8; hence not 73 divides 7673 by NAT_4:9;
7673 = 79*97 + 10; hence not 79 divides 7673 by NAT_4:9;
7673 = 83*92 + 37; hence not 83 divides 7673 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7673 & n is prime
holds not n divides 7673 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7681 is prime
proof
now
7681 = 2*3840 + 1; hence not 2 divides 7681 by NAT_4:9;
7681 = 3*2560 + 1; hence not 3 divides 7681 by NAT_4:9;
7681 = 5*1536 + 1; hence not 5 divides 7681 by NAT_4:9;
7681 = 7*1097 + 2; hence not 7 divides 7681 by NAT_4:9;
7681 = 11*698 + 3; hence not 11 divides 7681 by NAT_4:9;
7681 = 13*590 + 11; hence not 13 divides 7681 by NAT_4:9;
7681 = 17*451 + 14; hence not 17 divides 7681 by NAT_4:9;
7681 = 19*404 + 5; hence not 19 divides 7681 by NAT_4:9;
7681 = 23*333 + 22; hence not 23 divides 7681 by NAT_4:9;
7681 = 29*264 + 25; hence not 29 divides 7681 by NAT_4:9;
7681 = 31*247 + 24; hence not 31 divides 7681 by NAT_4:9;
7681 = 37*207 + 22; hence not 37 divides 7681 by NAT_4:9;
7681 = 41*187 + 14; hence not 41 divides 7681 by NAT_4:9;
7681 = 43*178 + 27; hence not 43 divides 7681 by NAT_4:9;
7681 = 47*163 + 20; hence not 47 divides 7681 by NAT_4:9;
7681 = 53*144 + 49; hence not 53 divides 7681 by NAT_4:9;
7681 = 59*130 + 11; hence not 59 divides 7681 by NAT_4:9;
7681 = 61*125 + 56; hence not 61 divides 7681 by NAT_4:9;
7681 = 67*114 + 43; hence not 67 divides 7681 by NAT_4:9;
7681 = 71*108 + 13; hence not 71 divides 7681 by NAT_4:9;
7681 = 73*105 + 16; hence not 73 divides 7681 by NAT_4:9;
7681 = 79*97 + 18; hence not 79 divides 7681 by NAT_4:9;
7681 = 83*92 + 45; hence not 83 divides 7681 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7681 & n is prime
holds not n divides 7681 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7687 is prime
proof
now
7687 = 2*3843 + 1; hence not 2 divides 7687 by NAT_4:9;
7687 = 3*2562 + 1; hence not 3 divides 7687 by NAT_4:9;
7687 = 5*1537 + 2; hence not 5 divides 7687 by NAT_4:9;
7687 = 7*1098 + 1; hence not 7 divides 7687 by NAT_4:9;
7687 = 11*698 + 9; hence not 11 divides 7687 by NAT_4:9;
7687 = 13*591 + 4; hence not 13 divides 7687 by NAT_4:9;
7687 = 17*452 + 3; hence not 17 divides 7687 by NAT_4:9;
7687 = 19*404 + 11; hence not 19 divides 7687 by NAT_4:9;
7687 = 23*334 + 5; hence not 23 divides 7687 by NAT_4:9;
7687 = 29*265 + 2; hence not 29 divides 7687 by NAT_4:9;
7687 = 31*247 + 30; hence not 31 divides 7687 by NAT_4:9;
7687 = 37*207 + 28; hence not 37 divides 7687 by NAT_4:9;
7687 = 41*187 + 20; hence not 41 divides 7687 by NAT_4:9;
7687 = 43*178 + 33; hence not 43 divides 7687 by NAT_4:9;
7687 = 47*163 + 26; hence not 47 divides 7687 by NAT_4:9;
7687 = 53*145 + 2; hence not 53 divides 7687 by NAT_4:9;
7687 = 59*130 + 17; hence not 59 divides 7687 by NAT_4:9;
7687 = 61*126 + 1; hence not 61 divides 7687 by NAT_4:9;
7687 = 67*114 + 49; hence not 67 divides 7687 by NAT_4:9;
7687 = 71*108 + 19; hence not 71 divides 7687 by NAT_4:9;
7687 = 73*105 + 22; hence not 73 divides 7687 by NAT_4:9;
7687 = 79*97 + 24; hence not 79 divides 7687 by NAT_4:9;
7687 = 83*92 + 51; hence not 83 divides 7687 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7687 & n is prime
holds not n divides 7687 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7691 is prime
proof
now
7691 = 2*3845 + 1; hence not 2 divides 7691 by NAT_4:9;
7691 = 3*2563 + 2; hence not 3 divides 7691 by NAT_4:9;
7691 = 5*1538 + 1; hence not 5 divides 7691 by NAT_4:9;
7691 = 7*1098 + 5; hence not 7 divides 7691 by NAT_4:9;
7691 = 11*699 + 2; hence not 11 divides 7691 by NAT_4:9;
7691 = 13*591 + 8; hence not 13 divides 7691 by NAT_4:9;
7691 = 17*452 + 7; hence not 17 divides 7691 by NAT_4:9;
7691 = 19*404 + 15; hence not 19 divides 7691 by NAT_4:9;
7691 = 23*334 + 9; hence not 23 divides 7691 by NAT_4:9;
7691 = 29*265 + 6; hence not 29 divides 7691 by NAT_4:9;
7691 = 31*248 + 3; hence not 31 divides 7691 by NAT_4:9;
7691 = 37*207 + 32; hence not 37 divides 7691 by NAT_4:9;
7691 = 41*187 + 24; hence not 41 divides 7691 by NAT_4:9;
7691 = 43*178 + 37; hence not 43 divides 7691 by NAT_4:9;
7691 = 47*163 + 30; hence not 47 divides 7691 by NAT_4:9;
7691 = 53*145 + 6; hence not 53 divides 7691 by NAT_4:9;
7691 = 59*130 + 21; hence not 59 divides 7691 by NAT_4:9;
7691 = 61*126 + 5; hence not 61 divides 7691 by NAT_4:9;
7691 = 67*114 + 53; hence not 67 divides 7691 by NAT_4:9;
7691 = 71*108 + 23; hence not 71 divides 7691 by NAT_4:9;
7691 = 73*105 + 26; hence not 73 divides 7691 by NAT_4:9;
7691 = 79*97 + 28; hence not 79 divides 7691 by NAT_4:9;
7691 = 83*92 + 55; hence not 83 divides 7691 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7691 & n is prime
holds not n divides 7691 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7699 is prime
proof
now
7699 = 2*3849 + 1; hence not 2 divides 7699 by NAT_4:9;
7699 = 3*2566 + 1; hence not 3 divides 7699 by NAT_4:9;
7699 = 5*1539 + 4; hence not 5 divides 7699 by NAT_4:9;
7699 = 7*1099 + 6; hence not 7 divides 7699 by NAT_4:9;
7699 = 11*699 + 10; hence not 11 divides 7699 by NAT_4:9;
7699 = 13*592 + 3; hence not 13 divides 7699 by NAT_4:9;
7699 = 17*452 + 15; hence not 17 divides 7699 by NAT_4:9;
7699 = 19*405 + 4; hence not 19 divides 7699 by NAT_4:9;
7699 = 23*334 + 17; hence not 23 divides 7699 by NAT_4:9;
7699 = 29*265 + 14; hence not 29 divides 7699 by NAT_4:9;
7699 = 31*248 + 11; hence not 31 divides 7699 by NAT_4:9;
7699 = 37*208 + 3; hence not 37 divides 7699 by NAT_4:9;
7699 = 41*187 + 32; hence not 41 divides 7699 by NAT_4:9;
7699 = 43*179 + 2; hence not 43 divides 7699 by NAT_4:9;
7699 = 47*163 + 38; hence not 47 divides 7699 by NAT_4:9;
7699 = 53*145 + 14; hence not 53 divides 7699 by NAT_4:9;
7699 = 59*130 + 29; hence not 59 divides 7699 by NAT_4:9;
7699 = 61*126 + 13; hence not 61 divides 7699 by NAT_4:9;
7699 = 67*114 + 61; hence not 67 divides 7699 by NAT_4:9;
7699 = 71*108 + 31; hence not 71 divides 7699 by NAT_4:9;
7699 = 73*105 + 34; hence not 73 divides 7699 by NAT_4:9;
7699 = 79*97 + 36; hence not 79 divides 7699 by NAT_4:9;
7699 = 83*92 + 63; hence not 83 divides 7699 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7699 & n is prime
holds not n divides 7699 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7703 is prime
proof
now
7703 = 2*3851 + 1; hence not 2 divides 7703 by NAT_4:9;
7703 = 3*2567 + 2; hence not 3 divides 7703 by NAT_4:9;
7703 = 5*1540 + 3; hence not 5 divides 7703 by NAT_4:9;
7703 = 7*1100 + 3; hence not 7 divides 7703 by NAT_4:9;
7703 = 11*700 + 3; hence not 11 divides 7703 by NAT_4:9;
7703 = 13*592 + 7; hence not 13 divides 7703 by NAT_4:9;
7703 = 17*453 + 2; hence not 17 divides 7703 by NAT_4:9;
7703 = 19*405 + 8; hence not 19 divides 7703 by NAT_4:9;
7703 = 23*334 + 21; hence not 23 divides 7703 by NAT_4:9;
7703 = 29*265 + 18; hence not 29 divides 7703 by NAT_4:9;
7703 = 31*248 + 15; hence not 31 divides 7703 by NAT_4:9;
7703 = 37*208 + 7; hence not 37 divides 7703 by NAT_4:9;
7703 = 41*187 + 36; hence not 41 divides 7703 by NAT_4:9;
7703 = 43*179 + 6; hence not 43 divides 7703 by NAT_4:9;
7703 = 47*163 + 42; hence not 47 divides 7703 by NAT_4:9;
7703 = 53*145 + 18; hence not 53 divides 7703 by NAT_4:9;
7703 = 59*130 + 33; hence not 59 divides 7703 by NAT_4:9;
7703 = 61*126 + 17; hence not 61 divides 7703 by NAT_4:9;
7703 = 67*114 + 65; hence not 67 divides 7703 by NAT_4:9;
7703 = 71*108 + 35; hence not 71 divides 7703 by NAT_4:9;
7703 = 73*105 + 38; hence not 73 divides 7703 by NAT_4:9;
7703 = 79*97 + 40; hence not 79 divides 7703 by NAT_4:9;
7703 = 83*92 + 67; hence not 83 divides 7703 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7703 & n is prime
holds not n divides 7703 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7717 is prime
proof
now
7717 = 2*3858 + 1; hence not 2 divides 7717 by NAT_4:9;
7717 = 3*2572 + 1; hence not 3 divides 7717 by NAT_4:9;
7717 = 5*1543 + 2; hence not 5 divides 7717 by NAT_4:9;
7717 = 7*1102 + 3; hence not 7 divides 7717 by NAT_4:9;
7717 = 11*701 + 6; hence not 11 divides 7717 by NAT_4:9;
7717 = 13*593 + 8; hence not 13 divides 7717 by NAT_4:9;
7717 = 17*453 + 16; hence not 17 divides 7717 by NAT_4:9;
7717 = 19*406 + 3; hence not 19 divides 7717 by NAT_4:9;
7717 = 23*335 + 12; hence not 23 divides 7717 by NAT_4:9;
7717 = 29*266 + 3; hence not 29 divides 7717 by NAT_4:9;
7717 = 31*248 + 29; hence not 31 divides 7717 by NAT_4:9;
7717 = 37*208 + 21; hence not 37 divides 7717 by NAT_4:9;
7717 = 41*188 + 9; hence not 41 divides 7717 by NAT_4:9;
7717 = 43*179 + 20; hence not 43 divides 7717 by NAT_4:9;
7717 = 47*164 + 9; hence not 47 divides 7717 by NAT_4:9;
7717 = 53*145 + 32; hence not 53 divides 7717 by NAT_4:9;
7717 = 59*130 + 47; hence not 59 divides 7717 by NAT_4:9;
7717 = 61*126 + 31; hence not 61 divides 7717 by NAT_4:9;
7717 = 67*115 + 12; hence not 67 divides 7717 by NAT_4:9;
7717 = 71*108 + 49; hence not 71 divides 7717 by NAT_4:9;
7717 = 73*105 + 52; hence not 73 divides 7717 by NAT_4:9;
7717 = 79*97 + 54; hence not 79 divides 7717 by NAT_4:9;
7717 = 83*92 + 81; hence not 83 divides 7717 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7717 & n is prime
holds not n divides 7717 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7723 is prime
proof
now
7723 = 2*3861 + 1; hence not 2 divides 7723 by NAT_4:9;
7723 = 3*2574 + 1; hence not 3 divides 7723 by NAT_4:9;
7723 = 5*1544 + 3; hence not 5 divides 7723 by NAT_4:9;
7723 = 7*1103 + 2; hence not 7 divides 7723 by NAT_4:9;
7723 = 11*702 + 1; hence not 11 divides 7723 by NAT_4:9;
7723 = 13*594 + 1; hence not 13 divides 7723 by NAT_4:9;
7723 = 17*454 + 5; hence not 17 divides 7723 by NAT_4:9;
7723 = 19*406 + 9; hence not 19 divides 7723 by NAT_4:9;
7723 = 23*335 + 18; hence not 23 divides 7723 by NAT_4:9;
7723 = 29*266 + 9; hence not 29 divides 7723 by NAT_4:9;
7723 = 31*249 + 4; hence not 31 divides 7723 by NAT_4:9;
7723 = 37*208 + 27; hence not 37 divides 7723 by NAT_4:9;
7723 = 41*188 + 15; hence not 41 divides 7723 by NAT_4:9;
7723 = 43*179 + 26; hence not 43 divides 7723 by NAT_4:9;
7723 = 47*164 + 15; hence not 47 divides 7723 by NAT_4:9;
7723 = 53*145 + 38; hence not 53 divides 7723 by NAT_4:9;
7723 = 59*130 + 53; hence not 59 divides 7723 by NAT_4:9;
7723 = 61*126 + 37; hence not 61 divides 7723 by NAT_4:9;
7723 = 67*115 + 18; hence not 67 divides 7723 by NAT_4:9;
7723 = 71*108 + 55; hence not 71 divides 7723 by NAT_4:9;
7723 = 73*105 + 58; hence not 73 divides 7723 by NAT_4:9;
7723 = 79*97 + 60; hence not 79 divides 7723 by NAT_4:9;
7723 = 83*93 + 4; hence not 83 divides 7723 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7723 & n is prime
holds not n divides 7723 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7727 is prime
proof
now
7727 = 2*3863 + 1; hence not 2 divides 7727 by NAT_4:9;
7727 = 3*2575 + 2; hence not 3 divides 7727 by NAT_4:9;
7727 = 5*1545 + 2; hence not 5 divides 7727 by NAT_4:9;
7727 = 7*1103 + 6; hence not 7 divides 7727 by NAT_4:9;
7727 = 11*702 + 5; hence not 11 divides 7727 by NAT_4:9;
7727 = 13*594 + 5; hence not 13 divides 7727 by NAT_4:9;
7727 = 17*454 + 9; hence not 17 divides 7727 by NAT_4:9;
7727 = 19*406 + 13; hence not 19 divides 7727 by NAT_4:9;
7727 = 23*335 + 22; hence not 23 divides 7727 by NAT_4:9;
7727 = 29*266 + 13; hence not 29 divides 7727 by NAT_4:9;
7727 = 31*249 + 8; hence not 31 divides 7727 by NAT_4:9;
7727 = 37*208 + 31; hence not 37 divides 7727 by NAT_4:9;
7727 = 41*188 + 19; hence not 41 divides 7727 by NAT_4:9;
7727 = 43*179 + 30; hence not 43 divides 7727 by NAT_4:9;
7727 = 47*164 + 19; hence not 47 divides 7727 by NAT_4:9;
7727 = 53*145 + 42; hence not 53 divides 7727 by NAT_4:9;
7727 = 59*130 + 57; hence not 59 divides 7727 by NAT_4:9;
7727 = 61*126 + 41; hence not 61 divides 7727 by NAT_4:9;
7727 = 67*115 + 22; hence not 67 divides 7727 by NAT_4:9;
7727 = 71*108 + 59; hence not 71 divides 7727 by NAT_4:9;
7727 = 73*105 + 62; hence not 73 divides 7727 by NAT_4:9;
7727 = 79*97 + 64; hence not 79 divides 7727 by NAT_4:9;
7727 = 83*93 + 8; hence not 83 divides 7727 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7727 & n is prime
holds not n divides 7727 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7741 is prime
proof
now
7741 = 2*3870 + 1; hence not 2 divides 7741 by NAT_4:9;
7741 = 3*2580 + 1; hence not 3 divides 7741 by NAT_4:9;
7741 = 5*1548 + 1; hence not 5 divides 7741 by NAT_4:9;
7741 = 7*1105 + 6; hence not 7 divides 7741 by NAT_4:9;
7741 = 11*703 + 8; hence not 11 divides 7741 by NAT_4:9;
7741 = 13*595 + 6; hence not 13 divides 7741 by NAT_4:9;
7741 = 17*455 + 6; hence not 17 divides 7741 by NAT_4:9;
7741 = 19*407 + 8; hence not 19 divides 7741 by NAT_4:9;
7741 = 23*336 + 13; hence not 23 divides 7741 by NAT_4:9;
7741 = 29*266 + 27; hence not 29 divides 7741 by NAT_4:9;
7741 = 31*249 + 22; hence not 31 divides 7741 by NAT_4:9;
7741 = 37*209 + 8; hence not 37 divides 7741 by NAT_4:9;
7741 = 41*188 + 33; hence not 41 divides 7741 by NAT_4:9;
7741 = 43*180 + 1; hence not 43 divides 7741 by NAT_4:9;
7741 = 47*164 + 33; hence not 47 divides 7741 by NAT_4:9;
7741 = 53*146 + 3; hence not 53 divides 7741 by NAT_4:9;
7741 = 59*131 + 12; hence not 59 divides 7741 by NAT_4:9;
7741 = 61*126 + 55; hence not 61 divides 7741 by NAT_4:9;
7741 = 67*115 + 36; hence not 67 divides 7741 by NAT_4:9;
7741 = 71*109 + 2; hence not 71 divides 7741 by NAT_4:9;
7741 = 73*106 + 3; hence not 73 divides 7741 by NAT_4:9;
7741 = 79*97 + 78; hence not 79 divides 7741 by NAT_4:9;
7741 = 83*93 + 22; hence not 83 divides 7741 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7741 & n is prime
holds not n divides 7741 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7753 is prime
proof
now
7753 = 2*3876 + 1; hence not 2 divides 7753 by NAT_4:9;
7753 = 3*2584 + 1; hence not 3 divides 7753 by NAT_4:9;
7753 = 5*1550 + 3; hence not 5 divides 7753 by NAT_4:9;
7753 = 7*1107 + 4; hence not 7 divides 7753 by NAT_4:9;
7753 = 11*704 + 9; hence not 11 divides 7753 by NAT_4:9;
7753 = 13*596 + 5; hence not 13 divides 7753 by NAT_4:9;
7753 = 17*456 + 1; hence not 17 divides 7753 by NAT_4:9;
7753 = 19*408 + 1; hence not 19 divides 7753 by NAT_4:9;
7753 = 23*337 + 2; hence not 23 divides 7753 by NAT_4:9;
7753 = 29*267 + 10; hence not 29 divides 7753 by NAT_4:9;
7753 = 31*250 + 3; hence not 31 divides 7753 by NAT_4:9;
7753 = 37*209 + 20; hence not 37 divides 7753 by NAT_4:9;
7753 = 41*189 + 4; hence not 41 divides 7753 by NAT_4:9;
7753 = 43*180 + 13; hence not 43 divides 7753 by NAT_4:9;
7753 = 47*164 + 45; hence not 47 divides 7753 by NAT_4:9;
7753 = 53*146 + 15; hence not 53 divides 7753 by NAT_4:9;
7753 = 59*131 + 24; hence not 59 divides 7753 by NAT_4:9;
7753 = 61*127 + 6; hence not 61 divides 7753 by NAT_4:9;
7753 = 67*115 + 48; hence not 67 divides 7753 by NAT_4:9;
7753 = 71*109 + 14; hence not 71 divides 7753 by NAT_4:9;
7753 = 73*106 + 15; hence not 73 divides 7753 by NAT_4:9;
7753 = 79*98 + 11; hence not 79 divides 7753 by NAT_4:9;
7753 = 83*93 + 34; hence not 83 divides 7753 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7753 & n is prime
holds not n divides 7753 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7757 is prime
proof
now
7757 = 2*3878 + 1; hence not 2 divides 7757 by NAT_4:9;
7757 = 3*2585 + 2; hence not 3 divides 7757 by NAT_4:9;
7757 = 5*1551 + 2; hence not 5 divides 7757 by NAT_4:9;
7757 = 7*1108 + 1; hence not 7 divides 7757 by NAT_4:9;
7757 = 11*705 + 2; hence not 11 divides 7757 by NAT_4:9;
7757 = 13*596 + 9; hence not 13 divides 7757 by NAT_4:9;
7757 = 17*456 + 5; hence not 17 divides 7757 by NAT_4:9;
7757 = 19*408 + 5; hence not 19 divides 7757 by NAT_4:9;
7757 = 23*337 + 6; hence not 23 divides 7757 by NAT_4:9;
7757 = 29*267 + 14; hence not 29 divides 7757 by NAT_4:9;
7757 = 31*250 + 7; hence not 31 divides 7757 by NAT_4:9;
7757 = 37*209 + 24; hence not 37 divides 7757 by NAT_4:9;
7757 = 41*189 + 8; hence not 41 divides 7757 by NAT_4:9;
7757 = 43*180 + 17; hence not 43 divides 7757 by NAT_4:9;
7757 = 47*165 + 2; hence not 47 divides 7757 by NAT_4:9;
7757 = 53*146 + 19; hence not 53 divides 7757 by NAT_4:9;
7757 = 59*131 + 28; hence not 59 divides 7757 by NAT_4:9;
7757 = 61*127 + 10; hence not 61 divides 7757 by NAT_4:9;
7757 = 67*115 + 52; hence not 67 divides 7757 by NAT_4:9;
7757 = 71*109 + 18; hence not 71 divides 7757 by NAT_4:9;
7757 = 73*106 + 19; hence not 73 divides 7757 by NAT_4:9;
7757 = 79*98 + 15; hence not 79 divides 7757 by NAT_4:9;
7757 = 83*93 + 38; hence not 83 divides 7757 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7757 & n is prime
holds not n divides 7757 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7759 is prime
proof
now
7759 = 2*3879 + 1; hence not 2 divides 7759 by NAT_4:9;
7759 = 3*2586 + 1; hence not 3 divides 7759 by NAT_4:9;
7759 = 5*1551 + 4; hence not 5 divides 7759 by NAT_4:9;
7759 = 7*1108 + 3; hence not 7 divides 7759 by NAT_4:9;
7759 = 11*705 + 4; hence not 11 divides 7759 by NAT_4:9;
7759 = 13*596 + 11; hence not 13 divides 7759 by NAT_4:9;
7759 = 17*456 + 7; hence not 17 divides 7759 by NAT_4:9;
7759 = 19*408 + 7; hence not 19 divides 7759 by NAT_4:9;
7759 = 23*337 + 8; hence not 23 divides 7759 by NAT_4:9;
7759 = 29*267 + 16; hence not 29 divides 7759 by NAT_4:9;
7759 = 31*250 + 9; hence not 31 divides 7759 by NAT_4:9;
7759 = 37*209 + 26; hence not 37 divides 7759 by NAT_4:9;
7759 = 41*189 + 10; hence not 41 divides 7759 by NAT_4:9;
7759 = 43*180 + 19; hence not 43 divides 7759 by NAT_4:9;
7759 = 47*165 + 4; hence not 47 divides 7759 by NAT_4:9;
7759 = 53*146 + 21; hence not 53 divides 7759 by NAT_4:9;
7759 = 59*131 + 30; hence not 59 divides 7759 by NAT_4:9;
7759 = 61*127 + 12; hence not 61 divides 7759 by NAT_4:9;
7759 = 67*115 + 54; hence not 67 divides 7759 by NAT_4:9;
7759 = 71*109 + 20; hence not 71 divides 7759 by NAT_4:9;
7759 = 73*106 + 21; hence not 73 divides 7759 by NAT_4:9;
7759 = 79*98 + 17; hence not 79 divides 7759 by NAT_4:9;
7759 = 83*93 + 40; hence not 83 divides 7759 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7759 & n is prime
holds not n divides 7759 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
7789 is prime
proof
now
7789 = 2*3894 + 1; hence not 2 divides 7789 by NAT_4:9;
7789 = 3*2596 + 1; hence not 3 divides 7789 by NAT_4:9;
7789 = 5*1557 + 4; hence not 5 divides 7789 by NAT_4:9;
7789 = 7*1112 + 5; hence not 7 divides 7789 by NAT_4:9;
7789 = 11*708 + 1; hence not 11 divides 7789 by NAT_4:9;
7789 = 13*599 + 2; hence not 13 divides 7789 by NAT_4:9;
7789 = 17*458 + 3; hence not 17 divides 7789 by NAT_4:9;
7789 = 19*409 + 18; hence not 19 divides 7789 by NAT_4:9;
7789 = 23*338 + 15; hence not 23 divides 7789 by NAT_4:9;
7789 = 29*268 + 17; hence not 29 divides 7789 by NAT_4:9;
7789 = 31*251 + 8; hence not 31 divides 7789 by NAT_4:9;
7789 = 37*210 + 19; hence not 37 divides 7789 by NAT_4:9;
7789 = 41*189 + 40; hence not 41 divides 7789 by NAT_4:9;
7789 = 43*181 + 6; hence not 43 divides 7789 by NAT_4:9;
7789 = 47*165 + 34; hence not 47 divides 7789 by NAT_4:9;
7789 = 53*146 + 51; hence not 53 divides 7789 by NAT_4:9;
7789 = 59*132 + 1; hence not 59 divides 7789 by NAT_4:9;
7789 = 61*127 + 42; hence not 61 divides 7789 by NAT_4:9;
7789 = 67*116 + 17; hence not 67 divides 7789 by NAT_4:9;
7789 = 71*109 + 50; hence not 71 divides 7789 by NAT_4:9;
7789 = 73*106 + 51; hence not 73 divides 7789 by NAT_4:9;
7789 = 79*98 + 47; hence not 79 divides 7789 by NAT_4:9;
7789 = 83*93 + 70; hence not 83 divides 7789 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7789 & n is prime
holds not n divides 7789 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7793 is prime
proof
now
7793 = 2*3896 + 1; hence not 2 divides 7793 by NAT_4:9;
7793 = 3*2597 + 2; hence not 3 divides 7793 by NAT_4:9;
7793 = 5*1558 + 3; hence not 5 divides 7793 by NAT_4:9;
7793 = 7*1113 + 2; hence not 7 divides 7793 by NAT_4:9;
7793 = 11*708 + 5; hence not 11 divides 7793 by NAT_4:9;
7793 = 13*599 + 6; hence not 13 divides 7793 by NAT_4:9;
7793 = 17*458 + 7; hence not 17 divides 7793 by NAT_4:9;
7793 = 19*410 + 3; hence not 19 divides 7793 by NAT_4:9;
7793 = 23*338 + 19; hence not 23 divides 7793 by NAT_4:9;
7793 = 29*268 + 21; hence not 29 divides 7793 by NAT_4:9;
7793 = 31*251 + 12; hence not 31 divides 7793 by NAT_4:9;
7793 = 37*210 + 23; hence not 37 divides 7793 by NAT_4:9;
7793 = 41*190 + 3; hence not 41 divides 7793 by NAT_4:9;
7793 = 43*181 + 10; hence not 43 divides 7793 by NAT_4:9;
7793 = 47*165 + 38; hence not 47 divides 7793 by NAT_4:9;
7793 = 53*147 + 2; hence not 53 divides 7793 by NAT_4:9;
7793 = 59*132 + 5; hence not 59 divides 7793 by NAT_4:9;
7793 = 61*127 + 46; hence not 61 divides 7793 by NAT_4:9;
7793 = 67*116 + 21; hence not 67 divides 7793 by NAT_4:9;
7793 = 71*109 + 54; hence not 71 divides 7793 by NAT_4:9;
7793 = 73*106 + 55; hence not 73 divides 7793 by NAT_4:9;
7793 = 79*98 + 51; hence not 79 divides 7793 by NAT_4:9;
7793 = 83*93 + 74; hence not 83 divides 7793 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7793 & n is prime
holds not n divides 7793 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
7817 is prime
proof
now
7817 = 2*3908 + 1; hence not 2 divides 7817 by NAT_4:9;
7817 = 3*2605 + 2; hence not 3 divides 7817 by NAT_4:9;
7817 = 5*1563 + 2; hence not 5 divides 7817 by NAT_4:9;
7817 = 7*1116 + 5; hence not 7 divides 7817 by NAT_4:9;
7817 = 11*710 + 7; hence not 11 divides 7817 by NAT_4:9;
7817 = 13*601 + 4; hence not 13 divides 7817 by NAT_4:9;
7817 = 17*459 + 14; hence not 17 divides 7817 by NAT_4:9;
7817 = 19*411 + 8; hence not 19 divides 7817 by NAT_4:9;
7817 = 23*339 + 20; hence not 23 divides 7817 by NAT_4:9;
7817 = 29*269 + 16; hence not 29 divides 7817 by NAT_4:9;
7817 = 31*252 + 5; hence not 31 divides 7817 by NAT_4:9;
7817 = 37*211 + 10; hence not 37 divides 7817 by NAT_4:9;
7817 = 41*190 + 27; hence not 41 divides 7817 by NAT_4:9;
7817 = 43*181 + 34; hence not 43 divides 7817 by NAT_4:9;
7817 = 47*166 + 15; hence not 47 divides 7817 by NAT_4:9;
7817 = 53*147 + 26; hence not 53 divides 7817 by NAT_4:9;
7817 = 59*132 + 29; hence not 59 divides 7817 by NAT_4:9;
7817 = 61*128 + 9; hence not 61 divides 7817 by NAT_4:9;
7817 = 67*116 + 45; hence not 67 divides 7817 by NAT_4:9;
7817 = 71*110 + 7; hence not 71 divides 7817 by NAT_4:9;
7817 = 73*107 + 6; hence not 73 divides 7817 by NAT_4:9;
7817 = 79*98 + 75; hence not 79 divides 7817 by NAT_4:9;
7817 = 83*94 + 15; hence not 83 divides 7817 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7817 & n is prime
holds not n divides 7817 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7823 is prime
proof
now
7823 = 2*3911 + 1; hence not 2 divides 7823 by NAT_4:9;
7823 = 3*2607 + 2; hence not 3 divides 7823 by NAT_4:9;
7823 = 5*1564 + 3; hence not 5 divides 7823 by NAT_4:9;
7823 = 7*1117 + 4; hence not 7 divides 7823 by NAT_4:9;
7823 = 11*711 + 2; hence not 11 divides 7823 by NAT_4:9;
7823 = 13*601 + 10; hence not 13 divides 7823 by NAT_4:9;
7823 = 17*460 + 3; hence not 17 divides 7823 by NAT_4:9;
7823 = 19*411 + 14; hence not 19 divides 7823 by NAT_4:9;
7823 = 23*340 + 3; hence not 23 divides 7823 by NAT_4:9;
7823 = 29*269 + 22; hence not 29 divides 7823 by NAT_4:9;
7823 = 31*252 + 11; hence not 31 divides 7823 by NAT_4:9;
7823 = 37*211 + 16; hence not 37 divides 7823 by NAT_4:9;
7823 = 41*190 + 33; hence not 41 divides 7823 by NAT_4:9;
7823 = 43*181 + 40; hence not 43 divides 7823 by NAT_4:9;
7823 = 47*166 + 21; hence not 47 divides 7823 by NAT_4:9;
7823 = 53*147 + 32; hence not 53 divides 7823 by NAT_4:9;
7823 = 59*132 + 35; hence not 59 divides 7823 by NAT_4:9;
7823 = 61*128 + 15; hence not 61 divides 7823 by NAT_4:9;
7823 = 67*116 + 51; hence not 67 divides 7823 by NAT_4:9;
7823 = 71*110 + 13; hence not 71 divides 7823 by NAT_4:9;
7823 = 73*107 + 12; hence not 73 divides 7823 by NAT_4:9;
7823 = 79*99 + 2; hence not 79 divides 7823 by NAT_4:9;
7823 = 83*94 + 21; hence not 83 divides 7823 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7823 & n is prime
holds not n divides 7823 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7829 is prime
proof
now
7829 = 2*3914 + 1; hence not 2 divides 7829 by NAT_4:9;
7829 = 3*2609 + 2; hence not 3 divides 7829 by NAT_4:9;
7829 = 5*1565 + 4; hence not 5 divides 7829 by NAT_4:9;
7829 = 7*1118 + 3; hence not 7 divides 7829 by NAT_4:9;
7829 = 11*711 + 8; hence not 11 divides 7829 by NAT_4:9;
7829 = 13*602 + 3; hence not 13 divides 7829 by NAT_4:9;
7829 = 17*460 + 9; hence not 17 divides 7829 by NAT_4:9;
7829 = 19*412 + 1; hence not 19 divides 7829 by NAT_4:9;
7829 = 23*340 + 9; hence not 23 divides 7829 by NAT_4:9;
7829 = 29*269 + 28; hence not 29 divides 7829 by NAT_4:9;
7829 = 31*252 + 17; hence not 31 divides 7829 by NAT_4:9;
7829 = 37*211 + 22; hence not 37 divides 7829 by NAT_4:9;
7829 = 41*190 + 39; hence not 41 divides 7829 by NAT_4:9;
7829 = 43*182 + 3; hence not 43 divides 7829 by NAT_4:9;
7829 = 47*166 + 27; hence not 47 divides 7829 by NAT_4:9;
7829 = 53*147 + 38; hence not 53 divides 7829 by NAT_4:9;
7829 = 59*132 + 41; hence not 59 divides 7829 by NAT_4:9;
7829 = 61*128 + 21; hence not 61 divides 7829 by NAT_4:9;
7829 = 67*116 + 57; hence not 67 divides 7829 by NAT_4:9;
7829 = 71*110 + 19; hence not 71 divides 7829 by NAT_4:9;
7829 = 73*107 + 18; hence not 73 divides 7829 by NAT_4:9;
7829 = 79*99 + 8; hence not 79 divides 7829 by NAT_4:9;
7829 = 83*94 + 27; hence not 83 divides 7829 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7829 & n is prime
holds not n divides 7829 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7841 is prime
proof
now
7841 = 2*3920 + 1; hence not 2 divides 7841 by NAT_4:9;
7841 = 3*2613 + 2; hence not 3 divides 7841 by NAT_4:9;
7841 = 5*1568 + 1; hence not 5 divides 7841 by NAT_4:9;
7841 = 7*1120 + 1; hence not 7 divides 7841 by NAT_4:9;
7841 = 11*712 + 9; hence not 11 divides 7841 by NAT_4:9;
7841 = 13*603 + 2; hence not 13 divides 7841 by NAT_4:9;
7841 = 17*461 + 4; hence not 17 divides 7841 by NAT_4:9;
7841 = 19*412 + 13; hence not 19 divides 7841 by NAT_4:9;
7841 = 23*340 + 21; hence not 23 divides 7841 by NAT_4:9;
7841 = 29*270 + 11; hence not 29 divides 7841 by NAT_4:9;
7841 = 31*252 + 29; hence not 31 divides 7841 by NAT_4:9;
7841 = 37*211 + 34; hence not 37 divides 7841 by NAT_4:9;
7841 = 41*191 + 10; hence not 41 divides 7841 by NAT_4:9;
7841 = 43*182 + 15; hence not 43 divides 7841 by NAT_4:9;
7841 = 47*166 + 39; hence not 47 divides 7841 by NAT_4:9;
7841 = 53*147 + 50; hence not 53 divides 7841 by NAT_4:9;
7841 = 59*132 + 53; hence not 59 divides 7841 by NAT_4:9;
7841 = 61*128 + 33; hence not 61 divides 7841 by NAT_4:9;
7841 = 67*117 + 2; hence not 67 divides 7841 by NAT_4:9;
7841 = 71*110 + 31; hence not 71 divides 7841 by NAT_4:9;
7841 = 73*107 + 30; hence not 73 divides 7841 by NAT_4:9;
7841 = 79*99 + 20; hence not 79 divides 7841 by NAT_4:9;
7841 = 83*94 + 39; hence not 83 divides 7841 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7841 & n is prime
holds not n divides 7841 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7853 is prime
proof
now
7853 = 2*3926 + 1; hence not 2 divides 7853 by NAT_4:9;
7853 = 3*2617 + 2; hence not 3 divides 7853 by NAT_4:9;
7853 = 5*1570 + 3; hence not 5 divides 7853 by NAT_4:9;
7853 = 7*1121 + 6; hence not 7 divides 7853 by NAT_4:9;
7853 = 11*713 + 10; hence not 11 divides 7853 by NAT_4:9;
7853 = 13*604 + 1; hence not 13 divides 7853 by NAT_4:9;
7853 = 17*461 + 16; hence not 17 divides 7853 by NAT_4:9;
7853 = 19*413 + 6; hence not 19 divides 7853 by NAT_4:9;
7853 = 23*341 + 10; hence not 23 divides 7853 by NAT_4:9;
7853 = 29*270 + 23; hence not 29 divides 7853 by NAT_4:9;
7853 = 31*253 + 10; hence not 31 divides 7853 by NAT_4:9;
7853 = 37*212 + 9; hence not 37 divides 7853 by NAT_4:9;
7853 = 41*191 + 22; hence not 41 divides 7853 by NAT_4:9;
7853 = 43*182 + 27; hence not 43 divides 7853 by NAT_4:9;
7853 = 47*167 + 4; hence not 47 divides 7853 by NAT_4:9;
7853 = 53*148 + 9; hence not 53 divides 7853 by NAT_4:9;
7853 = 59*133 + 6; hence not 59 divides 7853 by NAT_4:9;
7853 = 61*128 + 45; hence not 61 divides 7853 by NAT_4:9;
7853 = 67*117 + 14; hence not 67 divides 7853 by NAT_4:9;
7853 = 71*110 + 43; hence not 71 divides 7853 by NAT_4:9;
7853 = 73*107 + 42; hence not 73 divides 7853 by NAT_4:9;
7853 = 79*99 + 32; hence not 79 divides 7853 by NAT_4:9;
7853 = 83*94 + 51; hence not 83 divides 7853 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7853 & n is prime
holds not n divides 7853 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
7867 is prime
proof
now
7867 = 2*3933 + 1; hence not 2 divides 7867 by NAT_4:9;
7867 = 3*2622 + 1; hence not 3 divides 7867 by NAT_4:9;
7867 = 5*1573 + 2; hence not 5 divides 7867 by NAT_4:9;
7867 = 7*1123 + 6; hence not 7 divides 7867 by NAT_4:9;
7867 = 11*715 + 2; hence not 11 divides 7867 by NAT_4:9;
7867 = 13*605 + 2; hence not 13 divides 7867 by NAT_4:9;
7867 = 17*462 + 13; hence not 17 divides 7867 by NAT_4:9;
7867 = 19*414 + 1; hence not 19 divides 7867 by NAT_4:9;
7867 = 23*342 + 1; hence not 23 divides 7867 by NAT_4:9;
7867 = 29*271 + 8; hence not 29 divides 7867 by NAT_4:9;
7867 = 31*253 + 24; hence not 31 divides 7867 by NAT_4:9;
7867 = 37*212 + 23; hence not 37 divides 7867 by NAT_4:9;
7867 = 41*191 + 36; hence not 41 divides 7867 by NAT_4:9;
7867 = 43*182 + 41; hence not 43 divides 7867 by NAT_4:9;
7867 = 47*167 + 18; hence not 47 divides 7867 by NAT_4:9;
7867 = 53*148 + 23; hence not 53 divides 7867 by NAT_4:9;
7867 = 59*133 + 20; hence not 59 divides 7867 by NAT_4:9;
7867 = 61*128 + 59; hence not 61 divides 7867 by NAT_4:9;
7867 = 67*117 + 28; hence not 67 divides 7867 by NAT_4:9;
7867 = 71*110 + 57; hence not 71 divides 7867 by NAT_4:9;
7867 = 73*107 + 56; hence not 73 divides 7867 by NAT_4:9;
7867 = 79*99 + 46; hence not 79 divides 7867 by NAT_4:9;
7867 = 83*94 + 65; hence not 83 divides 7867 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7867 & n is prime
holds not n divides 7867 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7873 is prime
proof
now
7873 = 2*3936 + 1; hence not 2 divides 7873 by NAT_4:9;
7873 = 3*2624 + 1; hence not 3 divides 7873 by NAT_4:9;
7873 = 5*1574 + 3; hence not 5 divides 7873 by NAT_4:9;
7873 = 7*1124 + 5; hence not 7 divides 7873 by NAT_4:9;
7873 = 11*715 + 8; hence not 11 divides 7873 by NAT_4:9;
7873 = 13*605 + 8; hence not 13 divides 7873 by NAT_4:9;
7873 = 17*463 + 2; hence not 17 divides 7873 by NAT_4:9;
7873 = 19*414 + 7; hence not 19 divides 7873 by NAT_4:9;
7873 = 23*342 + 7; hence not 23 divides 7873 by NAT_4:9;
7873 = 29*271 + 14; hence not 29 divides 7873 by NAT_4:9;
7873 = 31*253 + 30; hence not 31 divides 7873 by NAT_4:9;
7873 = 37*212 + 29; hence not 37 divides 7873 by NAT_4:9;
7873 = 41*192 + 1; hence not 41 divides 7873 by NAT_4:9;
7873 = 43*183 + 4; hence not 43 divides 7873 by NAT_4:9;
7873 = 47*167 + 24; hence not 47 divides 7873 by NAT_4:9;
7873 = 53*148 + 29; hence not 53 divides 7873 by NAT_4:9;
7873 = 59*133 + 26; hence not 59 divides 7873 by NAT_4:9;
7873 = 61*129 + 4; hence not 61 divides 7873 by NAT_4:9;
7873 = 67*117 + 34; hence not 67 divides 7873 by NAT_4:9;
7873 = 71*110 + 63; hence not 71 divides 7873 by NAT_4:9;
7873 = 73*107 + 62; hence not 73 divides 7873 by NAT_4:9;
7873 = 79*99 + 52; hence not 79 divides 7873 by NAT_4:9;
7873 = 83*94 + 71; hence not 83 divides 7873 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7873 & n is prime
holds not n divides 7873 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7877 is prime
proof
now
7877 = 2*3938 + 1; hence not 2 divides 7877 by NAT_4:9;
7877 = 3*2625 + 2; hence not 3 divides 7877 by NAT_4:9;
7877 = 5*1575 + 2; hence not 5 divides 7877 by NAT_4:9;
7877 = 7*1125 + 2; hence not 7 divides 7877 by NAT_4:9;
7877 = 11*716 + 1; hence not 11 divides 7877 by NAT_4:9;
7877 = 13*605 + 12; hence not 13 divides 7877 by NAT_4:9;
7877 = 17*463 + 6; hence not 17 divides 7877 by NAT_4:9;
7877 = 19*414 + 11; hence not 19 divides 7877 by NAT_4:9;
7877 = 23*342 + 11; hence not 23 divides 7877 by NAT_4:9;
7877 = 29*271 + 18; hence not 29 divides 7877 by NAT_4:9;
7877 = 31*254 + 3; hence not 31 divides 7877 by NAT_4:9;
7877 = 37*212 + 33; hence not 37 divides 7877 by NAT_4:9;
7877 = 41*192 + 5; hence not 41 divides 7877 by NAT_4:9;
7877 = 43*183 + 8; hence not 43 divides 7877 by NAT_4:9;
7877 = 47*167 + 28; hence not 47 divides 7877 by NAT_4:9;
7877 = 53*148 + 33; hence not 53 divides 7877 by NAT_4:9;
7877 = 59*133 + 30; hence not 59 divides 7877 by NAT_4:9;
7877 = 61*129 + 8; hence not 61 divides 7877 by NAT_4:9;
7877 = 67*117 + 38; hence not 67 divides 7877 by NAT_4:9;
7877 = 71*110 + 67; hence not 71 divides 7877 by NAT_4:9;
7877 = 73*107 + 66; hence not 73 divides 7877 by NAT_4:9;
7877 = 79*99 + 56; hence not 79 divides 7877 by NAT_4:9;
7877 = 83*94 + 75; hence not 83 divides 7877 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7877 & n is prime
holds not n divides 7877 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7879 is prime
proof
now
7879 = 2*3939 + 1; hence not 2 divides 7879 by NAT_4:9;
7879 = 3*2626 + 1; hence not 3 divides 7879 by NAT_4:9;
7879 = 5*1575 + 4; hence not 5 divides 7879 by NAT_4:9;
7879 = 7*1125 + 4; hence not 7 divides 7879 by NAT_4:9;
7879 = 11*716 + 3; hence not 11 divides 7879 by NAT_4:9;
7879 = 13*606 + 1; hence not 13 divides 7879 by NAT_4:9;
7879 = 17*463 + 8; hence not 17 divides 7879 by NAT_4:9;
7879 = 19*414 + 13; hence not 19 divides 7879 by NAT_4:9;
7879 = 23*342 + 13; hence not 23 divides 7879 by NAT_4:9;
7879 = 29*271 + 20; hence not 29 divides 7879 by NAT_4:9;
7879 = 31*254 + 5; hence not 31 divides 7879 by NAT_4:9;
7879 = 37*212 + 35; hence not 37 divides 7879 by NAT_4:9;
7879 = 41*192 + 7; hence not 41 divides 7879 by NAT_4:9;
7879 = 43*183 + 10; hence not 43 divides 7879 by NAT_4:9;
7879 = 47*167 + 30; hence not 47 divides 7879 by NAT_4:9;
7879 = 53*148 + 35; hence not 53 divides 7879 by NAT_4:9;
7879 = 59*133 + 32; hence not 59 divides 7879 by NAT_4:9;
7879 = 61*129 + 10; hence not 61 divides 7879 by NAT_4:9;
7879 = 67*117 + 40; hence not 67 divides 7879 by NAT_4:9;
7879 = 71*110 + 69; hence not 71 divides 7879 by NAT_4:9;
7879 = 73*107 + 68; hence not 73 divides 7879 by NAT_4:9;
7879 = 79*99 + 58; hence not 79 divides 7879 by NAT_4:9;
7879 = 83*94 + 77; hence not 83 divides 7879 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7879 & n is prime
holds not n divides 7879 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7883 is prime
proof
now
7883 = 2*3941 + 1; hence not 2 divides 7883 by NAT_4:9;
7883 = 3*2627 + 2; hence not 3 divides 7883 by NAT_4:9;
7883 = 5*1576 + 3; hence not 5 divides 7883 by NAT_4:9;
7883 = 7*1126 + 1; hence not 7 divides 7883 by NAT_4:9;
7883 = 11*716 + 7; hence not 11 divides 7883 by NAT_4:9;
7883 = 13*606 + 5; hence not 13 divides 7883 by NAT_4:9;
7883 = 17*463 + 12; hence not 17 divides 7883 by NAT_4:9;
7883 = 19*414 + 17; hence not 19 divides 7883 by NAT_4:9;
7883 = 23*342 + 17; hence not 23 divides 7883 by NAT_4:9;
7883 = 29*271 + 24; hence not 29 divides 7883 by NAT_4:9;
7883 = 31*254 + 9; hence not 31 divides 7883 by NAT_4:9;
7883 = 37*213 + 2; hence not 37 divides 7883 by NAT_4:9;
7883 = 41*192 + 11; hence not 41 divides 7883 by NAT_4:9;
7883 = 43*183 + 14; hence not 43 divides 7883 by NAT_4:9;
7883 = 47*167 + 34; hence not 47 divides 7883 by NAT_4:9;
7883 = 53*148 + 39; hence not 53 divides 7883 by NAT_4:9;
7883 = 59*133 + 36; hence not 59 divides 7883 by NAT_4:9;
7883 = 61*129 + 14; hence not 61 divides 7883 by NAT_4:9;
7883 = 67*117 + 44; hence not 67 divides 7883 by NAT_4:9;
7883 = 71*111 + 2; hence not 71 divides 7883 by NAT_4:9;
7883 = 73*107 + 72; hence not 73 divides 7883 by NAT_4:9;
7883 = 79*99 + 62; hence not 79 divides 7883 by NAT_4:9;
7883 = 83*94 + 81; hence not 83 divides 7883 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7883 & n is prime
holds not n divides 7883 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
7901 is prime
proof
now
7901 = 2*3950 + 1; hence not 2 divides 7901 by NAT_4:9;
7901 = 3*2633 + 2; hence not 3 divides 7901 by NAT_4:9;
7901 = 5*1580 + 1; hence not 5 divides 7901 by NAT_4:9;
7901 = 7*1128 + 5; hence not 7 divides 7901 by NAT_4:9;
7901 = 11*718 + 3; hence not 11 divides 7901 by NAT_4:9;
7901 = 13*607 + 10; hence not 13 divides 7901 by NAT_4:9;
7901 = 17*464 + 13; hence not 17 divides 7901 by NAT_4:9;
7901 = 19*415 + 16; hence not 19 divides 7901 by NAT_4:9;
7901 = 23*343 + 12; hence not 23 divides 7901 by NAT_4:9;
7901 = 29*272 + 13; hence not 29 divides 7901 by NAT_4:9;
7901 = 31*254 + 27; hence not 31 divides 7901 by NAT_4:9;
7901 = 37*213 + 20; hence not 37 divides 7901 by NAT_4:9;
7901 = 41*192 + 29; hence not 41 divides 7901 by NAT_4:9;
7901 = 43*183 + 32; hence not 43 divides 7901 by NAT_4:9;
7901 = 47*168 + 5; hence not 47 divides 7901 by NAT_4:9;
7901 = 53*149 + 4; hence not 53 divides 7901 by NAT_4:9;
7901 = 59*133 + 54; hence not 59 divides 7901 by NAT_4:9;
7901 = 61*129 + 32; hence not 61 divides 7901 by NAT_4:9;
7901 = 67*117 + 62; hence not 67 divides 7901 by NAT_4:9;
7901 = 71*111 + 20; hence not 71 divides 7901 by NAT_4:9;
7901 = 73*108 + 17; hence not 73 divides 7901 by NAT_4:9;
7901 = 79*100 + 1; hence not 79 divides 7901 by NAT_4:9;
7901 = 83*95 + 16; hence not 83 divides 7901 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7901 & n is prime
holds not n divides 7901 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7907 is prime
proof
now
7907 = 2*3953 + 1; hence not 2 divides 7907 by NAT_4:9;
7907 = 3*2635 + 2; hence not 3 divides 7907 by NAT_4:9;
7907 = 5*1581 + 2; hence not 5 divides 7907 by NAT_4:9;
7907 = 7*1129 + 4; hence not 7 divides 7907 by NAT_4:9;
7907 = 11*718 + 9; hence not 11 divides 7907 by NAT_4:9;
7907 = 13*608 + 3; hence not 13 divides 7907 by NAT_4:9;
7907 = 17*465 + 2; hence not 17 divides 7907 by NAT_4:9;
7907 = 19*416 + 3; hence not 19 divides 7907 by NAT_4:9;
7907 = 23*343 + 18; hence not 23 divides 7907 by NAT_4:9;
7907 = 29*272 + 19; hence not 29 divides 7907 by NAT_4:9;
7907 = 31*255 + 2; hence not 31 divides 7907 by NAT_4:9;
7907 = 37*213 + 26; hence not 37 divides 7907 by NAT_4:9;
7907 = 41*192 + 35; hence not 41 divides 7907 by NAT_4:9;
7907 = 43*183 + 38; hence not 43 divides 7907 by NAT_4:9;
7907 = 47*168 + 11; hence not 47 divides 7907 by NAT_4:9;
7907 = 53*149 + 10; hence not 53 divides 7907 by NAT_4:9;
7907 = 59*134 + 1; hence not 59 divides 7907 by NAT_4:9;
7907 = 61*129 + 38; hence not 61 divides 7907 by NAT_4:9;
7907 = 67*118 + 1; hence not 67 divides 7907 by NAT_4:9;
7907 = 71*111 + 26; hence not 71 divides 7907 by NAT_4:9;
7907 = 73*108 + 23; hence not 73 divides 7907 by NAT_4:9;
7907 = 79*100 + 7; hence not 79 divides 7907 by NAT_4:9;
7907 = 83*95 + 22; hence not 83 divides 7907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7907 & n is prime
holds not n divides 7907 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7919 is prime
proof
now
7919 = 2*3959 + 1; hence not 2 divides 7919 by NAT_4:9;
7919 = 3*2639 + 2; hence not 3 divides 7919 by NAT_4:9;
7919 = 5*1583 + 4; hence not 5 divides 7919 by NAT_4:9;
7919 = 7*1131 + 2; hence not 7 divides 7919 by NAT_4:9;
7919 = 11*719 + 10; hence not 11 divides 7919 by NAT_4:9;
7919 = 13*609 + 2; hence not 13 divides 7919 by NAT_4:9;
7919 = 17*465 + 14; hence not 17 divides 7919 by NAT_4:9;
7919 = 19*416 + 15; hence not 19 divides 7919 by NAT_4:9;
7919 = 23*344 + 7; hence not 23 divides 7919 by NAT_4:9;
7919 = 29*273 + 2; hence not 29 divides 7919 by NAT_4:9;
7919 = 31*255 + 14; hence not 31 divides 7919 by NAT_4:9;
7919 = 37*214 + 1; hence not 37 divides 7919 by NAT_4:9;
7919 = 41*193 + 6; hence not 41 divides 7919 by NAT_4:9;
7919 = 43*184 + 7; hence not 43 divides 7919 by NAT_4:9;
7919 = 47*168 + 23; hence not 47 divides 7919 by NAT_4:9;
7919 = 53*149 + 22; hence not 53 divides 7919 by NAT_4:9;
7919 = 59*134 + 13; hence not 59 divides 7919 by NAT_4:9;
7919 = 61*129 + 50; hence not 61 divides 7919 by NAT_4:9;
7919 = 67*118 + 13; hence not 67 divides 7919 by NAT_4:9;
7919 = 71*111 + 38; hence not 71 divides 7919 by NAT_4:9;
7919 = 73*108 + 35; hence not 73 divides 7919 by NAT_4:9;
7919 = 79*100 + 19; hence not 79 divides 7919 by NAT_4:9;
7919 = 83*95 + 34; hence not 83 divides 7919 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7919 & n is prime
holds not n divides 7919 by XPRIMET1:46;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
7927 is prime
proof
now
7927 = 2*3963 + 1; hence not 2 divides 7927 by NAT_4:9;
7927 = 3*2642 + 1; hence not 3 divides 7927 by NAT_4:9;
7927 = 5*1585 + 2; hence not 5 divides 7927 by NAT_4:9;
7927 = 7*1132 + 3; hence not 7 divides 7927 by NAT_4:9;
7927 = 11*720 + 7; hence not 11 divides 7927 by NAT_4:9;
7927 = 13*609 + 10; hence not 13 divides 7927 by NAT_4:9;
7927 = 17*466 + 5; hence not 17 divides 7927 by NAT_4:9;
7927 = 19*417 + 4; hence not 19 divides 7927 by NAT_4:9;
7927 = 23*344 + 15; hence not 23 divides 7927 by NAT_4:9;
7927 = 29*273 + 10; hence not 29 divides 7927 by NAT_4:9;
7927 = 31*255 + 22; hence not 31 divides 7927 by NAT_4:9;
7927 = 37*214 + 9; hence not 37 divides 7927 by NAT_4:9;
7927 = 41*193 + 14; hence not 41 divides 7927 by NAT_4:9;
7927 = 43*184 + 15; hence not 43 divides 7927 by NAT_4:9;
7927 = 47*168 + 31; hence not 47 divides 7927 by NAT_4:9;
7927 = 53*149 + 30; hence not 53 divides 7927 by NAT_4:9;
7927 = 59*134 + 21; hence not 59 divides 7927 by NAT_4:9;
7927 = 61*129 + 58; hence not 61 divides 7927 by NAT_4:9;
7927 = 67*118 + 21; hence not 67 divides 7927 by NAT_4:9;
7927 = 71*111 + 46; hence not 71 divides 7927 by NAT_4:9;
7927 = 73*108 + 43; hence not 73 divides 7927 by NAT_4:9;
7927 = 79*100 + 27; hence not 79 divides 7927 by NAT_4:9;
7927 = 83*95 + 42; hence not 83 divides 7927 by NAT_4:9;
7927 = 89*89 + 6; hence not 89 divides 7927 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7927 & n is prime
holds not n divides 7927 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
7933 is prime
proof
now
7933 = 2*3966 + 1; hence not 2 divides 7933 by NAT_4:9;
7933 = 3*2644 + 1; hence not 3 divides 7933 by NAT_4:9;
7933 = 5*1586 + 3; hence not 5 divides 7933 by NAT_4:9;
7933 = 7*1133 + 2; hence not 7 divides 7933 by NAT_4:9;
7933 = 11*721 + 2; hence not 11 divides 7933 by NAT_4:9;
7933 = 13*610 + 3; hence not 13 divides 7933 by NAT_4:9;
7933 = 17*466 + 11; hence not 17 divides 7933 by NAT_4:9;
7933 = 19*417 + 10; hence not 19 divides 7933 by NAT_4:9;
7933 = 23*344 + 21; hence not 23 divides 7933 by NAT_4:9;
7933 = 29*273 + 16; hence not 29 divides 7933 by NAT_4:9;
7933 = 31*255 + 28; hence not 31 divides 7933 by NAT_4:9;
7933 = 37*214 + 15; hence not 37 divides 7933 by NAT_4:9;
7933 = 41*193 + 20; hence not 41 divides 7933 by NAT_4:9;
7933 = 43*184 + 21; hence not 43 divides 7933 by NAT_4:9;
7933 = 47*168 + 37; hence not 47 divides 7933 by NAT_4:9;
7933 = 53*149 + 36; hence not 53 divides 7933 by NAT_4:9;
7933 = 59*134 + 27; hence not 59 divides 7933 by NAT_4:9;
7933 = 61*130 + 3; hence not 61 divides 7933 by NAT_4:9;
7933 = 67*118 + 27; hence not 67 divides 7933 by NAT_4:9;
7933 = 71*111 + 52; hence not 71 divides 7933 by NAT_4:9;
7933 = 73*108 + 49; hence not 73 divides 7933 by NAT_4:9;
7933 = 79*100 + 33; hence not 79 divides 7933 by NAT_4:9;
7933 = 83*95 + 48; hence not 83 divides 7933 by NAT_4:9;
7933 = 89*89 + 12; hence not 89 divides 7933 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7933 & n is prime
holds not n divides 7933 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
7937 is prime
proof
now
7937 = 2*3968 + 1; hence not 2 divides 7937 by NAT_4:9;
7937 = 3*2645 + 2; hence not 3 divides 7937 by NAT_4:9;
7937 = 5*1587 + 2; hence not 5 divides 7937 by NAT_4:9;
7937 = 7*1133 + 6; hence not 7 divides 7937 by NAT_4:9;
7937 = 11*721 + 6; hence not 11 divides 7937 by NAT_4:9;
7937 = 13*610 + 7; hence not 13 divides 7937 by NAT_4:9;
7937 = 17*466 + 15; hence not 17 divides 7937 by NAT_4:9;
7937 = 19*417 + 14; hence not 19 divides 7937 by NAT_4:9;
7937 = 23*345 + 2; hence not 23 divides 7937 by NAT_4:9;
7937 = 29*273 + 20; hence not 29 divides 7937 by NAT_4:9;
7937 = 31*256 + 1; hence not 31 divides 7937 by NAT_4:9;
7937 = 37*214 + 19; hence not 37 divides 7937 by NAT_4:9;
7937 = 41*193 + 24; hence not 41 divides 7937 by NAT_4:9;
7937 = 43*184 + 25; hence not 43 divides 7937 by NAT_4:9;
7937 = 47*168 + 41; hence not 47 divides 7937 by NAT_4:9;
7937 = 53*149 + 40; hence not 53 divides 7937 by NAT_4:9;
7937 = 59*134 + 31; hence not 59 divides 7937 by NAT_4:9;
7937 = 61*130 + 7; hence not 61 divides 7937 by NAT_4:9;
7937 = 67*118 + 31; hence not 67 divides 7937 by NAT_4:9;
7937 = 71*111 + 56; hence not 71 divides 7937 by NAT_4:9;
7937 = 73*108 + 53; hence not 73 divides 7937 by NAT_4:9;
7937 = 79*100 + 37; hence not 79 divides 7937 by NAT_4:9;
7937 = 83*95 + 52; hence not 83 divides 7937 by NAT_4:9;
7937 = 89*89 + 16; hence not 89 divides 7937 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7937 & n is prime
holds not n divides 7937 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7949 is prime
proof
now
7949 = 2*3974 + 1; hence not 2 divides 7949 by NAT_4:9;
7949 = 3*2649 + 2; hence not 3 divides 7949 by NAT_4:9;
7949 = 5*1589 + 4; hence not 5 divides 7949 by NAT_4:9;
7949 = 7*1135 + 4; hence not 7 divides 7949 by NAT_4:9;
7949 = 11*722 + 7; hence not 11 divides 7949 by NAT_4:9;
7949 = 13*611 + 6; hence not 13 divides 7949 by NAT_4:9;
7949 = 17*467 + 10; hence not 17 divides 7949 by NAT_4:9;
7949 = 19*418 + 7; hence not 19 divides 7949 by NAT_4:9;
7949 = 23*345 + 14; hence not 23 divides 7949 by NAT_4:9;
7949 = 29*274 + 3; hence not 29 divides 7949 by NAT_4:9;
7949 = 31*256 + 13; hence not 31 divides 7949 by NAT_4:9;
7949 = 37*214 + 31; hence not 37 divides 7949 by NAT_4:9;
7949 = 41*193 + 36; hence not 41 divides 7949 by NAT_4:9;
7949 = 43*184 + 37; hence not 43 divides 7949 by NAT_4:9;
7949 = 47*169 + 6; hence not 47 divides 7949 by NAT_4:9;
7949 = 53*149 + 52; hence not 53 divides 7949 by NAT_4:9;
7949 = 59*134 + 43; hence not 59 divides 7949 by NAT_4:9;
7949 = 61*130 + 19; hence not 61 divides 7949 by NAT_4:9;
7949 = 67*118 + 43; hence not 67 divides 7949 by NAT_4:9;
7949 = 71*111 + 68; hence not 71 divides 7949 by NAT_4:9;
7949 = 73*108 + 65; hence not 73 divides 7949 by NAT_4:9;
7949 = 79*100 + 49; hence not 79 divides 7949 by NAT_4:9;
7949 = 83*95 + 64; hence not 83 divides 7949 by NAT_4:9;
7949 = 89*89 + 28; hence not 89 divides 7949 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7949 & n is prime
holds not n divides 7949 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
7951 is prime
proof
now
7951 = 2*3975 + 1; hence not 2 divides 7951 by NAT_4:9;
7951 = 3*2650 + 1; hence not 3 divides 7951 by NAT_4:9;
7951 = 5*1590 + 1; hence not 5 divides 7951 by NAT_4:9;
7951 = 7*1135 + 6; hence not 7 divides 7951 by NAT_4:9;
7951 = 11*722 + 9; hence not 11 divides 7951 by NAT_4:9;
7951 = 13*611 + 8; hence not 13 divides 7951 by NAT_4:9;
7951 = 17*467 + 12; hence not 17 divides 7951 by NAT_4:9;
7951 = 19*418 + 9; hence not 19 divides 7951 by NAT_4:9;
7951 = 23*345 + 16; hence not 23 divides 7951 by NAT_4:9;
7951 = 29*274 + 5; hence not 29 divides 7951 by NAT_4:9;
7951 = 31*256 + 15; hence not 31 divides 7951 by NAT_4:9;
7951 = 37*214 + 33; hence not 37 divides 7951 by NAT_4:9;
7951 = 41*193 + 38; hence not 41 divides 7951 by NAT_4:9;
7951 = 43*184 + 39; hence not 43 divides 7951 by NAT_4:9;
7951 = 47*169 + 8; hence not 47 divides 7951 by NAT_4:9;
7951 = 53*150 + 1; hence not 53 divides 7951 by NAT_4:9;
7951 = 59*134 + 45; hence not 59 divides 7951 by NAT_4:9;
7951 = 61*130 + 21; hence not 61 divides 7951 by NAT_4:9;
7951 = 67*118 + 45; hence not 67 divides 7951 by NAT_4:9;
7951 = 71*111 + 70; hence not 71 divides 7951 by NAT_4:9;
7951 = 73*108 + 67; hence not 73 divides 7951 by NAT_4:9;
7951 = 79*100 + 51; hence not 79 divides 7951 by NAT_4:9;
7951 = 83*95 + 66; hence not 83 divides 7951 by NAT_4:9;
7951 = 89*89 + 30; hence not 89 divides 7951 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7951 & n is prime
holds not n divides 7951 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
7963 is prime
proof
now
7963 = 2*3981 + 1; hence not 2 divides 7963 by NAT_4:9;
7963 = 3*2654 + 1; hence not 3 divides 7963 by NAT_4:9;
7963 = 5*1592 + 3; hence not 5 divides 7963 by NAT_4:9;
7963 = 7*1137 + 4; hence not 7 divides 7963 by NAT_4:9;
7963 = 11*723 + 10; hence not 11 divides 7963 by NAT_4:9;
7963 = 13*612 + 7; hence not 13 divides 7963 by NAT_4:9;
7963 = 17*468 + 7; hence not 17 divides 7963 by NAT_4:9;
7963 = 19*419 + 2; hence not 19 divides 7963 by NAT_4:9;
7963 = 23*346 + 5; hence not 23 divides 7963 by NAT_4:9;
7963 = 29*274 + 17; hence not 29 divides 7963 by NAT_4:9;
7963 = 31*256 + 27; hence not 31 divides 7963 by NAT_4:9;
7963 = 37*215 + 8; hence not 37 divides 7963 by NAT_4:9;
7963 = 41*194 + 9; hence not 41 divides 7963 by NAT_4:9;
7963 = 43*185 + 8; hence not 43 divides 7963 by NAT_4:9;
7963 = 47*169 + 20; hence not 47 divides 7963 by NAT_4:9;
7963 = 53*150 + 13; hence not 53 divides 7963 by NAT_4:9;
7963 = 59*134 + 57; hence not 59 divides 7963 by NAT_4:9;
7963 = 61*130 + 33; hence not 61 divides 7963 by NAT_4:9;
7963 = 67*118 + 57; hence not 67 divides 7963 by NAT_4:9;
7963 = 71*112 + 11; hence not 71 divides 7963 by NAT_4:9;
7963 = 73*109 + 6; hence not 73 divides 7963 by NAT_4:9;
7963 = 79*100 + 63; hence not 79 divides 7963 by NAT_4:9;
7963 = 83*95 + 78; hence not 83 divides 7963 by NAT_4:9;
7963 = 89*89 + 42; hence not 89 divides 7963 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7963 & n is prime
holds not n divides 7963 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
7993 is prime
proof
now
7993 = 2*3996 + 1; hence not 2 divides 7993 by NAT_4:9;
7993 = 3*2664 + 1; hence not 3 divides 7993 by NAT_4:9;
7993 = 5*1598 + 3; hence not 5 divides 7993 by NAT_4:9;
7993 = 7*1141 + 6; hence not 7 divides 7993 by NAT_4:9;
7993 = 11*726 + 7; hence not 11 divides 7993 by NAT_4:9;
7993 = 13*614 + 11; hence not 13 divides 7993 by NAT_4:9;
7993 = 17*470 + 3; hence not 17 divides 7993 by NAT_4:9;
7993 = 19*420 + 13; hence not 19 divides 7993 by NAT_4:9;
7993 = 23*347 + 12; hence not 23 divides 7993 by NAT_4:9;
7993 = 29*275 + 18; hence not 29 divides 7993 by NAT_4:9;
7993 = 31*257 + 26; hence not 31 divides 7993 by NAT_4:9;
7993 = 37*216 + 1; hence not 37 divides 7993 by NAT_4:9;
7993 = 41*194 + 39; hence not 41 divides 7993 by NAT_4:9;
7993 = 43*185 + 38; hence not 43 divides 7993 by NAT_4:9;
7993 = 47*170 + 3; hence not 47 divides 7993 by NAT_4:9;
7993 = 53*150 + 43; hence not 53 divides 7993 by NAT_4:9;
7993 = 59*135 + 28; hence not 59 divides 7993 by NAT_4:9;
7993 = 61*131 + 2; hence not 61 divides 7993 by NAT_4:9;
7993 = 67*119 + 20; hence not 67 divides 7993 by NAT_4:9;
7993 = 71*112 + 41; hence not 71 divides 7993 by NAT_4:9;
7993 = 73*109 + 36; hence not 73 divides 7993 by NAT_4:9;
7993 = 79*101 + 14; hence not 79 divides 7993 by NAT_4:9;
7993 = 83*96 + 25; hence not 83 divides 7993 by NAT_4:9;
7993 = 89*89 + 72; hence not 89 divides 7993 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 7993 & n is prime
holds not n divides 7993 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
8009 is prime
proof
now
8009 = 2*4004 + 1; hence not 2 divides 8009 by NAT_4:9;
8009 = 3*2669 + 2; hence not 3 divides 8009 by NAT_4:9;
8009 = 5*1601 + 4; hence not 5 divides 8009 by NAT_4:9;
8009 = 7*1144 + 1; hence not 7 divides 8009 by NAT_4:9;
8009 = 11*728 + 1; hence not 11 divides 8009 by NAT_4:9;
8009 = 13*616 + 1; hence not 13 divides 8009 by NAT_4:9;
8009 = 17*471 + 2; hence not 17 divides 8009 by NAT_4:9;
8009 = 19*421 + 10; hence not 19 divides 8009 by NAT_4:9;
8009 = 23*348 + 5; hence not 23 divides 8009 by NAT_4:9;
8009 = 29*276 + 5; hence not 29 divides 8009 by NAT_4:9;
8009 = 31*258 + 11; hence not 31 divides 8009 by NAT_4:9;
8009 = 37*216 + 17; hence not 37 divides 8009 by NAT_4:9;
8009 = 41*195 + 14; hence not 41 divides 8009 by NAT_4:9;
8009 = 43*186 + 11; hence not 43 divides 8009 by NAT_4:9;
8009 = 47*170 + 19; hence not 47 divides 8009 by NAT_4:9;
8009 = 53*151 + 6; hence not 53 divides 8009 by NAT_4:9;
8009 = 59*135 + 44; hence not 59 divides 8009 by NAT_4:9;
8009 = 61*131 + 18; hence not 61 divides 8009 by NAT_4:9;
8009 = 67*119 + 36; hence not 67 divides 8009 by NAT_4:9;
8009 = 71*112 + 57; hence not 71 divides 8009 by NAT_4:9;
8009 = 73*109 + 52; hence not 73 divides 8009 by NAT_4:9;
8009 = 79*101 + 30; hence not 79 divides 8009 by NAT_4:9;
8009 = 83*96 + 41; hence not 83 divides 8009 by NAT_4:9;
8009 = 89*89 + 88; hence not 89 divides 8009 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8009 & n is prime
holds not n divides 8009 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8011 is prime
proof
now
8011 = 2*4005 + 1; hence not 2 divides 8011 by NAT_4:9;
8011 = 3*2670 + 1; hence not 3 divides 8011 by NAT_4:9;
8011 = 5*1602 + 1; hence not 5 divides 8011 by NAT_4:9;
8011 = 7*1144 + 3; hence not 7 divides 8011 by NAT_4:9;
8011 = 11*728 + 3; hence not 11 divides 8011 by NAT_4:9;
8011 = 13*616 + 3; hence not 13 divides 8011 by NAT_4:9;
8011 = 17*471 + 4; hence not 17 divides 8011 by NAT_4:9;
8011 = 19*421 + 12; hence not 19 divides 8011 by NAT_4:9;
8011 = 23*348 + 7; hence not 23 divides 8011 by NAT_4:9;
8011 = 29*276 + 7; hence not 29 divides 8011 by NAT_4:9;
8011 = 31*258 + 13; hence not 31 divides 8011 by NAT_4:9;
8011 = 37*216 + 19; hence not 37 divides 8011 by NAT_4:9;
8011 = 41*195 + 16; hence not 41 divides 8011 by NAT_4:9;
8011 = 43*186 + 13; hence not 43 divides 8011 by NAT_4:9;
8011 = 47*170 + 21; hence not 47 divides 8011 by NAT_4:9;
8011 = 53*151 + 8; hence not 53 divides 8011 by NAT_4:9;
8011 = 59*135 + 46; hence not 59 divides 8011 by NAT_4:9;
8011 = 61*131 + 20; hence not 61 divides 8011 by NAT_4:9;
8011 = 67*119 + 38; hence not 67 divides 8011 by NAT_4:9;
8011 = 71*112 + 59; hence not 71 divides 8011 by NAT_4:9;
8011 = 73*109 + 54; hence not 73 divides 8011 by NAT_4:9;
8011 = 79*101 + 32; hence not 79 divides 8011 by NAT_4:9;
8011 = 83*96 + 43; hence not 83 divides 8011 by NAT_4:9;
8011 = 89*90 + 1; hence not 89 divides 8011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8011 & n is prime
holds not n divides 8011 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8017 is prime
proof
now
8017 = 2*4008 + 1; hence not 2 divides 8017 by NAT_4:9;
8017 = 3*2672 + 1; hence not 3 divides 8017 by NAT_4:9;
8017 = 5*1603 + 2; hence not 5 divides 8017 by NAT_4:9;
8017 = 7*1145 + 2; hence not 7 divides 8017 by NAT_4:9;
8017 = 11*728 + 9; hence not 11 divides 8017 by NAT_4:9;
8017 = 13*616 + 9; hence not 13 divides 8017 by NAT_4:9;
8017 = 17*471 + 10; hence not 17 divides 8017 by NAT_4:9;
8017 = 19*421 + 18; hence not 19 divides 8017 by NAT_4:9;
8017 = 23*348 + 13; hence not 23 divides 8017 by NAT_4:9;
8017 = 29*276 + 13; hence not 29 divides 8017 by NAT_4:9;
8017 = 31*258 + 19; hence not 31 divides 8017 by NAT_4:9;
8017 = 37*216 + 25; hence not 37 divides 8017 by NAT_4:9;
8017 = 41*195 + 22; hence not 41 divides 8017 by NAT_4:9;
8017 = 43*186 + 19; hence not 43 divides 8017 by NAT_4:9;
8017 = 47*170 + 27; hence not 47 divides 8017 by NAT_4:9;
8017 = 53*151 + 14; hence not 53 divides 8017 by NAT_4:9;
8017 = 59*135 + 52; hence not 59 divides 8017 by NAT_4:9;
8017 = 61*131 + 26; hence not 61 divides 8017 by NAT_4:9;
8017 = 67*119 + 44; hence not 67 divides 8017 by NAT_4:9;
8017 = 71*112 + 65; hence not 71 divides 8017 by NAT_4:9;
8017 = 73*109 + 60; hence not 73 divides 8017 by NAT_4:9;
8017 = 79*101 + 38; hence not 79 divides 8017 by NAT_4:9;
8017 = 83*96 + 49; hence not 83 divides 8017 by NAT_4:9;
8017 = 89*90 + 7; hence not 89 divides 8017 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8017 & n is prime
holds not n divides 8017 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
8039 is prime
proof
now
8039 = 2*4019 + 1; hence not 2 divides 8039 by NAT_4:9;
8039 = 3*2679 + 2; hence not 3 divides 8039 by NAT_4:9;
8039 = 5*1607 + 4; hence not 5 divides 8039 by NAT_4:9;
8039 = 7*1148 + 3; hence not 7 divides 8039 by NAT_4:9;
8039 = 11*730 + 9; hence not 11 divides 8039 by NAT_4:9;
8039 = 13*618 + 5; hence not 13 divides 8039 by NAT_4:9;
8039 = 17*472 + 15; hence not 17 divides 8039 by NAT_4:9;
8039 = 19*423 + 2; hence not 19 divides 8039 by NAT_4:9;
8039 = 23*349 + 12; hence not 23 divides 8039 by NAT_4:9;
8039 = 29*277 + 6; hence not 29 divides 8039 by NAT_4:9;
8039 = 31*259 + 10; hence not 31 divides 8039 by NAT_4:9;
8039 = 37*217 + 10; hence not 37 divides 8039 by NAT_4:9;
8039 = 41*196 + 3; hence not 41 divides 8039 by NAT_4:9;
8039 = 43*186 + 41; hence not 43 divides 8039 by NAT_4:9;
8039 = 47*171 + 2; hence not 47 divides 8039 by NAT_4:9;
8039 = 53*151 + 36; hence not 53 divides 8039 by NAT_4:9;
8039 = 59*136 + 15; hence not 59 divides 8039 by NAT_4:9;
8039 = 61*131 + 48; hence not 61 divides 8039 by NAT_4:9;
8039 = 67*119 + 66; hence not 67 divides 8039 by NAT_4:9;
8039 = 71*113 + 16; hence not 71 divides 8039 by NAT_4:9;
8039 = 73*110 + 9; hence not 73 divides 8039 by NAT_4:9;
8039 = 79*101 + 60; hence not 79 divides 8039 by NAT_4:9;
8039 = 83*96 + 71; hence not 83 divides 8039 by NAT_4:9;
8039 = 89*90 + 29; hence not 89 divides 8039 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8039 & n is prime
holds not n divides 8039 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8053 is prime
proof
now
8053 = 2*4026 + 1; hence not 2 divides 8053 by NAT_4:9;
8053 = 3*2684 + 1; hence not 3 divides 8053 by NAT_4:9;
8053 = 5*1610 + 3; hence not 5 divides 8053 by NAT_4:9;
8053 = 7*1150 + 3; hence not 7 divides 8053 by NAT_4:9;
8053 = 11*732 + 1; hence not 11 divides 8053 by NAT_4:9;
8053 = 13*619 + 6; hence not 13 divides 8053 by NAT_4:9;
8053 = 17*473 + 12; hence not 17 divides 8053 by NAT_4:9;
8053 = 19*423 + 16; hence not 19 divides 8053 by NAT_4:9;
8053 = 23*350 + 3; hence not 23 divides 8053 by NAT_4:9;
8053 = 29*277 + 20; hence not 29 divides 8053 by NAT_4:9;
8053 = 31*259 + 24; hence not 31 divides 8053 by NAT_4:9;
8053 = 37*217 + 24; hence not 37 divides 8053 by NAT_4:9;
8053 = 41*196 + 17; hence not 41 divides 8053 by NAT_4:9;
8053 = 43*187 + 12; hence not 43 divides 8053 by NAT_4:9;
8053 = 47*171 + 16; hence not 47 divides 8053 by NAT_4:9;
8053 = 53*151 + 50; hence not 53 divides 8053 by NAT_4:9;
8053 = 59*136 + 29; hence not 59 divides 8053 by NAT_4:9;
8053 = 61*132 + 1; hence not 61 divides 8053 by NAT_4:9;
8053 = 67*120 + 13; hence not 67 divides 8053 by NAT_4:9;
8053 = 71*113 + 30; hence not 71 divides 8053 by NAT_4:9;
8053 = 73*110 + 23; hence not 73 divides 8053 by NAT_4:9;
8053 = 79*101 + 74; hence not 79 divides 8053 by NAT_4:9;
8053 = 83*97 + 2; hence not 83 divides 8053 by NAT_4:9;
8053 = 89*90 + 43; hence not 89 divides 8053 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8053 & n is prime
holds not n divides 8053 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8059 is prime
proof
now
8059 = 2*4029 + 1; hence not 2 divides 8059 by NAT_4:9;
8059 = 3*2686 + 1; hence not 3 divides 8059 by NAT_4:9;
8059 = 5*1611 + 4; hence not 5 divides 8059 by NAT_4:9;
8059 = 7*1151 + 2; hence not 7 divides 8059 by NAT_4:9;
8059 = 11*732 + 7; hence not 11 divides 8059 by NAT_4:9;
8059 = 13*619 + 12; hence not 13 divides 8059 by NAT_4:9;
8059 = 17*474 + 1; hence not 17 divides 8059 by NAT_4:9;
8059 = 19*424 + 3; hence not 19 divides 8059 by NAT_4:9;
8059 = 23*350 + 9; hence not 23 divides 8059 by NAT_4:9;
8059 = 29*277 + 26; hence not 29 divides 8059 by NAT_4:9;
8059 = 31*259 + 30; hence not 31 divides 8059 by NAT_4:9;
8059 = 37*217 + 30; hence not 37 divides 8059 by NAT_4:9;
8059 = 41*196 + 23; hence not 41 divides 8059 by NAT_4:9;
8059 = 43*187 + 18; hence not 43 divides 8059 by NAT_4:9;
8059 = 47*171 + 22; hence not 47 divides 8059 by NAT_4:9;
8059 = 53*152 + 3; hence not 53 divides 8059 by NAT_4:9;
8059 = 59*136 + 35; hence not 59 divides 8059 by NAT_4:9;
8059 = 61*132 + 7; hence not 61 divides 8059 by NAT_4:9;
8059 = 67*120 + 19; hence not 67 divides 8059 by NAT_4:9;
8059 = 71*113 + 36; hence not 71 divides 8059 by NAT_4:9;
8059 = 73*110 + 29; hence not 73 divides 8059 by NAT_4:9;
8059 = 79*102 + 1; hence not 79 divides 8059 by NAT_4:9;
8059 = 83*97 + 8; hence not 83 divides 8059 by NAT_4:9;
8059 = 89*90 + 49; hence not 89 divides 8059 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8059 & n is prime
holds not n divides 8059 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8069 is prime
proof
now
8069 = 2*4034 + 1; hence not 2 divides 8069 by NAT_4:9;
8069 = 3*2689 + 2; hence not 3 divides 8069 by NAT_4:9;
8069 = 5*1613 + 4; hence not 5 divides 8069 by NAT_4:9;
8069 = 7*1152 + 5; hence not 7 divides 8069 by NAT_4:9;
8069 = 11*733 + 6; hence not 11 divides 8069 by NAT_4:9;
8069 = 13*620 + 9; hence not 13 divides 8069 by NAT_4:9;
8069 = 17*474 + 11; hence not 17 divides 8069 by NAT_4:9;
8069 = 19*424 + 13; hence not 19 divides 8069 by NAT_4:9;
8069 = 23*350 + 19; hence not 23 divides 8069 by NAT_4:9;
8069 = 29*278 + 7; hence not 29 divides 8069 by NAT_4:9;
8069 = 31*260 + 9; hence not 31 divides 8069 by NAT_4:9;
8069 = 37*218 + 3; hence not 37 divides 8069 by NAT_4:9;
8069 = 41*196 + 33; hence not 41 divides 8069 by NAT_4:9;
8069 = 43*187 + 28; hence not 43 divides 8069 by NAT_4:9;
8069 = 47*171 + 32; hence not 47 divides 8069 by NAT_4:9;
8069 = 53*152 + 13; hence not 53 divides 8069 by NAT_4:9;
8069 = 59*136 + 45; hence not 59 divides 8069 by NAT_4:9;
8069 = 61*132 + 17; hence not 61 divides 8069 by NAT_4:9;
8069 = 67*120 + 29; hence not 67 divides 8069 by NAT_4:9;
8069 = 71*113 + 46; hence not 71 divides 8069 by NAT_4:9;
8069 = 73*110 + 39; hence not 73 divides 8069 by NAT_4:9;
8069 = 79*102 + 11; hence not 79 divides 8069 by NAT_4:9;
8069 = 83*97 + 18; hence not 83 divides 8069 by NAT_4:9;
8069 = 89*90 + 59; hence not 89 divides 8069 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8069 & n is prime
holds not n divides 8069 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8081 is prime
proof
now
8081 = 2*4040 + 1; hence not 2 divides 8081 by NAT_4:9;
8081 = 3*2693 + 2; hence not 3 divides 8081 by NAT_4:9;
8081 = 5*1616 + 1; hence not 5 divides 8081 by NAT_4:9;
8081 = 7*1154 + 3; hence not 7 divides 8081 by NAT_4:9;
8081 = 11*734 + 7; hence not 11 divides 8081 by NAT_4:9;
8081 = 13*621 + 8; hence not 13 divides 8081 by NAT_4:9;
8081 = 17*475 + 6; hence not 17 divides 8081 by NAT_4:9;
8081 = 19*425 + 6; hence not 19 divides 8081 by NAT_4:9;
8081 = 23*351 + 8; hence not 23 divides 8081 by NAT_4:9;
8081 = 29*278 + 19; hence not 29 divides 8081 by NAT_4:9;
8081 = 31*260 + 21; hence not 31 divides 8081 by NAT_4:9;
8081 = 37*218 + 15; hence not 37 divides 8081 by NAT_4:9;
8081 = 41*197 + 4; hence not 41 divides 8081 by NAT_4:9;
8081 = 43*187 + 40; hence not 43 divides 8081 by NAT_4:9;
8081 = 47*171 + 44; hence not 47 divides 8081 by NAT_4:9;
8081 = 53*152 + 25; hence not 53 divides 8081 by NAT_4:9;
8081 = 59*136 + 57; hence not 59 divides 8081 by NAT_4:9;
8081 = 61*132 + 29; hence not 61 divides 8081 by NAT_4:9;
8081 = 67*120 + 41; hence not 67 divides 8081 by NAT_4:9;
8081 = 71*113 + 58; hence not 71 divides 8081 by NAT_4:9;
8081 = 73*110 + 51; hence not 73 divides 8081 by NAT_4:9;
8081 = 79*102 + 23; hence not 79 divides 8081 by NAT_4:9;
8081 = 83*97 + 30; hence not 83 divides 8081 by NAT_4:9;
8081 = 89*90 + 71; hence not 89 divides 8081 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8081 & n is prime
holds not n divides 8081 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8087 is prime
proof
now
8087 = 2*4043 + 1; hence not 2 divides 8087 by NAT_4:9;
8087 = 3*2695 + 2; hence not 3 divides 8087 by NAT_4:9;
8087 = 5*1617 + 2; hence not 5 divides 8087 by NAT_4:9;
8087 = 7*1155 + 2; hence not 7 divides 8087 by NAT_4:9;
8087 = 11*735 + 2; hence not 11 divides 8087 by NAT_4:9;
8087 = 13*622 + 1; hence not 13 divides 8087 by NAT_4:9;
8087 = 17*475 + 12; hence not 17 divides 8087 by NAT_4:9;
8087 = 19*425 + 12; hence not 19 divides 8087 by NAT_4:9;
8087 = 23*351 + 14; hence not 23 divides 8087 by NAT_4:9;
8087 = 29*278 + 25; hence not 29 divides 8087 by NAT_4:9;
8087 = 31*260 + 27; hence not 31 divides 8087 by NAT_4:9;
8087 = 37*218 + 21; hence not 37 divides 8087 by NAT_4:9;
8087 = 41*197 + 10; hence not 41 divides 8087 by NAT_4:9;
8087 = 43*188 + 3; hence not 43 divides 8087 by NAT_4:9;
8087 = 47*172 + 3; hence not 47 divides 8087 by NAT_4:9;
8087 = 53*152 + 31; hence not 53 divides 8087 by NAT_4:9;
8087 = 59*137 + 4; hence not 59 divides 8087 by NAT_4:9;
8087 = 61*132 + 35; hence not 61 divides 8087 by NAT_4:9;
8087 = 67*120 + 47; hence not 67 divides 8087 by NAT_4:9;
8087 = 71*113 + 64; hence not 71 divides 8087 by NAT_4:9;
8087 = 73*110 + 57; hence not 73 divides 8087 by NAT_4:9;
8087 = 79*102 + 29; hence not 79 divides 8087 by NAT_4:9;
8087 = 83*97 + 36; hence not 83 divides 8087 by NAT_4:9;
8087 = 89*90 + 77; hence not 89 divides 8087 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8087 & n is prime
holds not n divides 8087 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8089 is prime
proof
now
8089 = 2*4044 + 1; hence not 2 divides 8089 by NAT_4:9;
8089 = 3*2696 + 1; hence not 3 divides 8089 by NAT_4:9;
8089 = 5*1617 + 4; hence not 5 divides 8089 by NAT_4:9;
8089 = 7*1155 + 4; hence not 7 divides 8089 by NAT_4:9;
8089 = 11*735 + 4; hence not 11 divides 8089 by NAT_4:9;
8089 = 13*622 + 3; hence not 13 divides 8089 by NAT_4:9;
8089 = 17*475 + 14; hence not 17 divides 8089 by NAT_4:9;
8089 = 19*425 + 14; hence not 19 divides 8089 by NAT_4:9;
8089 = 23*351 + 16; hence not 23 divides 8089 by NAT_4:9;
8089 = 29*278 + 27; hence not 29 divides 8089 by NAT_4:9;
8089 = 31*260 + 29; hence not 31 divides 8089 by NAT_4:9;
8089 = 37*218 + 23; hence not 37 divides 8089 by NAT_4:9;
8089 = 41*197 + 12; hence not 41 divides 8089 by NAT_4:9;
8089 = 43*188 + 5; hence not 43 divides 8089 by NAT_4:9;
8089 = 47*172 + 5; hence not 47 divides 8089 by NAT_4:9;
8089 = 53*152 + 33; hence not 53 divides 8089 by NAT_4:9;
8089 = 59*137 + 6; hence not 59 divides 8089 by NAT_4:9;
8089 = 61*132 + 37; hence not 61 divides 8089 by NAT_4:9;
8089 = 67*120 + 49; hence not 67 divides 8089 by NAT_4:9;
8089 = 71*113 + 66; hence not 71 divides 8089 by NAT_4:9;
8089 = 73*110 + 59; hence not 73 divides 8089 by NAT_4:9;
8089 = 79*102 + 31; hence not 79 divides 8089 by NAT_4:9;
8089 = 83*97 + 38; hence not 83 divides 8089 by NAT_4:9;
8089 = 89*90 + 79; hence not 89 divides 8089 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8089 & n is prime
holds not n divides 8089 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8093 is prime
proof
now
8093 = 2*4046 + 1; hence not 2 divides 8093 by NAT_4:9;
8093 = 3*2697 + 2; hence not 3 divides 8093 by NAT_4:9;
8093 = 5*1618 + 3; hence not 5 divides 8093 by NAT_4:9;
8093 = 7*1156 + 1; hence not 7 divides 8093 by NAT_4:9;
8093 = 11*735 + 8; hence not 11 divides 8093 by NAT_4:9;
8093 = 13*622 + 7; hence not 13 divides 8093 by NAT_4:9;
8093 = 17*476 + 1; hence not 17 divides 8093 by NAT_4:9;
8093 = 19*425 + 18; hence not 19 divides 8093 by NAT_4:9;
8093 = 23*351 + 20; hence not 23 divides 8093 by NAT_4:9;
8093 = 29*279 + 2; hence not 29 divides 8093 by NAT_4:9;
8093 = 31*261 + 2; hence not 31 divides 8093 by NAT_4:9;
8093 = 37*218 + 27; hence not 37 divides 8093 by NAT_4:9;
8093 = 41*197 + 16; hence not 41 divides 8093 by NAT_4:9;
8093 = 43*188 + 9; hence not 43 divides 8093 by NAT_4:9;
8093 = 47*172 + 9; hence not 47 divides 8093 by NAT_4:9;
8093 = 53*152 + 37; hence not 53 divides 8093 by NAT_4:9;
8093 = 59*137 + 10; hence not 59 divides 8093 by NAT_4:9;
8093 = 61*132 + 41; hence not 61 divides 8093 by NAT_4:9;
8093 = 67*120 + 53; hence not 67 divides 8093 by NAT_4:9;
8093 = 71*113 + 70; hence not 71 divides 8093 by NAT_4:9;
8093 = 73*110 + 63; hence not 73 divides 8093 by NAT_4:9;
8093 = 79*102 + 35; hence not 79 divides 8093 by NAT_4:9;
8093 = 83*97 + 42; hence not 83 divides 8093 by NAT_4:9;
8093 = 89*90 + 83; hence not 89 divides 8093 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8093 & n is prime
holds not n divides 8093 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8101 is prime
proof
now
8101 = 2*4050 + 1; hence not 2 divides 8101 by NAT_4:9;
8101 = 3*2700 + 1; hence not 3 divides 8101 by NAT_4:9;
8101 = 5*1620 + 1; hence not 5 divides 8101 by NAT_4:9;
8101 = 7*1157 + 2; hence not 7 divides 8101 by NAT_4:9;
8101 = 11*736 + 5; hence not 11 divides 8101 by NAT_4:9;
8101 = 13*623 + 2; hence not 13 divides 8101 by NAT_4:9;
8101 = 17*476 + 9; hence not 17 divides 8101 by NAT_4:9;
8101 = 19*426 + 7; hence not 19 divides 8101 by NAT_4:9;
8101 = 23*352 + 5; hence not 23 divides 8101 by NAT_4:9;
8101 = 29*279 + 10; hence not 29 divides 8101 by NAT_4:9;
8101 = 31*261 + 10; hence not 31 divides 8101 by NAT_4:9;
8101 = 37*218 + 35; hence not 37 divides 8101 by NAT_4:9;
8101 = 41*197 + 24; hence not 41 divides 8101 by NAT_4:9;
8101 = 43*188 + 17; hence not 43 divides 8101 by NAT_4:9;
8101 = 47*172 + 17; hence not 47 divides 8101 by NAT_4:9;
8101 = 53*152 + 45; hence not 53 divides 8101 by NAT_4:9;
8101 = 59*137 + 18; hence not 59 divides 8101 by NAT_4:9;
8101 = 61*132 + 49; hence not 61 divides 8101 by NAT_4:9;
8101 = 67*120 + 61; hence not 67 divides 8101 by NAT_4:9;
8101 = 71*114 + 7; hence not 71 divides 8101 by NAT_4:9;
8101 = 73*110 + 71; hence not 73 divides 8101 by NAT_4:9;
8101 = 79*102 + 43; hence not 79 divides 8101 by NAT_4:9;
8101 = 83*97 + 50; hence not 83 divides 8101 by NAT_4:9;
8101 = 89*91 + 2; hence not 89 divides 8101 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8101 & n is prime
holds not n divides 8101 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8111 is prime
proof
now
8111 = 2*4055 + 1; hence not 2 divides 8111 by NAT_4:9;
8111 = 3*2703 + 2; hence not 3 divides 8111 by NAT_4:9;
8111 = 5*1622 + 1; hence not 5 divides 8111 by NAT_4:9;
8111 = 7*1158 + 5; hence not 7 divides 8111 by NAT_4:9;
8111 = 11*737 + 4; hence not 11 divides 8111 by NAT_4:9;
8111 = 13*623 + 12; hence not 13 divides 8111 by NAT_4:9;
8111 = 17*477 + 2; hence not 17 divides 8111 by NAT_4:9;
8111 = 19*426 + 17; hence not 19 divides 8111 by NAT_4:9;
8111 = 23*352 + 15; hence not 23 divides 8111 by NAT_4:9;
8111 = 29*279 + 20; hence not 29 divides 8111 by NAT_4:9;
8111 = 31*261 + 20; hence not 31 divides 8111 by NAT_4:9;
8111 = 37*219 + 8; hence not 37 divides 8111 by NAT_4:9;
8111 = 41*197 + 34; hence not 41 divides 8111 by NAT_4:9;
8111 = 43*188 + 27; hence not 43 divides 8111 by NAT_4:9;
8111 = 47*172 + 27; hence not 47 divides 8111 by NAT_4:9;
8111 = 53*153 + 2; hence not 53 divides 8111 by NAT_4:9;
8111 = 59*137 + 28; hence not 59 divides 8111 by NAT_4:9;
8111 = 61*132 + 59; hence not 61 divides 8111 by NAT_4:9;
8111 = 67*121 + 4; hence not 67 divides 8111 by NAT_4:9;
8111 = 71*114 + 17; hence not 71 divides 8111 by NAT_4:9;
8111 = 73*111 + 8; hence not 73 divides 8111 by NAT_4:9;
8111 = 79*102 + 53; hence not 79 divides 8111 by NAT_4:9;
8111 = 83*97 + 60; hence not 83 divides 8111 by NAT_4:9;
8111 = 89*91 + 12; hence not 89 divides 8111 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8111 & n is prime
holds not n divides 8111 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8117 is prime
proof
now
8117 = 2*4058 + 1; hence not 2 divides 8117 by NAT_4:9;
8117 = 3*2705 + 2; hence not 3 divides 8117 by NAT_4:9;
8117 = 5*1623 + 2; hence not 5 divides 8117 by NAT_4:9;
8117 = 7*1159 + 4; hence not 7 divides 8117 by NAT_4:9;
8117 = 11*737 + 10; hence not 11 divides 8117 by NAT_4:9;
8117 = 13*624 + 5; hence not 13 divides 8117 by NAT_4:9;
8117 = 17*477 + 8; hence not 17 divides 8117 by NAT_4:9;
8117 = 19*427 + 4; hence not 19 divides 8117 by NAT_4:9;
8117 = 23*352 + 21; hence not 23 divides 8117 by NAT_4:9;
8117 = 29*279 + 26; hence not 29 divides 8117 by NAT_4:9;
8117 = 31*261 + 26; hence not 31 divides 8117 by NAT_4:9;
8117 = 37*219 + 14; hence not 37 divides 8117 by NAT_4:9;
8117 = 41*197 + 40; hence not 41 divides 8117 by NAT_4:9;
8117 = 43*188 + 33; hence not 43 divides 8117 by NAT_4:9;
8117 = 47*172 + 33; hence not 47 divides 8117 by NAT_4:9;
8117 = 53*153 + 8; hence not 53 divides 8117 by NAT_4:9;
8117 = 59*137 + 34; hence not 59 divides 8117 by NAT_4:9;
8117 = 61*133 + 4; hence not 61 divides 8117 by NAT_4:9;
8117 = 67*121 + 10; hence not 67 divides 8117 by NAT_4:9;
8117 = 71*114 + 23; hence not 71 divides 8117 by NAT_4:9;
8117 = 73*111 + 14; hence not 73 divides 8117 by NAT_4:9;
8117 = 79*102 + 59; hence not 79 divides 8117 by NAT_4:9;
8117 = 83*97 + 66; hence not 83 divides 8117 by NAT_4:9;
8117 = 89*91 + 18; hence not 89 divides 8117 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8117 & n is prime
holds not n divides 8117 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8123 is prime
proof
now
8123 = 2*4061 + 1; hence not 2 divides 8123 by NAT_4:9;
8123 = 3*2707 + 2; hence not 3 divides 8123 by NAT_4:9;
8123 = 5*1624 + 3; hence not 5 divides 8123 by NAT_4:9;
8123 = 7*1160 + 3; hence not 7 divides 8123 by NAT_4:9;
8123 = 11*738 + 5; hence not 11 divides 8123 by NAT_4:9;
8123 = 13*624 + 11; hence not 13 divides 8123 by NAT_4:9;
8123 = 17*477 + 14; hence not 17 divides 8123 by NAT_4:9;
8123 = 19*427 + 10; hence not 19 divides 8123 by NAT_4:9;
8123 = 23*353 + 4; hence not 23 divides 8123 by NAT_4:9;
8123 = 29*280 + 3; hence not 29 divides 8123 by NAT_4:9;
8123 = 31*262 + 1; hence not 31 divides 8123 by NAT_4:9;
8123 = 37*219 + 20; hence not 37 divides 8123 by NAT_4:9;
8123 = 41*198 + 5; hence not 41 divides 8123 by NAT_4:9;
8123 = 43*188 + 39; hence not 43 divides 8123 by NAT_4:9;
8123 = 47*172 + 39; hence not 47 divides 8123 by NAT_4:9;
8123 = 53*153 + 14; hence not 53 divides 8123 by NAT_4:9;
8123 = 59*137 + 40; hence not 59 divides 8123 by NAT_4:9;
8123 = 61*133 + 10; hence not 61 divides 8123 by NAT_4:9;
8123 = 67*121 + 16; hence not 67 divides 8123 by NAT_4:9;
8123 = 71*114 + 29; hence not 71 divides 8123 by NAT_4:9;
8123 = 73*111 + 20; hence not 73 divides 8123 by NAT_4:9;
8123 = 79*102 + 65; hence not 79 divides 8123 by NAT_4:9;
8123 = 83*97 + 72; hence not 83 divides 8123 by NAT_4:9;
8123 = 89*91 + 24; hence not 89 divides 8123 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8123 & n is prime
holds not n divides 8123 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
8147 is prime
proof
now
8147 = 2*4073 + 1; hence not 2 divides 8147 by NAT_4:9;
8147 = 3*2715 + 2; hence not 3 divides 8147 by NAT_4:9;
8147 = 5*1629 + 2; hence not 5 divides 8147 by NAT_4:9;
8147 = 7*1163 + 6; hence not 7 divides 8147 by NAT_4:9;
8147 = 11*740 + 7; hence not 11 divides 8147 by NAT_4:9;
8147 = 13*626 + 9; hence not 13 divides 8147 by NAT_4:9;
8147 = 17*479 + 4; hence not 17 divides 8147 by NAT_4:9;
8147 = 19*428 + 15; hence not 19 divides 8147 by NAT_4:9;
8147 = 23*354 + 5; hence not 23 divides 8147 by NAT_4:9;
8147 = 29*280 + 27; hence not 29 divides 8147 by NAT_4:9;
8147 = 31*262 + 25; hence not 31 divides 8147 by NAT_4:9;
8147 = 37*220 + 7; hence not 37 divides 8147 by NAT_4:9;
8147 = 41*198 + 29; hence not 41 divides 8147 by NAT_4:9;
8147 = 43*189 + 20; hence not 43 divides 8147 by NAT_4:9;
8147 = 47*173 + 16; hence not 47 divides 8147 by NAT_4:9;
8147 = 53*153 + 38; hence not 53 divides 8147 by NAT_4:9;
8147 = 59*138 + 5; hence not 59 divides 8147 by NAT_4:9;
8147 = 61*133 + 34; hence not 61 divides 8147 by NAT_4:9;
8147 = 67*121 + 40; hence not 67 divides 8147 by NAT_4:9;
8147 = 71*114 + 53; hence not 71 divides 8147 by NAT_4:9;
8147 = 73*111 + 44; hence not 73 divides 8147 by NAT_4:9;
8147 = 79*103 + 10; hence not 79 divides 8147 by NAT_4:9;
8147 = 83*98 + 13; hence not 83 divides 8147 by NAT_4:9;
8147 = 89*91 + 48; hence not 89 divides 8147 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8147 & n is prime
holds not n divides 8147 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8161 is prime
proof
now
8161 = 2*4080 + 1; hence not 2 divides 8161 by NAT_4:9;
8161 = 3*2720 + 1; hence not 3 divides 8161 by NAT_4:9;
8161 = 5*1632 + 1; hence not 5 divides 8161 by NAT_4:9;
8161 = 7*1165 + 6; hence not 7 divides 8161 by NAT_4:9;
8161 = 11*741 + 10; hence not 11 divides 8161 by NAT_4:9;
8161 = 13*627 + 10; hence not 13 divides 8161 by NAT_4:9;
8161 = 17*480 + 1; hence not 17 divides 8161 by NAT_4:9;
8161 = 19*429 + 10; hence not 19 divides 8161 by NAT_4:9;
8161 = 23*354 + 19; hence not 23 divides 8161 by NAT_4:9;
8161 = 29*281 + 12; hence not 29 divides 8161 by NAT_4:9;
8161 = 31*263 + 8; hence not 31 divides 8161 by NAT_4:9;
8161 = 37*220 + 21; hence not 37 divides 8161 by NAT_4:9;
8161 = 41*199 + 2; hence not 41 divides 8161 by NAT_4:9;
8161 = 43*189 + 34; hence not 43 divides 8161 by NAT_4:9;
8161 = 47*173 + 30; hence not 47 divides 8161 by NAT_4:9;
8161 = 53*153 + 52; hence not 53 divides 8161 by NAT_4:9;
8161 = 59*138 + 19; hence not 59 divides 8161 by NAT_4:9;
8161 = 61*133 + 48; hence not 61 divides 8161 by NAT_4:9;
8161 = 67*121 + 54; hence not 67 divides 8161 by NAT_4:9;
8161 = 71*114 + 67; hence not 71 divides 8161 by NAT_4:9;
8161 = 73*111 + 58; hence not 73 divides 8161 by NAT_4:9;
8161 = 79*103 + 24; hence not 79 divides 8161 by NAT_4:9;
8161 = 83*98 + 27; hence not 83 divides 8161 by NAT_4:9;
8161 = 89*91 + 62; hence not 89 divides 8161 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8161 & n is prime
holds not n divides 8161 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8167 is prime
proof
now
8167 = 2*4083 + 1; hence not 2 divides 8167 by NAT_4:9;
8167 = 3*2722 + 1; hence not 3 divides 8167 by NAT_4:9;
8167 = 5*1633 + 2; hence not 5 divides 8167 by NAT_4:9;
8167 = 7*1166 + 5; hence not 7 divides 8167 by NAT_4:9;
8167 = 11*742 + 5; hence not 11 divides 8167 by NAT_4:9;
8167 = 13*628 + 3; hence not 13 divides 8167 by NAT_4:9;
8167 = 17*480 + 7; hence not 17 divides 8167 by NAT_4:9;
8167 = 19*429 + 16; hence not 19 divides 8167 by NAT_4:9;
8167 = 23*355 + 2; hence not 23 divides 8167 by NAT_4:9;
8167 = 29*281 + 18; hence not 29 divides 8167 by NAT_4:9;
8167 = 31*263 + 14; hence not 31 divides 8167 by NAT_4:9;
8167 = 37*220 + 27; hence not 37 divides 8167 by NAT_4:9;
8167 = 41*199 + 8; hence not 41 divides 8167 by NAT_4:9;
8167 = 43*189 + 40; hence not 43 divides 8167 by NAT_4:9;
8167 = 47*173 + 36; hence not 47 divides 8167 by NAT_4:9;
8167 = 53*154 + 5; hence not 53 divides 8167 by NAT_4:9;
8167 = 59*138 + 25; hence not 59 divides 8167 by NAT_4:9;
8167 = 61*133 + 54; hence not 61 divides 8167 by NAT_4:9;
8167 = 67*121 + 60; hence not 67 divides 8167 by NAT_4:9;
8167 = 71*115 + 2; hence not 71 divides 8167 by NAT_4:9;
8167 = 73*111 + 64; hence not 73 divides 8167 by NAT_4:9;
8167 = 79*103 + 30; hence not 79 divides 8167 by NAT_4:9;
8167 = 83*98 + 33; hence not 83 divides 8167 by NAT_4:9;
8167 = 89*91 + 68; hence not 89 divides 8167 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8167 & n is prime
holds not n divides 8167 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8171 is prime
proof
now
8171 = 2*4085 + 1; hence not 2 divides 8171 by NAT_4:9;
8171 = 3*2723 + 2; hence not 3 divides 8171 by NAT_4:9;
8171 = 5*1634 + 1; hence not 5 divides 8171 by NAT_4:9;
8171 = 7*1167 + 2; hence not 7 divides 8171 by NAT_4:9;
8171 = 11*742 + 9; hence not 11 divides 8171 by NAT_4:9;
8171 = 13*628 + 7; hence not 13 divides 8171 by NAT_4:9;
8171 = 17*480 + 11; hence not 17 divides 8171 by NAT_4:9;
8171 = 19*430 + 1; hence not 19 divides 8171 by NAT_4:9;
8171 = 23*355 + 6; hence not 23 divides 8171 by NAT_4:9;
8171 = 29*281 + 22; hence not 29 divides 8171 by NAT_4:9;
8171 = 31*263 + 18; hence not 31 divides 8171 by NAT_4:9;
8171 = 37*220 + 31; hence not 37 divides 8171 by NAT_4:9;
8171 = 41*199 + 12; hence not 41 divides 8171 by NAT_4:9;
8171 = 43*190 + 1; hence not 43 divides 8171 by NAT_4:9;
8171 = 47*173 + 40; hence not 47 divides 8171 by NAT_4:9;
8171 = 53*154 + 9; hence not 53 divides 8171 by NAT_4:9;
8171 = 59*138 + 29; hence not 59 divides 8171 by NAT_4:9;
8171 = 61*133 + 58; hence not 61 divides 8171 by NAT_4:9;
8171 = 67*121 + 64; hence not 67 divides 8171 by NAT_4:9;
8171 = 71*115 + 6; hence not 71 divides 8171 by NAT_4:9;
8171 = 73*111 + 68; hence not 73 divides 8171 by NAT_4:9;
8171 = 79*103 + 34; hence not 79 divides 8171 by NAT_4:9;
8171 = 83*98 + 37; hence not 83 divides 8171 by NAT_4:9;
8171 = 89*91 + 72; hence not 89 divides 8171 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8171 & n is prime
holds not n divides 8171 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8179 is prime
proof
now
8179 = 2*4089 + 1; hence not 2 divides 8179 by NAT_4:9;
8179 = 3*2726 + 1; hence not 3 divides 8179 by NAT_4:9;
8179 = 5*1635 + 4; hence not 5 divides 8179 by NAT_4:9;
8179 = 7*1168 + 3; hence not 7 divides 8179 by NAT_4:9;
8179 = 11*743 + 6; hence not 11 divides 8179 by NAT_4:9;
8179 = 13*629 + 2; hence not 13 divides 8179 by NAT_4:9;
8179 = 17*481 + 2; hence not 17 divides 8179 by NAT_4:9;
8179 = 19*430 + 9; hence not 19 divides 8179 by NAT_4:9;
8179 = 23*355 + 14; hence not 23 divides 8179 by NAT_4:9;
8179 = 29*282 + 1; hence not 29 divides 8179 by NAT_4:9;
8179 = 31*263 + 26; hence not 31 divides 8179 by NAT_4:9;
8179 = 37*221 + 2; hence not 37 divides 8179 by NAT_4:9;
8179 = 41*199 + 20; hence not 41 divides 8179 by NAT_4:9;
8179 = 43*190 + 9; hence not 43 divides 8179 by NAT_4:9;
8179 = 47*174 + 1; hence not 47 divides 8179 by NAT_4:9;
8179 = 53*154 + 17; hence not 53 divides 8179 by NAT_4:9;
8179 = 59*138 + 37; hence not 59 divides 8179 by NAT_4:9;
8179 = 61*134 + 5; hence not 61 divides 8179 by NAT_4:9;
8179 = 67*122 + 5; hence not 67 divides 8179 by NAT_4:9;
8179 = 71*115 + 14; hence not 71 divides 8179 by NAT_4:9;
8179 = 73*112 + 3; hence not 73 divides 8179 by NAT_4:9;
8179 = 79*103 + 42; hence not 79 divides 8179 by NAT_4:9;
8179 = 83*98 + 45; hence not 83 divides 8179 by NAT_4:9;
8179 = 89*91 + 80; hence not 89 divides 8179 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8179 & n is prime
holds not n divides 8179 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8191 is prime
proof
now
8191 = 2*4095 + 1; hence not 2 divides 8191 by NAT_4:9;
8191 = 3*2730 + 1; hence not 3 divides 8191 by NAT_4:9;
8191 = 5*1638 + 1; hence not 5 divides 8191 by NAT_4:9;
8191 = 7*1170 + 1; hence not 7 divides 8191 by NAT_4:9;
8191 = 11*744 + 7; hence not 11 divides 8191 by NAT_4:9;
8191 = 13*630 + 1; hence not 13 divides 8191 by NAT_4:9;
8191 = 17*481 + 14; hence not 17 divides 8191 by NAT_4:9;
8191 = 19*431 + 2; hence not 19 divides 8191 by NAT_4:9;
8191 = 23*356 + 3; hence not 23 divides 8191 by NAT_4:9;
8191 = 29*282 + 13; hence not 29 divides 8191 by NAT_4:9;
8191 = 31*264 + 7; hence not 31 divides 8191 by NAT_4:9;
8191 = 37*221 + 14; hence not 37 divides 8191 by NAT_4:9;
8191 = 41*199 + 32; hence not 41 divides 8191 by NAT_4:9;
8191 = 43*190 + 21; hence not 43 divides 8191 by NAT_4:9;
8191 = 47*174 + 13; hence not 47 divides 8191 by NAT_4:9;
8191 = 53*154 + 29; hence not 53 divides 8191 by NAT_4:9;
8191 = 59*138 + 49; hence not 59 divides 8191 by NAT_4:9;
8191 = 61*134 + 17; hence not 61 divides 8191 by NAT_4:9;
8191 = 67*122 + 17; hence not 67 divides 8191 by NAT_4:9;
8191 = 71*115 + 26; hence not 71 divides 8191 by NAT_4:9;
8191 = 73*112 + 15; hence not 73 divides 8191 by NAT_4:9;
8191 = 79*103 + 54; hence not 79 divides 8191 by NAT_4:9;
8191 = 83*98 + 57; hence not 83 divides 8191 by NAT_4:9;
8191 = 89*92 + 3; hence not 89 divides 8191 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8191 & n is prime
holds not n divides 8191 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
8209 is prime
proof
now
8209 = 2*4104 + 1; hence not 2 divides 8209 by NAT_4:9;
8209 = 3*2736 + 1; hence not 3 divides 8209 by NAT_4:9;
8209 = 5*1641 + 4; hence not 5 divides 8209 by NAT_4:9;
8209 = 7*1172 + 5; hence not 7 divides 8209 by NAT_4:9;
8209 = 11*746 + 3; hence not 11 divides 8209 by NAT_4:9;
8209 = 13*631 + 6; hence not 13 divides 8209 by NAT_4:9;
8209 = 17*482 + 15; hence not 17 divides 8209 by NAT_4:9;
8209 = 19*432 + 1; hence not 19 divides 8209 by NAT_4:9;
8209 = 23*356 + 21; hence not 23 divides 8209 by NAT_4:9;
8209 = 29*283 + 2; hence not 29 divides 8209 by NAT_4:9;
8209 = 31*264 + 25; hence not 31 divides 8209 by NAT_4:9;
8209 = 37*221 + 32; hence not 37 divides 8209 by NAT_4:9;
8209 = 41*200 + 9; hence not 41 divides 8209 by NAT_4:9;
8209 = 43*190 + 39; hence not 43 divides 8209 by NAT_4:9;
8209 = 47*174 + 31; hence not 47 divides 8209 by NAT_4:9;
8209 = 53*154 + 47; hence not 53 divides 8209 by NAT_4:9;
8209 = 59*139 + 8; hence not 59 divides 8209 by NAT_4:9;
8209 = 61*134 + 35; hence not 61 divides 8209 by NAT_4:9;
8209 = 67*122 + 35; hence not 67 divides 8209 by NAT_4:9;
8209 = 71*115 + 44; hence not 71 divides 8209 by NAT_4:9;
8209 = 73*112 + 33; hence not 73 divides 8209 by NAT_4:9;
8209 = 79*103 + 72; hence not 79 divides 8209 by NAT_4:9;
8209 = 83*98 + 75; hence not 83 divides 8209 by NAT_4:9;
8209 = 89*92 + 21; hence not 89 divides 8209 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8209 & n is prime
holds not n divides 8209 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8219 is prime
proof
now
8219 = 2*4109 + 1; hence not 2 divides 8219 by NAT_4:9;
8219 = 3*2739 + 2; hence not 3 divides 8219 by NAT_4:9;
8219 = 5*1643 + 4; hence not 5 divides 8219 by NAT_4:9;
8219 = 7*1174 + 1; hence not 7 divides 8219 by NAT_4:9;
8219 = 11*747 + 2; hence not 11 divides 8219 by NAT_4:9;
8219 = 13*632 + 3; hence not 13 divides 8219 by NAT_4:9;
8219 = 17*483 + 8; hence not 17 divides 8219 by NAT_4:9;
8219 = 19*432 + 11; hence not 19 divides 8219 by NAT_4:9;
8219 = 23*357 + 8; hence not 23 divides 8219 by NAT_4:9;
8219 = 29*283 + 12; hence not 29 divides 8219 by NAT_4:9;
8219 = 31*265 + 4; hence not 31 divides 8219 by NAT_4:9;
8219 = 37*222 + 5; hence not 37 divides 8219 by NAT_4:9;
8219 = 41*200 + 19; hence not 41 divides 8219 by NAT_4:9;
8219 = 43*191 + 6; hence not 43 divides 8219 by NAT_4:9;
8219 = 47*174 + 41; hence not 47 divides 8219 by NAT_4:9;
8219 = 53*155 + 4; hence not 53 divides 8219 by NAT_4:9;
8219 = 59*139 + 18; hence not 59 divides 8219 by NAT_4:9;
8219 = 61*134 + 45; hence not 61 divides 8219 by NAT_4:9;
8219 = 67*122 + 45; hence not 67 divides 8219 by NAT_4:9;
8219 = 71*115 + 54; hence not 71 divides 8219 by NAT_4:9;
8219 = 73*112 + 43; hence not 73 divides 8219 by NAT_4:9;
8219 = 79*104 + 3; hence not 79 divides 8219 by NAT_4:9;
8219 = 83*99 + 2; hence not 83 divides 8219 by NAT_4:9;
8219 = 89*92 + 31; hence not 89 divides 8219 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8219 & n is prime
holds not n divides 8219 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8221 is prime
proof
now
8221 = 2*4110 + 1; hence not 2 divides 8221 by NAT_4:9;
8221 = 3*2740 + 1; hence not 3 divides 8221 by NAT_4:9;
8221 = 5*1644 + 1; hence not 5 divides 8221 by NAT_4:9;
8221 = 7*1174 + 3; hence not 7 divides 8221 by NAT_4:9;
8221 = 11*747 + 4; hence not 11 divides 8221 by NAT_4:9;
8221 = 13*632 + 5; hence not 13 divides 8221 by NAT_4:9;
8221 = 17*483 + 10; hence not 17 divides 8221 by NAT_4:9;
8221 = 19*432 + 13; hence not 19 divides 8221 by NAT_4:9;
8221 = 23*357 + 10; hence not 23 divides 8221 by NAT_4:9;
8221 = 29*283 + 14; hence not 29 divides 8221 by NAT_4:9;
8221 = 31*265 + 6; hence not 31 divides 8221 by NAT_4:9;
8221 = 37*222 + 7; hence not 37 divides 8221 by NAT_4:9;
8221 = 41*200 + 21; hence not 41 divides 8221 by NAT_4:9;
8221 = 43*191 + 8; hence not 43 divides 8221 by NAT_4:9;
8221 = 47*174 + 43; hence not 47 divides 8221 by NAT_4:9;
8221 = 53*155 + 6; hence not 53 divides 8221 by NAT_4:9;
8221 = 59*139 + 20; hence not 59 divides 8221 by NAT_4:9;
8221 = 61*134 + 47; hence not 61 divides 8221 by NAT_4:9;
8221 = 67*122 + 47; hence not 67 divides 8221 by NAT_4:9;
8221 = 71*115 + 56; hence not 71 divides 8221 by NAT_4:9;
8221 = 73*112 + 45; hence not 73 divides 8221 by NAT_4:9;
8221 = 79*104 + 5; hence not 79 divides 8221 by NAT_4:9;
8221 = 83*99 + 4; hence not 83 divides 8221 by NAT_4:9;
8221 = 89*92 + 33; hence not 89 divides 8221 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8221 & n is prime
holds not n divides 8221 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8231 is prime
proof
now
8231 = 2*4115 + 1; hence not 2 divides 8231 by NAT_4:9;
8231 = 3*2743 + 2; hence not 3 divides 8231 by NAT_4:9;
8231 = 5*1646 + 1; hence not 5 divides 8231 by NAT_4:9;
8231 = 7*1175 + 6; hence not 7 divides 8231 by NAT_4:9;
8231 = 11*748 + 3; hence not 11 divides 8231 by NAT_4:9;
8231 = 13*633 + 2; hence not 13 divides 8231 by NAT_4:9;
8231 = 17*484 + 3; hence not 17 divides 8231 by NAT_4:9;
8231 = 19*433 + 4; hence not 19 divides 8231 by NAT_4:9;
8231 = 23*357 + 20; hence not 23 divides 8231 by NAT_4:9;
8231 = 29*283 + 24; hence not 29 divides 8231 by NAT_4:9;
8231 = 31*265 + 16; hence not 31 divides 8231 by NAT_4:9;
8231 = 37*222 + 17; hence not 37 divides 8231 by NAT_4:9;
8231 = 41*200 + 31; hence not 41 divides 8231 by NAT_4:9;
8231 = 43*191 + 18; hence not 43 divides 8231 by NAT_4:9;
8231 = 47*175 + 6; hence not 47 divides 8231 by NAT_4:9;
8231 = 53*155 + 16; hence not 53 divides 8231 by NAT_4:9;
8231 = 59*139 + 30; hence not 59 divides 8231 by NAT_4:9;
8231 = 61*134 + 57; hence not 61 divides 8231 by NAT_4:9;
8231 = 67*122 + 57; hence not 67 divides 8231 by NAT_4:9;
8231 = 71*115 + 66; hence not 71 divides 8231 by NAT_4:9;
8231 = 73*112 + 55; hence not 73 divides 8231 by NAT_4:9;
8231 = 79*104 + 15; hence not 79 divides 8231 by NAT_4:9;
8231 = 83*99 + 14; hence not 83 divides 8231 by NAT_4:9;
8231 = 89*92 + 43; hence not 89 divides 8231 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8231 & n is prime
holds not n divides 8231 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8233 is prime
proof
now
8233 = 2*4116 + 1; hence not 2 divides 8233 by NAT_4:9;
8233 = 3*2744 + 1; hence not 3 divides 8233 by NAT_4:9;
8233 = 5*1646 + 3; hence not 5 divides 8233 by NAT_4:9;
8233 = 7*1176 + 1; hence not 7 divides 8233 by NAT_4:9;
8233 = 11*748 + 5; hence not 11 divides 8233 by NAT_4:9;
8233 = 13*633 + 4; hence not 13 divides 8233 by NAT_4:9;
8233 = 17*484 + 5; hence not 17 divides 8233 by NAT_4:9;
8233 = 19*433 + 6; hence not 19 divides 8233 by NAT_4:9;
8233 = 23*357 + 22; hence not 23 divides 8233 by NAT_4:9;
8233 = 29*283 + 26; hence not 29 divides 8233 by NAT_4:9;
8233 = 31*265 + 18; hence not 31 divides 8233 by NAT_4:9;
8233 = 37*222 + 19; hence not 37 divides 8233 by NAT_4:9;
8233 = 41*200 + 33; hence not 41 divides 8233 by NAT_4:9;
8233 = 43*191 + 20; hence not 43 divides 8233 by NAT_4:9;
8233 = 47*175 + 8; hence not 47 divides 8233 by NAT_4:9;
8233 = 53*155 + 18; hence not 53 divides 8233 by NAT_4:9;
8233 = 59*139 + 32; hence not 59 divides 8233 by NAT_4:9;
8233 = 61*134 + 59; hence not 61 divides 8233 by NAT_4:9;
8233 = 67*122 + 59; hence not 67 divides 8233 by NAT_4:9;
8233 = 71*115 + 68; hence not 71 divides 8233 by NAT_4:9;
8233 = 73*112 + 57; hence not 73 divides 8233 by NAT_4:9;
8233 = 79*104 + 17; hence not 79 divides 8233 by NAT_4:9;
8233 = 83*99 + 16; hence not 83 divides 8233 by NAT_4:9;
8233 = 89*92 + 45; hence not 89 divides 8233 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8233 & n is prime
holds not n divides 8233 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8237 is prime
proof
now
8237 = 2*4118 + 1; hence not 2 divides 8237 by NAT_4:9;
8237 = 3*2745 + 2; hence not 3 divides 8237 by NAT_4:9;
8237 = 5*1647 + 2; hence not 5 divides 8237 by NAT_4:9;
8237 = 7*1176 + 5; hence not 7 divides 8237 by NAT_4:9;
8237 = 11*748 + 9; hence not 11 divides 8237 by NAT_4:9;
8237 = 13*633 + 8; hence not 13 divides 8237 by NAT_4:9;
8237 = 17*484 + 9; hence not 17 divides 8237 by NAT_4:9;
8237 = 19*433 + 10; hence not 19 divides 8237 by NAT_4:9;
8237 = 23*358 + 3; hence not 23 divides 8237 by NAT_4:9;
8237 = 29*284 + 1; hence not 29 divides 8237 by NAT_4:9;
8237 = 31*265 + 22; hence not 31 divides 8237 by NAT_4:9;
8237 = 37*222 + 23; hence not 37 divides 8237 by NAT_4:9;
8237 = 41*200 + 37; hence not 41 divides 8237 by NAT_4:9;
8237 = 43*191 + 24; hence not 43 divides 8237 by NAT_4:9;
8237 = 47*175 + 12; hence not 47 divides 8237 by NAT_4:9;
8237 = 53*155 + 22; hence not 53 divides 8237 by NAT_4:9;
8237 = 59*139 + 36; hence not 59 divides 8237 by NAT_4:9;
8237 = 61*135 + 2; hence not 61 divides 8237 by NAT_4:9;
8237 = 67*122 + 63; hence not 67 divides 8237 by NAT_4:9;
8237 = 71*116 + 1; hence not 71 divides 8237 by NAT_4:9;
8237 = 73*112 + 61; hence not 73 divides 8237 by NAT_4:9;
8237 = 79*104 + 21; hence not 79 divides 8237 by NAT_4:9;
8237 = 83*99 + 20; hence not 83 divides 8237 by NAT_4:9;
8237 = 89*92 + 49; hence not 89 divides 8237 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8237 & n is prime
holds not n divides 8237 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8243 is prime
proof
now
8243 = 2*4121 + 1; hence not 2 divides 8243 by NAT_4:9;
8243 = 3*2747 + 2; hence not 3 divides 8243 by NAT_4:9;
8243 = 5*1648 + 3; hence not 5 divides 8243 by NAT_4:9;
8243 = 7*1177 + 4; hence not 7 divides 8243 by NAT_4:9;
8243 = 11*749 + 4; hence not 11 divides 8243 by NAT_4:9;
8243 = 13*634 + 1; hence not 13 divides 8243 by NAT_4:9;
8243 = 17*484 + 15; hence not 17 divides 8243 by NAT_4:9;
8243 = 19*433 + 16; hence not 19 divides 8243 by NAT_4:9;
8243 = 23*358 + 9; hence not 23 divides 8243 by NAT_4:9;
8243 = 29*284 + 7; hence not 29 divides 8243 by NAT_4:9;
8243 = 31*265 + 28; hence not 31 divides 8243 by NAT_4:9;
8243 = 37*222 + 29; hence not 37 divides 8243 by NAT_4:9;
8243 = 41*201 + 2; hence not 41 divides 8243 by NAT_4:9;
8243 = 43*191 + 30; hence not 43 divides 8243 by NAT_4:9;
8243 = 47*175 + 18; hence not 47 divides 8243 by NAT_4:9;
8243 = 53*155 + 28; hence not 53 divides 8243 by NAT_4:9;
8243 = 59*139 + 42; hence not 59 divides 8243 by NAT_4:9;
8243 = 61*135 + 8; hence not 61 divides 8243 by NAT_4:9;
8243 = 67*123 + 2; hence not 67 divides 8243 by NAT_4:9;
8243 = 71*116 + 7; hence not 71 divides 8243 by NAT_4:9;
8243 = 73*112 + 67; hence not 73 divides 8243 by NAT_4:9;
8243 = 79*104 + 27; hence not 79 divides 8243 by NAT_4:9;
8243 = 83*99 + 26; hence not 83 divides 8243 by NAT_4:9;
8243 = 89*92 + 55; hence not 89 divides 8243 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8243 & n is prime
holds not n divides 8243 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
8263 is prime
proof
now
8263 = 2*4131 + 1; hence not 2 divides 8263 by NAT_4:9;
8263 = 3*2754 + 1; hence not 3 divides 8263 by NAT_4:9;
8263 = 5*1652 + 3; hence not 5 divides 8263 by NAT_4:9;
8263 = 7*1180 + 3; hence not 7 divides 8263 by NAT_4:9;
8263 = 11*751 + 2; hence not 11 divides 8263 by NAT_4:9;
8263 = 13*635 + 8; hence not 13 divides 8263 by NAT_4:9;
8263 = 17*486 + 1; hence not 17 divides 8263 by NAT_4:9;
8263 = 19*434 + 17; hence not 19 divides 8263 by NAT_4:9;
8263 = 23*359 + 6; hence not 23 divides 8263 by NAT_4:9;
8263 = 29*284 + 27; hence not 29 divides 8263 by NAT_4:9;
8263 = 31*266 + 17; hence not 31 divides 8263 by NAT_4:9;
8263 = 37*223 + 12; hence not 37 divides 8263 by NAT_4:9;
8263 = 41*201 + 22; hence not 41 divides 8263 by NAT_4:9;
8263 = 43*192 + 7; hence not 43 divides 8263 by NAT_4:9;
8263 = 47*175 + 38; hence not 47 divides 8263 by NAT_4:9;
8263 = 53*155 + 48; hence not 53 divides 8263 by NAT_4:9;
8263 = 59*140 + 3; hence not 59 divides 8263 by NAT_4:9;
8263 = 61*135 + 28; hence not 61 divides 8263 by NAT_4:9;
8263 = 67*123 + 22; hence not 67 divides 8263 by NAT_4:9;
8263 = 71*116 + 27; hence not 71 divides 8263 by NAT_4:9;
8263 = 73*113 + 14; hence not 73 divides 8263 by NAT_4:9;
8263 = 79*104 + 47; hence not 79 divides 8263 by NAT_4:9;
8263 = 83*99 + 46; hence not 83 divides 8263 by NAT_4:9;
8263 = 89*92 + 75; hence not 89 divides 8263 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8263 & n is prime
holds not n divides 8263 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8269 is prime
proof
now
8269 = 2*4134 + 1; hence not 2 divides 8269 by NAT_4:9;
8269 = 3*2756 + 1; hence not 3 divides 8269 by NAT_4:9;
8269 = 5*1653 + 4; hence not 5 divides 8269 by NAT_4:9;
8269 = 7*1181 + 2; hence not 7 divides 8269 by NAT_4:9;
8269 = 11*751 + 8; hence not 11 divides 8269 by NAT_4:9;
8269 = 13*636 + 1; hence not 13 divides 8269 by NAT_4:9;
8269 = 17*486 + 7; hence not 17 divides 8269 by NAT_4:9;
8269 = 19*435 + 4; hence not 19 divides 8269 by NAT_4:9;
8269 = 23*359 + 12; hence not 23 divides 8269 by NAT_4:9;
8269 = 29*285 + 4; hence not 29 divides 8269 by NAT_4:9;
8269 = 31*266 + 23; hence not 31 divides 8269 by NAT_4:9;
8269 = 37*223 + 18; hence not 37 divides 8269 by NAT_4:9;
8269 = 41*201 + 28; hence not 41 divides 8269 by NAT_4:9;
8269 = 43*192 + 13; hence not 43 divides 8269 by NAT_4:9;
8269 = 47*175 + 44; hence not 47 divides 8269 by NAT_4:9;
8269 = 53*156 + 1; hence not 53 divides 8269 by NAT_4:9;
8269 = 59*140 + 9; hence not 59 divides 8269 by NAT_4:9;
8269 = 61*135 + 34; hence not 61 divides 8269 by NAT_4:9;
8269 = 67*123 + 28; hence not 67 divides 8269 by NAT_4:9;
8269 = 71*116 + 33; hence not 71 divides 8269 by NAT_4:9;
8269 = 73*113 + 20; hence not 73 divides 8269 by NAT_4:9;
8269 = 79*104 + 53; hence not 79 divides 8269 by NAT_4:9;
8269 = 83*99 + 52; hence not 83 divides 8269 by NAT_4:9;
8269 = 89*92 + 81; hence not 89 divides 8269 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8269 & n is prime
holds not n divides 8269 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8273 is prime
proof
now
8273 = 2*4136 + 1; hence not 2 divides 8273 by NAT_4:9;
8273 = 3*2757 + 2; hence not 3 divides 8273 by NAT_4:9;
8273 = 5*1654 + 3; hence not 5 divides 8273 by NAT_4:9;
8273 = 7*1181 + 6; hence not 7 divides 8273 by NAT_4:9;
8273 = 11*752 + 1; hence not 11 divides 8273 by NAT_4:9;
8273 = 13*636 + 5; hence not 13 divides 8273 by NAT_4:9;
8273 = 17*486 + 11; hence not 17 divides 8273 by NAT_4:9;
8273 = 19*435 + 8; hence not 19 divides 8273 by NAT_4:9;
8273 = 23*359 + 16; hence not 23 divides 8273 by NAT_4:9;
8273 = 29*285 + 8; hence not 29 divides 8273 by NAT_4:9;
8273 = 31*266 + 27; hence not 31 divides 8273 by NAT_4:9;
8273 = 37*223 + 22; hence not 37 divides 8273 by NAT_4:9;
8273 = 41*201 + 32; hence not 41 divides 8273 by NAT_4:9;
8273 = 43*192 + 17; hence not 43 divides 8273 by NAT_4:9;
8273 = 47*176 + 1; hence not 47 divides 8273 by NAT_4:9;
8273 = 53*156 + 5; hence not 53 divides 8273 by NAT_4:9;
8273 = 59*140 + 13; hence not 59 divides 8273 by NAT_4:9;
8273 = 61*135 + 38; hence not 61 divides 8273 by NAT_4:9;
8273 = 67*123 + 32; hence not 67 divides 8273 by NAT_4:9;
8273 = 71*116 + 37; hence not 71 divides 8273 by NAT_4:9;
8273 = 73*113 + 24; hence not 73 divides 8273 by NAT_4:9;
8273 = 79*104 + 57; hence not 79 divides 8273 by NAT_4:9;
8273 = 83*99 + 56; hence not 83 divides 8273 by NAT_4:9;
8273 = 89*92 + 85; hence not 89 divides 8273 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8273 & n is prime
holds not n divides 8273 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8287 is prime
proof
now
8287 = 2*4143 + 1; hence not 2 divides 8287 by NAT_4:9;
8287 = 3*2762 + 1; hence not 3 divides 8287 by NAT_4:9;
8287 = 5*1657 + 2; hence not 5 divides 8287 by NAT_4:9;
8287 = 7*1183 + 6; hence not 7 divides 8287 by NAT_4:9;
8287 = 11*753 + 4; hence not 11 divides 8287 by NAT_4:9;
8287 = 13*637 + 6; hence not 13 divides 8287 by NAT_4:9;
8287 = 17*487 + 8; hence not 17 divides 8287 by NAT_4:9;
8287 = 19*436 + 3; hence not 19 divides 8287 by NAT_4:9;
8287 = 23*360 + 7; hence not 23 divides 8287 by NAT_4:9;
8287 = 29*285 + 22; hence not 29 divides 8287 by NAT_4:9;
8287 = 31*267 + 10; hence not 31 divides 8287 by NAT_4:9;
8287 = 37*223 + 36; hence not 37 divides 8287 by NAT_4:9;
8287 = 41*202 + 5; hence not 41 divides 8287 by NAT_4:9;
8287 = 43*192 + 31; hence not 43 divides 8287 by NAT_4:9;
8287 = 47*176 + 15; hence not 47 divides 8287 by NAT_4:9;
8287 = 53*156 + 19; hence not 53 divides 8287 by NAT_4:9;
8287 = 59*140 + 27; hence not 59 divides 8287 by NAT_4:9;
8287 = 61*135 + 52; hence not 61 divides 8287 by NAT_4:9;
8287 = 67*123 + 46; hence not 67 divides 8287 by NAT_4:9;
8287 = 71*116 + 51; hence not 71 divides 8287 by NAT_4:9;
8287 = 73*113 + 38; hence not 73 divides 8287 by NAT_4:9;
8287 = 79*104 + 71; hence not 79 divides 8287 by NAT_4:9;
8287 = 83*99 + 70; hence not 83 divides 8287 by NAT_4:9;
8287 = 89*93 + 10; hence not 89 divides 8287 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8287 & n is prime
holds not n divides 8287 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8291 is prime
proof
now
8291 = 2*4145 + 1; hence not 2 divides 8291 by NAT_4:9;
8291 = 3*2763 + 2; hence not 3 divides 8291 by NAT_4:9;
8291 = 5*1658 + 1; hence not 5 divides 8291 by NAT_4:9;
8291 = 7*1184 + 3; hence not 7 divides 8291 by NAT_4:9;
8291 = 11*753 + 8; hence not 11 divides 8291 by NAT_4:9;
8291 = 13*637 + 10; hence not 13 divides 8291 by NAT_4:9;
8291 = 17*487 + 12; hence not 17 divides 8291 by NAT_4:9;
8291 = 19*436 + 7; hence not 19 divides 8291 by NAT_4:9;
8291 = 23*360 + 11; hence not 23 divides 8291 by NAT_4:9;
8291 = 29*285 + 26; hence not 29 divides 8291 by NAT_4:9;
8291 = 31*267 + 14; hence not 31 divides 8291 by NAT_4:9;
8291 = 37*224 + 3; hence not 37 divides 8291 by NAT_4:9;
8291 = 41*202 + 9; hence not 41 divides 8291 by NAT_4:9;
8291 = 43*192 + 35; hence not 43 divides 8291 by NAT_4:9;
8291 = 47*176 + 19; hence not 47 divides 8291 by NAT_4:9;
8291 = 53*156 + 23; hence not 53 divides 8291 by NAT_4:9;
8291 = 59*140 + 31; hence not 59 divides 8291 by NAT_4:9;
8291 = 61*135 + 56; hence not 61 divides 8291 by NAT_4:9;
8291 = 67*123 + 50; hence not 67 divides 8291 by NAT_4:9;
8291 = 71*116 + 55; hence not 71 divides 8291 by NAT_4:9;
8291 = 73*113 + 42; hence not 73 divides 8291 by NAT_4:9;
8291 = 79*104 + 75; hence not 79 divides 8291 by NAT_4:9;
8291 = 83*99 + 74; hence not 83 divides 8291 by NAT_4:9;
8291 = 89*93 + 14; hence not 89 divides 8291 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8291 & n is prime
holds not n divides 8291 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8293 is prime
proof
now
8293 = 2*4146 + 1; hence not 2 divides 8293 by NAT_4:9;
8293 = 3*2764 + 1; hence not 3 divides 8293 by NAT_4:9;
8293 = 5*1658 + 3; hence not 5 divides 8293 by NAT_4:9;
8293 = 7*1184 + 5; hence not 7 divides 8293 by NAT_4:9;
8293 = 11*753 + 10; hence not 11 divides 8293 by NAT_4:9;
8293 = 13*637 + 12; hence not 13 divides 8293 by NAT_4:9;
8293 = 17*487 + 14; hence not 17 divides 8293 by NAT_4:9;
8293 = 19*436 + 9; hence not 19 divides 8293 by NAT_4:9;
8293 = 23*360 + 13; hence not 23 divides 8293 by NAT_4:9;
8293 = 29*285 + 28; hence not 29 divides 8293 by NAT_4:9;
8293 = 31*267 + 16; hence not 31 divides 8293 by NAT_4:9;
8293 = 37*224 + 5; hence not 37 divides 8293 by NAT_4:9;
8293 = 41*202 + 11; hence not 41 divides 8293 by NAT_4:9;
8293 = 43*192 + 37; hence not 43 divides 8293 by NAT_4:9;
8293 = 47*176 + 21; hence not 47 divides 8293 by NAT_4:9;
8293 = 53*156 + 25; hence not 53 divides 8293 by NAT_4:9;
8293 = 59*140 + 33; hence not 59 divides 8293 by NAT_4:9;
8293 = 61*135 + 58; hence not 61 divides 8293 by NAT_4:9;
8293 = 67*123 + 52; hence not 67 divides 8293 by NAT_4:9;
8293 = 71*116 + 57; hence not 71 divides 8293 by NAT_4:9;
8293 = 73*113 + 44; hence not 73 divides 8293 by NAT_4:9;
8293 = 79*104 + 77; hence not 79 divides 8293 by NAT_4:9;
8293 = 83*99 + 76; hence not 83 divides 8293 by NAT_4:9;
8293 = 89*93 + 16; hence not 89 divides 8293 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8293 & n is prime
holds not n divides 8293 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8297 is prime
proof
now
8297 = 2*4148 + 1; hence not 2 divides 8297 by NAT_4:9;
8297 = 3*2765 + 2; hence not 3 divides 8297 by NAT_4:9;
8297 = 5*1659 + 2; hence not 5 divides 8297 by NAT_4:9;
8297 = 7*1185 + 2; hence not 7 divides 8297 by NAT_4:9;
8297 = 11*754 + 3; hence not 11 divides 8297 by NAT_4:9;
8297 = 13*638 + 3; hence not 13 divides 8297 by NAT_4:9;
8297 = 17*488 + 1; hence not 17 divides 8297 by NAT_4:9;
8297 = 19*436 + 13; hence not 19 divides 8297 by NAT_4:9;
8297 = 23*360 + 17; hence not 23 divides 8297 by NAT_4:9;
8297 = 29*286 + 3; hence not 29 divides 8297 by NAT_4:9;
8297 = 31*267 + 20; hence not 31 divides 8297 by NAT_4:9;
8297 = 37*224 + 9; hence not 37 divides 8297 by NAT_4:9;
8297 = 41*202 + 15; hence not 41 divides 8297 by NAT_4:9;
8297 = 43*192 + 41; hence not 43 divides 8297 by NAT_4:9;
8297 = 47*176 + 25; hence not 47 divides 8297 by NAT_4:9;
8297 = 53*156 + 29; hence not 53 divides 8297 by NAT_4:9;
8297 = 59*140 + 37; hence not 59 divides 8297 by NAT_4:9;
8297 = 61*136 + 1; hence not 61 divides 8297 by NAT_4:9;
8297 = 67*123 + 56; hence not 67 divides 8297 by NAT_4:9;
8297 = 71*116 + 61; hence not 71 divides 8297 by NAT_4:9;
8297 = 73*113 + 48; hence not 73 divides 8297 by NAT_4:9;
8297 = 79*105 + 2; hence not 79 divides 8297 by NAT_4:9;
8297 = 83*99 + 80; hence not 83 divides 8297 by NAT_4:9;
8297 = 89*93 + 20; hence not 89 divides 8297 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8297 & n is prime
holds not n divides 8297 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8311 is prime
proof
now
8311 = 2*4155 + 1; hence not 2 divides 8311 by NAT_4:9;
8311 = 3*2770 + 1; hence not 3 divides 8311 by NAT_4:9;
8311 = 5*1662 + 1; hence not 5 divides 8311 by NAT_4:9;
8311 = 7*1187 + 2; hence not 7 divides 8311 by NAT_4:9;
8311 = 11*755 + 6; hence not 11 divides 8311 by NAT_4:9;
8311 = 13*639 + 4; hence not 13 divides 8311 by NAT_4:9;
8311 = 17*488 + 15; hence not 17 divides 8311 by NAT_4:9;
8311 = 19*437 + 8; hence not 19 divides 8311 by NAT_4:9;
8311 = 23*361 + 8; hence not 23 divides 8311 by NAT_4:9;
8311 = 29*286 + 17; hence not 29 divides 8311 by NAT_4:9;
8311 = 31*268 + 3; hence not 31 divides 8311 by NAT_4:9;
8311 = 37*224 + 23; hence not 37 divides 8311 by NAT_4:9;
8311 = 41*202 + 29; hence not 41 divides 8311 by NAT_4:9;
8311 = 43*193 + 12; hence not 43 divides 8311 by NAT_4:9;
8311 = 47*176 + 39; hence not 47 divides 8311 by NAT_4:9;
8311 = 53*156 + 43; hence not 53 divides 8311 by NAT_4:9;
8311 = 59*140 + 51; hence not 59 divides 8311 by NAT_4:9;
8311 = 61*136 + 15; hence not 61 divides 8311 by NAT_4:9;
8311 = 67*124 + 3; hence not 67 divides 8311 by NAT_4:9;
8311 = 71*117 + 4; hence not 71 divides 8311 by NAT_4:9;
8311 = 73*113 + 62; hence not 73 divides 8311 by NAT_4:9;
8311 = 79*105 + 16; hence not 79 divides 8311 by NAT_4:9;
8311 = 83*100 + 11; hence not 83 divides 8311 by NAT_4:9;
8311 = 89*93 + 34; hence not 89 divides 8311 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8311 & n is prime
holds not n divides 8311 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8317 is prime
proof
now
8317 = 2*4158 + 1; hence not 2 divides 8317 by NAT_4:9;
8317 = 3*2772 + 1; hence not 3 divides 8317 by NAT_4:9;
8317 = 5*1663 + 2; hence not 5 divides 8317 by NAT_4:9;
8317 = 7*1188 + 1; hence not 7 divides 8317 by NAT_4:9;
8317 = 11*756 + 1; hence not 11 divides 8317 by NAT_4:9;
8317 = 13*639 + 10; hence not 13 divides 8317 by NAT_4:9;
8317 = 17*489 + 4; hence not 17 divides 8317 by NAT_4:9;
8317 = 19*437 + 14; hence not 19 divides 8317 by NAT_4:9;
8317 = 23*361 + 14; hence not 23 divides 8317 by NAT_4:9;
8317 = 29*286 + 23; hence not 29 divides 8317 by NAT_4:9;
8317 = 31*268 + 9; hence not 31 divides 8317 by NAT_4:9;
8317 = 37*224 + 29; hence not 37 divides 8317 by NAT_4:9;
8317 = 41*202 + 35; hence not 41 divides 8317 by NAT_4:9;
8317 = 43*193 + 18; hence not 43 divides 8317 by NAT_4:9;
8317 = 47*176 + 45; hence not 47 divides 8317 by NAT_4:9;
8317 = 53*156 + 49; hence not 53 divides 8317 by NAT_4:9;
8317 = 59*140 + 57; hence not 59 divides 8317 by NAT_4:9;
8317 = 61*136 + 21; hence not 61 divides 8317 by NAT_4:9;
8317 = 67*124 + 9; hence not 67 divides 8317 by NAT_4:9;
8317 = 71*117 + 10; hence not 71 divides 8317 by NAT_4:9;
8317 = 73*113 + 68; hence not 73 divides 8317 by NAT_4:9;
8317 = 79*105 + 22; hence not 79 divides 8317 by NAT_4:9;
8317 = 83*100 + 17; hence not 83 divides 8317 by NAT_4:9;
8317 = 89*93 + 40; hence not 89 divides 8317 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8317 & n is prime
holds not n divides 8317 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8329 is prime
proof
now
8329 = 2*4164 + 1; hence not 2 divides 8329 by NAT_4:9;
8329 = 3*2776 + 1; hence not 3 divides 8329 by NAT_4:9;
8329 = 5*1665 + 4; hence not 5 divides 8329 by NAT_4:9;
8329 = 7*1189 + 6; hence not 7 divides 8329 by NAT_4:9;
8329 = 11*757 + 2; hence not 11 divides 8329 by NAT_4:9;
8329 = 13*640 + 9; hence not 13 divides 8329 by NAT_4:9;
8329 = 17*489 + 16; hence not 17 divides 8329 by NAT_4:9;
8329 = 19*438 + 7; hence not 19 divides 8329 by NAT_4:9;
8329 = 23*362 + 3; hence not 23 divides 8329 by NAT_4:9;
8329 = 29*287 + 6; hence not 29 divides 8329 by NAT_4:9;
8329 = 31*268 + 21; hence not 31 divides 8329 by NAT_4:9;
8329 = 37*225 + 4; hence not 37 divides 8329 by NAT_4:9;
8329 = 41*203 + 6; hence not 41 divides 8329 by NAT_4:9;
8329 = 43*193 + 30; hence not 43 divides 8329 by NAT_4:9;
8329 = 47*177 + 10; hence not 47 divides 8329 by NAT_4:9;
8329 = 53*157 + 8; hence not 53 divides 8329 by NAT_4:9;
8329 = 59*141 + 10; hence not 59 divides 8329 by NAT_4:9;
8329 = 61*136 + 33; hence not 61 divides 8329 by NAT_4:9;
8329 = 67*124 + 21; hence not 67 divides 8329 by NAT_4:9;
8329 = 71*117 + 22; hence not 71 divides 8329 by NAT_4:9;
8329 = 73*114 + 7; hence not 73 divides 8329 by NAT_4:9;
8329 = 79*105 + 34; hence not 79 divides 8329 by NAT_4:9;
8329 = 83*100 + 29; hence not 83 divides 8329 by NAT_4:9;
8329 = 89*93 + 52; hence not 89 divides 8329 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8329 & n is prime
holds not n divides 8329 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
8353 is prime
proof
now
8353 = 2*4176 + 1; hence not 2 divides 8353 by NAT_4:9;
8353 = 3*2784 + 1; hence not 3 divides 8353 by NAT_4:9;
8353 = 5*1670 + 3; hence not 5 divides 8353 by NAT_4:9;
8353 = 7*1193 + 2; hence not 7 divides 8353 by NAT_4:9;
8353 = 11*759 + 4; hence not 11 divides 8353 by NAT_4:9;
8353 = 13*642 + 7; hence not 13 divides 8353 by NAT_4:9;
8353 = 17*491 + 6; hence not 17 divides 8353 by NAT_4:9;
8353 = 19*439 + 12; hence not 19 divides 8353 by NAT_4:9;
8353 = 23*363 + 4; hence not 23 divides 8353 by NAT_4:9;
8353 = 29*288 + 1; hence not 29 divides 8353 by NAT_4:9;
8353 = 31*269 + 14; hence not 31 divides 8353 by NAT_4:9;
8353 = 37*225 + 28; hence not 37 divides 8353 by NAT_4:9;
8353 = 41*203 + 30; hence not 41 divides 8353 by NAT_4:9;
8353 = 43*194 + 11; hence not 43 divides 8353 by NAT_4:9;
8353 = 47*177 + 34; hence not 47 divides 8353 by NAT_4:9;
8353 = 53*157 + 32; hence not 53 divides 8353 by NAT_4:9;
8353 = 59*141 + 34; hence not 59 divides 8353 by NAT_4:9;
8353 = 61*136 + 57; hence not 61 divides 8353 by NAT_4:9;
8353 = 67*124 + 45; hence not 67 divides 8353 by NAT_4:9;
8353 = 71*117 + 46; hence not 71 divides 8353 by NAT_4:9;
8353 = 73*114 + 31; hence not 73 divides 8353 by NAT_4:9;
8353 = 79*105 + 58; hence not 79 divides 8353 by NAT_4:9;
8353 = 83*100 + 53; hence not 83 divides 8353 by NAT_4:9;
8353 = 89*93 + 76; hence not 89 divides 8353 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8353 & n is prime
holds not n divides 8353 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8363 is prime
proof
now
8363 = 2*4181 + 1; hence not 2 divides 8363 by NAT_4:9;
8363 = 3*2787 + 2; hence not 3 divides 8363 by NAT_4:9;
8363 = 5*1672 + 3; hence not 5 divides 8363 by NAT_4:9;
8363 = 7*1194 + 5; hence not 7 divides 8363 by NAT_4:9;
8363 = 11*760 + 3; hence not 11 divides 8363 by NAT_4:9;
8363 = 13*643 + 4; hence not 13 divides 8363 by NAT_4:9;
8363 = 17*491 + 16; hence not 17 divides 8363 by NAT_4:9;
8363 = 19*440 + 3; hence not 19 divides 8363 by NAT_4:9;
8363 = 23*363 + 14; hence not 23 divides 8363 by NAT_4:9;
8363 = 29*288 + 11; hence not 29 divides 8363 by NAT_4:9;
8363 = 31*269 + 24; hence not 31 divides 8363 by NAT_4:9;
8363 = 37*226 + 1; hence not 37 divides 8363 by NAT_4:9;
8363 = 41*203 + 40; hence not 41 divides 8363 by NAT_4:9;
8363 = 43*194 + 21; hence not 43 divides 8363 by NAT_4:9;
8363 = 47*177 + 44; hence not 47 divides 8363 by NAT_4:9;
8363 = 53*157 + 42; hence not 53 divides 8363 by NAT_4:9;
8363 = 59*141 + 44; hence not 59 divides 8363 by NAT_4:9;
8363 = 61*137 + 6; hence not 61 divides 8363 by NAT_4:9;
8363 = 67*124 + 55; hence not 67 divides 8363 by NAT_4:9;
8363 = 71*117 + 56; hence not 71 divides 8363 by NAT_4:9;
8363 = 73*114 + 41; hence not 73 divides 8363 by NAT_4:9;
8363 = 79*105 + 68; hence not 79 divides 8363 by NAT_4:9;
8363 = 83*100 + 63; hence not 83 divides 8363 by NAT_4:9;
8363 = 89*93 + 86; hence not 89 divides 8363 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8363 & n is prime
holds not n divides 8363 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8369 is prime
proof
now
8369 = 2*4184 + 1; hence not 2 divides 8369 by NAT_4:9;
8369 = 3*2789 + 2; hence not 3 divides 8369 by NAT_4:9;
8369 = 5*1673 + 4; hence not 5 divides 8369 by NAT_4:9;
8369 = 7*1195 + 4; hence not 7 divides 8369 by NAT_4:9;
8369 = 11*760 + 9; hence not 11 divides 8369 by NAT_4:9;
8369 = 13*643 + 10; hence not 13 divides 8369 by NAT_4:9;
8369 = 17*492 + 5; hence not 17 divides 8369 by NAT_4:9;
8369 = 19*440 + 9; hence not 19 divides 8369 by NAT_4:9;
8369 = 23*363 + 20; hence not 23 divides 8369 by NAT_4:9;
8369 = 29*288 + 17; hence not 29 divides 8369 by NAT_4:9;
8369 = 31*269 + 30; hence not 31 divides 8369 by NAT_4:9;
8369 = 37*226 + 7; hence not 37 divides 8369 by NAT_4:9;
8369 = 41*204 + 5; hence not 41 divides 8369 by NAT_4:9;
8369 = 43*194 + 27; hence not 43 divides 8369 by NAT_4:9;
8369 = 47*178 + 3; hence not 47 divides 8369 by NAT_4:9;
8369 = 53*157 + 48; hence not 53 divides 8369 by NAT_4:9;
8369 = 59*141 + 50; hence not 59 divides 8369 by NAT_4:9;
8369 = 61*137 + 12; hence not 61 divides 8369 by NAT_4:9;
8369 = 67*124 + 61; hence not 67 divides 8369 by NAT_4:9;
8369 = 71*117 + 62; hence not 71 divides 8369 by NAT_4:9;
8369 = 73*114 + 47; hence not 73 divides 8369 by NAT_4:9;
8369 = 79*105 + 74; hence not 79 divides 8369 by NAT_4:9;
8369 = 83*100 + 69; hence not 83 divides 8369 by NAT_4:9;
8369 = 89*94 + 3; hence not 89 divides 8369 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8369 & n is prime
holds not n divides 8369 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8377 is prime
proof
now
8377 = 2*4188 + 1; hence not 2 divides 8377 by NAT_4:9;
8377 = 3*2792 + 1; hence not 3 divides 8377 by NAT_4:9;
8377 = 5*1675 + 2; hence not 5 divides 8377 by NAT_4:9;
8377 = 7*1196 + 5; hence not 7 divides 8377 by NAT_4:9;
8377 = 11*761 + 6; hence not 11 divides 8377 by NAT_4:9;
8377 = 13*644 + 5; hence not 13 divides 8377 by NAT_4:9;
8377 = 17*492 + 13; hence not 17 divides 8377 by NAT_4:9;
8377 = 19*440 + 17; hence not 19 divides 8377 by NAT_4:9;
8377 = 23*364 + 5; hence not 23 divides 8377 by NAT_4:9;
8377 = 29*288 + 25; hence not 29 divides 8377 by NAT_4:9;
8377 = 31*270 + 7; hence not 31 divides 8377 by NAT_4:9;
8377 = 37*226 + 15; hence not 37 divides 8377 by NAT_4:9;
8377 = 41*204 + 13; hence not 41 divides 8377 by NAT_4:9;
8377 = 43*194 + 35; hence not 43 divides 8377 by NAT_4:9;
8377 = 47*178 + 11; hence not 47 divides 8377 by NAT_4:9;
8377 = 53*158 + 3; hence not 53 divides 8377 by NAT_4:9;
8377 = 59*141 + 58; hence not 59 divides 8377 by NAT_4:9;
8377 = 61*137 + 20; hence not 61 divides 8377 by NAT_4:9;
8377 = 67*125 + 2; hence not 67 divides 8377 by NAT_4:9;
8377 = 71*117 + 70; hence not 71 divides 8377 by NAT_4:9;
8377 = 73*114 + 55; hence not 73 divides 8377 by NAT_4:9;
8377 = 79*106 + 3; hence not 79 divides 8377 by NAT_4:9;
8377 = 83*100 + 77; hence not 83 divides 8377 by NAT_4:9;
8377 = 89*94 + 11; hence not 89 divides 8377 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8377 & n is prime
holds not n divides 8377 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8387 is prime
proof
now
8387 = 2*4193 + 1; hence not 2 divides 8387 by NAT_4:9;
8387 = 3*2795 + 2; hence not 3 divides 8387 by NAT_4:9;
8387 = 5*1677 + 2; hence not 5 divides 8387 by NAT_4:9;
8387 = 7*1198 + 1; hence not 7 divides 8387 by NAT_4:9;
8387 = 11*762 + 5; hence not 11 divides 8387 by NAT_4:9;
8387 = 13*645 + 2; hence not 13 divides 8387 by NAT_4:9;
8387 = 17*493 + 6; hence not 17 divides 8387 by NAT_4:9;
8387 = 19*441 + 8; hence not 19 divides 8387 by NAT_4:9;
8387 = 23*364 + 15; hence not 23 divides 8387 by NAT_4:9;
8387 = 29*289 + 6; hence not 29 divides 8387 by NAT_4:9;
8387 = 31*270 + 17; hence not 31 divides 8387 by NAT_4:9;
8387 = 37*226 + 25; hence not 37 divides 8387 by NAT_4:9;
8387 = 41*204 + 23; hence not 41 divides 8387 by NAT_4:9;
8387 = 43*195 + 2; hence not 43 divides 8387 by NAT_4:9;
8387 = 47*178 + 21; hence not 47 divides 8387 by NAT_4:9;
8387 = 53*158 + 13; hence not 53 divides 8387 by NAT_4:9;
8387 = 59*142 + 9; hence not 59 divides 8387 by NAT_4:9;
8387 = 61*137 + 30; hence not 61 divides 8387 by NAT_4:9;
8387 = 67*125 + 12; hence not 67 divides 8387 by NAT_4:9;
8387 = 71*118 + 9; hence not 71 divides 8387 by NAT_4:9;
8387 = 73*114 + 65; hence not 73 divides 8387 by NAT_4:9;
8387 = 79*106 + 13; hence not 79 divides 8387 by NAT_4:9;
8387 = 83*101 + 4; hence not 83 divides 8387 by NAT_4:9;
8387 = 89*94 + 21; hence not 89 divides 8387 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8387 & n is prime
holds not n divides 8387 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8389 is prime
proof
now
8389 = 2*4194 + 1; hence not 2 divides 8389 by NAT_4:9;
8389 = 3*2796 + 1; hence not 3 divides 8389 by NAT_4:9;
8389 = 5*1677 + 4; hence not 5 divides 8389 by NAT_4:9;
8389 = 7*1198 + 3; hence not 7 divides 8389 by NAT_4:9;
8389 = 11*762 + 7; hence not 11 divides 8389 by NAT_4:9;
8389 = 13*645 + 4; hence not 13 divides 8389 by NAT_4:9;
8389 = 17*493 + 8; hence not 17 divides 8389 by NAT_4:9;
8389 = 19*441 + 10; hence not 19 divides 8389 by NAT_4:9;
8389 = 23*364 + 17; hence not 23 divides 8389 by NAT_4:9;
8389 = 29*289 + 8; hence not 29 divides 8389 by NAT_4:9;
8389 = 31*270 + 19; hence not 31 divides 8389 by NAT_4:9;
8389 = 37*226 + 27; hence not 37 divides 8389 by NAT_4:9;
8389 = 41*204 + 25; hence not 41 divides 8389 by NAT_4:9;
8389 = 43*195 + 4; hence not 43 divides 8389 by NAT_4:9;
8389 = 47*178 + 23; hence not 47 divides 8389 by NAT_4:9;
8389 = 53*158 + 15; hence not 53 divides 8389 by NAT_4:9;
8389 = 59*142 + 11; hence not 59 divides 8389 by NAT_4:9;
8389 = 61*137 + 32; hence not 61 divides 8389 by NAT_4:9;
8389 = 67*125 + 14; hence not 67 divides 8389 by NAT_4:9;
8389 = 71*118 + 11; hence not 71 divides 8389 by NAT_4:9;
8389 = 73*114 + 67; hence not 73 divides 8389 by NAT_4:9;
8389 = 79*106 + 15; hence not 79 divides 8389 by NAT_4:9;
8389 = 83*101 + 6; hence not 83 divides 8389 by NAT_4:9;
8389 = 89*94 + 23; hence not 89 divides 8389 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8389 & n is prime
holds not n divides 8389 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
8419 is prime
proof
now
8419 = 2*4209 + 1; hence not 2 divides 8419 by NAT_4:9;
8419 = 3*2806 + 1; hence not 3 divides 8419 by NAT_4:9;
8419 = 5*1683 + 4; hence not 5 divides 8419 by NAT_4:9;
8419 = 7*1202 + 5; hence not 7 divides 8419 by NAT_4:9;
8419 = 11*765 + 4; hence not 11 divides 8419 by NAT_4:9;
8419 = 13*647 + 8; hence not 13 divides 8419 by NAT_4:9;
8419 = 17*495 + 4; hence not 17 divides 8419 by NAT_4:9;
8419 = 19*443 + 2; hence not 19 divides 8419 by NAT_4:9;
8419 = 23*366 + 1; hence not 23 divides 8419 by NAT_4:9;
8419 = 29*290 + 9; hence not 29 divides 8419 by NAT_4:9;
8419 = 31*271 + 18; hence not 31 divides 8419 by NAT_4:9;
8419 = 37*227 + 20; hence not 37 divides 8419 by NAT_4:9;
8419 = 41*205 + 14; hence not 41 divides 8419 by NAT_4:9;
8419 = 43*195 + 34; hence not 43 divides 8419 by NAT_4:9;
8419 = 47*179 + 6; hence not 47 divides 8419 by NAT_4:9;
8419 = 53*158 + 45; hence not 53 divides 8419 by NAT_4:9;
8419 = 59*142 + 41; hence not 59 divides 8419 by NAT_4:9;
8419 = 61*138 + 1; hence not 61 divides 8419 by NAT_4:9;
8419 = 67*125 + 44; hence not 67 divides 8419 by NAT_4:9;
8419 = 71*118 + 41; hence not 71 divides 8419 by NAT_4:9;
8419 = 73*115 + 24; hence not 73 divides 8419 by NAT_4:9;
8419 = 79*106 + 45; hence not 79 divides 8419 by NAT_4:9;
8419 = 83*101 + 36; hence not 83 divides 8419 by NAT_4:9;
8419 = 89*94 + 53; hence not 89 divides 8419 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8419 & n is prime
holds not n divides 8419 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8423 is prime
proof
now
8423 = 2*4211 + 1; hence not 2 divides 8423 by NAT_4:9;
8423 = 3*2807 + 2; hence not 3 divides 8423 by NAT_4:9;
8423 = 5*1684 + 3; hence not 5 divides 8423 by NAT_4:9;
8423 = 7*1203 + 2; hence not 7 divides 8423 by NAT_4:9;
8423 = 11*765 + 8; hence not 11 divides 8423 by NAT_4:9;
8423 = 13*647 + 12; hence not 13 divides 8423 by NAT_4:9;
8423 = 17*495 + 8; hence not 17 divides 8423 by NAT_4:9;
8423 = 19*443 + 6; hence not 19 divides 8423 by NAT_4:9;
8423 = 23*366 + 5; hence not 23 divides 8423 by NAT_4:9;
8423 = 29*290 + 13; hence not 29 divides 8423 by NAT_4:9;
8423 = 31*271 + 22; hence not 31 divides 8423 by NAT_4:9;
8423 = 37*227 + 24; hence not 37 divides 8423 by NAT_4:9;
8423 = 41*205 + 18; hence not 41 divides 8423 by NAT_4:9;
8423 = 43*195 + 38; hence not 43 divides 8423 by NAT_4:9;
8423 = 47*179 + 10; hence not 47 divides 8423 by NAT_4:9;
8423 = 53*158 + 49; hence not 53 divides 8423 by NAT_4:9;
8423 = 59*142 + 45; hence not 59 divides 8423 by NAT_4:9;
8423 = 61*138 + 5; hence not 61 divides 8423 by NAT_4:9;
8423 = 67*125 + 48; hence not 67 divides 8423 by NAT_4:9;
8423 = 71*118 + 45; hence not 71 divides 8423 by NAT_4:9;
8423 = 73*115 + 28; hence not 73 divides 8423 by NAT_4:9;
8423 = 79*106 + 49; hence not 79 divides 8423 by NAT_4:9;
8423 = 83*101 + 40; hence not 83 divides 8423 by NAT_4:9;
8423 = 89*94 + 57; hence not 89 divides 8423 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8423 & n is prime
holds not n divides 8423 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8429 is prime
proof
now
8429 = 2*4214 + 1; hence not 2 divides 8429 by NAT_4:9;
8429 = 3*2809 + 2; hence not 3 divides 8429 by NAT_4:9;
8429 = 5*1685 + 4; hence not 5 divides 8429 by NAT_4:9;
8429 = 7*1204 + 1; hence not 7 divides 8429 by NAT_4:9;
8429 = 11*766 + 3; hence not 11 divides 8429 by NAT_4:9;
8429 = 13*648 + 5; hence not 13 divides 8429 by NAT_4:9;
8429 = 17*495 + 14; hence not 17 divides 8429 by NAT_4:9;
8429 = 19*443 + 12; hence not 19 divides 8429 by NAT_4:9;
8429 = 23*366 + 11; hence not 23 divides 8429 by NAT_4:9;
8429 = 29*290 + 19; hence not 29 divides 8429 by NAT_4:9;
8429 = 31*271 + 28; hence not 31 divides 8429 by NAT_4:9;
8429 = 37*227 + 30; hence not 37 divides 8429 by NAT_4:9;
8429 = 41*205 + 24; hence not 41 divides 8429 by NAT_4:9;
8429 = 43*196 + 1; hence not 43 divides 8429 by NAT_4:9;
8429 = 47*179 + 16; hence not 47 divides 8429 by NAT_4:9;
8429 = 53*159 + 2; hence not 53 divides 8429 by NAT_4:9;
8429 = 59*142 + 51; hence not 59 divides 8429 by NAT_4:9;
8429 = 61*138 + 11; hence not 61 divides 8429 by NAT_4:9;
8429 = 67*125 + 54; hence not 67 divides 8429 by NAT_4:9;
8429 = 71*118 + 51; hence not 71 divides 8429 by NAT_4:9;
8429 = 73*115 + 34; hence not 73 divides 8429 by NAT_4:9;
8429 = 79*106 + 55; hence not 79 divides 8429 by NAT_4:9;
8429 = 83*101 + 46; hence not 83 divides 8429 by NAT_4:9;
8429 = 89*94 + 63; hence not 89 divides 8429 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8429 & n is prime
holds not n divides 8429 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8431 is prime
proof
now
8431 = 2*4215 + 1; hence not 2 divides 8431 by NAT_4:9;
8431 = 3*2810 + 1; hence not 3 divides 8431 by NAT_4:9;
8431 = 5*1686 + 1; hence not 5 divides 8431 by NAT_4:9;
8431 = 7*1204 + 3; hence not 7 divides 8431 by NAT_4:9;
8431 = 11*766 + 5; hence not 11 divides 8431 by NAT_4:9;
8431 = 13*648 + 7; hence not 13 divides 8431 by NAT_4:9;
8431 = 17*495 + 16; hence not 17 divides 8431 by NAT_4:9;
8431 = 19*443 + 14; hence not 19 divides 8431 by NAT_4:9;
8431 = 23*366 + 13; hence not 23 divides 8431 by NAT_4:9;
8431 = 29*290 + 21; hence not 29 divides 8431 by NAT_4:9;
8431 = 31*271 + 30; hence not 31 divides 8431 by NAT_4:9;
8431 = 37*227 + 32; hence not 37 divides 8431 by NAT_4:9;
8431 = 41*205 + 26; hence not 41 divides 8431 by NAT_4:9;
8431 = 43*196 + 3; hence not 43 divides 8431 by NAT_4:9;
8431 = 47*179 + 18; hence not 47 divides 8431 by NAT_4:9;
8431 = 53*159 + 4; hence not 53 divides 8431 by NAT_4:9;
8431 = 59*142 + 53; hence not 59 divides 8431 by NAT_4:9;
8431 = 61*138 + 13; hence not 61 divides 8431 by NAT_4:9;
8431 = 67*125 + 56; hence not 67 divides 8431 by NAT_4:9;
8431 = 71*118 + 53; hence not 71 divides 8431 by NAT_4:9;
8431 = 73*115 + 36; hence not 73 divides 8431 by NAT_4:9;
8431 = 79*106 + 57; hence not 79 divides 8431 by NAT_4:9;
8431 = 83*101 + 48; hence not 83 divides 8431 by NAT_4:9;
8431 = 89*94 + 65; hence not 89 divides 8431 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8431 & n is prime
holds not n divides 8431 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8443 is prime
proof
now
8443 = 2*4221 + 1; hence not 2 divides 8443 by NAT_4:9;
8443 = 3*2814 + 1; hence not 3 divides 8443 by NAT_4:9;
8443 = 5*1688 + 3; hence not 5 divides 8443 by NAT_4:9;
8443 = 7*1206 + 1; hence not 7 divides 8443 by NAT_4:9;
8443 = 11*767 + 6; hence not 11 divides 8443 by NAT_4:9;
8443 = 13*649 + 6; hence not 13 divides 8443 by NAT_4:9;
8443 = 17*496 + 11; hence not 17 divides 8443 by NAT_4:9;
8443 = 19*444 + 7; hence not 19 divides 8443 by NAT_4:9;
8443 = 23*367 + 2; hence not 23 divides 8443 by NAT_4:9;
8443 = 29*291 + 4; hence not 29 divides 8443 by NAT_4:9;
8443 = 31*272 + 11; hence not 31 divides 8443 by NAT_4:9;
8443 = 37*228 + 7; hence not 37 divides 8443 by NAT_4:9;
8443 = 41*205 + 38; hence not 41 divides 8443 by NAT_4:9;
8443 = 43*196 + 15; hence not 43 divides 8443 by NAT_4:9;
8443 = 47*179 + 30; hence not 47 divides 8443 by NAT_4:9;
8443 = 53*159 + 16; hence not 53 divides 8443 by NAT_4:9;
8443 = 59*143 + 6; hence not 59 divides 8443 by NAT_4:9;
8443 = 61*138 + 25; hence not 61 divides 8443 by NAT_4:9;
8443 = 67*126 + 1; hence not 67 divides 8443 by NAT_4:9;
8443 = 71*118 + 65; hence not 71 divides 8443 by NAT_4:9;
8443 = 73*115 + 48; hence not 73 divides 8443 by NAT_4:9;
8443 = 79*106 + 69; hence not 79 divides 8443 by NAT_4:9;
8443 = 83*101 + 60; hence not 83 divides 8443 by NAT_4:9;
8443 = 89*94 + 77; hence not 89 divides 8443 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8443 & n is prime
holds not n divides 8443 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8447 is prime
proof
now
8447 = 2*4223 + 1; hence not 2 divides 8447 by NAT_4:9;
8447 = 3*2815 + 2; hence not 3 divides 8447 by NAT_4:9;
8447 = 5*1689 + 2; hence not 5 divides 8447 by NAT_4:9;
8447 = 7*1206 + 5; hence not 7 divides 8447 by NAT_4:9;
8447 = 11*767 + 10; hence not 11 divides 8447 by NAT_4:9;
8447 = 13*649 + 10; hence not 13 divides 8447 by NAT_4:9;
8447 = 17*496 + 15; hence not 17 divides 8447 by NAT_4:9;
8447 = 19*444 + 11; hence not 19 divides 8447 by NAT_4:9;
8447 = 23*367 + 6; hence not 23 divides 8447 by NAT_4:9;
8447 = 29*291 + 8; hence not 29 divides 8447 by NAT_4:9;
8447 = 31*272 + 15; hence not 31 divides 8447 by NAT_4:9;
8447 = 37*228 + 11; hence not 37 divides 8447 by NAT_4:9;
8447 = 41*206 + 1; hence not 41 divides 8447 by NAT_4:9;
8447 = 43*196 + 19; hence not 43 divides 8447 by NAT_4:9;
8447 = 47*179 + 34; hence not 47 divides 8447 by NAT_4:9;
8447 = 53*159 + 20; hence not 53 divides 8447 by NAT_4:9;
8447 = 59*143 + 10; hence not 59 divides 8447 by NAT_4:9;
8447 = 61*138 + 29; hence not 61 divides 8447 by NAT_4:9;
8447 = 67*126 + 5; hence not 67 divides 8447 by NAT_4:9;
8447 = 71*118 + 69; hence not 71 divides 8447 by NAT_4:9;
8447 = 73*115 + 52; hence not 73 divides 8447 by NAT_4:9;
8447 = 79*106 + 73; hence not 79 divides 8447 by NAT_4:9;
8447 = 83*101 + 64; hence not 83 divides 8447 by NAT_4:9;
8447 = 89*94 + 81; hence not 89 divides 8447 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8447 & n is prime
holds not n divides 8447 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8461 is prime
proof
now
8461 = 2*4230 + 1; hence not 2 divides 8461 by NAT_4:9;
8461 = 3*2820 + 1; hence not 3 divides 8461 by NAT_4:9;
8461 = 5*1692 + 1; hence not 5 divides 8461 by NAT_4:9;
8461 = 7*1208 + 5; hence not 7 divides 8461 by NAT_4:9;
8461 = 11*769 + 2; hence not 11 divides 8461 by NAT_4:9;
8461 = 13*650 + 11; hence not 13 divides 8461 by NAT_4:9;
8461 = 17*497 + 12; hence not 17 divides 8461 by NAT_4:9;
8461 = 19*445 + 6; hence not 19 divides 8461 by NAT_4:9;
8461 = 23*367 + 20; hence not 23 divides 8461 by NAT_4:9;
8461 = 29*291 + 22; hence not 29 divides 8461 by NAT_4:9;
8461 = 31*272 + 29; hence not 31 divides 8461 by NAT_4:9;
8461 = 37*228 + 25; hence not 37 divides 8461 by NAT_4:9;
8461 = 41*206 + 15; hence not 41 divides 8461 by NAT_4:9;
8461 = 43*196 + 33; hence not 43 divides 8461 by NAT_4:9;
8461 = 47*180 + 1; hence not 47 divides 8461 by NAT_4:9;
8461 = 53*159 + 34; hence not 53 divides 8461 by NAT_4:9;
8461 = 59*143 + 24; hence not 59 divides 8461 by NAT_4:9;
8461 = 61*138 + 43; hence not 61 divides 8461 by NAT_4:9;
8461 = 67*126 + 19; hence not 67 divides 8461 by NAT_4:9;
8461 = 71*119 + 12; hence not 71 divides 8461 by NAT_4:9;
8461 = 73*115 + 66; hence not 73 divides 8461 by NAT_4:9;
8461 = 79*107 + 8; hence not 79 divides 8461 by NAT_4:9;
8461 = 83*101 + 78; hence not 83 divides 8461 by NAT_4:9;
8461 = 89*95 + 6; hence not 89 divides 8461 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8461 & n is prime
holds not n divides 8461 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8467 is prime
proof
now
8467 = 2*4233 + 1; hence not 2 divides 8467 by NAT_4:9;
8467 = 3*2822 + 1; hence not 3 divides 8467 by NAT_4:9;
8467 = 5*1693 + 2; hence not 5 divides 8467 by NAT_4:9;
8467 = 7*1209 + 4; hence not 7 divides 8467 by NAT_4:9;
8467 = 11*769 + 8; hence not 11 divides 8467 by NAT_4:9;
8467 = 13*651 + 4; hence not 13 divides 8467 by NAT_4:9;
8467 = 17*498 + 1; hence not 17 divides 8467 by NAT_4:9;
8467 = 19*445 + 12; hence not 19 divides 8467 by NAT_4:9;
8467 = 23*368 + 3; hence not 23 divides 8467 by NAT_4:9;
8467 = 29*291 + 28; hence not 29 divides 8467 by NAT_4:9;
8467 = 31*273 + 4; hence not 31 divides 8467 by NAT_4:9;
8467 = 37*228 + 31; hence not 37 divides 8467 by NAT_4:9;
8467 = 41*206 + 21; hence not 41 divides 8467 by NAT_4:9;
8467 = 43*196 + 39; hence not 43 divides 8467 by NAT_4:9;
8467 = 47*180 + 7; hence not 47 divides 8467 by NAT_4:9;
8467 = 53*159 + 40; hence not 53 divides 8467 by NAT_4:9;
8467 = 59*143 + 30; hence not 59 divides 8467 by NAT_4:9;
8467 = 61*138 + 49; hence not 61 divides 8467 by NAT_4:9;
8467 = 67*126 + 25; hence not 67 divides 8467 by NAT_4:9;
8467 = 71*119 + 18; hence not 71 divides 8467 by NAT_4:9;
8467 = 73*115 + 72; hence not 73 divides 8467 by NAT_4:9;
8467 = 79*107 + 14; hence not 79 divides 8467 by NAT_4:9;
8467 = 83*102 + 1; hence not 83 divides 8467 by NAT_4:9;
8467 = 89*95 + 12; hence not 89 divides 8467 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8467 & n is prime
holds not n divides 8467 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 33
theorem
8501 is prime
proof
now
8501 = 2*4250 + 1; hence not 2 divides 8501 by NAT_4:9;
8501 = 3*2833 + 2; hence not 3 divides 8501 by NAT_4:9;
8501 = 5*1700 + 1; hence not 5 divides 8501 by NAT_4:9;
8501 = 7*1214 + 3; hence not 7 divides 8501 by NAT_4:9;
8501 = 11*772 + 9; hence not 11 divides 8501 by NAT_4:9;
8501 = 13*653 + 12; hence not 13 divides 8501 by NAT_4:9;
8501 = 17*500 + 1; hence not 17 divides 8501 by NAT_4:9;
8501 = 19*447 + 8; hence not 19 divides 8501 by NAT_4:9;
8501 = 23*369 + 14; hence not 23 divides 8501 by NAT_4:9;
8501 = 29*293 + 4; hence not 29 divides 8501 by NAT_4:9;
8501 = 31*274 + 7; hence not 31 divides 8501 by NAT_4:9;
8501 = 37*229 + 28; hence not 37 divides 8501 by NAT_4:9;
8501 = 41*207 + 14; hence not 41 divides 8501 by NAT_4:9;
8501 = 43*197 + 30; hence not 43 divides 8501 by NAT_4:9;
8501 = 47*180 + 41; hence not 47 divides 8501 by NAT_4:9;
8501 = 53*160 + 21; hence not 53 divides 8501 by NAT_4:9;
8501 = 59*144 + 5; hence not 59 divides 8501 by NAT_4:9;
8501 = 61*139 + 22; hence not 61 divides 8501 by NAT_4:9;
8501 = 67*126 + 59; hence not 67 divides 8501 by NAT_4:9;
8501 = 71*119 + 52; hence not 71 divides 8501 by NAT_4:9;
8501 = 73*116 + 33; hence not 73 divides 8501 by NAT_4:9;
8501 = 79*107 + 48; hence not 79 divides 8501 by NAT_4:9;
8501 = 83*102 + 35; hence not 83 divides 8501 by NAT_4:9;
8501 = 89*95 + 46; hence not 89 divides 8501 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8501 & n is prime
holds not n divides 8501 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8513 is prime
proof
now
8513 = 2*4256 + 1; hence not 2 divides 8513 by NAT_4:9;
8513 = 3*2837 + 2; hence not 3 divides 8513 by NAT_4:9;
8513 = 5*1702 + 3; hence not 5 divides 8513 by NAT_4:9;
8513 = 7*1216 + 1; hence not 7 divides 8513 by NAT_4:9;
8513 = 11*773 + 10; hence not 11 divides 8513 by NAT_4:9;
8513 = 13*654 + 11; hence not 13 divides 8513 by NAT_4:9;
8513 = 17*500 + 13; hence not 17 divides 8513 by NAT_4:9;
8513 = 19*448 + 1; hence not 19 divides 8513 by NAT_4:9;
8513 = 23*370 + 3; hence not 23 divides 8513 by NAT_4:9;
8513 = 29*293 + 16; hence not 29 divides 8513 by NAT_4:9;
8513 = 31*274 + 19; hence not 31 divides 8513 by NAT_4:9;
8513 = 37*230 + 3; hence not 37 divides 8513 by NAT_4:9;
8513 = 41*207 + 26; hence not 41 divides 8513 by NAT_4:9;
8513 = 43*197 + 42; hence not 43 divides 8513 by NAT_4:9;
8513 = 47*181 + 6; hence not 47 divides 8513 by NAT_4:9;
8513 = 53*160 + 33; hence not 53 divides 8513 by NAT_4:9;
8513 = 59*144 + 17; hence not 59 divides 8513 by NAT_4:9;
8513 = 61*139 + 34; hence not 61 divides 8513 by NAT_4:9;
8513 = 67*127 + 4; hence not 67 divides 8513 by NAT_4:9;
8513 = 71*119 + 64; hence not 71 divides 8513 by NAT_4:9;
8513 = 73*116 + 45; hence not 73 divides 8513 by NAT_4:9;
8513 = 79*107 + 60; hence not 79 divides 8513 by NAT_4:9;
8513 = 83*102 + 47; hence not 83 divides 8513 by NAT_4:9;
8513 = 89*95 + 58; hence not 89 divides 8513 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8513 & n is prime
holds not n divides 8513 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8521 is prime
proof
now
8521 = 2*4260 + 1; hence not 2 divides 8521 by NAT_4:9;
8521 = 3*2840 + 1; hence not 3 divides 8521 by NAT_4:9;
8521 = 5*1704 + 1; hence not 5 divides 8521 by NAT_4:9;
8521 = 7*1217 + 2; hence not 7 divides 8521 by NAT_4:9;
8521 = 11*774 + 7; hence not 11 divides 8521 by NAT_4:9;
8521 = 13*655 + 6; hence not 13 divides 8521 by NAT_4:9;
8521 = 17*501 + 4; hence not 17 divides 8521 by NAT_4:9;
8521 = 19*448 + 9; hence not 19 divides 8521 by NAT_4:9;
8521 = 23*370 + 11; hence not 23 divides 8521 by NAT_4:9;
8521 = 29*293 + 24; hence not 29 divides 8521 by NAT_4:9;
8521 = 31*274 + 27; hence not 31 divides 8521 by NAT_4:9;
8521 = 37*230 + 11; hence not 37 divides 8521 by NAT_4:9;
8521 = 41*207 + 34; hence not 41 divides 8521 by NAT_4:9;
8521 = 43*198 + 7; hence not 43 divides 8521 by NAT_4:9;
8521 = 47*181 + 14; hence not 47 divides 8521 by NAT_4:9;
8521 = 53*160 + 41; hence not 53 divides 8521 by NAT_4:9;
8521 = 59*144 + 25; hence not 59 divides 8521 by NAT_4:9;
8521 = 61*139 + 42; hence not 61 divides 8521 by NAT_4:9;
8521 = 67*127 + 12; hence not 67 divides 8521 by NAT_4:9;
8521 = 71*120 + 1; hence not 71 divides 8521 by NAT_4:9;
8521 = 73*116 + 53; hence not 73 divides 8521 by NAT_4:9;
8521 = 79*107 + 68; hence not 79 divides 8521 by NAT_4:9;
8521 = 83*102 + 55; hence not 83 divides 8521 by NAT_4:9;
8521 = 89*95 + 66; hence not 89 divides 8521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8521 & n is prime
holds not n divides 8521 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8527 is prime
proof
now
8527 = 2*4263 + 1; hence not 2 divides 8527 by NAT_4:9;
8527 = 3*2842 + 1; hence not 3 divides 8527 by NAT_4:9;
8527 = 5*1705 + 2; hence not 5 divides 8527 by NAT_4:9;
8527 = 7*1218 + 1; hence not 7 divides 8527 by NAT_4:9;
8527 = 11*775 + 2; hence not 11 divides 8527 by NAT_4:9;
8527 = 13*655 + 12; hence not 13 divides 8527 by NAT_4:9;
8527 = 17*501 + 10; hence not 17 divides 8527 by NAT_4:9;
8527 = 19*448 + 15; hence not 19 divides 8527 by NAT_4:9;
8527 = 23*370 + 17; hence not 23 divides 8527 by NAT_4:9;
8527 = 29*294 + 1; hence not 29 divides 8527 by NAT_4:9;
8527 = 31*275 + 2; hence not 31 divides 8527 by NAT_4:9;
8527 = 37*230 + 17; hence not 37 divides 8527 by NAT_4:9;
8527 = 41*207 + 40; hence not 41 divides 8527 by NAT_4:9;
8527 = 43*198 + 13; hence not 43 divides 8527 by NAT_4:9;
8527 = 47*181 + 20; hence not 47 divides 8527 by NAT_4:9;
8527 = 53*160 + 47; hence not 53 divides 8527 by NAT_4:9;
8527 = 59*144 + 31; hence not 59 divides 8527 by NAT_4:9;
8527 = 61*139 + 48; hence not 61 divides 8527 by NAT_4:9;
8527 = 67*127 + 18; hence not 67 divides 8527 by NAT_4:9;
8527 = 71*120 + 7; hence not 71 divides 8527 by NAT_4:9;
8527 = 73*116 + 59; hence not 73 divides 8527 by NAT_4:9;
8527 = 79*107 + 74; hence not 79 divides 8527 by NAT_4:9;
8527 = 83*102 + 61; hence not 83 divides 8527 by NAT_4:9;
8527 = 89*95 + 72; hence not 89 divides 8527 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8527 & n is prime
holds not n divides 8527 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8537 is prime
proof
now
8537 = 2*4268 + 1; hence not 2 divides 8537 by NAT_4:9;
8537 = 3*2845 + 2; hence not 3 divides 8537 by NAT_4:9;
8537 = 5*1707 + 2; hence not 5 divides 8537 by NAT_4:9;
8537 = 7*1219 + 4; hence not 7 divides 8537 by NAT_4:9;
8537 = 11*776 + 1; hence not 11 divides 8537 by NAT_4:9;
8537 = 13*656 + 9; hence not 13 divides 8537 by NAT_4:9;
8537 = 17*502 + 3; hence not 17 divides 8537 by NAT_4:9;
8537 = 19*449 + 6; hence not 19 divides 8537 by NAT_4:9;
8537 = 23*371 + 4; hence not 23 divides 8537 by NAT_4:9;
8537 = 29*294 + 11; hence not 29 divides 8537 by NAT_4:9;
8537 = 31*275 + 12; hence not 31 divides 8537 by NAT_4:9;
8537 = 37*230 + 27; hence not 37 divides 8537 by NAT_4:9;
8537 = 41*208 + 9; hence not 41 divides 8537 by NAT_4:9;
8537 = 43*198 + 23; hence not 43 divides 8537 by NAT_4:9;
8537 = 47*181 + 30; hence not 47 divides 8537 by NAT_4:9;
8537 = 53*161 + 4; hence not 53 divides 8537 by NAT_4:9;
8537 = 59*144 + 41; hence not 59 divides 8537 by NAT_4:9;
8537 = 61*139 + 58; hence not 61 divides 8537 by NAT_4:9;
8537 = 67*127 + 28; hence not 67 divides 8537 by NAT_4:9;
8537 = 71*120 + 17; hence not 71 divides 8537 by NAT_4:9;
8537 = 73*116 + 69; hence not 73 divides 8537 by NAT_4:9;
8537 = 79*108 + 5; hence not 79 divides 8537 by NAT_4:9;
8537 = 83*102 + 71; hence not 83 divides 8537 by NAT_4:9;
8537 = 89*95 + 82; hence not 89 divides 8537 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8537 & n is prime
holds not n divides 8537 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8539 is prime
proof
now
8539 = 2*4269 + 1; hence not 2 divides 8539 by NAT_4:9;
8539 = 3*2846 + 1; hence not 3 divides 8539 by NAT_4:9;
8539 = 5*1707 + 4; hence not 5 divides 8539 by NAT_4:9;
8539 = 7*1219 + 6; hence not 7 divides 8539 by NAT_4:9;
8539 = 11*776 + 3; hence not 11 divides 8539 by NAT_4:9;
8539 = 13*656 + 11; hence not 13 divides 8539 by NAT_4:9;
8539 = 17*502 + 5; hence not 17 divides 8539 by NAT_4:9;
8539 = 19*449 + 8; hence not 19 divides 8539 by NAT_4:9;
8539 = 23*371 + 6; hence not 23 divides 8539 by NAT_4:9;
8539 = 29*294 + 13; hence not 29 divides 8539 by NAT_4:9;
8539 = 31*275 + 14; hence not 31 divides 8539 by NAT_4:9;
8539 = 37*230 + 29; hence not 37 divides 8539 by NAT_4:9;
8539 = 41*208 + 11; hence not 41 divides 8539 by NAT_4:9;
8539 = 43*198 + 25; hence not 43 divides 8539 by NAT_4:9;
8539 = 47*181 + 32; hence not 47 divides 8539 by NAT_4:9;
8539 = 53*161 + 6; hence not 53 divides 8539 by NAT_4:9;
8539 = 59*144 + 43; hence not 59 divides 8539 by NAT_4:9;
8539 = 61*139 + 60; hence not 61 divides 8539 by NAT_4:9;
8539 = 67*127 + 30; hence not 67 divides 8539 by NAT_4:9;
8539 = 71*120 + 19; hence not 71 divides 8539 by NAT_4:9;
8539 = 73*116 + 71; hence not 73 divides 8539 by NAT_4:9;
8539 = 79*108 + 7; hence not 79 divides 8539 by NAT_4:9;
8539 = 83*102 + 73; hence not 83 divides 8539 by NAT_4:9;
8539 = 89*95 + 84; hence not 89 divides 8539 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8539 & n is prime
holds not n divides 8539 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8543 is prime
proof
now
8543 = 2*4271 + 1; hence not 2 divides 8543 by NAT_4:9;
8543 = 3*2847 + 2; hence not 3 divides 8543 by NAT_4:9;
8543 = 5*1708 + 3; hence not 5 divides 8543 by NAT_4:9;
8543 = 7*1220 + 3; hence not 7 divides 8543 by NAT_4:9;
8543 = 11*776 + 7; hence not 11 divides 8543 by NAT_4:9;
8543 = 13*657 + 2; hence not 13 divides 8543 by NAT_4:9;
8543 = 17*502 + 9; hence not 17 divides 8543 by NAT_4:9;
8543 = 19*449 + 12; hence not 19 divides 8543 by NAT_4:9;
8543 = 23*371 + 10; hence not 23 divides 8543 by NAT_4:9;
8543 = 29*294 + 17; hence not 29 divides 8543 by NAT_4:9;
8543 = 31*275 + 18; hence not 31 divides 8543 by NAT_4:9;
8543 = 37*230 + 33; hence not 37 divides 8543 by NAT_4:9;
8543 = 41*208 + 15; hence not 41 divides 8543 by NAT_4:9;
8543 = 43*198 + 29; hence not 43 divides 8543 by NAT_4:9;
8543 = 47*181 + 36; hence not 47 divides 8543 by NAT_4:9;
8543 = 53*161 + 10; hence not 53 divides 8543 by NAT_4:9;
8543 = 59*144 + 47; hence not 59 divides 8543 by NAT_4:9;
8543 = 61*140 + 3; hence not 61 divides 8543 by NAT_4:9;
8543 = 67*127 + 34; hence not 67 divides 8543 by NAT_4:9;
8543 = 71*120 + 23; hence not 71 divides 8543 by NAT_4:9;
8543 = 73*117 + 2; hence not 73 divides 8543 by NAT_4:9;
8543 = 79*108 + 11; hence not 79 divides 8543 by NAT_4:9;
8543 = 83*102 + 77; hence not 83 divides 8543 by NAT_4:9;
8543 = 89*95 + 88; hence not 89 divides 8543 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8543 & n is prime
holds not n divides 8543 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
8563 is prime
proof
now
8563 = 2*4281 + 1; hence not 2 divides 8563 by NAT_4:9;
8563 = 3*2854 + 1; hence not 3 divides 8563 by NAT_4:9;
8563 = 5*1712 + 3; hence not 5 divides 8563 by NAT_4:9;
8563 = 7*1223 + 2; hence not 7 divides 8563 by NAT_4:9;
8563 = 11*778 + 5; hence not 11 divides 8563 by NAT_4:9;
8563 = 13*658 + 9; hence not 13 divides 8563 by NAT_4:9;
8563 = 17*503 + 12; hence not 17 divides 8563 by NAT_4:9;
8563 = 19*450 + 13; hence not 19 divides 8563 by NAT_4:9;
8563 = 23*372 + 7; hence not 23 divides 8563 by NAT_4:9;
8563 = 29*295 + 8; hence not 29 divides 8563 by NAT_4:9;
8563 = 31*276 + 7; hence not 31 divides 8563 by NAT_4:9;
8563 = 37*231 + 16; hence not 37 divides 8563 by NAT_4:9;
8563 = 41*208 + 35; hence not 41 divides 8563 by NAT_4:9;
8563 = 43*199 + 6; hence not 43 divides 8563 by NAT_4:9;
8563 = 47*182 + 9; hence not 47 divides 8563 by NAT_4:9;
8563 = 53*161 + 30; hence not 53 divides 8563 by NAT_4:9;
8563 = 59*145 + 8; hence not 59 divides 8563 by NAT_4:9;
8563 = 61*140 + 23; hence not 61 divides 8563 by NAT_4:9;
8563 = 67*127 + 54; hence not 67 divides 8563 by NAT_4:9;
8563 = 71*120 + 43; hence not 71 divides 8563 by NAT_4:9;
8563 = 73*117 + 22; hence not 73 divides 8563 by NAT_4:9;
8563 = 79*108 + 31; hence not 79 divides 8563 by NAT_4:9;
8563 = 83*103 + 14; hence not 83 divides 8563 by NAT_4:9;
8563 = 89*96 + 19; hence not 89 divides 8563 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8563 & n is prime
holds not n divides 8563 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8573 is prime
proof
now
8573 = 2*4286 + 1; hence not 2 divides 8573 by NAT_4:9;
8573 = 3*2857 + 2; hence not 3 divides 8573 by NAT_4:9;
8573 = 5*1714 + 3; hence not 5 divides 8573 by NAT_4:9;
8573 = 7*1224 + 5; hence not 7 divides 8573 by NAT_4:9;
8573 = 11*779 + 4; hence not 11 divides 8573 by NAT_4:9;
8573 = 13*659 + 6; hence not 13 divides 8573 by NAT_4:9;
8573 = 17*504 + 5; hence not 17 divides 8573 by NAT_4:9;
8573 = 19*451 + 4; hence not 19 divides 8573 by NAT_4:9;
8573 = 23*372 + 17; hence not 23 divides 8573 by NAT_4:9;
8573 = 29*295 + 18; hence not 29 divides 8573 by NAT_4:9;
8573 = 31*276 + 17; hence not 31 divides 8573 by NAT_4:9;
8573 = 37*231 + 26; hence not 37 divides 8573 by NAT_4:9;
8573 = 41*209 + 4; hence not 41 divides 8573 by NAT_4:9;
8573 = 43*199 + 16; hence not 43 divides 8573 by NAT_4:9;
8573 = 47*182 + 19; hence not 47 divides 8573 by NAT_4:9;
8573 = 53*161 + 40; hence not 53 divides 8573 by NAT_4:9;
8573 = 59*145 + 18; hence not 59 divides 8573 by NAT_4:9;
8573 = 61*140 + 33; hence not 61 divides 8573 by NAT_4:9;
8573 = 67*127 + 64; hence not 67 divides 8573 by NAT_4:9;
8573 = 71*120 + 53; hence not 71 divides 8573 by NAT_4:9;
8573 = 73*117 + 32; hence not 73 divides 8573 by NAT_4:9;
8573 = 79*108 + 41; hence not 79 divides 8573 by NAT_4:9;
8573 = 83*103 + 24; hence not 83 divides 8573 by NAT_4:9;
8573 = 89*96 + 29; hence not 89 divides 8573 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8573 & n is prime
holds not n divides 8573 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8581 is prime
proof
now
8581 = 2*4290 + 1; hence not 2 divides 8581 by NAT_4:9;
8581 = 3*2860 + 1; hence not 3 divides 8581 by NAT_4:9;
8581 = 5*1716 + 1; hence not 5 divides 8581 by NAT_4:9;
8581 = 7*1225 + 6; hence not 7 divides 8581 by NAT_4:9;
8581 = 11*780 + 1; hence not 11 divides 8581 by NAT_4:9;
8581 = 13*660 + 1; hence not 13 divides 8581 by NAT_4:9;
8581 = 17*504 + 13; hence not 17 divides 8581 by NAT_4:9;
8581 = 19*451 + 12; hence not 19 divides 8581 by NAT_4:9;
8581 = 23*373 + 2; hence not 23 divides 8581 by NAT_4:9;
8581 = 29*295 + 26; hence not 29 divides 8581 by NAT_4:9;
8581 = 31*276 + 25; hence not 31 divides 8581 by NAT_4:9;
8581 = 37*231 + 34; hence not 37 divides 8581 by NAT_4:9;
8581 = 41*209 + 12; hence not 41 divides 8581 by NAT_4:9;
8581 = 43*199 + 24; hence not 43 divides 8581 by NAT_4:9;
8581 = 47*182 + 27; hence not 47 divides 8581 by NAT_4:9;
8581 = 53*161 + 48; hence not 53 divides 8581 by NAT_4:9;
8581 = 59*145 + 26; hence not 59 divides 8581 by NAT_4:9;
8581 = 61*140 + 41; hence not 61 divides 8581 by NAT_4:9;
8581 = 67*128 + 5; hence not 67 divides 8581 by NAT_4:9;
8581 = 71*120 + 61; hence not 71 divides 8581 by NAT_4:9;
8581 = 73*117 + 40; hence not 73 divides 8581 by NAT_4:9;
8581 = 79*108 + 49; hence not 79 divides 8581 by NAT_4:9;
8581 = 83*103 + 32; hence not 83 divides 8581 by NAT_4:9;
8581 = 89*96 + 37; hence not 89 divides 8581 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8581 & n is prime
holds not n divides 8581 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
8597 is prime
proof
now
8597 = 2*4298 + 1; hence not 2 divides 8597 by NAT_4:9;
8597 = 3*2865 + 2; hence not 3 divides 8597 by NAT_4:9;
8597 = 5*1719 + 2; hence not 5 divides 8597 by NAT_4:9;
8597 = 7*1228 + 1; hence not 7 divides 8597 by NAT_4:9;
8597 = 11*781 + 6; hence not 11 divides 8597 by NAT_4:9;
8597 = 13*661 + 4; hence not 13 divides 8597 by NAT_4:9;
8597 = 17*505 + 12; hence not 17 divides 8597 by NAT_4:9;
8597 = 19*452 + 9; hence not 19 divides 8597 by NAT_4:9;
8597 = 23*373 + 18; hence not 23 divides 8597 by NAT_4:9;
8597 = 29*296 + 13; hence not 29 divides 8597 by NAT_4:9;
8597 = 31*277 + 10; hence not 31 divides 8597 by NAT_4:9;
8597 = 37*232 + 13; hence not 37 divides 8597 by NAT_4:9;
8597 = 41*209 + 28; hence not 41 divides 8597 by NAT_4:9;
8597 = 43*199 + 40; hence not 43 divides 8597 by NAT_4:9;
8597 = 47*182 + 43; hence not 47 divides 8597 by NAT_4:9;
8597 = 53*162 + 11; hence not 53 divides 8597 by NAT_4:9;
8597 = 59*145 + 42; hence not 59 divides 8597 by NAT_4:9;
8597 = 61*140 + 57; hence not 61 divides 8597 by NAT_4:9;
8597 = 67*128 + 21; hence not 67 divides 8597 by NAT_4:9;
8597 = 71*121 + 6; hence not 71 divides 8597 by NAT_4:9;
8597 = 73*117 + 56; hence not 73 divides 8597 by NAT_4:9;
8597 = 79*108 + 65; hence not 79 divides 8597 by NAT_4:9;
8597 = 83*103 + 48; hence not 83 divides 8597 by NAT_4:9;
8597 = 89*96 + 53; hence not 89 divides 8597 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8597 & n is prime
holds not n divides 8597 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8599 is prime
proof
now
8599 = 2*4299 + 1; hence not 2 divides 8599 by NAT_4:9;
8599 = 3*2866 + 1; hence not 3 divides 8599 by NAT_4:9;
8599 = 5*1719 + 4; hence not 5 divides 8599 by NAT_4:9;
8599 = 7*1228 + 3; hence not 7 divides 8599 by NAT_4:9;
8599 = 11*781 + 8; hence not 11 divides 8599 by NAT_4:9;
8599 = 13*661 + 6; hence not 13 divides 8599 by NAT_4:9;
8599 = 17*505 + 14; hence not 17 divides 8599 by NAT_4:9;
8599 = 19*452 + 11; hence not 19 divides 8599 by NAT_4:9;
8599 = 23*373 + 20; hence not 23 divides 8599 by NAT_4:9;
8599 = 29*296 + 15; hence not 29 divides 8599 by NAT_4:9;
8599 = 31*277 + 12; hence not 31 divides 8599 by NAT_4:9;
8599 = 37*232 + 15; hence not 37 divides 8599 by NAT_4:9;
8599 = 41*209 + 30; hence not 41 divides 8599 by NAT_4:9;
8599 = 43*199 + 42; hence not 43 divides 8599 by NAT_4:9;
8599 = 47*182 + 45; hence not 47 divides 8599 by NAT_4:9;
8599 = 53*162 + 13; hence not 53 divides 8599 by NAT_4:9;
8599 = 59*145 + 44; hence not 59 divides 8599 by NAT_4:9;
8599 = 61*140 + 59; hence not 61 divides 8599 by NAT_4:9;
8599 = 67*128 + 23; hence not 67 divides 8599 by NAT_4:9;
8599 = 71*121 + 8; hence not 71 divides 8599 by NAT_4:9;
8599 = 73*117 + 58; hence not 73 divides 8599 by NAT_4:9;
8599 = 79*108 + 67; hence not 79 divides 8599 by NAT_4:9;
8599 = 83*103 + 50; hence not 83 divides 8599 by NAT_4:9;
8599 = 89*96 + 55; hence not 89 divides 8599 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8599 & n is prime
holds not n divides 8599 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8609 is prime
proof
now
8609 = 2*4304 + 1; hence not 2 divides 8609 by NAT_4:9;
8609 = 3*2869 + 2; hence not 3 divides 8609 by NAT_4:9;
8609 = 5*1721 + 4; hence not 5 divides 8609 by NAT_4:9;
8609 = 7*1229 + 6; hence not 7 divides 8609 by NAT_4:9;
8609 = 11*782 + 7; hence not 11 divides 8609 by NAT_4:9;
8609 = 13*662 + 3; hence not 13 divides 8609 by NAT_4:9;
8609 = 17*506 + 7; hence not 17 divides 8609 by NAT_4:9;
8609 = 19*453 + 2; hence not 19 divides 8609 by NAT_4:9;
8609 = 23*374 + 7; hence not 23 divides 8609 by NAT_4:9;
8609 = 29*296 + 25; hence not 29 divides 8609 by NAT_4:9;
8609 = 31*277 + 22; hence not 31 divides 8609 by NAT_4:9;
8609 = 37*232 + 25; hence not 37 divides 8609 by NAT_4:9;
8609 = 41*209 + 40; hence not 41 divides 8609 by NAT_4:9;
8609 = 43*200 + 9; hence not 43 divides 8609 by NAT_4:9;
8609 = 47*183 + 8; hence not 47 divides 8609 by NAT_4:9;
8609 = 53*162 + 23; hence not 53 divides 8609 by NAT_4:9;
8609 = 59*145 + 54; hence not 59 divides 8609 by NAT_4:9;
8609 = 61*141 + 8; hence not 61 divides 8609 by NAT_4:9;
8609 = 67*128 + 33; hence not 67 divides 8609 by NAT_4:9;
8609 = 71*121 + 18; hence not 71 divides 8609 by NAT_4:9;
8609 = 73*117 + 68; hence not 73 divides 8609 by NAT_4:9;
8609 = 79*108 + 77; hence not 79 divides 8609 by NAT_4:9;
8609 = 83*103 + 60; hence not 83 divides 8609 by NAT_4:9;
8609 = 89*96 + 65; hence not 89 divides 8609 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8609 & n is prime
holds not n divides 8609 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
8623 is prime
proof
now
8623 = 2*4311 + 1; hence not 2 divides 8623 by NAT_4:9;
8623 = 3*2874 + 1; hence not 3 divides 8623 by NAT_4:9;
8623 = 5*1724 + 3; hence not 5 divides 8623 by NAT_4:9;
8623 = 7*1231 + 6; hence not 7 divides 8623 by NAT_4:9;
8623 = 11*783 + 10; hence not 11 divides 8623 by NAT_4:9;
8623 = 13*663 + 4; hence not 13 divides 8623 by NAT_4:9;
8623 = 17*507 + 4; hence not 17 divides 8623 by NAT_4:9;
8623 = 19*453 + 16; hence not 19 divides 8623 by NAT_4:9;
8623 = 23*374 + 21; hence not 23 divides 8623 by NAT_4:9;
8623 = 29*297 + 10; hence not 29 divides 8623 by NAT_4:9;
8623 = 31*278 + 5; hence not 31 divides 8623 by NAT_4:9;
8623 = 37*233 + 2; hence not 37 divides 8623 by NAT_4:9;
8623 = 41*210 + 13; hence not 41 divides 8623 by NAT_4:9;
8623 = 43*200 + 23; hence not 43 divides 8623 by NAT_4:9;
8623 = 47*183 + 22; hence not 47 divides 8623 by NAT_4:9;
8623 = 53*162 + 37; hence not 53 divides 8623 by NAT_4:9;
8623 = 59*146 + 9; hence not 59 divides 8623 by NAT_4:9;
8623 = 61*141 + 22; hence not 61 divides 8623 by NAT_4:9;
8623 = 67*128 + 47; hence not 67 divides 8623 by NAT_4:9;
8623 = 71*121 + 32; hence not 71 divides 8623 by NAT_4:9;
8623 = 73*118 + 9; hence not 73 divides 8623 by NAT_4:9;
8623 = 79*109 + 12; hence not 79 divides 8623 by NAT_4:9;
8623 = 83*103 + 74; hence not 83 divides 8623 by NAT_4:9;
8623 = 89*96 + 79; hence not 89 divides 8623 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8623 & n is prime
holds not n divides 8623 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8627 is prime
proof
now
8627 = 2*4313 + 1; hence not 2 divides 8627 by NAT_4:9;
8627 = 3*2875 + 2; hence not 3 divides 8627 by NAT_4:9;
8627 = 5*1725 + 2; hence not 5 divides 8627 by NAT_4:9;
8627 = 7*1232 + 3; hence not 7 divides 8627 by NAT_4:9;
8627 = 11*784 + 3; hence not 11 divides 8627 by NAT_4:9;
8627 = 13*663 + 8; hence not 13 divides 8627 by NAT_4:9;
8627 = 17*507 + 8; hence not 17 divides 8627 by NAT_4:9;
8627 = 19*454 + 1; hence not 19 divides 8627 by NAT_4:9;
8627 = 23*375 + 2; hence not 23 divides 8627 by NAT_4:9;
8627 = 29*297 + 14; hence not 29 divides 8627 by NAT_4:9;
8627 = 31*278 + 9; hence not 31 divides 8627 by NAT_4:9;
8627 = 37*233 + 6; hence not 37 divides 8627 by NAT_4:9;
8627 = 41*210 + 17; hence not 41 divides 8627 by NAT_4:9;
8627 = 43*200 + 27; hence not 43 divides 8627 by NAT_4:9;
8627 = 47*183 + 26; hence not 47 divides 8627 by NAT_4:9;
8627 = 53*162 + 41; hence not 53 divides 8627 by NAT_4:9;
8627 = 59*146 + 13; hence not 59 divides 8627 by NAT_4:9;
8627 = 61*141 + 26; hence not 61 divides 8627 by NAT_4:9;
8627 = 67*128 + 51; hence not 67 divides 8627 by NAT_4:9;
8627 = 71*121 + 36; hence not 71 divides 8627 by NAT_4:9;
8627 = 73*118 + 13; hence not 73 divides 8627 by NAT_4:9;
8627 = 79*109 + 16; hence not 79 divides 8627 by NAT_4:9;
8627 = 83*103 + 78; hence not 83 divides 8627 by NAT_4:9;
8627 = 89*96 + 83; hence not 89 divides 8627 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8627 & n is prime
holds not n divides 8627 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8629 is prime
proof
now
8629 = 2*4314 + 1; hence not 2 divides 8629 by NAT_4:9;
8629 = 3*2876 + 1; hence not 3 divides 8629 by NAT_4:9;
8629 = 5*1725 + 4; hence not 5 divides 8629 by NAT_4:9;
8629 = 7*1232 + 5; hence not 7 divides 8629 by NAT_4:9;
8629 = 11*784 + 5; hence not 11 divides 8629 by NAT_4:9;
8629 = 13*663 + 10; hence not 13 divides 8629 by NAT_4:9;
8629 = 17*507 + 10; hence not 17 divides 8629 by NAT_4:9;
8629 = 19*454 + 3; hence not 19 divides 8629 by NAT_4:9;
8629 = 23*375 + 4; hence not 23 divides 8629 by NAT_4:9;
8629 = 29*297 + 16; hence not 29 divides 8629 by NAT_4:9;
8629 = 31*278 + 11; hence not 31 divides 8629 by NAT_4:9;
8629 = 37*233 + 8; hence not 37 divides 8629 by NAT_4:9;
8629 = 41*210 + 19; hence not 41 divides 8629 by NAT_4:9;
8629 = 43*200 + 29; hence not 43 divides 8629 by NAT_4:9;
8629 = 47*183 + 28; hence not 47 divides 8629 by NAT_4:9;
8629 = 53*162 + 43; hence not 53 divides 8629 by NAT_4:9;
8629 = 59*146 + 15; hence not 59 divides 8629 by NAT_4:9;
8629 = 61*141 + 28; hence not 61 divides 8629 by NAT_4:9;
8629 = 67*128 + 53; hence not 67 divides 8629 by NAT_4:9;
8629 = 71*121 + 38; hence not 71 divides 8629 by NAT_4:9;
8629 = 73*118 + 15; hence not 73 divides 8629 by NAT_4:9;
8629 = 79*109 + 18; hence not 79 divides 8629 by NAT_4:9;
8629 = 83*103 + 80; hence not 83 divides 8629 by NAT_4:9;
8629 = 89*96 + 85; hence not 89 divides 8629 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8629 & n is prime
holds not n divides 8629 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8641 is prime
proof
now
8641 = 2*4320 + 1; hence not 2 divides 8641 by NAT_4:9;
8641 = 3*2880 + 1; hence not 3 divides 8641 by NAT_4:9;
8641 = 5*1728 + 1; hence not 5 divides 8641 by NAT_4:9;
8641 = 7*1234 + 3; hence not 7 divides 8641 by NAT_4:9;
8641 = 11*785 + 6; hence not 11 divides 8641 by NAT_4:9;
8641 = 13*664 + 9; hence not 13 divides 8641 by NAT_4:9;
8641 = 17*508 + 5; hence not 17 divides 8641 by NAT_4:9;
8641 = 19*454 + 15; hence not 19 divides 8641 by NAT_4:9;
8641 = 23*375 + 16; hence not 23 divides 8641 by NAT_4:9;
8641 = 29*297 + 28; hence not 29 divides 8641 by NAT_4:9;
8641 = 31*278 + 23; hence not 31 divides 8641 by NAT_4:9;
8641 = 37*233 + 20; hence not 37 divides 8641 by NAT_4:9;
8641 = 41*210 + 31; hence not 41 divides 8641 by NAT_4:9;
8641 = 43*200 + 41; hence not 43 divides 8641 by NAT_4:9;
8641 = 47*183 + 40; hence not 47 divides 8641 by NAT_4:9;
8641 = 53*163 + 2; hence not 53 divides 8641 by NAT_4:9;
8641 = 59*146 + 27; hence not 59 divides 8641 by NAT_4:9;
8641 = 61*141 + 40; hence not 61 divides 8641 by NAT_4:9;
8641 = 67*128 + 65; hence not 67 divides 8641 by NAT_4:9;
8641 = 71*121 + 50; hence not 71 divides 8641 by NAT_4:9;
8641 = 73*118 + 27; hence not 73 divides 8641 by NAT_4:9;
8641 = 79*109 + 30; hence not 79 divides 8641 by NAT_4:9;
8641 = 83*104 + 9; hence not 83 divides 8641 by NAT_4:9;
8641 = 89*97 + 8; hence not 89 divides 8641 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8641 & n is prime
holds not n divides 8641 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8647 is prime
proof
now
8647 = 2*4323 + 1; hence not 2 divides 8647 by NAT_4:9;
8647 = 3*2882 + 1; hence not 3 divides 8647 by NAT_4:9;
8647 = 5*1729 + 2; hence not 5 divides 8647 by NAT_4:9;
8647 = 7*1235 + 2; hence not 7 divides 8647 by NAT_4:9;
8647 = 11*786 + 1; hence not 11 divides 8647 by NAT_4:9;
8647 = 13*665 + 2; hence not 13 divides 8647 by NAT_4:9;
8647 = 17*508 + 11; hence not 17 divides 8647 by NAT_4:9;
8647 = 19*455 + 2; hence not 19 divides 8647 by NAT_4:9;
8647 = 23*375 + 22; hence not 23 divides 8647 by NAT_4:9;
8647 = 29*298 + 5; hence not 29 divides 8647 by NAT_4:9;
8647 = 31*278 + 29; hence not 31 divides 8647 by NAT_4:9;
8647 = 37*233 + 26; hence not 37 divides 8647 by NAT_4:9;
8647 = 41*210 + 37; hence not 41 divides 8647 by NAT_4:9;
8647 = 43*201 + 4; hence not 43 divides 8647 by NAT_4:9;
8647 = 47*183 + 46; hence not 47 divides 8647 by NAT_4:9;
8647 = 53*163 + 8; hence not 53 divides 8647 by NAT_4:9;
8647 = 59*146 + 33; hence not 59 divides 8647 by NAT_4:9;
8647 = 61*141 + 46; hence not 61 divides 8647 by NAT_4:9;
8647 = 67*129 + 4; hence not 67 divides 8647 by NAT_4:9;
8647 = 71*121 + 56; hence not 71 divides 8647 by NAT_4:9;
8647 = 73*118 + 33; hence not 73 divides 8647 by NAT_4:9;
8647 = 79*109 + 36; hence not 79 divides 8647 by NAT_4:9;
8647 = 83*104 + 15; hence not 83 divides 8647 by NAT_4:9;
8647 = 89*97 + 14; hence not 89 divides 8647 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8647 & n is prime
holds not n divides 8647 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
8663 is prime
proof
now
8663 = 2*4331 + 1; hence not 2 divides 8663 by NAT_4:9;
8663 = 3*2887 + 2; hence not 3 divides 8663 by NAT_4:9;
8663 = 5*1732 + 3; hence not 5 divides 8663 by NAT_4:9;
8663 = 7*1237 + 4; hence not 7 divides 8663 by NAT_4:9;
8663 = 11*787 + 6; hence not 11 divides 8663 by NAT_4:9;
8663 = 13*666 + 5; hence not 13 divides 8663 by NAT_4:9;
8663 = 17*509 + 10; hence not 17 divides 8663 by NAT_4:9;
8663 = 19*455 + 18; hence not 19 divides 8663 by NAT_4:9;
8663 = 23*376 + 15; hence not 23 divides 8663 by NAT_4:9;
8663 = 29*298 + 21; hence not 29 divides 8663 by NAT_4:9;
8663 = 31*279 + 14; hence not 31 divides 8663 by NAT_4:9;
8663 = 37*234 + 5; hence not 37 divides 8663 by NAT_4:9;
8663 = 41*211 + 12; hence not 41 divides 8663 by NAT_4:9;
8663 = 43*201 + 20; hence not 43 divides 8663 by NAT_4:9;
8663 = 47*184 + 15; hence not 47 divides 8663 by NAT_4:9;
8663 = 53*163 + 24; hence not 53 divides 8663 by NAT_4:9;
8663 = 59*146 + 49; hence not 59 divides 8663 by NAT_4:9;
8663 = 61*142 + 1; hence not 61 divides 8663 by NAT_4:9;
8663 = 67*129 + 20; hence not 67 divides 8663 by NAT_4:9;
8663 = 71*122 + 1; hence not 71 divides 8663 by NAT_4:9;
8663 = 73*118 + 49; hence not 73 divides 8663 by NAT_4:9;
8663 = 79*109 + 52; hence not 79 divides 8663 by NAT_4:9;
8663 = 83*104 + 31; hence not 83 divides 8663 by NAT_4:9;
8663 = 89*97 + 30; hence not 89 divides 8663 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8663 & n is prime
holds not n divides 8663 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8669 is prime
proof
now
8669 = 2*4334 + 1; hence not 2 divides 8669 by NAT_4:9;
8669 = 3*2889 + 2; hence not 3 divides 8669 by NAT_4:9;
8669 = 5*1733 + 4; hence not 5 divides 8669 by NAT_4:9;
8669 = 7*1238 + 3; hence not 7 divides 8669 by NAT_4:9;
8669 = 11*788 + 1; hence not 11 divides 8669 by NAT_4:9;
8669 = 13*666 + 11; hence not 13 divides 8669 by NAT_4:9;
8669 = 17*509 + 16; hence not 17 divides 8669 by NAT_4:9;
8669 = 19*456 + 5; hence not 19 divides 8669 by NAT_4:9;
8669 = 23*376 + 21; hence not 23 divides 8669 by NAT_4:9;
8669 = 29*298 + 27; hence not 29 divides 8669 by NAT_4:9;
8669 = 31*279 + 20; hence not 31 divides 8669 by NAT_4:9;
8669 = 37*234 + 11; hence not 37 divides 8669 by NAT_4:9;
8669 = 41*211 + 18; hence not 41 divides 8669 by NAT_4:9;
8669 = 43*201 + 26; hence not 43 divides 8669 by NAT_4:9;
8669 = 47*184 + 21; hence not 47 divides 8669 by NAT_4:9;
8669 = 53*163 + 30; hence not 53 divides 8669 by NAT_4:9;
8669 = 59*146 + 55; hence not 59 divides 8669 by NAT_4:9;
8669 = 61*142 + 7; hence not 61 divides 8669 by NAT_4:9;
8669 = 67*129 + 26; hence not 67 divides 8669 by NAT_4:9;
8669 = 71*122 + 7; hence not 71 divides 8669 by NAT_4:9;
8669 = 73*118 + 55; hence not 73 divides 8669 by NAT_4:9;
8669 = 79*109 + 58; hence not 79 divides 8669 by NAT_4:9;
8669 = 83*104 + 37; hence not 83 divides 8669 by NAT_4:9;
8669 = 89*97 + 36; hence not 89 divides 8669 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8669 & n is prime
holds not n divides 8669 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8677 is prime
proof
now
8677 = 2*4338 + 1; hence not 2 divides 8677 by NAT_4:9;
8677 = 3*2892 + 1; hence not 3 divides 8677 by NAT_4:9;
8677 = 5*1735 + 2; hence not 5 divides 8677 by NAT_4:9;
8677 = 7*1239 + 4; hence not 7 divides 8677 by NAT_4:9;
8677 = 11*788 + 9; hence not 11 divides 8677 by NAT_4:9;
8677 = 13*667 + 6; hence not 13 divides 8677 by NAT_4:9;
8677 = 17*510 + 7; hence not 17 divides 8677 by NAT_4:9;
8677 = 19*456 + 13; hence not 19 divides 8677 by NAT_4:9;
8677 = 23*377 + 6; hence not 23 divides 8677 by NAT_4:9;
8677 = 29*299 + 6; hence not 29 divides 8677 by NAT_4:9;
8677 = 31*279 + 28; hence not 31 divides 8677 by NAT_4:9;
8677 = 37*234 + 19; hence not 37 divides 8677 by NAT_4:9;
8677 = 41*211 + 26; hence not 41 divides 8677 by NAT_4:9;
8677 = 43*201 + 34; hence not 43 divides 8677 by NAT_4:9;
8677 = 47*184 + 29; hence not 47 divides 8677 by NAT_4:9;
8677 = 53*163 + 38; hence not 53 divides 8677 by NAT_4:9;
8677 = 59*147 + 4; hence not 59 divides 8677 by NAT_4:9;
8677 = 61*142 + 15; hence not 61 divides 8677 by NAT_4:9;
8677 = 67*129 + 34; hence not 67 divides 8677 by NAT_4:9;
8677 = 71*122 + 15; hence not 71 divides 8677 by NAT_4:9;
8677 = 73*118 + 63; hence not 73 divides 8677 by NAT_4:9;
8677 = 79*109 + 66; hence not 79 divides 8677 by NAT_4:9;
8677 = 83*104 + 45; hence not 83 divides 8677 by NAT_4:9;
8677 = 89*97 + 44; hence not 89 divides 8677 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8677 & n is prime
holds not n divides 8677 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8681 is prime
proof
now
8681 = 2*4340 + 1; hence not 2 divides 8681 by NAT_4:9;
8681 = 3*2893 + 2; hence not 3 divides 8681 by NAT_4:9;
8681 = 5*1736 + 1; hence not 5 divides 8681 by NAT_4:9;
8681 = 7*1240 + 1; hence not 7 divides 8681 by NAT_4:9;
8681 = 11*789 + 2; hence not 11 divides 8681 by NAT_4:9;
8681 = 13*667 + 10; hence not 13 divides 8681 by NAT_4:9;
8681 = 17*510 + 11; hence not 17 divides 8681 by NAT_4:9;
8681 = 19*456 + 17; hence not 19 divides 8681 by NAT_4:9;
8681 = 23*377 + 10; hence not 23 divides 8681 by NAT_4:9;
8681 = 29*299 + 10; hence not 29 divides 8681 by NAT_4:9;
8681 = 31*280 + 1; hence not 31 divides 8681 by NAT_4:9;
8681 = 37*234 + 23; hence not 37 divides 8681 by NAT_4:9;
8681 = 41*211 + 30; hence not 41 divides 8681 by NAT_4:9;
8681 = 43*201 + 38; hence not 43 divides 8681 by NAT_4:9;
8681 = 47*184 + 33; hence not 47 divides 8681 by NAT_4:9;
8681 = 53*163 + 42; hence not 53 divides 8681 by NAT_4:9;
8681 = 59*147 + 8; hence not 59 divides 8681 by NAT_4:9;
8681 = 61*142 + 19; hence not 61 divides 8681 by NAT_4:9;
8681 = 67*129 + 38; hence not 67 divides 8681 by NAT_4:9;
8681 = 71*122 + 19; hence not 71 divides 8681 by NAT_4:9;
8681 = 73*118 + 67; hence not 73 divides 8681 by NAT_4:9;
8681 = 79*109 + 70; hence not 79 divides 8681 by NAT_4:9;
8681 = 83*104 + 49; hence not 83 divides 8681 by NAT_4:9;
8681 = 89*97 + 48; hence not 89 divides 8681 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8681 & n is prime
holds not n divides 8681 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8689 is prime
proof
now
8689 = 2*4344 + 1; hence not 2 divides 8689 by NAT_4:9;
8689 = 3*2896 + 1; hence not 3 divides 8689 by NAT_4:9;
8689 = 5*1737 + 4; hence not 5 divides 8689 by NAT_4:9;
8689 = 7*1241 + 2; hence not 7 divides 8689 by NAT_4:9;
8689 = 11*789 + 10; hence not 11 divides 8689 by NAT_4:9;
8689 = 13*668 + 5; hence not 13 divides 8689 by NAT_4:9;
8689 = 17*511 + 2; hence not 17 divides 8689 by NAT_4:9;
8689 = 19*457 + 6; hence not 19 divides 8689 by NAT_4:9;
8689 = 23*377 + 18; hence not 23 divides 8689 by NAT_4:9;
8689 = 29*299 + 18; hence not 29 divides 8689 by NAT_4:9;
8689 = 31*280 + 9; hence not 31 divides 8689 by NAT_4:9;
8689 = 37*234 + 31; hence not 37 divides 8689 by NAT_4:9;
8689 = 41*211 + 38; hence not 41 divides 8689 by NAT_4:9;
8689 = 43*202 + 3; hence not 43 divides 8689 by NAT_4:9;
8689 = 47*184 + 41; hence not 47 divides 8689 by NAT_4:9;
8689 = 53*163 + 50; hence not 53 divides 8689 by NAT_4:9;
8689 = 59*147 + 16; hence not 59 divides 8689 by NAT_4:9;
8689 = 61*142 + 27; hence not 61 divides 8689 by NAT_4:9;
8689 = 67*129 + 46; hence not 67 divides 8689 by NAT_4:9;
8689 = 71*122 + 27; hence not 71 divides 8689 by NAT_4:9;
8689 = 73*119 + 2; hence not 73 divides 8689 by NAT_4:9;
8689 = 79*109 + 78; hence not 79 divides 8689 by NAT_4:9;
8689 = 83*104 + 57; hence not 83 divides 8689 by NAT_4:9;
8689 = 89*97 + 56; hence not 89 divides 8689 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8689 & n is prime
holds not n divides 8689 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8693 is prime
proof
now
8693 = 2*4346 + 1; hence not 2 divides 8693 by NAT_4:9;
8693 = 3*2897 + 2; hence not 3 divides 8693 by NAT_4:9;
8693 = 5*1738 + 3; hence not 5 divides 8693 by NAT_4:9;
8693 = 7*1241 + 6; hence not 7 divides 8693 by NAT_4:9;
8693 = 11*790 + 3; hence not 11 divides 8693 by NAT_4:9;
8693 = 13*668 + 9; hence not 13 divides 8693 by NAT_4:9;
8693 = 17*511 + 6; hence not 17 divides 8693 by NAT_4:9;
8693 = 19*457 + 10; hence not 19 divides 8693 by NAT_4:9;
8693 = 23*377 + 22; hence not 23 divides 8693 by NAT_4:9;
8693 = 29*299 + 22; hence not 29 divides 8693 by NAT_4:9;
8693 = 31*280 + 13; hence not 31 divides 8693 by NAT_4:9;
8693 = 37*234 + 35; hence not 37 divides 8693 by NAT_4:9;
8693 = 41*212 + 1; hence not 41 divides 8693 by NAT_4:9;
8693 = 43*202 + 7; hence not 43 divides 8693 by NAT_4:9;
8693 = 47*184 + 45; hence not 47 divides 8693 by NAT_4:9;
8693 = 53*164 + 1; hence not 53 divides 8693 by NAT_4:9;
8693 = 59*147 + 20; hence not 59 divides 8693 by NAT_4:9;
8693 = 61*142 + 31; hence not 61 divides 8693 by NAT_4:9;
8693 = 67*129 + 50; hence not 67 divides 8693 by NAT_4:9;
8693 = 71*122 + 31; hence not 71 divides 8693 by NAT_4:9;
8693 = 73*119 + 6; hence not 73 divides 8693 by NAT_4:9;
8693 = 79*110 + 3; hence not 79 divides 8693 by NAT_4:9;
8693 = 83*104 + 61; hence not 83 divides 8693 by NAT_4:9;
8693 = 89*97 + 60; hence not 89 divides 8693 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8693 & n is prime
holds not n divides 8693 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8699 is prime
proof
now
8699 = 2*4349 + 1; hence not 2 divides 8699 by NAT_4:9;
8699 = 3*2899 + 2; hence not 3 divides 8699 by NAT_4:9;
8699 = 5*1739 + 4; hence not 5 divides 8699 by NAT_4:9;
8699 = 7*1242 + 5; hence not 7 divides 8699 by NAT_4:9;
8699 = 11*790 + 9; hence not 11 divides 8699 by NAT_4:9;
8699 = 13*669 + 2; hence not 13 divides 8699 by NAT_4:9;
8699 = 17*511 + 12; hence not 17 divides 8699 by NAT_4:9;
8699 = 19*457 + 16; hence not 19 divides 8699 by NAT_4:9;
8699 = 23*378 + 5; hence not 23 divides 8699 by NAT_4:9;
8699 = 29*299 + 28; hence not 29 divides 8699 by NAT_4:9;
8699 = 31*280 + 19; hence not 31 divides 8699 by NAT_4:9;
8699 = 37*235 + 4; hence not 37 divides 8699 by NAT_4:9;
8699 = 41*212 + 7; hence not 41 divides 8699 by NAT_4:9;
8699 = 43*202 + 13; hence not 43 divides 8699 by NAT_4:9;
8699 = 47*185 + 4; hence not 47 divides 8699 by NAT_4:9;
8699 = 53*164 + 7; hence not 53 divides 8699 by NAT_4:9;
8699 = 59*147 + 26; hence not 59 divides 8699 by NAT_4:9;
8699 = 61*142 + 37; hence not 61 divides 8699 by NAT_4:9;
8699 = 67*129 + 56; hence not 67 divides 8699 by NAT_4:9;
8699 = 71*122 + 37; hence not 71 divides 8699 by NAT_4:9;
8699 = 73*119 + 12; hence not 73 divides 8699 by NAT_4:9;
8699 = 79*110 + 9; hence not 79 divides 8699 by NAT_4:9;
8699 = 83*104 + 67; hence not 83 divides 8699 by NAT_4:9;
8699 = 89*97 + 66; hence not 89 divides 8699 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8699 & n is prime
holds not n divides 8699 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8707 is prime
proof
now
8707 = 2*4353 + 1; hence not 2 divides 8707 by NAT_4:9;
8707 = 3*2902 + 1; hence not 3 divides 8707 by NAT_4:9;
8707 = 5*1741 + 2; hence not 5 divides 8707 by NAT_4:9;
8707 = 7*1243 + 6; hence not 7 divides 8707 by NAT_4:9;
8707 = 11*791 + 6; hence not 11 divides 8707 by NAT_4:9;
8707 = 13*669 + 10; hence not 13 divides 8707 by NAT_4:9;
8707 = 17*512 + 3; hence not 17 divides 8707 by NAT_4:9;
8707 = 19*458 + 5; hence not 19 divides 8707 by NAT_4:9;
8707 = 23*378 + 13; hence not 23 divides 8707 by NAT_4:9;
8707 = 29*300 + 7; hence not 29 divides 8707 by NAT_4:9;
8707 = 31*280 + 27; hence not 31 divides 8707 by NAT_4:9;
8707 = 37*235 + 12; hence not 37 divides 8707 by NAT_4:9;
8707 = 41*212 + 15; hence not 41 divides 8707 by NAT_4:9;
8707 = 43*202 + 21; hence not 43 divides 8707 by NAT_4:9;
8707 = 47*185 + 12; hence not 47 divides 8707 by NAT_4:9;
8707 = 53*164 + 15; hence not 53 divides 8707 by NAT_4:9;
8707 = 59*147 + 34; hence not 59 divides 8707 by NAT_4:9;
8707 = 61*142 + 45; hence not 61 divides 8707 by NAT_4:9;
8707 = 67*129 + 64; hence not 67 divides 8707 by NAT_4:9;
8707 = 71*122 + 45; hence not 71 divides 8707 by NAT_4:9;
8707 = 73*119 + 20; hence not 73 divides 8707 by NAT_4:9;
8707 = 79*110 + 17; hence not 79 divides 8707 by NAT_4:9;
8707 = 83*104 + 75; hence not 83 divides 8707 by NAT_4:9;
8707 = 89*97 + 74; hence not 89 divides 8707 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8707 & n is prime
holds not n divides 8707 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8713 is prime
proof
now
8713 = 2*4356 + 1; hence not 2 divides 8713 by NAT_4:9;
8713 = 3*2904 + 1; hence not 3 divides 8713 by NAT_4:9;
8713 = 5*1742 + 3; hence not 5 divides 8713 by NAT_4:9;
8713 = 7*1244 + 5; hence not 7 divides 8713 by NAT_4:9;
8713 = 11*792 + 1; hence not 11 divides 8713 by NAT_4:9;
8713 = 13*670 + 3; hence not 13 divides 8713 by NAT_4:9;
8713 = 17*512 + 9; hence not 17 divides 8713 by NAT_4:9;
8713 = 19*458 + 11; hence not 19 divides 8713 by NAT_4:9;
8713 = 23*378 + 19; hence not 23 divides 8713 by NAT_4:9;
8713 = 29*300 + 13; hence not 29 divides 8713 by NAT_4:9;
8713 = 31*281 + 2; hence not 31 divides 8713 by NAT_4:9;
8713 = 37*235 + 18; hence not 37 divides 8713 by NAT_4:9;
8713 = 41*212 + 21; hence not 41 divides 8713 by NAT_4:9;
8713 = 43*202 + 27; hence not 43 divides 8713 by NAT_4:9;
8713 = 47*185 + 18; hence not 47 divides 8713 by NAT_4:9;
8713 = 53*164 + 21; hence not 53 divides 8713 by NAT_4:9;
8713 = 59*147 + 40; hence not 59 divides 8713 by NAT_4:9;
8713 = 61*142 + 51; hence not 61 divides 8713 by NAT_4:9;
8713 = 67*130 + 3; hence not 67 divides 8713 by NAT_4:9;
8713 = 71*122 + 51; hence not 71 divides 8713 by NAT_4:9;
8713 = 73*119 + 26; hence not 73 divides 8713 by NAT_4:9;
8713 = 79*110 + 23; hence not 79 divides 8713 by NAT_4:9;
8713 = 83*104 + 81; hence not 83 divides 8713 by NAT_4:9;
8713 = 89*97 + 80; hence not 89 divides 8713 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8713 & n is prime
holds not n divides 8713 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8719 is prime
proof
now
8719 = 2*4359 + 1; hence not 2 divides 8719 by NAT_4:9;
8719 = 3*2906 + 1; hence not 3 divides 8719 by NAT_4:9;
8719 = 5*1743 + 4; hence not 5 divides 8719 by NAT_4:9;
8719 = 7*1245 + 4; hence not 7 divides 8719 by NAT_4:9;
8719 = 11*792 + 7; hence not 11 divides 8719 by NAT_4:9;
8719 = 13*670 + 9; hence not 13 divides 8719 by NAT_4:9;
8719 = 17*512 + 15; hence not 17 divides 8719 by NAT_4:9;
8719 = 19*458 + 17; hence not 19 divides 8719 by NAT_4:9;
8719 = 23*379 + 2; hence not 23 divides 8719 by NAT_4:9;
8719 = 29*300 + 19; hence not 29 divides 8719 by NAT_4:9;
8719 = 31*281 + 8; hence not 31 divides 8719 by NAT_4:9;
8719 = 37*235 + 24; hence not 37 divides 8719 by NAT_4:9;
8719 = 41*212 + 27; hence not 41 divides 8719 by NAT_4:9;
8719 = 43*202 + 33; hence not 43 divides 8719 by NAT_4:9;
8719 = 47*185 + 24; hence not 47 divides 8719 by NAT_4:9;
8719 = 53*164 + 27; hence not 53 divides 8719 by NAT_4:9;
8719 = 59*147 + 46; hence not 59 divides 8719 by NAT_4:9;
8719 = 61*142 + 57; hence not 61 divides 8719 by NAT_4:9;
8719 = 67*130 + 9; hence not 67 divides 8719 by NAT_4:9;
8719 = 71*122 + 57; hence not 71 divides 8719 by NAT_4:9;
8719 = 73*119 + 32; hence not 73 divides 8719 by NAT_4:9;
8719 = 79*110 + 29; hence not 79 divides 8719 by NAT_4:9;
8719 = 83*105 + 4; hence not 83 divides 8719 by NAT_4:9;
8719 = 89*97 + 86; hence not 89 divides 8719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8719 & n is prime
holds not n divides 8719 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8731 is prime
proof
now
8731 = 2*4365 + 1; hence not 2 divides 8731 by NAT_4:9;
8731 = 3*2910 + 1; hence not 3 divides 8731 by NAT_4:9;
8731 = 5*1746 + 1; hence not 5 divides 8731 by NAT_4:9;
8731 = 7*1247 + 2; hence not 7 divides 8731 by NAT_4:9;
8731 = 11*793 + 8; hence not 11 divides 8731 by NAT_4:9;
8731 = 13*671 + 8; hence not 13 divides 8731 by NAT_4:9;
8731 = 17*513 + 10; hence not 17 divides 8731 by NAT_4:9;
8731 = 19*459 + 10; hence not 19 divides 8731 by NAT_4:9;
8731 = 23*379 + 14; hence not 23 divides 8731 by NAT_4:9;
8731 = 29*301 + 2; hence not 29 divides 8731 by NAT_4:9;
8731 = 31*281 + 20; hence not 31 divides 8731 by NAT_4:9;
8731 = 37*235 + 36; hence not 37 divides 8731 by NAT_4:9;
8731 = 41*212 + 39; hence not 41 divides 8731 by NAT_4:9;
8731 = 43*203 + 2; hence not 43 divides 8731 by NAT_4:9;
8731 = 47*185 + 36; hence not 47 divides 8731 by NAT_4:9;
8731 = 53*164 + 39; hence not 53 divides 8731 by NAT_4:9;
8731 = 59*147 + 58; hence not 59 divides 8731 by NAT_4:9;
8731 = 61*143 + 8; hence not 61 divides 8731 by NAT_4:9;
8731 = 67*130 + 21; hence not 67 divides 8731 by NAT_4:9;
8731 = 71*122 + 69; hence not 71 divides 8731 by NAT_4:9;
8731 = 73*119 + 44; hence not 73 divides 8731 by NAT_4:9;
8731 = 79*110 + 41; hence not 79 divides 8731 by NAT_4:9;
8731 = 83*105 + 16; hence not 83 divides 8731 by NAT_4:9;
8731 = 89*98 + 9; hence not 89 divides 8731 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8731 & n is prime
holds not n divides 8731 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8737 is prime
proof
now
8737 = 2*4368 + 1; hence not 2 divides 8737 by NAT_4:9;
8737 = 3*2912 + 1; hence not 3 divides 8737 by NAT_4:9;
8737 = 5*1747 + 2; hence not 5 divides 8737 by NAT_4:9;
8737 = 7*1248 + 1; hence not 7 divides 8737 by NAT_4:9;
8737 = 11*794 + 3; hence not 11 divides 8737 by NAT_4:9;
8737 = 13*672 + 1; hence not 13 divides 8737 by NAT_4:9;
8737 = 17*513 + 16; hence not 17 divides 8737 by NAT_4:9;
8737 = 19*459 + 16; hence not 19 divides 8737 by NAT_4:9;
8737 = 23*379 + 20; hence not 23 divides 8737 by NAT_4:9;
8737 = 29*301 + 8; hence not 29 divides 8737 by NAT_4:9;
8737 = 31*281 + 26; hence not 31 divides 8737 by NAT_4:9;
8737 = 37*236 + 5; hence not 37 divides 8737 by NAT_4:9;
8737 = 41*213 + 4; hence not 41 divides 8737 by NAT_4:9;
8737 = 43*203 + 8; hence not 43 divides 8737 by NAT_4:9;
8737 = 47*185 + 42; hence not 47 divides 8737 by NAT_4:9;
8737 = 53*164 + 45; hence not 53 divides 8737 by NAT_4:9;
8737 = 59*148 + 5; hence not 59 divides 8737 by NAT_4:9;
8737 = 61*143 + 14; hence not 61 divides 8737 by NAT_4:9;
8737 = 67*130 + 27; hence not 67 divides 8737 by NAT_4:9;
8737 = 71*123 + 4; hence not 71 divides 8737 by NAT_4:9;
8737 = 73*119 + 50; hence not 73 divides 8737 by NAT_4:9;
8737 = 79*110 + 47; hence not 79 divides 8737 by NAT_4:9;
8737 = 83*105 + 22; hence not 83 divides 8737 by NAT_4:9;
8737 = 89*98 + 15; hence not 89 divides 8737 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8737 & n is prime
holds not n divides 8737 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8741 is prime
proof
now
8741 = 2*4370 + 1; hence not 2 divides 8741 by NAT_4:9;
8741 = 3*2913 + 2; hence not 3 divides 8741 by NAT_4:9;
8741 = 5*1748 + 1; hence not 5 divides 8741 by NAT_4:9;
8741 = 7*1248 + 5; hence not 7 divides 8741 by NAT_4:9;
8741 = 11*794 + 7; hence not 11 divides 8741 by NAT_4:9;
8741 = 13*672 + 5; hence not 13 divides 8741 by NAT_4:9;
8741 = 17*514 + 3; hence not 17 divides 8741 by NAT_4:9;
8741 = 19*460 + 1; hence not 19 divides 8741 by NAT_4:9;
8741 = 23*380 + 1; hence not 23 divides 8741 by NAT_4:9;
8741 = 29*301 + 12; hence not 29 divides 8741 by NAT_4:9;
8741 = 31*281 + 30; hence not 31 divides 8741 by NAT_4:9;
8741 = 37*236 + 9; hence not 37 divides 8741 by NAT_4:9;
8741 = 41*213 + 8; hence not 41 divides 8741 by NAT_4:9;
8741 = 43*203 + 12; hence not 43 divides 8741 by NAT_4:9;
8741 = 47*185 + 46; hence not 47 divides 8741 by NAT_4:9;
8741 = 53*164 + 49; hence not 53 divides 8741 by NAT_4:9;
8741 = 59*148 + 9; hence not 59 divides 8741 by NAT_4:9;
8741 = 61*143 + 18; hence not 61 divides 8741 by NAT_4:9;
8741 = 67*130 + 31; hence not 67 divides 8741 by NAT_4:9;
8741 = 71*123 + 8; hence not 71 divides 8741 by NAT_4:9;
8741 = 73*119 + 54; hence not 73 divides 8741 by NAT_4:9;
8741 = 79*110 + 51; hence not 79 divides 8741 by NAT_4:9;
8741 = 83*105 + 26; hence not 83 divides 8741 by NAT_4:9;
8741 = 89*98 + 19; hence not 89 divides 8741 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8741 & n is prime
holds not n divides 8741 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8747 is prime
proof
now
8747 = 2*4373 + 1; hence not 2 divides 8747 by NAT_4:9;
8747 = 3*2915 + 2; hence not 3 divides 8747 by NAT_4:9;
8747 = 5*1749 + 2; hence not 5 divides 8747 by NAT_4:9;
8747 = 7*1249 + 4; hence not 7 divides 8747 by NAT_4:9;
8747 = 11*795 + 2; hence not 11 divides 8747 by NAT_4:9;
8747 = 13*672 + 11; hence not 13 divides 8747 by NAT_4:9;
8747 = 17*514 + 9; hence not 17 divides 8747 by NAT_4:9;
8747 = 19*460 + 7; hence not 19 divides 8747 by NAT_4:9;
8747 = 23*380 + 7; hence not 23 divides 8747 by NAT_4:9;
8747 = 29*301 + 18; hence not 29 divides 8747 by NAT_4:9;
8747 = 31*282 + 5; hence not 31 divides 8747 by NAT_4:9;
8747 = 37*236 + 15; hence not 37 divides 8747 by NAT_4:9;
8747 = 41*213 + 14; hence not 41 divides 8747 by NAT_4:9;
8747 = 43*203 + 18; hence not 43 divides 8747 by NAT_4:9;
8747 = 47*186 + 5; hence not 47 divides 8747 by NAT_4:9;
8747 = 53*165 + 2; hence not 53 divides 8747 by NAT_4:9;
8747 = 59*148 + 15; hence not 59 divides 8747 by NAT_4:9;
8747 = 61*143 + 24; hence not 61 divides 8747 by NAT_4:9;
8747 = 67*130 + 37; hence not 67 divides 8747 by NAT_4:9;
8747 = 71*123 + 14; hence not 71 divides 8747 by NAT_4:9;
8747 = 73*119 + 60; hence not 73 divides 8747 by NAT_4:9;
8747 = 79*110 + 57; hence not 79 divides 8747 by NAT_4:9;
8747 = 83*105 + 32; hence not 83 divides 8747 by NAT_4:9;
8747 = 89*98 + 25; hence not 89 divides 8747 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8747 & n is prime
holds not n divides 8747 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8753 is prime
proof
now
8753 = 2*4376 + 1; hence not 2 divides 8753 by NAT_4:9;
8753 = 3*2917 + 2; hence not 3 divides 8753 by NAT_4:9;
8753 = 5*1750 + 3; hence not 5 divides 8753 by NAT_4:9;
8753 = 7*1250 + 3; hence not 7 divides 8753 by NAT_4:9;
8753 = 11*795 + 8; hence not 11 divides 8753 by NAT_4:9;
8753 = 13*673 + 4; hence not 13 divides 8753 by NAT_4:9;
8753 = 17*514 + 15; hence not 17 divides 8753 by NAT_4:9;
8753 = 19*460 + 13; hence not 19 divides 8753 by NAT_4:9;
8753 = 23*380 + 13; hence not 23 divides 8753 by NAT_4:9;
8753 = 29*301 + 24; hence not 29 divides 8753 by NAT_4:9;
8753 = 31*282 + 11; hence not 31 divides 8753 by NAT_4:9;
8753 = 37*236 + 21; hence not 37 divides 8753 by NAT_4:9;
8753 = 41*213 + 20; hence not 41 divides 8753 by NAT_4:9;
8753 = 43*203 + 24; hence not 43 divides 8753 by NAT_4:9;
8753 = 47*186 + 11; hence not 47 divides 8753 by NAT_4:9;
8753 = 53*165 + 8; hence not 53 divides 8753 by NAT_4:9;
8753 = 59*148 + 21; hence not 59 divides 8753 by NAT_4:9;
8753 = 61*143 + 30; hence not 61 divides 8753 by NAT_4:9;
8753 = 67*130 + 43; hence not 67 divides 8753 by NAT_4:9;
8753 = 71*123 + 20; hence not 71 divides 8753 by NAT_4:9;
8753 = 73*119 + 66; hence not 73 divides 8753 by NAT_4:9;
8753 = 79*110 + 63; hence not 79 divides 8753 by NAT_4:9;
8753 = 83*105 + 38; hence not 83 divides 8753 by NAT_4:9;
8753 = 89*98 + 31; hence not 89 divides 8753 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8753 & n is prime
holds not n divides 8753 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8761 is prime
proof
now
8761 = 2*4380 + 1; hence not 2 divides 8761 by NAT_4:9;
8761 = 3*2920 + 1; hence not 3 divides 8761 by NAT_4:9;
8761 = 5*1752 + 1; hence not 5 divides 8761 by NAT_4:9;
8761 = 7*1251 + 4; hence not 7 divides 8761 by NAT_4:9;
8761 = 11*796 + 5; hence not 11 divides 8761 by NAT_4:9;
8761 = 13*673 + 12; hence not 13 divides 8761 by NAT_4:9;
8761 = 17*515 + 6; hence not 17 divides 8761 by NAT_4:9;
8761 = 19*461 + 2; hence not 19 divides 8761 by NAT_4:9;
8761 = 23*380 + 21; hence not 23 divides 8761 by NAT_4:9;
8761 = 29*302 + 3; hence not 29 divides 8761 by NAT_4:9;
8761 = 31*282 + 19; hence not 31 divides 8761 by NAT_4:9;
8761 = 37*236 + 29; hence not 37 divides 8761 by NAT_4:9;
8761 = 41*213 + 28; hence not 41 divides 8761 by NAT_4:9;
8761 = 43*203 + 32; hence not 43 divides 8761 by NAT_4:9;
8761 = 47*186 + 19; hence not 47 divides 8761 by NAT_4:9;
8761 = 53*165 + 16; hence not 53 divides 8761 by NAT_4:9;
8761 = 59*148 + 29; hence not 59 divides 8761 by NAT_4:9;
8761 = 61*143 + 38; hence not 61 divides 8761 by NAT_4:9;
8761 = 67*130 + 51; hence not 67 divides 8761 by NAT_4:9;
8761 = 71*123 + 28; hence not 71 divides 8761 by NAT_4:9;
8761 = 73*120 + 1; hence not 73 divides 8761 by NAT_4:9;
8761 = 79*110 + 71; hence not 79 divides 8761 by NAT_4:9;
8761 = 83*105 + 46; hence not 83 divides 8761 by NAT_4:9;
8761 = 89*98 + 39; hence not 89 divides 8761 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8761 & n is prime
holds not n divides 8761 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
8779 is prime
proof
now
8779 = 2*4389 + 1; hence not 2 divides 8779 by NAT_4:9;
8779 = 3*2926 + 1; hence not 3 divides 8779 by NAT_4:9;
8779 = 5*1755 + 4; hence not 5 divides 8779 by NAT_4:9;
8779 = 7*1254 + 1; hence not 7 divides 8779 by NAT_4:9;
8779 = 11*798 + 1; hence not 11 divides 8779 by NAT_4:9;
8779 = 13*675 + 4; hence not 13 divides 8779 by NAT_4:9;
8779 = 17*516 + 7; hence not 17 divides 8779 by NAT_4:9;
8779 = 19*462 + 1; hence not 19 divides 8779 by NAT_4:9;
8779 = 23*381 + 16; hence not 23 divides 8779 by NAT_4:9;
8779 = 29*302 + 21; hence not 29 divides 8779 by NAT_4:9;
8779 = 31*283 + 6; hence not 31 divides 8779 by NAT_4:9;
8779 = 37*237 + 10; hence not 37 divides 8779 by NAT_4:9;
8779 = 41*214 + 5; hence not 41 divides 8779 by NAT_4:9;
8779 = 43*204 + 7; hence not 43 divides 8779 by NAT_4:9;
8779 = 47*186 + 37; hence not 47 divides 8779 by NAT_4:9;
8779 = 53*165 + 34; hence not 53 divides 8779 by NAT_4:9;
8779 = 59*148 + 47; hence not 59 divides 8779 by NAT_4:9;
8779 = 61*143 + 56; hence not 61 divides 8779 by NAT_4:9;
8779 = 67*131 + 2; hence not 67 divides 8779 by NAT_4:9;
8779 = 71*123 + 46; hence not 71 divides 8779 by NAT_4:9;
8779 = 73*120 + 19; hence not 73 divides 8779 by NAT_4:9;
8779 = 79*111 + 10; hence not 79 divides 8779 by NAT_4:9;
8779 = 83*105 + 64; hence not 83 divides 8779 by NAT_4:9;
8779 = 89*98 + 57; hence not 89 divides 8779 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8779 & n is prime
holds not n divides 8779 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8783 is prime
proof
now
8783 = 2*4391 + 1; hence not 2 divides 8783 by NAT_4:9;
8783 = 3*2927 + 2; hence not 3 divides 8783 by NAT_4:9;
8783 = 5*1756 + 3; hence not 5 divides 8783 by NAT_4:9;
8783 = 7*1254 + 5; hence not 7 divides 8783 by NAT_4:9;
8783 = 11*798 + 5; hence not 11 divides 8783 by NAT_4:9;
8783 = 13*675 + 8; hence not 13 divides 8783 by NAT_4:9;
8783 = 17*516 + 11; hence not 17 divides 8783 by NAT_4:9;
8783 = 19*462 + 5; hence not 19 divides 8783 by NAT_4:9;
8783 = 23*381 + 20; hence not 23 divides 8783 by NAT_4:9;
8783 = 29*302 + 25; hence not 29 divides 8783 by NAT_4:9;
8783 = 31*283 + 10; hence not 31 divides 8783 by NAT_4:9;
8783 = 37*237 + 14; hence not 37 divides 8783 by NAT_4:9;
8783 = 41*214 + 9; hence not 41 divides 8783 by NAT_4:9;
8783 = 43*204 + 11; hence not 43 divides 8783 by NAT_4:9;
8783 = 47*186 + 41; hence not 47 divides 8783 by NAT_4:9;
8783 = 53*165 + 38; hence not 53 divides 8783 by NAT_4:9;
8783 = 59*148 + 51; hence not 59 divides 8783 by NAT_4:9;
8783 = 61*143 + 60; hence not 61 divides 8783 by NAT_4:9;
8783 = 67*131 + 6; hence not 67 divides 8783 by NAT_4:9;
8783 = 71*123 + 50; hence not 71 divides 8783 by NAT_4:9;
8783 = 73*120 + 23; hence not 73 divides 8783 by NAT_4:9;
8783 = 79*111 + 14; hence not 79 divides 8783 by NAT_4:9;
8783 = 83*105 + 68; hence not 83 divides 8783 by NAT_4:9;
8783 = 89*98 + 61; hence not 89 divides 8783 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8783 & n is prime
holds not n divides 8783 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
8803 is prime
proof
now
8803 = 2*4401 + 1; hence not 2 divides 8803 by NAT_4:9;
8803 = 3*2934 + 1; hence not 3 divides 8803 by NAT_4:9;
8803 = 5*1760 + 3; hence not 5 divides 8803 by NAT_4:9;
8803 = 7*1257 + 4; hence not 7 divides 8803 by NAT_4:9;
8803 = 11*800 + 3; hence not 11 divides 8803 by NAT_4:9;
8803 = 13*677 + 2; hence not 13 divides 8803 by NAT_4:9;
8803 = 17*517 + 14; hence not 17 divides 8803 by NAT_4:9;
8803 = 19*463 + 6; hence not 19 divides 8803 by NAT_4:9;
8803 = 23*382 + 17; hence not 23 divides 8803 by NAT_4:9;
8803 = 29*303 + 16; hence not 29 divides 8803 by NAT_4:9;
8803 = 31*283 + 30; hence not 31 divides 8803 by NAT_4:9;
8803 = 37*237 + 34; hence not 37 divides 8803 by NAT_4:9;
8803 = 41*214 + 29; hence not 41 divides 8803 by NAT_4:9;
8803 = 43*204 + 31; hence not 43 divides 8803 by NAT_4:9;
8803 = 47*187 + 14; hence not 47 divides 8803 by NAT_4:9;
8803 = 53*166 + 5; hence not 53 divides 8803 by NAT_4:9;
8803 = 59*149 + 12; hence not 59 divides 8803 by NAT_4:9;
8803 = 61*144 + 19; hence not 61 divides 8803 by NAT_4:9;
8803 = 67*131 + 26; hence not 67 divides 8803 by NAT_4:9;
8803 = 71*123 + 70; hence not 71 divides 8803 by NAT_4:9;
8803 = 73*120 + 43; hence not 73 divides 8803 by NAT_4:9;
8803 = 79*111 + 34; hence not 79 divides 8803 by NAT_4:9;
8803 = 83*106 + 5; hence not 83 divides 8803 by NAT_4:9;
8803 = 89*98 + 81; hence not 89 divides 8803 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8803 & n is prime
holds not n divides 8803 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8807 is prime
proof
now
8807 = 2*4403 + 1; hence not 2 divides 8807 by NAT_4:9;
8807 = 3*2935 + 2; hence not 3 divides 8807 by NAT_4:9;
8807 = 5*1761 + 2; hence not 5 divides 8807 by NAT_4:9;
8807 = 7*1258 + 1; hence not 7 divides 8807 by NAT_4:9;
8807 = 11*800 + 7; hence not 11 divides 8807 by NAT_4:9;
8807 = 13*677 + 6; hence not 13 divides 8807 by NAT_4:9;
8807 = 17*518 + 1; hence not 17 divides 8807 by NAT_4:9;
8807 = 19*463 + 10; hence not 19 divides 8807 by NAT_4:9;
8807 = 23*382 + 21; hence not 23 divides 8807 by NAT_4:9;
8807 = 29*303 + 20; hence not 29 divides 8807 by NAT_4:9;
8807 = 31*284 + 3; hence not 31 divides 8807 by NAT_4:9;
8807 = 37*238 + 1; hence not 37 divides 8807 by NAT_4:9;
8807 = 41*214 + 33; hence not 41 divides 8807 by NAT_4:9;
8807 = 43*204 + 35; hence not 43 divides 8807 by NAT_4:9;
8807 = 47*187 + 18; hence not 47 divides 8807 by NAT_4:9;
8807 = 53*166 + 9; hence not 53 divides 8807 by NAT_4:9;
8807 = 59*149 + 16; hence not 59 divides 8807 by NAT_4:9;
8807 = 61*144 + 23; hence not 61 divides 8807 by NAT_4:9;
8807 = 67*131 + 30; hence not 67 divides 8807 by NAT_4:9;
8807 = 71*124 + 3; hence not 71 divides 8807 by NAT_4:9;
8807 = 73*120 + 47; hence not 73 divides 8807 by NAT_4:9;
8807 = 79*111 + 38; hence not 79 divides 8807 by NAT_4:9;
8807 = 83*106 + 9; hence not 83 divides 8807 by NAT_4:9;
8807 = 89*98 + 85; hence not 89 divides 8807 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8807 & n is prime
holds not n divides 8807 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8819 is prime
proof
now
8819 = 2*4409 + 1; hence not 2 divides 8819 by NAT_4:9;
8819 = 3*2939 + 2; hence not 3 divides 8819 by NAT_4:9;
8819 = 5*1763 + 4; hence not 5 divides 8819 by NAT_4:9;
8819 = 7*1259 + 6; hence not 7 divides 8819 by NAT_4:9;
8819 = 11*801 + 8; hence not 11 divides 8819 by NAT_4:9;
8819 = 13*678 + 5; hence not 13 divides 8819 by NAT_4:9;
8819 = 17*518 + 13; hence not 17 divides 8819 by NAT_4:9;
8819 = 19*464 + 3; hence not 19 divides 8819 by NAT_4:9;
8819 = 23*383 + 10; hence not 23 divides 8819 by NAT_4:9;
8819 = 29*304 + 3; hence not 29 divides 8819 by NAT_4:9;
8819 = 31*284 + 15; hence not 31 divides 8819 by NAT_4:9;
8819 = 37*238 + 13; hence not 37 divides 8819 by NAT_4:9;
8819 = 41*215 + 4; hence not 41 divides 8819 by NAT_4:9;
8819 = 43*205 + 4; hence not 43 divides 8819 by NAT_4:9;
8819 = 47*187 + 30; hence not 47 divides 8819 by NAT_4:9;
8819 = 53*166 + 21; hence not 53 divides 8819 by NAT_4:9;
8819 = 59*149 + 28; hence not 59 divides 8819 by NAT_4:9;
8819 = 61*144 + 35; hence not 61 divides 8819 by NAT_4:9;
8819 = 67*131 + 42; hence not 67 divides 8819 by NAT_4:9;
8819 = 71*124 + 15; hence not 71 divides 8819 by NAT_4:9;
8819 = 73*120 + 59; hence not 73 divides 8819 by NAT_4:9;
8819 = 79*111 + 50; hence not 79 divides 8819 by NAT_4:9;
8819 = 83*106 + 21; hence not 83 divides 8819 by NAT_4:9;
8819 = 89*99 + 8; hence not 89 divides 8819 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8819 & n is prime
holds not n divides 8819 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8821 is prime
proof
now
8821 = 2*4410 + 1; hence not 2 divides 8821 by NAT_4:9;
8821 = 3*2940 + 1; hence not 3 divides 8821 by NAT_4:9;
8821 = 5*1764 + 1; hence not 5 divides 8821 by NAT_4:9;
8821 = 7*1260 + 1; hence not 7 divides 8821 by NAT_4:9;
8821 = 11*801 + 10; hence not 11 divides 8821 by NAT_4:9;
8821 = 13*678 + 7; hence not 13 divides 8821 by NAT_4:9;
8821 = 17*518 + 15; hence not 17 divides 8821 by NAT_4:9;
8821 = 19*464 + 5; hence not 19 divides 8821 by NAT_4:9;
8821 = 23*383 + 12; hence not 23 divides 8821 by NAT_4:9;
8821 = 29*304 + 5; hence not 29 divides 8821 by NAT_4:9;
8821 = 31*284 + 17; hence not 31 divides 8821 by NAT_4:9;
8821 = 37*238 + 15; hence not 37 divides 8821 by NAT_4:9;
8821 = 41*215 + 6; hence not 41 divides 8821 by NAT_4:9;
8821 = 43*205 + 6; hence not 43 divides 8821 by NAT_4:9;
8821 = 47*187 + 32; hence not 47 divides 8821 by NAT_4:9;
8821 = 53*166 + 23; hence not 53 divides 8821 by NAT_4:9;
8821 = 59*149 + 30; hence not 59 divides 8821 by NAT_4:9;
8821 = 61*144 + 37; hence not 61 divides 8821 by NAT_4:9;
8821 = 67*131 + 44; hence not 67 divides 8821 by NAT_4:9;
8821 = 71*124 + 17; hence not 71 divides 8821 by NAT_4:9;
8821 = 73*120 + 61; hence not 73 divides 8821 by NAT_4:9;
8821 = 79*111 + 52; hence not 79 divides 8821 by NAT_4:9;
8821 = 83*106 + 23; hence not 83 divides 8821 by NAT_4:9;
8821 = 89*99 + 10; hence not 89 divides 8821 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8821 & n is prime
holds not n divides 8821 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8831 is prime
proof
now
8831 = 2*4415 + 1; hence not 2 divides 8831 by NAT_4:9;
8831 = 3*2943 + 2; hence not 3 divides 8831 by NAT_4:9;
8831 = 5*1766 + 1; hence not 5 divides 8831 by NAT_4:9;
8831 = 7*1261 + 4; hence not 7 divides 8831 by NAT_4:9;
8831 = 11*802 + 9; hence not 11 divides 8831 by NAT_4:9;
8831 = 13*679 + 4; hence not 13 divides 8831 by NAT_4:9;
8831 = 17*519 + 8; hence not 17 divides 8831 by NAT_4:9;
8831 = 19*464 + 15; hence not 19 divides 8831 by NAT_4:9;
8831 = 23*383 + 22; hence not 23 divides 8831 by NAT_4:9;
8831 = 29*304 + 15; hence not 29 divides 8831 by NAT_4:9;
8831 = 31*284 + 27; hence not 31 divides 8831 by NAT_4:9;
8831 = 37*238 + 25; hence not 37 divides 8831 by NAT_4:9;
8831 = 41*215 + 16; hence not 41 divides 8831 by NAT_4:9;
8831 = 43*205 + 16; hence not 43 divides 8831 by NAT_4:9;
8831 = 47*187 + 42; hence not 47 divides 8831 by NAT_4:9;
8831 = 53*166 + 33; hence not 53 divides 8831 by NAT_4:9;
8831 = 59*149 + 40; hence not 59 divides 8831 by NAT_4:9;
8831 = 61*144 + 47; hence not 61 divides 8831 by NAT_4:9;
8831 = 67*131 + 54; hence not 67 divides 8831 by NAT_4:9;
8831 = 71*124 + 27; hence not 71 divides 8831 by NAT_4:9;
8831 = 73*120 + 71; hence not 73 divides 8831 by NAT_4:9;
8831 = 79*111 + 62; hence not 79 divides 8831 by NAT_4:9;
8831 = 83*106 + 33; hence not 83 divides 8831 by NAT_4:9;
8831 = 89*99 + 20; hence not 89 divides 8831 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8831 & n is prime
holds not n divides 8831 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8837 is prime
proof
now
8837 = 2*4418 + 1; hence not 2 divides 8837 by NAT_4:9;
8837 = 3*2945 + 2; hence not 3 divides 8837 by NAT_4:9;
8837 = 5*1767 + 2; hence not 5 divides 8837 by NAT_4:9;
8837 = 7*1262 + 3; hence not 7 divides 8837 by NAT_4:9;
8837 = 11*803 + 4; hence not 11 divides 8837 by NAT_4:9;
8837 = 13*679 + 10; hence not 13 divides 8837 by NAT_4:9;
8837 = 17*519 + 14; hence not 17 divides 8837 by NAT_4:9;
8837 = 19*465 + 2; hence not 19 divides 8837 by NAT_4:9;
8837 = 23*384 + 5; hence not 23 divides 8837 by NAT_4:9;
8837 = 29*304 + 21; hence not 29 divides 8837 by NAT_4:9;
8837 = 31*285 + 2; hence not 31 divides 8837 by NAT_4:9;
8837 = 37*238 + 31; hence not 37 divides 8837 by NAT_4:9;
8837 = 41*215 + 22; hence not 41 divides 8837 by NAT_4:9;
8837 = 43*205 + 22; hence not 43 divides 8837 by NAT_4:9;
8837 = 47*188 + 1; hence not 47 divides 8837 by NAT_4:9;
8837 = 53*166 + 39; hence not 53 divides 8837 by NAT_4:9;
8837 = 59*149 + 46; hence not 59 divides 8837 by NAT_4:9;
8837 = 61*144 + 53; hence not 61 divides 8837 by NAT_4:9;
8837 = 67*131 + 60; hence not 67 divides 8837 by NAT_4:9;
8837 = 71*124 + 33; hence not 71 divides 8837 by NAT_4:9;
8837 = 73*121 + 4; hence not 73 divides 8837 by NAT_4:9;
8837 = 79*111 + 68; hence not 79 divides 8837 by NAT_4:9;
8837 = 83*106 + 39; hence not 83 divides 8837 by NAT_4:9;
8837 = 89*99 + 26; hence not 89 divides 8837 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8837 & n is prime
holds not n divides 8837 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8839 is prime
proof
now
8839 = 2*4419 + 1; hence not 2 divides 8839 by NAT_4:9;
8839 = 3*2946 + 1; hence not 3 divides 8839 by NAT_4:9;
8839 = 5*1767 + 4; hence not 5 divides 8839 by NAT_4:9;
8839 = 7*1262 + 5; hence not 7 divides 8839 by NAT_4:9;
8839 = 11*803 + 6; hence not 11 divides 8839 by NAT_4:9;
8839 = 13*679 + 12; hence not 13 divides 8839 by NAT_4:9;
8839 = 17*519 + 16; hence not 17 divides 8839 by NAT_4:9;
8839 = 19*465 + 4; hence not 19 divides 8839 by NAT_4:9;
8839 = 23*384 + 7; hence not 23 divides 8839 by NAT_4:9;
8839 = 29*304 + 23; hence not 29 divides 8839 by NAT_4:9;
8839 = 31*285 + 4; hence not 31 divides 8839 by NAT_4:9;
8839 = 37*238 + 33; hence not 37 divides 8839 by NAT_4:9;
8839 = 41*215 + 24; hence not 41 divides 8839 by NAT_4:9;
8839 = 43*205 + 24; hence not 43 divides 8839 by NAT_4:9;
8839 = 47*188 + 3; hence not 47 divides 8839 by NAT_4:9;
8839 = 53*166 + 41; hence not 53 divides 8839 by NAT_4:9;
8839 = 59*149 + 48; hence not 59 divides 8839 by NAT_4:9;
8839 = 61*144 + 55; hence not 61 divides 8839 by NAT_4:9;
8839 = 67*131 + 62; hence not 67 divides 8839 by NAT_4:9;
8839 = 71*124 + 35; hence not 71 divides 8839 by NAT_4:9;
8839 = 73*121 + 6; hence not 73 divides 8839 by NAT_4:9;
8839 = 79*111 + 70; hence not 79 divides 8839 by NAT_4:9;
8839 = 83*106 + 41; hence not 83 divides 8839 by NAT_4:9;
8839 = 89*99 + 28; hence not 89 divides 8839 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8839 & n is prime
holds not n divides 8839 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8849 is prime
proof
now
8849 = 2*4424 + 1; hence not 2 divides 8849 by NAT_4:9;
8849 = 3*2949 + 2; hence not 3 divides 8849 by NAT_4:9;
8849 = 5*1769 + 4; hence not 5 divides 8849 by NAT_4:9;
8849 = 7*1264 + 1; hence not 7 divides 8849 by NAT_4:9;
8849 = 11*804 + 5; hence not 11 divides 8849 by NAT_4:9;
8849 = 13*680 + 9; hence not 13 divides 8849 by NAT_4:9;
8849 = 17*520 + 9; hence not 17 divides 8849 by NAT_4:9;
8849 = 19*465 + 14; hence not 19 divides 8849 by NAT_4:9;
8849 = 23*384 + 17; hence not 23 divides 8849 by NAT_4:9;
8849 = 29*305 + 4; hence not 29 divides 8849 by NAT_4:9;
8849 = 31*285 + 14; hence not 31 divides 8849 by NAT_4:9;
8849 = 37*239 + 6; hence not 37 divides 8849 by NAT_4:9;
8849 = 41*215 + 34; hence not 41 divides 8849 by NAT_4:9;
8849 = 43*205 + 34; hence not 43 divides 8849 by NAT_4:9;
8849 = 47*188 + 13; hence not 47 divides 8849 by NAT_4:9;
8849 = 53*166 + 51; hence not 53 divides 8849 by NAT_4:9;
8849 = 59*149 + 58; hence not 59 divides 8849 by NAT_4:9;
8849 = 61*145 + 4; hence not 61 divides 8849 by NAT_4:9;
8849 = 67*132 + 5; hence not 67 divides 8849 by NAT_4:9;
8849 = 71*124 + 45; hence not 71 divides 8849 by NAT_4:9;
8849 = 73*121 + 16; hence not 73 divides 8849 by NAT_4:9;
8849 = 79*112 + 1; hence not 79 divides 8849 by NAT_4:9;
8849 = 83*106 + 51; hence not 83 divides 8849 by NAT_4:9;
8849 = 89*99 + 38; hence not 89 divides 8849 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8849 & n is prime
holds not n divides 8849 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8861 is prime
proof
now
8861 = 2*4430 + 1; hence not 2 divides 8861 by NAT_4:9;
8861 = 3*2953 + 2; hence not 3 divides 8861 by NAT_4:9;
8861 = 5*1772 + 1; hence not 5 divides 8861 by NAT_4:9;
8861 = 7*1265 + 6; hence not 7 divides 8861 by NAT_4:9;
8861 = 11*805 + 6; hence not 11 divides 8861 by NAT_4:9;
8861 = 13*681 + 8; hence not 13 divides 8861 by NAT_4:9;
8861 = 17*521 + 4; hence not 17 divides 8861 by NAT_4:9;
8861 = 19*466 + 7; hence not 19 divides 8861 by NAT_4:9;
8861 = 23*385 + 6; hence not 23 divides 8861 by NAT_4:9;
8861 = 29*305 + 16; hence not 29 divides 8861 by NAT_4:9;
8861 = 31*285 + 26; hence not 31 divides 8861 by NAT_4:9;
8861 = 37*239 + 18; hence not 37 divides 8861 by NAT_4:9;
8861 = 41*216 + 5; hence not 41 divides 8861 by NAT_4:9;
8861 = 43*206 + 3; hence not 43 divides 8861 by NAT_4:9;
8861 = 47*188 + 25; hence not 47 divides 8861 by NAT_4:9;
8861 = 53*167 + 10; hence not 53 divides 8861 by NAT_4:9;
8861 = 59*150 + 11; hence not 59 divides 8861 by NAT_4:9;
8861 = 61*145 + 16; hence not 61 divides 8861 by NAT_4:9;
8861 = 67*132 + 17; hence not 67 divides 8861 by NAT_4:9;
8861 = 71*124 + 57; hence not 71 divides 8861 by NAT_4:9;
8861 = 73*121 + 28; hence not 73 divides 8861 by NAT_4:9;
8861 = 79*112 + 13; hence not 79 divides 8861 by NAT_4:9;
8861 = 83*106 + 63; hence not 83 divides 8861 by NAT_4:9;
8861 = 89*99 + 50; hence not 89 divides 8861 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8861 & n is prime
holds not n divides 8861 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8863 is prime
proof
now
8863 = 2*4431 + 1; hence not 2 divides 8863 by NAT_4:9;
8863 = 3*2954 + 1; hence not 3 divides 8863 by NAT_4:9;
8863 = 5*1772 + 3; hence not 5 divides 8863 by NAT_4:9;
8863 = 7*1266 + 1; hence not 7 divides 8863 by NAT_4:9;
8863 = 11*805 + 8; hence not 11 divides 8863 by NAT_4:9;
8863 = 13*681 + 10; hence not 13 divides 8863 by NAT_4:9;
8863 = 17*521 + 6; hence not 17 divides 8863 by NAT_4:9;
8863 = 19*466 + 9; hence not 19 divides 8863 by NAT_4:9;
8863 = 23*385 + 8; hence not 23 divides 8863 by NAT_4:9;
8863 = 29*305 + 18; hence not 29 divides 8863 by NAT_4:9;
8863 = 31*285 + 28; hence not 31 divides 8863 by NAT_4:9;
8863 = 37*239 + 20; hence not 37 divides 8863 by NAT_4:9;
8863 = 41*216 + 7; hence not 41 divides 8863 by NAT_4:9;
8863 = 43*206 + 5; hence not 43 divides 8863 by NAT_4:9;
8863 = 47*188 + 27; hence not 47 divides 8863 by NAT_4:9;
8863 = 53*167 + 12; hence not 53 divides 8863 by NAT_4:9;
8863 = 59*150 + 13; hence not 59 divides 8863 by NAT_4:9;
8863 = 61*145 + 18; hence not 61 divides 8863 by NAT_4:9;
8863 = 67*132 + 19; hence not 67 divides 8863 by NAT_4:9;
8863 = 71*124 + 59; hence not 71 divides 8863 by NAT_4:9;
8863 = 73*121 + 30; hence not 73 divides 8863 by NAT_4:9;
8863 = 79*112 + 15; hence not 79 divides 8863 by NAT_4:9;
8863 = 83*106 + 65; hence not 83 divides 8863 by NAT_4:9;
8863 = 89*99 + 52; hence not 89 divides 8863 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8863 & n is prime
holds not n divides 8863 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8867 is prime
proof
now
8867 = 2*4433 + 1; hence not 2 divides 8867 by NAT_4:9;
8867 = 3*2955 + 2; hence not 3 divides 8867 by NAT_4:9;
8867 = 5*1773 + 2; hence not 5 divides 8867 by NAT_4:9;
8867 = 7*1266 + 5; hence not 7 divides 8867 by NAT_4:9;
8867 = 11*806 + 1; hence not 11 divides 8867 by NAT_4:9;
8867 = 13*682 + 1; hence not 13 divides 8867 by NAT_4:9;
8867 = 17*521 + 10; hence not 17 divides 8867 by NAT_4:9;
8867 = 19*466 + 13; hence not 19 divides 8867 by NAT_4:9;
8867 = 23*385 + 12; hence not 23 divides 8867 by NAT_4:9;
8867 = 29*305 + 22; hence not 29 divides 8867 by NAT_4:9;
8867 = 31*286 + 1; hence not 31 divides 8867 by NAT_4:9;
8867 = 37*239 + 24; hence not 37 divides 8867 by NAT_4:9;
8867 = 41*216 + 11; hence not 41 divides 8867 by NAT_4:9;
8867 = 43*206 + 9; hence not 43 divides 8867 by NAT_4:9;
8867 = 47*188 + 31; hence not 47 divides 8867 by NAT_4:9;
8867 = 53*167 + 16; hence not 53 divides 8867 by NAT_4:9;
8867 = 59*150 + 17; hence not 59 divides 8867 by NAT_4:9;
8867 = 61*145 + 22; hence not 61 divides 8867 by NAT_4:9;
8867 = 67*132 + 23; hence not 67 divides 8867 by NAT_4:9;
8867 = 71*124 + 63; hence not 71 divides 8867 by NAT_4:9;
8867 = 73*121 + 34; hence not 73 divides 8867 by NAT_4:9;
8867 = 79*112 + 19; hence not 79 divides 8867 by NAT_4:9;
8867 = 83*106 + 69; hence not 83 divides 8867 by NAT_4:9;
8867 = 89*99 + 56; hence not 89 divides 8867 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8867 & n is prime
holds not n divides 8867 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
8887 is prime
proof
now
8887 = 2*4443 + 1; hence not 2 divides 8887 by NAT_4:9;
8887 = 3*2962 + 1; hence not 3 divides 8887 by NAT_4:9;
8887 = 5*1777 + 2; hence not 5 divides 8887 by NAT_4:9;
8887 = 7*1269 + 4; hence not 7 divides 8887 by NAT_4:9;
8887 = 11*807 + 10; hence not 11 divides 8887 by NAT_4:9;
8887 = 13*683 + 8; hence not 13 divides 8887 by NAT_4:9;
8887 = 17*522 + 13; hence not 17 divides 8887 by NAT_4:9;
8887 = 19*467 + 14; hence not 19 divides 8887 by NAT_4:9;
8887 = 23*386 + 9; hence not 23 divides 8887 by NAT_4:9;
8887 = 29*306 + 13; hence not 29 divides 8887 by NAT_4:9;
8887 = 31*286 + 21; hence not 31 divides 8887 by NAT_4:9;
8887 = 37*240 + 7; hence not 37 divides 8887 by NAT_4:9;
8887 = 41*216 + 31; hence not 41 divides 8887 by NAT_4:9;
8887 = 43*206 + 29; hence not 43 divides 8887 by NAT_4:9;
8887 = 47*189 + 4; hence not 47 divides 8887 by NAT_4:9;
8887 = 53*167 + 36; hence not 53 divides 8887 by NAT_4:9;
8887 = 59*150 + 37; hence not 59 divides 8887 by NAT_4:9;
8887 = 61*145 + 42; hence not 61 divides 8887 by NAT_4:9;
8887 = 67*132 + 43; hence not 67 divides 8887 by NAT_4:9;
8887 = 71*125 + 12; hence not 71 divides 8887 by NAT_4:9;
8887 = 73*121 + 54; hence not 73 divides 8887 by NAT_4:9;
8887 = 79*112 + 39; hence not 79 divides 8887 by NAT_4:9;
8887 = 83*107 + 6; hence not 83 divides 8887 by NAT_4:9;
8887 = 89*99 + 76; hence not 89 divides 8887 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8887 & n is prime
holds not n divides 8887 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8893 is prime
proof
now
8893 = 2*4446 + 1; hence not 2 divides 8893 by NAT_4:9;
8893 = 3*2964 + 1; hence not 3 divides 8893 by NAT_4:9;
8893 = 5*1778 + 3; hence not 5 divides 8893 by NAT_4:9;
8893 = 7*1270 + 3; hence not 7 divides 8893 by NAT_4:9;
8893 = 11*808 + 5; hence not 11 divides 8893 by NAT_4:9;
8893 = 13*684 + 1; hence not 13 divides 8893 by NAT_4:9;
8893 = 17*523 + 2; hence not 17 divides 8893 by NAT_4:9;
8893 = 19*468 + 1; hence not 19 divides 8893 by NAT_4:9;
8893 = 23*386 + 15; hence not 23 divides 8893 by NAT_4:9;
8893 = 29*306 + 19; hence not 29 divides 8893 by NAT_4:9;
8893 = 31*286 + 27; hence not 31 divides 8893 by NAT_4:9;
8893 = 37*240 + 13; hence not 37 divides 8893 by NAT_4:9;
8893 = 41*216 + 37; hence not 41 divides 8893 by NAT_4:9;
8893 = 43*206 + 35; hence not 43 divides 8893 by NAT_4:9;
8893 = 47*189 + 10; hence not 47 divides 8893 by NAT_4:9;
8893 = 53*167 + 42; hence not 53 divides 8893 by NAT_4:9;
8893 = 59*150 + 43; hence not 59 divides 8893 by NAT_4:9;
8893 = 61*145 + 48; hence not 61 divides 8893 by NAT_4:9;
8893 = 67*132 + 49; hence not 67 divides 8893 by NAT_4:9;
8893 = 71*125 + 18; hence not 71 divides 8893 by NAT_4:9;
8893 = 73*121 + 60; hence not 73 divides 8893 by NAT_4:9;
8893 = 79*112 + 45; hence not 79 divides 8893 by NAT_4:9;
8893 = 83*107 + 12; hence not 83 divides 8893 by NAT_4:9;
8893 = 89*99 + 82; hence not 89 divides 8893 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8893 & n is prime
holds not n divides 8893 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 29
theorem
8923 is prime
proof
now
8923 = 2*4461 + 1; hence not 2 divides 8923 by NAT_4:9;
8923 = 3*2974 + 1; hence not 3 divides 8923 by NAT_4:9;
8923 = 5*1784 + 3; hence not 5 divides 8923 by NAT_4:9;
8923 = 7*1274 + 5; hence not 7 divides 8923 by NAT_4:9;
8923 = 11*811 + 2; hence not 11 divides 8923 by NAT_4:9;
8923 = 13*686 + 5; hence not 13 divides 8923 by NAT_4:9;
8923 = 17*524 + 15; hence not 17 divides 8923 by NAT_4:9;
8923 = 19*469 + 12; hence not 19 divides 8923 by NAT_4:9;
8923 = 23*387 + 22; hence not 23 divides 8923 by NAT_4:9;
8923 = 29*307 + 20; hence not 29 divides 8923 by NAT_4:9;
8923 = 31*287 + 26; hence not 31 divides 8923 by NAT_4:9;
8923 = 37*241 + 6; hence not 37 divides 8923 by NAT_4:9;
8923 = 41*217 + 26; hence not 41 divides 8923 by NAT_4:9;
8923 = 43*207 + 22; hence not 43 divides 8923 by NAT_4:9;
8923 = 47*189 + 40; hence not 47 divides 8923 by NAT_4:9;
8923 = 53*168 + 19; hence not 53 divides 8923 by NAT_4:9;
8923 = 59*151 + 14; hence not 59 divides 8923 by NAT_4:9;
8923 = 61*146 + 17; hence not 61 divides 8923 by NAT_4:9;
8923 = 67*133 + 12; hence not 67 divides 8923 by NAT_4:9;
8923 = 71*125 + 48; hence not 71 divides 8923 by NAT_4:9;
8923 = 73*122 + 17; hence not 73 divides 8923 by NAT_4:9;
8923 = 79*112 + 75; hence not 79 divides 8923 by NAT_4:9;
8923 = 83*107 + 42; hence not 83 divides 8923 by NAT_4:9;
8923 = 89*100 + 23; hence not 89 divides 8923 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8923 & n is prime
holds not n divides 8923 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8929 is prime
proof
now
8929 = 2*4464 + 1; hence not 2 divides 8929 by NAT_4:9;
8929 = 3*2976 + 1; hence not 3 divides 8929 by NAT_4:9;
8929 = 5*1785 + 4; hence not 5 divides 8929 by NAT_4:9;
8929 = 7*1275 + 4; hence not 7 divides 8929 by NAT_4:9;
8929 = 11*811 + 8; hence not 11 divides 8929 by NAT_4:9;
8929 = 13*686 + 11; hence not 13 divides 8929 by NAT_4:9;
8929 = 17*525 + 4; hence not 17 divides 8929 by NAT_4:9;
8929 = 19*469 + 18; hence not 19 divides 8929 by NAT_4:9;
8929 = 23*388 + 5; hence not 23 divides 8929 by NAT_4:9;
8929 = 29*307 + 26; hence not 29 divides 8929 by NAT_4:9;
8929 = 31*288 + 1; hence not 31 divides 8929 by NAT_4:9;
8929 = 37*241 + 12; hence not 37 divides 8929 by NAT_4:9;
8929 = 41*217 + 32; hence not 41 divides 8929 by NAT_4:9;
8929 = 43*207 + 28; hence not 43 divides 8929 by NAT_4:9;
8929 = 47*189 + 46; hence not 47 divides 8929 by NAT_4:9;
8929 = 53*168 + 25; hence not 53 divides 8929 by NAT_4:9;
8929 = 59*151 + 20; hence not 59 divides 8929 by NAT_4:9;
8929 = 61*146 + 23; hence not 61 divides 8929 by NAT_4:9;
8929 = 67*133 + 18; hence not 67 divides 8929 by NAT_4:9;
8929 = 71*125 + 54; hence not 71 divides 8929 by NAT_4:9;
8929 = 73*122 + 23; hence not 73 divides 8929 by NAT_4:9;
8929 = 79*113 + 2; hence not 79 divides 8929 by NAT_4:9;
8929 = 83*107 + 48; hence not 83 divides 8929 by NAT_4:9;
8929 = 89*100 + 29; hence not 89 divides 8929 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8929 & n is prime
holds not n divides 8929 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
8933 is prime
proof
now
8933 = 2*4466 + 1; hence not 2 divides 8933 by NAT_4:9;
8933 = 3*2977 + 2; hence not 3 divides 8933 by NAT_4:9;
8933 = 5*1786 + 3; hence not 5 divides 8933 by NAT_4:9;
8933 = 7*1276 + 1; hence not 7 divides 8933 by NAT_4:9;
8933 = 11*812 + 1; hence not 11 divides 8933 by NAT_4:9;
8933 = 13*687 + 2; hence not 13 divides 8933 by NAT_4:9;
8933 = 17*525 + 8; hence not 17 divides 8933 by NAT_4:9;
8933 = 19*470 + 3; hence not 19 divides 8933 by NAT_4:9;
8933 = 23*388 + 9; hence not 23 divides 8933 by NAT_4:9;
8933 = 29*308 + 1; hence not 29 divides 8933 by NAT_4:9;
8933 = 31*288 + 5; hence not 31 divides 8933 by NAT_4:9;
8933 = 37*241 + 16; hence not 37 divides 8933 by NAT_4:9;
8933 = 41*217 + 36; hence not 41 divides 8933 by NAT_4:9;
8933 = 43*207 + 32; hence not 43 divides 8933 by NAT_4:9;
8933 = 47*190 + 3; hence not 47 divides 8933 by NAT_4:9;
8933 = 53*168 + 29; hence not 53 divides 8933 by NAT_4:9;
8933 = 59*151 + 24; hence not 59 divides 8933 by NAT_4:9;
8933 = 61*146 + 27; hence not 61 divides 8933 by NAT_4:9;
8933 = 67*133 + 22; hence not 67 divides 8933 by NAT_4:9;
8933 = 71*125 + 58; hence not 71 divides 8933 by NAT_4:9;
8933 = 73*122 + 27; hence not 73 divides 8933 by NAT_4:9;
8933 = 79*113 + 6; hence not 79 divides 8933 by NAT_4:9;
8933 = 83*107 + 52; hence not 83 divides 8933 by NAT_4:9;
8933 = 89*100 + 33; hence not 89 divides 8933 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8933 & n is prime
holds not n divides 8933 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
8941 is prime
proof
now
8941 = 2*4470 + 1; hence not 2 divides 8941 by NAT_4:9;
8941 = 3*2980 + 1; hence not 3 divides 8941 by NAT_4:9;
8941 = 5*1788 + 1; hence not 5 divides 8941 by NAT_4:9;
8941 = 7*1277 + 2; hence not 7 divides 8941 by NAT_4:9;
8941 = 11*812 + 9; hence not 11 divides 8941 by NAT_4:9;
8941 = 13*687 + 10; hence not 13 divides 8941 by NAT_4:9;
8941 = 17*525 + 16; hence not 17 divides 8941 by NAT_4:9;
8941 = 19*470 + 11; hence not 19 divides 8941 by NAT_4:9;
8941 = 23*388 + 17; hence not 23 divides 8941 by NAT_4:9;
8941 = 29*308 + 9; hence not 29 divides 8941 by NAT_4:9;
8941 = 31*288 + 13; hence not 31 divides 8941 by NAT_4:9;
8941 = 37*241 + 24; hence not 37 divides 8941 by NAT_4:9;
8941 = 41*218 + 3; hence not 41 divides 8941 by NAT_4:9;
8941 = 43*207 + 40; hence not 43 divides 8941 by NAT_4:9;
8941 = 47*190 + 11; hence not 47 divides 8941 by NAT_4:9;
8941 = 53*168 + 37; hence not 53 divides 8941 by NAT_4:9;
8941 = 59*151 + 32; hence not 59 divides 8941 by NAT_4:9;
8941 = 61*146 + 35; hence not 61 divides 8941 by NAT_4:9;
8941 = 67*133 + 30; hence not 67 divides 8941 by NAT_4:9;
8941 = 71*125 + 66; hence not 71 divides 8941 by NAT_4:9;
8941 = 73*122 + 35; hence not 73 divides 8941 by NAT_4:9;
8941 = 79*113 + 14; hence not 79 divides 8941 by NAT_4:9;
8941 = 83*107 + 60; hence not 83 divides 8941 by NAT_4:9;
8941 = 89*100 + 41; hence not 89 divides 8941 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8941 & n is prime
holds not n divides 8941 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
8951 is prime
proof
now
8951 = 2*4475 + 1; hence not 2 divides 8951 by NAT_4:9;
8951 = 3*2983 + 2; hence not 3 divides 8951 by NAT_4:9;
8951 = 5*1790 + 1; hence not 5 divides 8951 by NAT_4:9;
8951 = 7*1278 + 5; hence not 7 divides 8951 by NAT_4:9;
8951 = 11*813 + 8; hence not 11 divides 8951 by NAT_4:9;
8951 = 13*688 + 7; hence not 13 divides 8951 by NAT_4:9;
8951 = 17*526 + 9; hence not 17 divides 8951 by NAT_4:9;
8951 = 19*471 + 2; hence not 19 divides 8951 by NAT_4:9;
8951 = 23*389 + 4; hence not 23 divides 8951 by NAT_4:9;
8951 = 29*308 + 19; hence not 29 divides 8951 by NAT_4:9;
8951 = 31*288 + 23; hence not 31 divides 8951 by NAT_4:9;
8951 = 37*241 + 34; hence not 37 divides 8951 by NAT_4:9;
8951 = 41*218 + 13; hence not 41 divides 8951 by NAT_4:9;
8951 = 43*208 + 7; hence not 43 divides 8951 by NAT_4:9;
8951 = 47*190 + 21; hence not 47 divides 8951 by NAT_4:9;
8951 = 53*168 + 47; hence not 53 divides 8951 by NAT_4:9;
8951 = 59*151 + 42; hence not 59 divides 8951 by NAT_4:9;
8951 = 61*146 + 45; hence not 61 divides 8951 by NAT_4:9;
8951 = 67*133 + 40; hence not 67 divides 8951 by NAT_4:9;
8951 = 71*126 + 5; hence not 71 divides 8951 by NAT_4:9;
8951 = 73*122 + 45; hence not 73 divides 8951 by NAT_4:9;
8951 = 79*113 + 24; hence not 79 divides 8951 by NAT_4:9;
8951 = 83*107 + 70; hence not 83 divides 8951 by NAT_4:9;
8951 = 89*100 + 51; hence not 89 divides 8951 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8951 & n is prime
holds not n divides 8951 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
8963 is prime
proof
now
8963 = 2*4481 + 1; hence not 2 divides 8963 by NAT_4:9;
8963 = 3*2987 + 2; hence not 3 divides 8963 by NAT_4:9;
8963 = 5*1792 + 3; hence not 5 divides 8963 by NAT_4:9;
8963 = 7*1280 + 3; hence not 7 divides 8963 by NAT_4:9;
8963 = 11*814 + 9; hence not 11 divides 8963 by NAT_4:9;
8963 = 13*689 + 6; hence not 13 divides 8963 by NAT_4:9;
8963 = 17*527 + 4; hence not 17 divides 8963 by NAT_4:9;
8963 = 19*471 + 14; hence not 19 divides 8963 by NAT_4:9;
8963 = 23*389 + 16; hence not 23 divides 8963 by NAT_4:9;
8963 = 29*309 + 2; hence not 29 divides 8963 by NAT_4:9;
8963 = 31*289 + 4; hence not 31 divides 8963 by NAT_4:9;
8963 = 37*242 + 9; hence not 37 divides 8963 by NAT_4:9;
8963 = 41*218 + 25; hence not 41 divides 8963 by NAT_4:9;
8963 = 43*208 + 19; hence not 43 divides 8963 by NAT_4:9;
8963 = 47*190 + 33; hence not 47 divides 8963 by NAT_4:9;
8963 = 53*169 + 6; hence not 53 divides 8963 by NAT_4:9;
8963 = 59*151 + 54; hence not 59 divides 8963 by NAT_4:9;
8963 = 61*146 + 57; hence not 61 divides 8963 by NAT_4:9;
8963 = 67*133 + 52; hence not 67 divides 8963 by NAT_4:9;
8963 = 71*126 + 17; hence not 71 divides 8963 by NAT_4:9;
8963 = 73*122 + 57; hence not 73 divides 8963 by NAT_4:9;
8963 = 79*113 + 36; hence not 79 divides 8963 by NAT_4:9;
8963 = 83*107 + 82; hence not 83 divides 8963 by NAT_4:9;
8963 = 89*100 + 63; hence not 89 divides 8963 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8963 & n is prime
holds not n divides 8963 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
8969 is prime
proof
now
8969 = 2*4484 + 1; hence not 2 divides 8969 by NAT_4:9;
8969 = 3*2989 + 2; hence not 3 divides 8969 by NAT_4:9;
8969 = 5*1793 + 4; hence not 5 divides 8969 by NAT_4:9;
8969 = 7*1281 + 2; hence not 7 divides 8969 by NAT_4:9;
8969 = 11*815 + 4; hence not 11 divides 8969 by NAT_4:9;
8969 = 13*689 + 12; hence not 13 divides 8969 by NAT_4:9;
8969 = 17*527 + 10; hence not 17 divides 8969 by NAT_4:9;
8969 = 19*472 + 1; hence not 19 divides 8969 by NAT_4:9;
8969 = 23*389 + 22; hence not 23 divides 8969 by NAT_4:9;
8969 = 29*309 + 8; hence not 29 divides 8969 by NAT_4:9;
8969 = 31*289 + 10; hence not 31 divides 8969 by NAT_4:9;
8969 = 37*242 + 15; hence not 37 divides 8969 by NAT_4:9;
8969 = 41*218 + 31; hence not 41 divides 8969 by NAT_4:9;
8969 = 43*208 + 25; hence not 43 divides 8969 by NAT_4:9;
8969 = 47*190 + 39; hence not 47 divides 8969 by NAT_4:9;
8969 = 53*169 + 12; hence not 53 divides 8969 by NAT_4:9;
8969 = 59*152 + 1; hence not 59 divides 8969 by NAT_4:9;
8969 = 61*147 + 2; hence not 61 divides 8969 by NAT_4:9;
8969 = 67*133 + 58; hence not 67 divides 8969 by NAT_4:9;
8969 = 71*126 + 23; hence not 71 divides 8969 by NAT_4:9;
8969 = 73*122 + 63; hence not 73 divides 8969 by NAT_4:9;
8969 = 79*113 + 42; hence not 79 divides 8969 by NAT_4:9;
8969 = 83*108 + 5; hence not 83 divides 8969 by NAT_4:9;
8969 = 89*100 + 69; hence not 89 divides 8969 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8969 & n is prime
holds not n divides 8969 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
8971 is prime
proof
now
8971 = 2*4485 + 1; hence not 2 divides 8971 by NAT_4:9;
8971 = 3*2990 + 1; hence not 3 divides 8971 by NAT_4:9;
8971 = 5*1794 + 1; hence not 5 divides 8971 by NAT_4:9;
8971 = 7*1281 + 4; hence not 7 divides 8971 by NAT_4:9;
8971 = 11*815 + 6; hence not 11 divides 8971 by NAT_4:9;
8971 = 13*690 + 1; hence not 13 divides 8971 by NAT_4:9;
8971 = 17*527 + 12; hence not 17 divides 8971 by NAT_4:9;
8971 = 19*472 + 3; hence not 19 divides 8971 by NAT_4:9;
8971 = 23*390 + 1; hence not 23 divides 8971 by NAT_4:9;
8971 = 29*309 + 10; hence not 29 divides 8971 by NAT_4:9;
8971 = 31*289 + 12; hence not 31 divides 8971 by NAT_4:9;
8971 = 37*242 + 17; hence not 37 divides 8971 by NAT_4:9;
8971 = 41*218 + 33; hence not 41 divides 8971 by NAT_4:9;
8971 = 43*208 + 27; hence not 43 divides 8971 by NAT_4:9;
8971 = 47*190 + 41; hence not 47 divides 8971 by NAT_4:9;
8971 = 53*169 + 14; hence not 53 divides 8971 by NAT_4:9;
8971 = 59*152 + 3; hence not 59 divides 8971 by NAT_4:9;
8971 = 61*147 + 4; hence not 61 divides 8971 by NAT_4:9;
8971 = 67*133 + 60; hence not 67 divides 8971 by NAT_4:9;
8971 = 71*126 + 25; hence not 71 divides 8971 by NAT_4:9;
8971 = 73*122 + 65; hence not 73 divides 8971 by NAT_4:9;
8971 = 79*113 + 44; hence not 79 divides 8971 by NAT_4:9;
8971 = 83*108 + 7; hence not 83 divides 8971 by NAT_4:9;
8971 = 89*100 + 71; hence not 89 divides 8971 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8971 & n is prime
holds not n divides 8971 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 27
theorem
8999 is prime
proof
now
8999 = 2*4499 + 1; hence not 2 divides 8999 by NAT_4:9;
8999 = 3*2999 + 2; hence not 3 divides 8999 by NAT_4:9;
8999 = 5*1799 + 4; hence not 5 divides 8999 by NAT_4:9;
8999 = 7*1285 + 4; hence not 7 divides 8999 by NAT_4:9;
8999 = 11*818 + 1; hence not 11 divides 8999 by NAT_4:9;
8999 = 13*692 + 3; hence not 13 divides 8999 by NAT_4:9;
8999 = 17*529 + 6; hence not 17 divides 8999 by NAT_4:9;
8999 = 19*473 + 12; hence not 19 divides 8999 by NAT_4:9;
8999 = 23*391 + 6; hence not 23 divides 8999 by NAT_4:9;
8999 = 29*310 + 9; hence not 29 divides 8999 by NAT_4:9;
8999 = 31*290 + 9; hence not 31 divides 8999 by NAT_4:9;
8999 = 37*243 + 8; hence not 37 divides 8999 by NAT_4:9;
8999 = 41*219 + 20; hence not 41 divides 8999 by NAT_4:9;
8999 = 43*209 + 12; hence not 43 divides 8999 by NAT_4:9;
8999 = 47*191 + 22; hence not 47 divides 8999 by NAT_4:9;
8999 = 53*169 + 42; hence not 53 divides 8999 by NAT_4:9;
8999 = 59*152 + 31; hence not 59 divides 8999 by NAT_4:9;
8999 = 61*147 + 32; hence not 61 divides 8999 by NAT_4:9;
8999 = 67*134 + 21; hence not 67 divides 8999 by NAT_4:9;
8999 = 71*126 + 53; hence not 71 divides 8999 by NAT_4:9;
8999 = 73*123 + 20; hence not 73 divides 8999 by NAT_4:9;
8999 = 79*113 + 72; hence not 79 divides 8999 by NAT_4:9;
8999 = 83*108 + 35; hence not 83 divides 8999 by NAT_4:9;
8999 = 89*101 + 10; hence not 89 divides 8999 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 8999 & n is prime
holds not n divides 8999 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9001 is prime
proof
now
9001 = 2*4500 + 1; hence not 2 divides 9001 by NAT_4:9;
9001 = 3*3000 + 1; hence not 3 divides 9001 by NAT_4:9;
9001 = 5*1800 + 1; hence not 5 divides 9001 by NAT_4:9;
9001 = 7*1285 + 6; hence not 7 divides 9001 by NAT_4:9;
9001 = 11*818 + 3; hence not 11 divides 9001 by NAT_4:9;
9001 = 13*692 + 5; hence not 13 divides 9001 by NAT_4:9;
9001 = 17*529 + 8; hence not 17 divides 9001 by NAT_4:9;
9001 = 19*473 + 14; hence not 19 divides 9001 by NAT_4:9;
9001 = 23*391 + 8; hence not 23 divides 9001 by NAT_4:9;
9001 = 29*310 + 11; hence not 29 divides 9001 by NAT_4:9;
9001 = 31*290 + 11; hence not 31 divides 9001 by NAT_4:9;
9001 = 37*243 + 10; hence not 37 divides 9001 by NAT_4:9;
9001 = 41*219 + 22; hence not 41 divides 9001 by NAT_4:9;
9001 = 43*209 + 14; hence not 43 divides 9001 by NAT_4:9;
9001 = 47*191 + 24; hence not 47 divides 9001 by NAT_4:9;
9001 = 53*169 + 44; hence not 53 divides 9001 by NAT_4:9;
9001 = 59*152 + 33; hence not 59 divides 9001 by NAT_4:9;
9001 = 61*147 + 34; hence not 61 divides 9001 by NAT_4:9;
9001 = 67*134 + 23; hence not 67 divides 9001 by NAT_4:9;
9001 = 71*126 + 55; hence not 71 divides 9001 by NAT_4:9;
9001 = 73*123 + 22; hence not 73 divides 9001 by NAT_4:9;
9001 = 79*113 + 74; hence not 79 divides 9001 by NAT_4:9;
9001 = 83*108 + 37; hence not 83 divides 9001 by NAT_4:9;
9001 = 89*101 + 12; hence not 89 divides 9001 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9001 & n is prime
holds not n divides 9001 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9007 is prime
proof
now
9007 = 2*4503 + 1; hence not 2 divides 9007 by NAT_4:9;
9007 = 3*3002 + 1; hence not 3 divides 9007 by NAT_4:9;
9007 = 5*1801 + 2; hence not 5 divides 9007 by NAT_4:9;
9007 = 7*1286 + 5; hence not 7 divides 9007 by NAT_4:9;
9007 = 11*818 + 9; hence not 11 divides 9007 by NAT_4:9;
9007 = 13*692 + 11; hence not 13 divides 9007 by NAT_4:9;
9007 = 17*529 + 14; hence not 17 divides 9007 by NAT_4:9;
9007 = 19*474 + 1; hence not 19 divides 9007 by NAT_4:9;
9007 = 23*391 + 14; hence not 23 divides 9007 by NAT_4:9;
9007 = 29*310 + 17; hence not 29 divides 9007 by NAT_4:9;
9007 = 31*290 + 17; hence not 31 divides 9007 by NAT_4:9;
9007 = 37*243 + 16; hence not 37 divides 9007 by NAT_4:9;
9007 = 41*219 + 28; hence not 41 divides 9007 by NAT_4:9;
9007 = 43*209 + 20; hence not 43 divides 9007 by NAT_4:9;
9007 = 47*191 + 30; hence not 47 divides 9007 by NAT_4:9;
9007 = 53*169 + 50; hence not 53 divides 9007 by NAT_4:9;
9007 = 59*152 + 39; hence not 59 divides 9007 by NAT_4:9;
9007 = 61*147 + 40; hence not 61 divides 9007 by NAT_4:9;
9007 = 67*134 + 29; hence not 67 divides 9007 by NAT_4:9;
9007 = 71*126 + 61; hence not 71 divides 9007 by NAT_4:9;
9007 = 73*123 + 28; hence not 73 divides 9007 by NAT_4:9;
9007 = 79*114 + 1; hence not 79 divides 9007 by NAT_4:9;
9007 = 83*108 + 43; hence not 83 divides 9007 by NAT_4:9;
9007 = 89*101 + 18; hence not 89 divides 9007 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9007 & n is prime
holds not n divides 9007 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9011 is prime
proof
now
9011 = 2*4505 + 1; hence not 2 divides 9011 by NAT_4:9;
9011 = 3*3003 + 2; hence not 3 divides 9011 by NAT_4:9;
9011 = 5*1802 + 1; hence not 5 divides 9011 by NAT_4:9;
9011 = 7*1287 + 2; hence not 7 divides 9011 by NAT_4:9;
9011 = 11*819 + 2; hence not 11 divides 9011 by NAT_4:9;
9011 = 13*693 + 2; hence not 13 divides 9011 by NAT_4:9;
9011 = 17*530 + 1; hence not 17 divides 9011 by NAT_4:9;
9011 = 19*474 + 5; hence not 19 divides 9011 by NAT_4:9;
9011 = 23*391 + 18; hence not 23 divides 9011 by NAT_4:9;
9011 = 29*310 + 21; hence not 29 divides 9011 by NAT_4:9;
9011 = 31*290 + 21; hence not 31 divides 9011 by NAT_4:9;
9011 = 37*243 + 20; hence not 37 divides 9011 by NAT_4:9;
9011 = 41*219 + 32; hence not 41 divides 9011 by NAT_4:9;
9011 = 43*209 + 24; hence not 43 divides 9011 by NAT_4:9;
9011 = 47*191 + 34; hence not 47 divides 9011 by NAT_4:9;
9011 = 53*170 + 1; hence not 53 divides 9011 by NAT_4:9;
9011 = 59*152 + 43; hence not 59 divides 9011 by NAT_4:9;
9011 = 61*147 + 44; hence not 61 divides 9011 by NAT_4:9;
9011 = 67*134 + 33; hence not 67 divides 9011 by NAT_4:9;
9011 = 71*126 + 65; hence not 71 divides 9011 by NAT_4:9;
9011 = 73*123 + 32; hence not 73 divides 9011 by NAT_4:9;
9011 = 79*114 + 5; hence not 79 divides 9011 by NAT_4:9;
9011 = 83*108 + 47; hence not 83 divides 9011 by NAT_4:9;
9011 = 89*101 + 22; hence not 89 divides 9011 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9011 & n is prime
holds not n divides 9011 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9013 is prime
proof
now
9013 = 2*4506 + 1; hence not 2 divides 9013 by NAT_4:9;
9013 = 3*3004 + 1; hence not 3 divides 9013 by NAT_4:9;
9013 = 5*1802 + 3; hence not 5 divides 9013 by NAT_4:9;
9013 = 7*1287 + 4; hence not 7 divides 9013 by NAT_4:9;
9013 = 11*819 + 4; hence not 11 divides 9013 by NAT_4:9;
9013 = 13*693 + 4; hence not 13 divides 9013 by NAT_4:9;
9013 = 17*530 + 3; hence not 17 divides 9013 by NAT_4:9;
9013 = 19*474 + 7; hence not 19 divides 9013 by NAT_4:9;
9013 = 23*391 + 20; hence not 23 divides 9013 by NAT_4:9;
9013 = 29*310 + 23; hence not 29 divides 9013 by NAT_4:9;
9013 = 31*290 + 23; hence not 31 divides 9013 by NAT_4:9;
9013 = 37*243 + 22; hence not 37 divides 9013 by NAT_4:9;
9013 = 41*219 + 34; hence not 41 divides 9013 by NAT_4:9;
9013 = 43*209 + 26; hence not 43 divides 9013 by NAT_4:9;
9013 = 47*191 + 36; hence not 47 divides 9013 by NAT_4:9;
9013 = 53*170 + 3; hence not 53 divides 9013 by NAT_4:9;
9013 = 59*152 + 45; hence not 59 divides 9013 by NAT_4:9;
9013 = 61*147 + 46; hence not 61 divides 9013 by NAT_4:9;
9013 = 67*134 + 35; hence not 67 divides 9013 by NAT_4:9;
9013 = 71*126 + 67; hence not 71 divides 9013 by NAT_4:9;
9013 = 73*123 + 34; hence not 73 divides 9013 by NAT_4:9;
9013 = 79*114 + 7; hence not 79 divides 9013 by NAT_4:9;
9013 = 83*108 + 49; hence not 83 divides 9013 by NAT_4:9;
9013 = 89*101 + 24; hence not 89 divides 9013 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9013 & n is prime
holds not n divides 9013 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
9029 is prime
proof
now
9029 = 2*4514 + 1; hence not 2 divides 9029 by NAT_4:9;
9029 = 3*3009 + 2; hence not 3 divides 9029 by NAT_4:9;
9029 = 5*1805 + 4; hence not 5 divides 9029 by NAT_4:9;
9029 = 7*1289 + 6; hence not 7 divides 9029 by NAT_4:9;
9029 = 11*820 + 9; hence not 11 divides 9029 by NAT_4:9;
9029 = 13*694 + 7; hence not 13 divides 9029 by NAT_4:9;
9029 = 17*531 + 2; hence not 17 divides 9029 by NAT_4:9;
9029 = 19*475 + 4; hence not 19 divides 9029 by NAT_4:9;
9029 = 23*392 + 13; hence not 23 divides 9029 by NAT_4:9;
9029 = 29*311 + 10; hence not 29 divides 9029 by NAT_4:9;
9029 = 31*291 + 8; hence not 31 divides 9029 by NAT_4:9;
9029 = 37*244 + 1; hence not 37 divides 9029 by NAT_4:9;
9029 = 41*220 + 9; hence not 41 divides 9029 by NAT_4:9;
9029 = 43*209 + 42; hence not 43 divides 9029 by NAT_4:9;
9029 = 47*192 + 5; hence not 47 divides 9029 by NAT_4:9;
9029 = 53*170 + 19; hence not 53 divides 9029 by NAT_4:9;
9029 = 59*153 + 2; hence not 59 divides 9029 by NAT_4:9;
9029 = 61*148 + 1; hence not 61 divides 9029 by NAT_4:9;
9029 = 67*134 + 51; hence not 67 divides 9029 by NAT_4:9;
9029 = 71*127 + 12; hence not 71 divides 9029 by NAT_4:9;
9029 = 73*123 + 50; hence not 73 divides 9029 by NAT_4:9;
9029 = 79*114 + 23; hence not 79 divides 9029 by NAT_4:9;
9029 = 83*108 + 65; hence not 83 divides 9029 by NAT_4:9;
9029 = 89*101 + 40; hence not 89 divides 9029 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9029 & n is prime
holds not n divides 9029 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9041 is prime
proof
now
9041 = 2*4520 + 1; hence not 2 divides 9041 by NAT_4:9;
9041 = 3*3013 + 2; hence not 3 divides 9041 by NAT_4:9;
9041 = 5*1808 + 1; hence not 5 divides 9041 by NAT_4:9;
9041 = 7*1291 + 4; hence not 7 divides 9041 by NAT_4:9;
9041 = 11*821 + 10; hence not 11 divides 9041 by NAT_4:9;
9041 = 13*695 + 6; hence not 13 divides 9041 by NAT_4:9;
9041 = 17*531 + 14; hence not 17 divides 9041 by NAT_4:9;
9041 = 19*475 + 16; hence not 19 divides 9041 by NAT_4:9;
9041 = 23*393 + 2; hence not 23 divides 9041 by NAT_4:9;
9041 = 29*311 + 22; hence not 29 divides 9041 by NAT_4:9;
9041 = 31*291 + 20; hence not 31 divides 9041 by NAT_4:9;
9041 = 37*244 + 13; hence not 37 divides 9041 by NAT_4:9;
9041 = 41*220 + 21; hence not 41 divides 9041 by NAT_4:9;
9041 = 43*210 + 11; hence not 43 divides 9041 by NAT_4:9;
9041 = 47*192 + 17; hence not 47 divides 9041 by NAT_4:9;
9041 = 53*170 + 31; hence not 53 divides 9041 by NAT_4:9;
9041 = 59*153 + 14; hence not 59 divides 9041 by NAT_4:9;
9041 = 61*148 + 13; hence not 61 divides 9041 by NAT_4:9;
9041 = 67*134 + 63; hence not 67 divides 9041 by NAT_4:9;
9041 = 71*127 + 24; hence not 71 divides 9041 by NAT_4:9;
9041 = 73*123 + 62; hence not 73 divides 9041 by NAT_4:9;
9041 = 79*114 + 35; hence not 79 divides 9041 by NAT_4:9;
9041 = 83*108 + 77; hence not 83 divides 9041 by NAT_4:9;
9041 = 89*101 + 52; hence not 89 divides 9041 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9041 & n is prime
holds not n divides 9041 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9043 is prime
proof
now
9043 = 2*4521 + 1; hence not 2 divides 9043 by NAT_4:9;
9043 = 3*3014 + 1; hence not 3 divides 9043 by NAT_4:9;
9043 = 5*1808 + 3; hence not 5 divides 9043 by NAT_4:9;
9043 = 7*1291 + 6; hence not 7 divides 9043 by NAT_4:9;
9043 = 11*822 + 1; hence not 11 divides 9043 by NAT_4:9;
9043 = 13*695 + 8; hence not 13 divides 9043 by NAT_4:9;
9043 = 17*531 + 16; hence not 17 divides 9043 by NAT_4:9;
9043 = 19*475 + 18; hence not 19 divides 9043 by NAT_4:9;
9043 = 23*393 + 4; hence not 23 divides 9043 by NAT_4:9;
9043 = 29*311 + 24; hence not 29 divides 9043 by NAT_4:9;
9043 = 31*291 + 22; hence not 31 divides 9043 by NAT_4:9;
9043 = 37*244 + 15; hence not 37 divides 9043 by NAT_4:9;
9043 = 41*220 + 23; hence not 41 divides 9043 by NAT_4:9;
9043 = 43*210 + 13; hence not 43 divides 9043 by NAT_4:9;
9043 = 47*192 + 19; hence not 47 divides 9043 by NAT_4:9;
9043 = 53*170 + 33; hence not 53 divides 9043 by NAT_4:9;
9043 = 59*153 + 16; hence not 59 divides 9043 by NAT_4:9;
9043 = 61*148 + 15; hence not 61 divides 9043 by NAT_4:9;
9043 = 67*134 + 65; hence not 67 divides 9043 by NAT_4:9;
9043 = 71*127 + 26; hence not 71 divides 9043 by NAT_4:9;
9043 = 73*123 + 64; hence not 73 divides 9043 by NAT_4:9;
9043 = 79*114 + 37; hence not 79 divides 9043 by NAT_4:9;
9043 = 83*108 + 79; hence not 83 divides 9043 by NAT_4:9;
9043 = 89*101 + 54; hence not 89 divides 9043 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9043 & n is prime
holds not n divides 9043 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9049 is prime
proof
now
9049 = 2*4524 + 1; hence not 2 divides 9049 by NAT_4:9;
9049 = 3*3016 + 1; hence not 3 divides 9049 by NAT_4:9;
9049 = 5*1809 + 4; hence not 5 divides 9049 by NAT_4:9;
9049 = 7*1292 + 5; hence not 7 divides 9049 by NAT_4:9;
9049 = 11*822 + 7; hence not 11 divides 9049 by NAT_4:9;
9049 = 13*696 + 1; hence not 13 divides 9049 by NAT_4:9;
9049 = 17*532 + 5; hence not 17 divides 9049 by NAT_4:9;
9049 = 19*476 + 5; hence not 19 divides 9049 by NAT_4:9;
9049 = 23*393 + 10; hence not 23 divides 9049 by NAT_4:9;
9049 = 29*312 + 1; hence not 29 divides 9049 by NAT_4:9;
9049 = 31*291 + 28; hence not 31 divides 9049 by NAT_4:9;
9049 = 37*244 + 21; hence not 37 divides 9049 by NAT_4:9;
9049 = 41*220 + 29; hence not 41 divides 9049 by NAT_4:9;
9049 = 43*210 + 19; hence not 43 divides 9049 by NAT_4:9;
9049 = 47*192 + 25; hence not 47 divides 9049 by NAT_4:9;
9049 = 53*170 + 39; hence not 53 divides 9049 by NAT_4:9;
9049 = 59*153 + 22; hence not 59 divides 9049 by NAT_4:9;
9049 = 61*148 + 21; hence not 61 divides 9049 by NAT_4:9;
9049 = 67*135 + 4; hence not 67 divides 9049 by NAT_4:9;
9049 = 71*127 + 32; hence not 71 divides 9049 by NAT_4:9;
9049 = 73*123 + 70; hence not 73 divides 9049 by NAT_4:9;
9049 = 79*114 + 43; hence not 79 divides 9049 by NAT_4:9;
9049 = 83*109 + 2; hence not 83 divides 9049 by NAT_4:9;
9049 = 89*101 + 60; hence not 89 divides 9049 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9049 & n is prime
holds not n divides 9049 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9059 is prime
proof
now
9059 = 2*4529 + 1; hence not 2 divides 9059 by NAT_4:9;
9059 = 3*3019 + 2; hence not 3 divides 9059 by NAT_4:9;
9059 = 5*1811 + 4; hence not 5 divides 9059 by NAT_4:9;
9059 = 7*1294 + 1; hence not 7 divides 9059 by NAT_4:9;
9059 = 11*823 + 6; hence not 11 divides 9059 by NAT_4:9;
9059 = 13*696 + 11; hence not 13 divides 9059 by NAT_4:9;
9059 = 17*532 + 15; hence not 17 divides 9059 by NAT_4:9;
9059 = 19*476 + 15; hence not 19 divides 9059 by NAT_4:9;
9059 = 23*393 + 20; hence not 23 divides 9059 by NAT_4:9;
9059 = 29*312 + 11; hence not 29 divides 9059 by NAT_4:9;
9059 = 31*292 + 7; hence not 31 divides 9059 by NAT_4:9;
9059 = 37*244 + 31; hence not 37 divides 9059 by NAT_4:9;
9059 = 41*220 + 39; hence not 41 divides 9059 by NAT_4:9;
9059 = 43*210 + 29; hence not 43 divides 9059 by NAT_4:9;
9059 = 47*192 + 35; hence not 47 divides 9059 by NAT_4:9;
9059 = 53*170 + 49; hence not 53 divides 9059 by NAT_4:9;
9059 = 59*153 + 32; hence not 59 divides 9059 by NAT_4:9;
9059 = 61*148 + 31; hence not 61 divides 9059 by NAT_4:9;
9059 = 67*135 + 14; hence not 67 divides 9059 by NAT_4:9;
9059 = 71*127 + 42; hence not 71 divides 9059 by NAT_4:9;
9059 = 73*124 + 7; hence not 73 divides 9059 by NAT_4:9;
9059 = 79*114 + 53; hence not 79 divides 9059 by NAT_4:9;
9059 = 83*109 + 12; hence not 83 divides 9059 by NAT_4:9;
9059 = 89*101 + 70; hence not 89 divides 9059 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9059 & n is prime
holds not n divides 9059 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9067 is prime
proof
now
9067 = 2*4533 + 1; hence not 2 divides 9067 by NAT_4:9;
9067 = 3*3022 + 1; hence not 3 divides 9067 by NAT_4:9;
9067 = 5*1813 + 2; hence not 5 divides 9067 by NAT_4:9;
9067 = 7*1295 + 2; hence not 7 divides 9067 by NAT_4:9;
9067 = 11*824 + 3; hence not 11 divides 9067 by NAT_4:9;
9067 = 13*697 + 6; hence not 13 divides 9067 by NAT_4:9;
9067 = 17*533 + 6; hence not 17 divides 9067 by NAT_4:9;
9067 = 19*477 + 4; hence not 19 divides 9067 by NAT_4:9;
9067 = 23*394 + 5; hence not 23 divides 9067 by NAT_4:9;
9067 = 29*312 + 19; hence not 29 divides 9067 by NAT_4:9;
9067 = 31*292 + 15; hence not 31 divides 9067 by NAT_4:9;
9067 = 37*245 + 2; hence not 37 divides 9067 by NAT_4:9;
9067 = 41*221 + 6; hence not 41 divides 9067 by NAT_4:9;
9067 = 43*210 + 37; hence not 43 divides 9067 by NAT_4:9;
9067 = 47*192 + 43; hence not 47 divides 9067 by NAT_4:9;
9067 = 53*171 + 4; hence not 53 divides 9067 by NAT_4:9;
9067 = 59*153 + 40; hence not 59 divides 9067 by NAT_4:9;
9067 = 61*148 + 39; hence not 61 divides 9067 by NAT_4:9;
9067 = 67*135 + 22; hence not 67 divides 9067 by NAT_4:9;
9067 = 71*127 + 50; hence not 71 divides 9067 by NAT_4:9;
9067 = 73*124 + 15; hence not 73 divides 9067 by NAT_4:9;
9067 = 79*114 + 61; hence not 79 divides 9067 by NAT_4:9;
9067 = 83*109 + 20; hence not 83 divides 9067 by NAT_4:9;
9067 = 89*101 + 78; hence not 89 divides 9067 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9067 & n is prime
holds not n divides 9067 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 23
theorem
9091 is prime
proof
now
9091 = 2*4545 + 1; hence not 2 divides 9091 by NAT_4:9;
9091 = 3*3030 + 1; hence not 3 divides 9091 by NAT_4:9;
9091 = 5*1818 + 1; hence not 5 divides 9091 by NAT_4:9;
9091 = 7*1298 + 5; hence not 7 divides 9091 by NAT_4:9;
9091 = 11*826 + 5; hence not 11 divides 9091 by NAT_4:9;
9091 = 13*699 + 4; hence not 13 divides 9091 by NAT_4:9;
9091 = 17*534 + 13; hence not 17 divides 9091 by NAT_4:9;
9091 = 19*478 + 9; hence not 19 divides 9091 by NAT_4:9;
9091 = 23*395 + 6; hence not 23 divides 9091 by NAT_4:9;
9091 = 29*313 + 14; hence not 29 divides 9091 by NAT_4:9;
9091 = 31*293 + 8; hence not 31 divides 9091 by NAT_4:9;
9091 = 37*245 + 26; hence not 37 divides 9091 by NAT_4:9;
9091 = 41*221 + 30; hence not 41 divides 9091 by NAT_4:9;
9091 = 43*211 + 18; hence not 43 divides 9091 by NAT_4:9;
9091 = 47*193 + 20; hence not 47 divides 9091 by NAT_4:9;
9091 = 53*171 + 28; hence not 53 divides 9091 by NAT_4:9;
9091 = 59*154 + 5; hence not 59 divides 9091 by NAT_4:9;
9091 = 61*149 + 2; hence not 61 divides 9091 by NAT_4:9;
9091 = 67*135 + 46; hence not 67 divides 9091 by NAT_4:9;
9091 = 71*128 + 3; hence not 71 divides 9091 by NAT_4:9;
9091 = 73*124 + 39; hence not 73 divides 9091 by NAT_4:9;
9091 = 79*115 + 6; hence not 79 divides 9091 by NAT_4:9;
9091 = 83*109 + 44; hence not 83 divides 9091 by NAT_4:9;
9091 = 89*102 + 13; hence not 89 divides 9091 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9091 & n is prime
holds not n divides 9091 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9103 is prime
proof
now
9103 = 2*4551 + 1; hence not 2 divides 9103 by NAT_4:9;
9103 = 3*3034 + 1; hence not 3 divides 9103 by NAT_4:9;
9103 = 5*1820 + 3; hence not 5 divides 9103 by NAT_4:9;
9103 = 7*1300 + 3; hence not 7 divides 9103 by NAT_4:9;
9103 = 11*827 + 6; hence not 11 divides 9103 by NAT_4:9;
9103 = 13*700 + 3; hence not 13 divides 9103 by NAT_4:9;
9103 = 17*535 + 8; hence not 17 divides 9103 by NAT_4:9;
9103 = 19*479 + 2; hence not 19 divides 9103 by NAT_4:9;
9103 = 23*395 + 18; hence not 23 divides 9103 by NAT_4:9;
9103 = 29*313 + 26; hence not 29 divides 9103 by NAT_4:9;
9103 = 31*293 + 20; hence not 31 divides 9103 by NAT_4:9;
9103 = 37*246 + 1; hence not 37 divides 9103 by NAT_4:9;
9103 = 41*222 + 1; hence not 41 divides 9103 by NAT_4:9;
9103 = 43*211 + 30; hence not 43 divides 9103 by NAT_4:9;
9103 = 47*193 + 32; hence not 47 divides 9103 by NAT_4:9;
9103 = 53*171 + 40; hence not 53 divides 9103 by NAT_4:9;
9103 = 59*154 + 17; hence not 59 divides 9103 by NAT_4:9;
9103 = 61*149 + 14; hence not 61 divides 9103 by NAT_4:9;
9103 = 67*135 + 58; hence not 67 divides 9103 by NAT_4:9;
9103 = 71*128 + 15; hence not 71 divides 9103 by NAT_4:9;
9103 = 73*124 + 51; hence not 73 divides 9103 by NAT_4:9;
9103 = 79*115 + 18; hence not 79 divides 9103 by NAT_4:9;
9103 = 83*109 + 56; hence not 83 divides 9103 by NAT_4:9;
9103 = 89*102 + 25; hence not 89 divides 9103 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9103 & n is prime
holds not n divides 9103 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9109 is prime
proof
now
9109 = 2*4554 + 1; hence not 2 divides 9109 by NAT_4:9;
9109 = 3*3036 + 1; hence not 3 divides 9109 by NAT_4:9;
9109 = 5*1821 + 4; hence not 5 divides 9109 by NAT_4:9;
9109 = 7*1301 + 2; hence not 7 divides 9109 by NAT_4:9;
9109 = 11*828 + 1; hence not 11 divides 9109 by NAT_4:9;
9109 = 13*700 + 9; hence not 13 divides 9109 by NAT_4:9;
9109 = 17*535 + 14; hence not 17 divides 9109 by NAT_4:9;
9109 = 19*479 + 8; hence not 19 divides 9109 by NAT_4:9;
9109 = 23*396 + 1; hence not 23 divides 9109 by NAT_4:9;
9109 = 29*314 + 3; hence not 29 divides 9109 by NAT_4:9;
9109 = 31*293 + 26; hence not 31 divides 9109 by NAT_4:9;
9109 = 37*246 + 7; hence not 37 divides 9109 by NAT_4:9;
9109 = 41*222 + 7; hence not 41 divides 9109 by NAT_4:9;
9109 = 43*211 + 36; hence not 43 divides 9109 by NAT_4:9;
9109 = 47*193 + 38; hence not 47 divides 9109 by NAT_4:9;
9109 = 53*171 + 46; hence not 53 divides 9109 by NAT_4:9;
9109 = 59*154 + 23; hence not 59 divides 9109 by NAT_4:9;
9109 = 61*149 + 20; hence not 61 divides 9109 by NAT_4:9;
9109 = 67*135 + 64; hence not 67 divides 9109 by NAT_4:9;
9109 = 71*128 + 21; hence not 71 divides 9109 by NAT_4:9;
9109 = 73*124 + 57; hence not 73 divides 9109 by NAT_4:9;
9109 = 79*115 + 24; hence not 79 divides 9109 by NAT_4:9;
9109 = 83*109 + 62; hence not 83 divides 9109 by NAT_4:9;
9109 = 89*102 + 31; hence not 89 divides 9109 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9109 & n is prime
holds not n divides 9109 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
9127 is prime
proof
now
9127 = 2*4563 + 1; hence not 2 divides 9127 by NAT_4:9;
9127 = 3*3042 + 1; hence not 3 divides 9127 by NAT_4:9;
9127 = 5*1825 + 2; hence not 5 divides 9127 by NAT_4:9;
9127 = 7*1303 + 6; hence not 7 divides 9127 by NAT_4:9;
9127 = 11*829 + 8; hence not 11 divides 9127 by NAT_4:9;
9127 = 13*702 + 1; hence not 13 divides 9127 by NAT_4:9;
9127 = 17*536 + 15; hence not 17 divides 9127 by NAT_4:9;
9127 = 19*480 + 7; hence not 19 divides 9127 by NAT_4:9;
9127 = 23*396 + 19; hence not 23 divides 9127 by NAT_4:9;
9127 = 29*314 + 21; hence not 29 divides 9127 by NAT_4:9;
9127 = 31*294 + 13; hence not 31 divides 9127 by NAT_4:9;
9127 = 37*246 + 25; hence not 37 divides 9127 by NAT_4:9;
9127 = 41*222 + 25; hence not 41 divides 9127 by NAT_4:9;
9127 = 43*212 + 11; hence not 43 divides 9127 by NAT_4:9;
9127 = 47*194 + 9; hence not 47 divides 9127 by NAT_4:9;
9127 = 53*172 + 11; hence not 53 divides 9127 by NAT_4:9;
9127 = 59*154 + 41; hence not 59 divides 9127 by NAT_4:9;
9127 = 61*149 + 38; hence not 61 divides 9127 by NAT_4:9;
9127 = 67*136 + 15; hence not 67 divides 9127 by NAT_4:9;
9127 = 71*128 + 39; hence not 71 divides 9127 by NAT_4:9;
9127 = 73*125 + 2; hence not 73 divides 9127 by NAT_4:9;
9127 = 79*115 + 42; hence not 79 divides 9127 by NAT_4:9;
9127 = 83*109 + 80; hence not 83 divides 9127 by NAT_4:9;
9127 = 89*102 + 49; hence not 89 divides 9127 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9127 & n is prime
holds not n divides 9127 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9133 is prime
proof
now
9133 = 2*4566 + 1; hence not 2 divides 9133 by NAT_4:9;
9133 = 3*3044 + 1; hence not 3 divides 9133 by NAT_4:9;
9133 = 5*1826 + 3; hence not 5 divides 9133 by NAT_4:9;
9133 = 7*1304 + 5; hence not 7 divides 9133 by NAT_4:9;
9133 = 11*830 + 3; hence not 11 divides 9133 by NAT_4:9;
9133 = 13*702 + 7; hence not 13 divides 9133 by NAT_4:9;
9133 = 17*537 + 4; hence not 17 divides 9133 by NAT_4:9;
9133 = 19*480 + 13; hence not 19 divides 9133 by NAT_4:9;
9133 = 23*397 + 2; hence not 23 divides 9133 by NAT_4:9;
9133 = 29*314 + 27; hence not 29 divides 9133 by NAT_4:9;
9133 = 31*294 + 19; hence not 31 divides 9133 by NAT_4:9;
9133 = 37*246 + 31; hence not 37 divides 9133 by NAT_4:9;
9133 = 41*222 + 31; hence not 41 divides 9133 by NAT_4:9;
9133 = 43*212 + 17; hence not 43 divides 9133 by NAT_4:9;
9133 = 47*194 + 15; hence not 47 divides 9133 by NAT_4:9;
9133 = 53*172 + 17; hence not 53 divides 9133 by NAT_4:9;
9133 = 59*154 + 47; hence not 59 divides 9133 by NAT_4:9;
9133 = 61*149 + 44; hence not 61 divides 9133 by NAT_4:9;
9133 = 67*136 + 21; hence not 67 divides 9133 by NAT_4:9;
9133 = 71*128 + 45; hence not 71 divides 9133 by NAT_4:9;
9133 = 73*125 + 8; hence not 73 divides 9133 by NAT_4:9;
9133 = 79*115 + 48; hence not 79 divides 9133 by NAT_4:9;
9133 = 83*110 + 3; hence not 83 divides 9133 by NAT_4:9;
9133 = 89*102 + 55; hence not 89 divides 9133 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9133 & n is prime
holds not n divides 9133 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9137 is prime
proof
now
9137 = 2*4568 + 1; hence not 2 divides 9137 by NAT_4:9;
9137 = 3*3045 + 2; hence not 3 divides 9137 by NAT_4:9;
9137 = 5*1827 + 2; hence not 5 divides 9137 by NAT_4:9;
9137 = 7*1305 + 2; hence not 7 divides 9137 by NAT_4:9;
9137 = 11*830 + 7; hence not 11 divides 9137 by NAT_4:9;
9137 = 13*702 + 11; hence not 13 divides 9137 by NAT_4:9;
9137 = 17*537 + 8; hence not 17 divides 9137 by NAT_4:9;
9137 = 19*480 + 17; hence not 19 divides 9137 by NAT_4:9;
9137 = 23*397 + 6; hence not 23 divides 9137 by NAT_4:9;
9137 = 29*315 + 2; hence not 29 divides 9137 by NAT_4:9;
9137 = 31*294 + 23; hence not 31 divides 9137 by NAT_4:9;
9137 = 37*246 + 35; hence not 37 divides 9137 by NAT_4:9;
9137 = 41*222 + 35; hence not 41 divides 9137 by NAT_4:9;
9137 = 43*212 + 21; hence not 43 divides 9137 by NAT_4:9;
9137 = 47*194 + 19; hence not 47 divides 9137 by NAT_4:9;
9137 = 53*172 + 21; hence not 53 divides 9137 by NAT_4:9;
9137 = 59*154 + 51; hence not 59 divides 9137 by NAT_4:9;
9137 = 61*149 + 48; hence not 61 divides 9137 by NAT_4:9;
9137 = 67*136 + 25; hence not 67 divides 9137 by NAT_4:9;
9137 = 71*128 + 49; hence not 71 divides 9137 by NAT_4:9;
9137 = 73*125 + 12; hence not 73 divides 9137 by NAT_4:9;
9137 = 79*115 + 52; hence not 79 divides 9137 by NAT_4:9;
9137 = 83*110 + 7; hence not 83 divides 9137 by NAT_4:9;
9137 = 89*102 + 59; hence not 89 divides 9137 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9137 & n is prime
holds not n divides 9137 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9151 is prime
proof
now
9151 = 2*4575 + 1; hence not 2 divides 9151 by NAT_4:9;
9151 = 3*3050 + 1; hence not 3 divides 9151 by NAT_4:9;
9151 = 5*1830 + 1; hence not 5 divides 9151 by NAT_4:9;
9151 = 7*1307 + 2; hence not 7 divides 9151 by NAT_4:9;
9151 = 11*831 + 10; hence not 11 divides 9151 by NAT_4:9;
9151 = 13*703 + 12; hence not 13 divides 9151 by NAT_4:9;
9151 = 17*538 + 5; hence not 17 divides 9151 by NAT_4:9;
9151 = 19*481 + 12; hence not 19 divides 9151 by NAT_4:9;
9151 = 23*397 + 20; hence not 23 divides 9151 by NAT_4:9;
9151 = 29*315 + 16; hence not 29 divides 9151 by NAT_4:9;
9151 = 31*295 + 6; hence not 31 divides 9151 by NAT_4:9;
9151 = 37*247 + 12; hence not 37 divides 9151 by NAT_4:9;
9151 = 41*223 + 8; hence not 41 divides 9151 by NAT_4:9;
9151 = 43*212 + 35; hence not 43 divides 9151 by NAT_4:9;
9151 = 47*194 + 33; hence not 47 divides 9151 by NAT_4:9;
9151 = 53*172 + 35; hence not 53 divides 9151 by NAT_4:9;
9151 = 59*155 + 6; hence not 59 divides 9151 by NAT_4:9;
9151 = 61*150 + 1; hence not 61 divides 9151 by NAT_4:9;
9151 = 67*136 + 39; hence not 67 divides 9151 by NAT_4:9;
9151 = 71*128 + 63; hence not 71 divides 9151 by NAT_4:9;
9151 = 73*125 + 26; hence not 73 divides 9151 by NAT_4:9;
9151 = 79*115 + 66; hence not 79 divides 9151 by NAT_4:9;
9151 = 83*110 + 21; hence not 83 divides 9151 by NAT_4:9;
9151 = 89*102 + 73; hence not 89 divides 9151 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9151 & n is prime
holds not n divides 9151 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9157 is prime
proof
now
9157 = 2*4578 + 1; hence not 2 divides 9157 by NAT_4:9;
9157 = 3*3052 + 1; hence not 3 divides 9157 by NAT_4:9;
9157 = 5*1831 + 2; hence not 5 divides 9157 by NAT_4:9;
9157 = 7*1308 + 1; hence not 7 divides 9157 by NAT_4:9;
9157 = 11*832 + 5; hence not 11 divides 9157 by NAT_4:9;
9157 = 13*704 + 5; hence not 13 divides 9157 by NAT_4:9;
9157 = 17*538 + 11; hence not 17 divides 9157 by NAT_4:9;
9157 = 19*481 + 18; hence not 19 divides 9157 by NAT_4:9;
9157 = 23*398 + 3; hence not 23 divides 9157 by NAT_4:9;
9157 = 29*315 + 22; hence not 29 divides 9157 by NAT_4:9;
9157 = 31*295 + 12; hence not 31 divides 9157 by NAT_4:9;
9157 = 37*247 + 18; hence not 37 divides 9157 by NAT_4:9;
9157 = 41*223 + 14; hence not 41 divides 9157 by NAT_4:9;
9157 = 43*212 + 41; hence not 43 divides 9157 by NAT_4:9;
9157 = 47*194 + 39; hence not 47 divides 9157 by NAT_4:9;
9157 = 53*172 + 41; hence not 53 divides 9157 by NAT_4:9;
9157 = 59*155 + 12; hence not 59 divides 9157 by NAT_4:9;
9157 = 61*150 + 7; hence not 61 divides 9157 by NAT_4:9;
9157 = 67*136 + 45; hence not 67 divides 9157 by NAT_4:9;
9157 = 71*128 + 69; hence not 71 divides 9157 by NAT_4:9;
9157 = 73*125 + 32; hence not 73 divides 9157 by NAT_4:9;
9157 = 79*115 + 72; hence not 79 divides 9157 by NAT_4:9;
9157 = 83*110 + 27; hence not 83 divides 9157 by NAT_4:9;
9157 = 89*102 + 79; hence not 89 divides 9157 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9157 & n is prime
holds not n divides 9157 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9161 is prime
proof
now
9161 = 2*4580 + 1; hence not 2 divides 9161 by NAT_4:9;
9161 = 3*3053 + 2; hence not 3 divides 9161 by NAT_4:9;
9161 = 5*1832 + 1; hence not 5 divides 9161 by NAT_4:9;
9161 = 7*1308 + 5; hence not 7 divides 9161 by NAT_4:9;
9161 = 11*832 + 9; hence not 11 divides 9161 by NAT_4:9;
9161 = 13*704 + 9; hence not 13 divides 9161 by NAT_4:9;
9161 = 17*538 + 15; hence not 17 divides 9161 by NAT_4:9;
9161 = 19*482 + 3; hence not 19 divides 9161 by NAT_4:9;
9161 = 23*398 + 7; hence not 23 divides 9161 by NAT_4:9;
9161 = 29*315 + 26; hence not 29 divides 9161 by NAT_4:9;
9161 = 31*295 + 16; hence not 31 divides 9161 by NAT_4:9;
9161 = 37*247 + 22; hence not 37 divides 9161 by NAT_4:9;
9161 = 41*223 + 18; hence not 41 divides 9161 by NAT_4:9;
9161 = 43*213 + 2; hence not 43 divides 9161 by NAT_4:9;
9161 = 47*194 + 43; hence not 47 divides 9161 by NAT_4:9;
9161 = 53*172 + 45; hence not 53 divides 9161 by NAT_4:9;
9161 = 59*155 + 16; hence not 59 divides 9161 by NAT_4:9;
9161 = 61*150 + 11; hence not 61 divides 9161 by NAT_4:9;
9161 = 67*136 + 49; hence not 67 divides 9161 by NAT_4:9;
9161 = 71*129 + 2; hence not 71 divides 9161 by NAT_4:9;
9161 = 73*125 + 36; hence not 73 divides 9161 by NAT_4:9;
9161 = 79*115 + 76; hence not 79 divides 9161 by NAT_4:9;
9161 = 83*110 + 31; hence not 83 divides 9161 by NAT_4:9;
9161 = 89*102 + 83; hence not 89 divides 9161 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9161 & n is prime
holds not n divides 9161 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9173 is prime
proof
now
9173 = 2*4586 + 1; hence not 2 divides 9173 by NAT_4:9;
9173 = 3*3057 + 2; hence not 3 divides 9173 by NAT_4:9;
9173 = 5*1834 + 3; hence not 5 divides 9173 by NAT_4:9;
9173 = 7*1310 + 3; hence not 7 divides 9173 by NAT_4:9;
9173 = 11*833 + 10; hence not 11 divides 9173 by NAT_4:9;
9173 = 13*705 + 8; hence not 13 divides 9173 by NAT_4:9;
9173 = 17*539 + 10; hence not 17 divides 9173 by NAT_4:9;
9173 = 19*482 + 15; hence not 19 divides 9173 by NAT_4:9;
9173 = 23*398 + 19; hence not 23 divides 9173 by NAT_4:9;
9173 = 29*316 + 9; hence not 29 divides 9173 by NAT_4:9;
9173 = 31*295 + 28; hence not 31 divides 9173 by NAT_4:9;
9173 = 37*247 + 34; hence not 37 divides 9173 by NAT_4:9;
9173 = 41*223 + 30; hence not 41 divides 9173 by NAT_4:9;
9173 = 43*213 + 14; hence not 43 divides 9173 by NAT_4:9;
9173 = 47*195 + 8; hence not 47 divides 9173 by NAT_4:9;
9173 = 53*173 + 4; hence not 53 divides 9173 by NAT_4:9;
9173 = 59*155 + 28; hence not 59 divides 9173 by NAT_4:9;
9173 = 61*150 + 23; hence not 61 divides 9173 by NAT_4:9;
9173 = 67*136 + 61; hence not 67 divides 9173 by NAT_4:9;
9173 = 71*129 + 14; hence not 71 divides 9173 by NAT_4:9;
9173 = 73*125 + 48; hence not 73 divides 9173 by NAT_4:9;
9173 = 79*116 + 9; hence not 79 divides 9173 by NAT_4:9;
9173 = 83*110 + 43; hence not 83 divides 9173 by NAT_4:9;
9173 = 89*103 + 6; hence not 89 divides 9173 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9173 & n is prime
holds not n divides 9173 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9181 is prime
proof
now
9181 = 2*4590 + 1; hence not 2 divides 9181 by NAT_4:9;
9181 = 3*3060 + 1; hence not 3 divides 9181 by NAT_4:9;
9181 = 5*1836 + 1; hence not 5 divides 9181 by NAT_4:9;
9181 = 7*1311 + 4; hence not 7 divides 9181 by NAT_4:9;
9181 = 11*834 + 7; hence not 11 divides 9181 by NAT_4:9;
9181 = 13*706 + 3; hence not 13 divides 9181 by NAT_4:9;
9181 = 17*540 + 1; hence not 17 divides 9181 by NAT_4:9;
9181 = 19*483 + 4; hence not 19 divides 9181 by NAT_4:9;
9181 = 23*399 + 4; hence not 23 divides 9181 by NAT_4:9;
9181 = 29*316 + 17; hence not 29 divides 9181 by NAT_4:9;
9181 = 31*296 + 5; hence not 31 divides 9181 by NAT_4:9;
9181 = 37*248 + 5; hence not 37 divides 9181 by NAT_4:9;
9181 = 41*223 + 38; hence not 41 divides 9181 by NAT_4:9;
9181 = 43*213 + 22; hence not 43 divides 9181 by NAT_4:9;
9181 = 47*195 + 16; hence not 47 divides 9181 by NAT_4:9;
9181 = 53*173 + 12; hence not 53 divides 9181 by NAT_4:9;
9181 = 59*155 + 36; hence not 59 divides 9181 by NAT_4:9;
9181 = 61*150 + 31; hence not 61 divides 9181 by NAT_4:9;
9181 = 67*137 + 2; hence not 67 divides 9181 by NAT_4:9;
9181 = 71*129 + 22; hence not 71 divides 9181 by NAT_4:9;
9181 = 73*125 + 56; hence not 73 divides 9181 by NAT_4:9;
9181 = 79*116 + 17; hence not 79 divides 9181 by NAT_4:9;
9181 = 83*110 + 51; hence not 83 divides 9181 by NAT_4:9;
9181 = 89*103 + 14; hence not 89 divides 9181 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9181 & n is prime
holds not n divides 9181 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9187 is prime
proof
now
9187 = 2*4593 + 1; hence not 2 divides 9187 by NAT_4:9;
9187 = 3*3062 + 1; hence not 3 divides 9187 by NAT_4:9;
9187 = 5*1837 + 2; hence not 5 divides 9187 by NAT_4:9;
9187 = 7*1312 + 3; hence not 7 divides 9187 by NAT_4:9;
9187 = 11*835 + 2; hence not 11 divides 9187 by NAT_4:9;
9187 = 13*706 + 9; hence not 13 divides 9187 by NAT_4:9;
9187 = 17*540 + 7; hence not 17 divides 9187 by NAT_4:9;
9187 = 19*483 + 10; hence not 19 divides 9187 by NAT_4:9;
9187 = 23*399 + 10; hence not 23 divides 9187 by NAT_4:9;
9187 = 29*316 + 23; hence not 29 divides 9187 by NAT_4:9;
9187 = 31*296 + 11; hence not 31 divides 9187 by NAT_4:9;
9187 = 37*248 + 11; hence not 37 divides 9187 by NAT_4:9;
9187 = 41*224 + 3; hence not 41 divides 9187 by NAT_4:9;
9187 = 43*213 + 28; hence not 43 divides 9187 by NAT_4:9;
9187 = 47*195 + 22; hence not 47 divides 9187 by NAT_4:9;
9187 = 53*173 + 18; hence not 53 divides 9187 by NAT_4:9;
9187 = 59*155 + 42; hence not 59 divides 9187 by NAT_4:9;
9187 = 61*150 + 37; hence not 61 divides 9187 by NAT_4:9;
9187 = 67*137 + 8; hence not 67 divides 9187 by NAT_4:9;
9187 = 71*129 + 28; hence not 71 divides 9187 by NAT_4:9;
9187 = 73*125 + 62; hence not 73 divides 9187 by NAT_4:9;
9187 = 79*116 + 23; hence not 79 divides 9187 by NAT_4:9;
9187 = 83*110 + 57; hence not 83 divides 9187 by NAT_4:9;
9187 = 89*103 + 20; hence not 89 divides 9187 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9187 & n is prime
holds not n divides 9187 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9199 is prime
proof
now
9199 = 2*4599 + 1; hence not 2 divides 9199 by NAT_4:9;
9199 = 3*3066 + 1; hence not 3 divides 9199 by NAT_4:9;
9199 = 5*1839 + 4; hence not 5 divides 9199 by NAT_4:9;
9199 = 7*1314 + 1; hence not 7 divides 9199 by NAT_4:9;
9199 = 11*836 + 3; hence not 11 divides 9199 by NAT_4:9;
9199 = 13*707 + 8; hence not 13 divides 9199 by NAT_4:9;
9199 = 17*541 + 2; hence not 17 divides 9199 by NAT_4:9;
9199 = 19*484 + 3; hence not 19 divides 9199 by NAT_4:9;
9199 = 23*399 + 22; hence not 23 divides 9199 by NAT_4:9;
9199 = 29*317 + 6; hence not 29 divides 9199 by NAT_4:9;
9199 = 31*296 + 23; hence not 31 divides 9199 by NAT_4:9;
9199 = 37*248 + 23; hence not 37 divides 9199 by NAT_4:9;
9199 = 41*224 + 15; hence not 41 divides 9199 by NAT_4:9;
9199 = 43*213 + 40; hence not 43 divides 9199 by NAT_4:9;
9199 = 47*195 + 34; hence not 47 divides 9199 by NAT_4:9;
9199 = 53*173 + 30; hence not 53 divides 9199 by NAT_4:9;
9199 = 59*155 + 54; hence not 59 divides 9199 by NAT_4:9;
9199 = 61*150 + 49; hence not 61 divides 9199 by NAT_4:9;
9199 = 67*137 + 20; hence not 67 divides 9199 by NAT_4:9;
9199 = 71*129 + 40; hence not 71 divides 9199 by NAT_4:9;
9199 = 73*126 + 1; hence not 73 divides 9199 by NAT_4:9;
9199 = 79*116 + 35; hence not 79 divides 9199 by NAT_4:9;
9199 = 83*110 + 69; hence not 83 divides 9199 by NAT_4:9;
9199 = 89*103 + 32; hence not 89 divides 9199 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9199 & n is prime
holds not n divides 9199 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9203 is prime
proof
now
9203 = 2*4601 + 1; hence not 2 divides 9203 by NAT_4:9;
9203 = 3*3067 + 2; hence not 3 divides 9203 by NAT_4:9;
9203 = 5*1840 + 3; hence not 5 divides 9203 by NAT_4:9;
9203 = 7*1314 + 5; hence not 7 divides 9203 by NAT_4:9;
9203 = 11*836 + 7; hence not 11 divides 9203 by NAT_4:9;
9203 = 13*707 + 12; hence not 13 divides 9203 by NAT_4:9;
9203 = 17*541 + 6; hence not 17 divides 9203 by NAT_4:9;
9203 = 19*484 + 7; hence not 19 divides 9203 by NAT_4:9;
9203 = 23*400 + 3; hence not 23 divides 9203 by NAT_4:9;
9203 = 29*317 + 10; hence not 29 divides 9203 by NAT_4:9;
9203 = 31*296 + 27; hence not 31 divides 9203 by NAT_4:9;
9203 = 37*248 + 27; hence not 37 divides 9203 by NAT_4:9;
9203 = 41*224 + 19; hence not 41 divides 9203 by NAT_4:9;
9203 = 43*214 + 1; hence not 43 divides 9203 by NAT_4:9;
9203 = 47*195 + 38; hence not 47 divides 9203 by NAT_4:9;
9203 = 53*173 + 34; hence not 53 divides 9203 by NAT_4:9;
9203 = 59*155 + 58; hence not 59 divides 9203 by NAT_4:9;
9203 = 61*150 + 53; hence not 61 divides 9203 by NAT_4:9;
9203 = 67*137 + 24; hence not 67 divides 9203 by NAT_4:9;
9203 = 71*129 + 44; hence not 71 divides 9203 by NAT_4:9;
9203 = 73*126 + 5; hence not 73 divides 9203 by NAT_4:9;
9203 = 79*116 + 39; hence not 79 divides 9203 by NAT_4:9;
9203 = 83*110 + 73; hence not 83 divides 9203 by NAT_4:9;
9203 = 89*103 + 36; hence not 89 divides 9203 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9203 & n is prime
holds not n divides 9203 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9209 is prime
proof
now
9209 = 2*4604 + 1; hence not 2 divides 9209 by NAT_4:9;
9209 = 3*3069 + 2; hence not 3 divides 9209 by NAT_4:9;
9209 = 5*1841 + 4; hence not 5 divides 9209 by NAT_4:9;
9209 = 7*1315 + 4; hence not 7 divides 9209 by NAT_4:9;
9209 = 11*837 + 2; hence not 11 divides 9209 by NAT_4:9;
9209 = 13*708 + 5; hence not 13 divides 9209 by NAT_4:9;
9209 = 17*541 + 12; hence not 17 divides 9209 by NAT_4:9;
9209 = 19*484 + 13; hence not 19 divides 9209 by NAT_4:9;
9209 = 23*400 + 9; hence not 23 divides 9209 by NAT_4:9;
9209 = 29*317 + 16; hence not 29 divides 9209 by NAT_4:9;
9209 = 31*297 + 2; hence not 31 divides 9209 by NAT_4:9;
9209 = 37*248 + 33; hence not 37 divides 9209 by NAT_4:9;
9209 = 41*224 + 25; hence not 41 divides 9209 by NAT_4:9;
9209 = 43*214 + 7; hence not 43 divides 9209 by NAT_4:9;
9209 = 47*195 + 44; hence not 47 divides 9209 by NAT_4:9;
9209 = 53*173 + 40; hence not 53 divides 9209 by NAT_4:9;
9209 = 59*156 + 5; hence not 59 divides 9209 by NAT_4:9;
9209 = 61*150 + 59; hence not 61 divides 9209 by NAT_4:9;
9209 = 67*137 + 30; hence not 67 divides 9209 by NAT_4:9;
9209 = 71*129 + 50; hence not 71 divides 9209 by NAT_4:9;
9209 = 73*126 + 11; hence not 73 divides 9209 by NAT_4:9;
9209 = 79*116 + 45; hence not 79 divides 9209 by NAT_4:9;
9209 = 83*110 + 79; hence not 83 divides 9209 by NAT_4:9;
9209 = 89*103 + 42; hence not 89 divides 9209 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9209 & n is prime
holds not n divides 9209 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9221 is prime
proof
now
9221 = 2*4610 + 1; hence not 2 divides 9221 by NAT_4:9;
9221 = 3*3073 + 2; hence not 3 divides 9221 by NAT_4:9;
9221 = 5*1844 + 1; hence not 5 divides 9221 by NAT_4:9;
9221 = 7*1317 + 2; hence not 7 divides 9221 by NAT_4:9;
9221 = 11*838 + 3; hence not 11 divides 9221 by NAT_4:9;
9221 = 13*709 + 4; hence not 13 divides 9221 by NAT_4:9;
9221 = 17*542 + 7; hence not 17 divides 9221 by NAT_4:9;
9221 = 19*485 + 6; hence not 19 divides 9221 by NAT_4:9;
9221 = 23*400 + 21; hence not 23 divides 9221 by NAT_4:9;
9221 = 29*317 + 28; hence not 29 divides 9221 by NAT_4:9;
9221 = 31*297 + 14; hence not 31 divides 9221 by NAT_4:9;
9221 = 37*249 + 8; hence not 37 divides 9221 by NAT_4:9;
9221 = 41*224 + 37; hence not 41 divides 9221 by NAT_4:9;
9221 = 43*214 + 19; hence not 43 divides 9221 by NAT_4:9;
9221 = 47*196 + 9; hence not 47 divides 9221 by NAT_4:9;
9221 = 53*173 + 52; hence not 53 divides 9221 by NAT_4:9;
9221 = 59*156 + 17; hence not 59 divides 9221 by NAT_4:9;
9221 = 61*151 + 10; hence not 61 divides 9221 by NAT_4:9;
9221 = 67*137 + 42; hence not 67 divides 9221 by NAT_4:9;
9221 = 71*129 + 62; hence not 71 divides 9221 by NAT_4:9;
9221 = 73*126 + 23; hence not 73 divides 9221 by NAT_4:9;
9221 = 79*116 + 57; hence not 79 divides 9221 by NAT_4:9;
9221 = 83*111 + 8; hence not 83 divides 9221 by NAT_4:9;
9221 = 89*103 + 54; hence not 89 divides 9221 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9221 & n is prime
holds not n divides 9221 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9227 is prime
proof
now
9227 = 2*4613 + 1; hence not 2 divides 9227 by NAT_4:9;
9227 = 3*3075 + 2; hence not 3 divides 9227 by NAT_4:9;
9227 = 5*1845 + 2; hence not 5 divides 9227 by NAT_4:9;
9227 = 7*1318 + 1; hence not 7 divides 9227 by NAT_4:9;
9227 = 11*838 + 9; hence not 11 divides 9227 by NAT_4:9;
9227 = 13*709 + 10; hence not 13 divides 9227 by NAT_4:9;
9227 = 17*542 + 13; hence not 17 divides 9227 by NAT_4:9;
9227 = 19*485 + 12; hence not 19 divides 9227 by NAT_4:9;
9227 = 23*401 + 4; hence not 23 divides 9227 by NAT_4:9;
9227 = 29*318 + 5; hence not 29 divides 9227 by NAT_4:9;
9227 = 31*297 + 20; hence not 31 divides 9227 by NAT_4:9;
9227 = 37*249 + 14; hence not 37 divides 9227 by NAT_4:9;
9227 = 41*225 + 2; hence not 41 divides 9227 by NAT_4:9;
9227 = 43*214 + 25; hence not 43 divides 9227 by NAT_4:9;
9227 = 47*196 + 15; hence not 47 divides 9227 by NAT_4:9;
9227 = 53*174 + 5; hence not 53 divides 9227 by NAT_4:9;
9227 = 59*156 + 23; hence not 59 divides 9227 by NAT_4:9;
9227 = 61*151 + 16; hence not 61 divides 9227 by NAT_4:9;
9227 = 67*137 + 48; hence not 67 divides 9227 by NAT_4:9;
9227 = 71*129 + 68; hence not 71 divides 9227 by NAT_4:9;
9227 = 73*126 + 29; hence not 73 divides 9227 by NAT_4:9;
9227 = 79*116 + 63; hence not 79 divides 9227 by NAT_4:9;
9227 = 83*111 + 14; hence not 83 divides 9227 by NAT_4:9;
9227 = 89*103 + 60; hence not 89 divides 9227 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9227 & n is prime
holds not n divides 9227 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9239 is prime
proof
now
9239 = 2*4619 + 1; hence not 2 divides 9239 by NAT_4:9;
9239 = 3*3079 + 2; hence not 3 divides 9239 by NAT_4:9;
9239 = 5*1847 + 4; hence not 5 divides 9239 by NAT_4:9;
9239 = 7*1319 + 6; hence not 7 divides 9239 by NAT_4:9;
9239 = 11*839 + 10; hence not 11 divides 9239 by NAT_4:9;
9239 = 13*710 + 9; hence not 13 divides 9239 by NAT_4:9;
9239 = 17*543 + 8; hence not 17 divides 9239 by NAT_4:9;
9239 = 19*486 + 5; hence not 19 divides 9239 by NAT_4:9;
9239 = 23*401 + 16; hence not 23 divides 9239 by NAT_4:9;
9239 = 29*318 + 17; hence not 29 divides 9239 by NAT_4:9;
9239 = 31*298 + 1; hence not 31 divides 9239 by NAT_4:9;
9239 = 37*249 + 26; hence not 37 divides 9239 by NAT_4:9;
9239 = 41*225 + 14; hence not 41 divides 9239 by NAT_4:9;
9239 = 43*214 + 37; hence not 43 divides 9239 by NAT_4:9;
9239 = 47*196 + 27; hence not 47 divides 9239 by NAT_4:9;
9239 = 53*174 + 17; hence not 53 divides 9239 by NAT_4:9;
9239 = 59*156 + 35; hence not 59 divides 9239 by NAT_4:9;
9239 = 61*151 + 28; hence not 61 divides 9239 by NAT_4:9;
9239 = 67*137 + 60; hence not 67 divides 9239 by NAT_4:9;
9239 = 71*130 + 9; hence not 71 divides 9239 by NAT_4:9;
9239 = 73*126 + 41; hence not 73 divides 9239 by NAT_4:9;
9239 = 79*116 + 75; hence not 79 divides 9239 by NAT_4:9;
9239 = 83*111 + 26; hence not 83 divides 9239 by NAT_4:9;
9239 = 89*103 + 72; hence not 89 divides 9239 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9239 & n is prime
holds not n divides 9239 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9241 is prime
proof
now
9241 = 2*4620 + 1; hence not 2 divides 9241 by NAT_4:9;
9241 = 3*3080 + 1; hence not 3 divides 9241 by NAT_4:9;
9241 = 5*1848 + 1; hence not 5 divides 9241 by NAT_4:9;
9241 = 7*1320 + 1; hence not 7 divides 9241 by NAT_4:9;
9241 = 11*840 + 1; hence not 11 divides 9241 by NAT_4:9;
9241 = 13*710 + 11; hence not 13 divides 9241 by NAT_4:9;
9241 = 17*543 + 10; hence not 17 divides 9241 by NAT_4:9;
9241 = 19*486 + 7; hence not 19 divides 9241 by NAT_4:9;
9241 = 23*401 + 18; hence not 23 divides 9241 by NAT_4:9;
9241 = 29*318 + 19; hence not 29 divides 9241 by NAT_4:9;
9241 = 31*298 + 3; hence not 31 divides 9241 by NAT_4:9;
9241 = 37*249 + 28; hence not 37 divides 9241 by NAT_4:9;
9241 = 41*225 + 16; hence not 41 divides 9241 by NAT_4:9;
9241 = 43*214 + 39; hence not 43 divides 9241 by NAT_4:9;
9241 = 47*196 + 29; hence not 47 divides 9241 by NAT_4:9;
9241 = 53*174 + 19; hence not 53 divides 9241 by NAT_4:9;
9241 = 59*156 + 37; hence not 59 divides 9241 by NAT_4:9;
9241 = 61*151 + 30; hence not 61 divides 9241 by NAT_4:9;
9241 = 67*137 + 62; hence not 67 divides 9241 by NAT_4:9;
9241 = 71*130 + 11; hence not 71 divides 9241 by NAT_4:9;
9241 = 73*126 + 43; hence not 73 divides 9241 by NAT_4:9;
9241 = 79*116 + 77; hence not 79 divides 9241 by NAT_4:9;
9241 = 83*111 + 28; hence not 83 divides 9241 by NAT_4:9;
9241 = 89*103 + 74; hence not 89 divides 9241 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9241 & n is prime
holds not n divides 9241 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
9257 is prime
proof
now
9257 = 2*4628 + 1; hence not 2 divides 9257 by NAT_4:9;
9257 = 3*3085 + 2; hence not 3 divides 9257 by NAT_4:9;
9257 = 5*1851 + 2; hence not 5 divides 9257 by NAT_4:9;
9257 = 7*1322 + 3; hence not 7 divides 9257 by NAT_4:9;
9257 = 11*841 + 6; hence not 11 divides 9257 by NAT_4:9;
9257 = 13*712 + 1; hence not 13 divides 9257 by NAT_4:9;
9257 = 17*544 + 9; hence not 17 divides 9257 by NAT_4:9;
9257 = 19*487 + 4; hence not 19 divides 9257 by NAT_4:9;
9257 = 23*402 + 11; hence not 23 divides 9257 by NAT_4:9;
9257 = 29*319 + 6; hence not 29 divides 9257 by NAT_4:9;
9257 = 31*298 + 19; hence not 31 divides 9257 by NAT_4:9;
9257 = 37*250 + 7; hence not 37 divides 9257 by NAT_4:9;
9257 = 41*225 + 32; hence not 41 divides 9257 by NAT_4:9;
9257 = 43*215 + 12; hence not 43 divides 9257 by NAT_4:9;
9257 = 47*196 + 45; hence not 47 divides 9257 by NAT_4:9;
9257 = 53*174 + 35; hence not 53 divides 9257 by NAT_4:9;
9257 = 59*156 + 53; hence not 59 divides 9257 by NAT_4:9;
9257 = 61*151 + 46; hence not 61 divides 9257 by NAT_4:9;
9257 = 67*138 + 11; hence not 67 divides 9257 by NAT_4:9;
9257 = 71*130 + 27; hence not 71 divides 9257 by NAT_4:9;
9257 = 73*126 + 59; hence not 73 divides 9257 by NAT_4:9;
9257 = 79*117 + 14; hence not 79 divides 9257 by NAT_4:9;
9257 = 83*111 + 44; hence not 83 divides 9257 by NAT_4:9;
9257 = 89*104 + 1; hence not 89 divides 9257 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9257 & n is prime
holds not n divides 9257 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 19
theorem
9277 is prime
proof
now
9277 = 2*4638 + 1; hence not 2 divides 9277 by NAT_4:9;
9277 = 3*3092 + 1; hence not 3 divides 9277 by NAT_4:9;
9277 = 5*1855 + 2; hence not 5 divides 9277 by NAT_4:9;
9277 = 7*1325 + 2; hence not 7 divides 9277 by NAT_4:9;
9277 = 11*843 + 4; hence not 11 divides 9277 by NAT_4:9;
9277 = 13*713 + 8; hence not 13 divides 9277 by NAT_4:9;
9277 = 17*545 + 12; hence not 17 divides 9277 by NAT_4:9;
9277 = 19*488 + 5; hence not 19 divides 9277 by NAT_4:9;
9277 = 23*403 + 8; hence not 23 divides 9277 by NAT_4:9;
9277 = 29*319 + 26; hence not 29 divides 9277 by NAT_4:9;
9277 = 31*299 + 8; hence not 31 divides 9277 by NAT_4:9;
9277 = 37*250 + 27; hence not 37 divides 9277 by NAT_4:9;
9277 = 41*226 + 11; hence not 41 divides 9277 by NAT_4:9;
9277 = 43*215 + 32; hence not 43 divides 9277 by NAT_4:9;
9277 = 47*197 + 18; hence not 47 divides 9277 by NAT_4:9;
9277 = 53*175 + 2; hence not 53 divides 9277 by NAT_4:9;
9277 = 59*157 + 14; hence not 59 divides 9277 by NAT_4:9;
9277 = 61*152 + 5; hence not 61 divides 9277 by NAT_4:9;
9277 = 67*138 + 31; hence not 67 divides 9277 by NAT_4:9;
9277 = 71*130 + 47; hence not 71 divides 9277 by NAT_4:9;
9277 = 73*127 + 6; hence not 73 divides 9277 by NAT_4:9;
9277 = 79*117 + 34; hence not 79 divides 9277 by NAT_4:9;
9277 = 83*111 + 64; hence not 83 divides 9277 by NAT_4:9;
9277 = 89*104 + 21; hence not 89 divides 9277 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9277 & n is prime
holds not n divides 9277 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9281 is prime
proof
now
9281 = 2*4640 + 1; hence not 2 divides 9281 by NAT_4:9;
9281 = 3*3093 + 2; hence not 3 divides 9281 by NAT_4:9;
9281 = 5*1856 + 1; hence not 5 divides 9281 by NAT_4:9;
9281 = 7*1325 + 6; hence not 7 divides 9281 by NAT_4:9;
9281 = 11*843 + 8; hence not 11 divides 9281 by NAT_4:9;
9281 = 13*713 + 12; hence not 13 divides 9281 by NAT_4:9;
9281 = 17*545 + 16; hence not 17 divides 9281 by NAT_4:9;
9281 = 19*488 + 9; hence not 19 divides 9281 by NAT_4:9;
9281 = 23*403 + 12; hence not 23 divides 9281 by NAT_4:9;
9281 = 29*320 + 1; hence not 29 divides 9281 by NAT_4:9;
9281 = 31*299 + 12; hence not 31 divides 9281 by NAT_4:9;
9281 = 37*250 + 31; hence not 37 divides 9281 by NAT_4:9;
9281 = 41*226 + 15; hence not 41 divides 9281 by NAT_4:9;
9281 = 43*215 + 36; hence not 43 divides 9281 by NAT_4:9;
9281 = 47*197 + 22; hence not 47 divides 9281 by NAT_4:9;
9281 = 53*175 + 6; hence not 53 divides 9281 by NAT_4:9;
9281 = 59*157 + 18; hence not 59 divides 9281 by NAT_4:9;
9281 = 61*152 + 9; hence not 61 divides 9281 by NAT_4:9;
9281 = 67*138 + 35; hence not 67 divides 9281 by NAT_4:9;
9281 = 71*130 + 51; hence not 71 divides 9281 by NAT_4:9;
9281 = 73*127 + 10; hence not 73 divides 9281 by NAT_4:9;
9281 = 79*117 + 38; hence not 79 divides 9281 by NAT_4:9;
9281 = 83*111 + 68; hence not 83 divides 9281 by NAT_4:9;
9281 = 89*104 + 25; hence not 89 divides 9281 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9281 & n is prime
holds not n divides 9281 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9283 is prime
proof
now
9283 = 2*4641 + 1; hence not 2 divides 9283 by NAT_4:9;
9283 = 3*3094 + 1; hence not 3 divides 9283 by NAT_4:9;
9283 = 5*1856 + 3; hence not 5 divides 9283 by NAT_4:9;
9283 = 7*1326 + 1; hence not 7 divides 9283 by NAT_4:9;
9283 = 11*843 + 10; hence not 11 divides 9283 by NAT_4:9;
9283 = 13*714 + 1; hence not 13 divides 9283 by NAT_4:9;
9283 = 17*546 + 1; hence not 17 divides 9283 by NAT_4:9;
9283 = 19*488 + 11; hence not 19 divides 9283 by NAT_4:9;
9283 = 23*403 + 14; hence not 23 divides 9283 by NAT_4:9;
9283 = 29*320 + 3; hence not 29 divides 9283 by NAT_4:9;
9283 = 31*299 + 14; hence not 31 divides 9283 by NAT_4:9;
9283 = 37*250 + 33; hence not 37 divides 9283 by NAT_4:9;
9283 = 41*226 + 17; hence not 41 divides 9283 by NAT_4:9;
9283 = 43*215 + 38; hence not 43 divides 9283 by NAT_4:9;
9283 = 47*197 + 24; hence not 47 divides 9283 by NAT_4:9;
9283 = 53*175 + 8; hence not 53 divides 9283 by NAT_4:9;
9283 = 59*157 + 20; hence not 59 divides 9283 by NAT_4:9;
9283 = 61*152 + 11; hence not 61 divides 9283 by NAT_4:9;
9283 = 67*138 + 37; hence not 67 divides 9283 by NAT_4:9;
9283 = 71*130 + 53; hence not 71 divides 9283 by NAT_4:9;
9283 = 73*127 + 12; hence not 73 divides 9283 by NAT_4:9;
9283 = 79*117 + 40; hence not 79 divides 9283 by NAT_4:9;
9283 = 83*111 + 70; hence not 83 divides 9283 by NAT_4:9;
9283 = 89*104 + 27; hence not 89 divides 9283 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9283 & n is prime
holds not n divides 9283 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9293 is prime
proof
now
9293 = 2*4646 + 1; hence not 2 divides 9293 by NAT_4:9;
9293 = 3*3097 + 2; hence not 3 divides 9293 by NAT_4:9;
9293 = 5*1858 + 3; hence not 5 divides 9293 by NAT_4:9;
9293 = 7*1327 + 4; hence not 7 divides 9293 by NAT_4:9;
9293 = 11*844 + 9; hence not 11 divides 9293 by NAT_4:9;
9293 = 13*714 + 11; hence not 13 divides 9293 by NAT_4:9;
9293 = 17*546 + 11; hence not 17 divides 9293 by NAT_4:9;
9293 = 19*489 + 2; hence not 19 divides 9293 by NAT_4:9;
9293 = 23*404 + 1; hence not 23 divides 9293 by NAT_4:9;
9293 = 29*320 + 13; hence not 29 divides 9293 by NAT_4:9;
9293 = 31*299 + 24; hence not 31 divides 9293 by NAT_4:9;
9293 = 37*251 + 6; hence not 37 divides 9293 by NAT_4:9;
9293 = 41*226 + 27; hence not 41 divides 9293 by NAT_4:9;
9293 = 43*216 + 5; hence not 43 divides 9293 by NAT_4:9;
9293 = 47*197 + 34; hence not 47 divides 9293 by NAT_4:9;
9293 = 53*175 + 18; hence not 53 divides 9293 by NAT_4:9;
9293 = 59*157 + 30; hence not 59 divides 9293 by NAT_4:9;
9293 = 61*152 + 21; hence not 61 divides 9293 by NAT_4:9;
9293 = 67*138 + 47; hence not 67 divides 9293 by NAT_4:9;
9293 = 71*130 + 63; hence not 71 divides 9293 by NAT_4:9;
9293 = 73*127 + 22; hence not 73 divides 9293 by NAT_4:9;
9293 = 79*117 + 50; hence not 79 divides 9293 by NAT_4:9;
9293 = 83*111 + 80; hence not 83 divides 9293 by NAT_4:9;
9293 = 89*104 + 37; hence not 89 divides 9293 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9293 & n is prime
holds not n divides 9293 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
9311 is prime
proof
now
9311 = 2*4655 + 1; hence not 2 divides 9311 by NAT_4:9;
9311 = 3*3103 + 2; hence not 3 divides 9311 by NAT_4:9;
9311 = 5*1862 + 1; hence not 5 divides 9311 by NAT_4:9;
9311 = 7*1330 + 1; hence not 7 divides 9311 by NAT_4:9;
9311 = 11*846 + 5; hence not 11 divides 9311 by NAT_4:9;
9311 = 13*716 + 3; hence not 13 divides 9311 by NAT_4:9;
9311 = 17*547 + 12; hence not 17 divides 9311 by NAT_4:9;
9311 = 19*490 + 1; hence not 19 divides 9311 by NAT_4:9;
9311 = 23*404 + 19; hence not 23 divides 9311 by NAT_4:9;
9311 = 29*321 + 2; hence not 29 divides 9311 by NAT_4:9;
9311 = 31*300 + 11; hence not 31 divides 9311 by NAT_4:9;
9311 = 37*251 + 24; hence not 37 divides 9311 by NAT_4:9;
9311 = 41*227 + 4; hence not 41 divides 9311 by NAT_4:9;
9311 = 43*216 + 23; hence not 43 divides 9311 by NAT_4:9;
9311 = 47*198 + 5; hence not 47 divides 9311 by NAT_4:9;
9311 = 53*175 + 36; hence not 53 divides 9311 by NAT_4:9;
9311 = 59*157 + 48; hence not 59 divides 9311 by NAT_4:9;
9311 = 61*152 + 39; hence not 61 divides 9311 by NAT_4:9;
9311 = 67*138 + 65; hence not 67 divides 9311 by NAT_4:9;
9311 = 71*131 + 10; hence not 71 divides 9311 by NAT_4:9;
9311 = 73*127 + 40; hence not 73 divides 9311 by NAT_4:9;
9311 = 79*117 + 68; hence not 79 divides 9311 by NAT_4:9;
9311 = 83*112 + 15; hence not 83 divides 9311 by NAT_4:9;
9311 = 89*104 + 55; hence not 89 divides 9311 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9311 & n is prime
holds not n divides 9311 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9319 is prime
proof
now
9319 = 2*4659 + 1; hence not 2 divides 9319 by NAT_4:9;
9319 = 3*3106 + 1; hence not 3 divides 9319 by NAT_4:9;
9319 = 5*1863 + 4; hence not 5 divides 9319 by NAT_4:9;
9319 = 7*1331 + 2; hence not 7 divides 9319 by NAT_4:9;
9319 = 11*847 + 2; hence not 11 divides 9319 by NAT_4:9;
9319 = 13*716 + 11; hence not 13 divides 9319 by NAT_4:9;
9319 = 17*548 + 3; hence not 17 divides 9319 by NAT_4:9;
9319 = 19*490 + 9; hence not 19 divides 9319 by NAT_4:9;
9319 = 23*405 + 4; hence not 23 divides 9319 by NAT_4:9;
9319 = 29*321 + 10; hence not 29 divides 9319 by NAT_4:9;
9319 = 31*300 + 19; hence not 31 divides 9319 by NAT_4:9;
9319 = 37*251 + 32; hence not 37 divides 9319 by NAT_4:9;
9319 = 41*227 + 12; hence not 41 divides 9319 by NAT_4:9;
9319 = 43*216 + 31; hence not 43 divides 9319 by NAT_4:9;
9319 = 47*198 + 13; hence not 47 divides 9319 by NAT_4:9;
9319 = 53*175 + 44; hence not 53 divides 9319 by NAT_4:9;
9319 = 59*157 + 56; hence not 59 divides 9319 by NAT_4:9;
9319 = 61*152 + 47; hence not 61 divides 9319 by NAT_4:9;
9319 = 67*139 + 6; hence not 67 divides 9319 by NAT_4:9;
9319 = 71*131 + 18; hence not 71 divides 9319 by NAT_4:9;
9319 = 73*127 + 48; hence not 73 divides 9319 by NAT_4:9;
9319 = 79*117 + 76; hence not 79 divides 9319 by NAT_4:9;
9319 = 83*112 + 23; hence not 83 divides 9319 by NAT_4:9;
9319 = 89*104 + 63; hence not 89 divides 9319 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9319 & n is prime
holds not n divides 9319 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9323 is prime
proof
now
9323 = 2*4661 + 1; hence not 2 divides 9323 by NAT_4:9;
9323 = 3*3107 + 2; hence not 3 divides 9323 by NAT_4:9;
9323 = 5*1864 + 3; hence not 5 divides 9323 by NAT_4:9;
9323 = 7*1331 + 6; hence not 7 divides 9323 by NAT_4:9;
9323 = 11*847 + 6; hence not 11 divides 9323 by NAT_4:9;
9323 = 13*717 + 2; hence not 13 divides 9323 by NAT_4:9;
9323 = 17*548 + 7; hence not 17 divides 9323 by NAT_4:9;
9323 = 19*490 + 13; hence not 19 divides 9323 by NAT_4:9;
9323 = 23*405 + 8; hence not 23 divides 9323 by NAT_4:9;
9323 = 29*321 + 14; hence not 29 divides 9323 by NAT_4:9;
9323 = 31*300 + 23; hence not 31 divides 9323 by NAT_4:9;
9323 = 37*251 + 36; hence not 37 divides 9323 by NAT_4:9;
9323 = 41*227 + 16; hence not 41 divides 9323 by NAT_4:9;
9323 = 43*216 + 35; hence not 43 divides 9323 by NAT_4:9;
9323 = 47*198 + 17; hence not 47 divides 9323 by NAT_4:9;
9323 = 53*175 + 48; hence not 53 divides 9323 by NAT_4:9;
9323 = 59*158 + 1; hence not 59 divides 9323 by NAT_4:9;
9323 = 61*152 + 51; hence not 61 divides 9323 by NAT_4:9;
9323 = 67*139 + 10; hence not 67 divides 9323 by NAT_4:9;
9323 = 71*131 + 22; hence not 71 divides 9323 by NAT_4:9;
9323 = 73*127 + 52; hence not 73 divides 9323 by NAT_4:9;
9323 = 79*118 + 1; hence not 79 divides 9323 by NAT_4:9;
9323 = 83*112 + 27; hence not 83 divides 9323 by NAT_4:9;
9323 = 89*104 + 67; hence not 89 divides 9323 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9323 & n is prime
holds not n divides 9323 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9337 is prime
proof
now
9337 = 2*4668 + 1; hence not 2 divides 9337 by NAT_4:9;
9337 = 3*3112 + 1; hence not 3 divides 9337 by NAT_4:9;
9337 = 5*1867 + 2; hence not 5 divides 9337 by NAT_4:9;
9337 = 7*1333 + 6; hence not 7 divides 9337 by NAT_4:9;
9337 = 11*848 + 9; hence not 11 divides 9337 by NAT_4:9;
9337 = 13*718 + 3; hence not 13 divides 9337 by NAT_4:9;
9337 = 17*549 + 4; hence not 17 divides 9337 by NAT_4:9;
9337 = 19*491 + 8; hence not 19 divides 9337 by NAT_4:9;
9337 = 23*405 + 22; hence not 23 divides 9337 by NAT_4:9;
9337 = 29*321 + 28; hence not 29 divides 9337 by NAT_4:9;
9337 = 31*301 + 6; hence not 31 divides 9337 by NAT_4:9;
9337 = 37*252 + 13; hence not 37 divides 9337 by NAT_4:9;
9337 = 41*227 + 30; hence not 41 divides 9337 by NAT_4:9;
9337 = 43*217 + 6; hence not 43 divides 9337 by NAT_4:9;
9337 = 47*198 + 31; hence not 47 divides 9337 by NAT_4:9;
9337 = 53*176 + 9; hence not 53 divides 9337 by NAT_4:9;
9337 = 59*158 + 15; hence not 59 divides 9337 by NAT_4:9;
9337 = 61*153 + 4; hence not 61 divides 9337 by NAT_4:9;
9337 = 67*139 + 24; hence not 67 divides 9337 by NAT_4:9;
9337 = 71*131 + 36; hence not 71 divides 9337 by NAT_4:9;
9337 = 73*127 + 66; hence not 73 divides 9337 by NAT_4:9;
9337 = 79*118 + 15; hence not 79 divides 9337 by NAT_4:9;
9337 = 83*112 + 41; hence not 83 divides 9337 by NAT_4:9;
9337 = 89*104 + 81; hence not 89 divides 9337 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9337 & n is prime
holds not n divides 9337 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9341 is prime
proof
now
9341 = 2*4670 + 1; hence not 2 divides 9341 by NAT_4:9;
9341 = 3*3113 + 2; hence not 3 divides 9341 by NAT_4:9;
9341 = 5*1868 + 1; hence not 5 divides 9341 by NAT_4:9;
9341 = 7*1334 + 3; hence not 7 divides 9341 by NAT_4:9;
9341 = 11*849 + 2; hence not 11 divides 9341 by NAT_4:9;
9341 = 13*718 + 7; hence not 13 divides 9341 by NAT_4:9;
9341 = 17*549 + 8; hence not 17 divides 9341 by NAT_4:9;
9341 = 19*491 + 12; hence not 19 divides 9341 by NAT_4:9;
9341 = 23*406 + 3; hence not 23 divides 9341 by NAT_4:9;
9341 = 29*322 + 3; hence not 29 divides 9341 by NAT_4:9;
9341 = 31*301 + 10; hence not 31 divides 9341 by NAT_4:9;
9341 = 37*252 + 17; hence not 37 divides 9341 by NAT_4:9;
9341 = 41*227 + 34; hence not 41 divides 9341 by NAT_4:9;
9341 = 43*217 + 10; hence not 43 divides 9341 by NAT_4:9;
9341 = 47*198 + 35; hence not 47 divides 9341 by NAT_4:9;
9341 = 53*176 + 13; hence not 53 divides 9341 by NAT_4:9;
9341 = 59*158 + 19; hence not 59 divides 9341 by NAT_4:9;
9341 = 61*153 + 8; hence not 61 divides 9341 by NAT_4:9;
9341 = 67*139 + 28; hence not 67 divides 9341 by NAT_4:9;
9341 = 71*131 + 40; hence not 71 divides 9341 by NAT_4:9;
9341 = 73*127 + 70; hence not 73 divides 9341 by NAT_4:9;
9341 = 79*118 + 19; hence not 79 divides 9341 by NAT_4:9;
9341 = 83*112 + 45; hence not 83 divides 9341 by NAT_4:9;
9341 = 89*104 + 85; hence not 89 divides 9341 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9341 & n is prime
holds not n divides 9341 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9343 is prime
proof
now
9343 = 2*4671 + 1; hence not 2 divides 9343 by NAT_4:9;
9343 = 3*3114 + 1; hence not 3 divides 9343 by NAT_4:9;
9343 = 5*1868 + 3; hence not 5 divides 9343 by NAT_4:9;
9343 = 7*1334 + 5; hence not 7 divides 9343 by NAT_4:9;
9343 = 11*849 + 4; hence not 11 divides 9343 by NAT_4:9;
9343 = 13*718 + 9; hence not 13 divides 9343 by NAT_4:9;
9343 = 17*549 + 10; hence not 17 divides 9343 by NAT_4:9;
9343 = 19*491 + 14; hence not 19 divides 9343 by NAT_4:9;
9343 = 23*406 + 5; hence not 23 divides 9343 by NAT_4:9;
9343 = 29*322 + 5; hence not 29 divides 9343 by NAT_4:9;
9343 = 31*301 + 12; hence not 31 divides 9343 by NAT_4:9;
9343 = 37*252 + 19; hence not 37 divides 9343 by NAT_4:9;
9343 = 41*227 + 36; hence not 41 divides 9343 by NAT_4:9;
9343 = 43*217 + 12; hence not 43 divides 9343 by NAT_4:9;
9343 = 47*198 + 37; hence not 47 divides 9343 by NAT_4:9;
9343 = 53*176 + 15; hence not 53 divides 9343 by NAT_4:9;
9343 = 59*158 + 21; hence not 59 divides 9343 by NAT_4:9;
9343 = 61*153 + 10; hence not 61 divides 9343 by NAT_4:9;
9343 = 67*139 + 30; hence not 67 divides 9343 by NAT_4:9;
9343 = 71*131 + 42; hence not 71 divides 9343 by NAT_4:9;
9343 = 73*127 + 72; hence not 73 divides 9343 by NAT_4:9;
9343 = 79*118 + 21; hence not 79 divides 9343 by NAT_4:9;
9343 = 83*112 + 47; hence not 83 divides 9343 by NAT_4:9;
9343 = 89*104 + 87; hence not 89 divides 9343 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9343 & n is prime
holds not n divides 9343 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9349 is prime
proof
now
9349 = 2*4674 + 1; hence not 2 divides 9349 by NAT_4:9;
9349 = 3*3116 + 1; hence not 3 divides 9349 by NAT_4:9;
9349 = 5*1869 + 4; hence not 5 divides 9349 by NAT_4:9;
9349 = 7*1335 + 4; hence not 7 divides 9349 by NAT_4:9;
9349 = 11*849 + 10; hence not 11 divides 9349 by NAT_4:9;
9349 = 13*719 + 2; hence not 13 divides 9349 by NAT_4:9;
9349 = 17*549 + 16; hence not 17 divides 9349 by NAT_4:9;
9349 = 19*492 + 1; hence not 19 divides 9349 by NAT_4:9;
9349 = 23*406 + 11; hence not 23 divides 9349 by NAT_4:9;
9349 = 29*322 + 11; hence not 29 divides 9349 by NAT_4:9;
9349 = 31*301 + 18; hence not 31 divides 9349 by NAT_4:9;
9349 = 37*252 + 25; hence not 37 divides 9349 by NAT_4:9;
9349 = 41*228 + 1; hence not 41 divides 9349 by NAT_4:9;
9349 = 43*217 + 18; hence not 43 divides 9349 by NAT_4:9;
9349 = 47*198 + 43; hence not 47 divides 9349 by NAT_4:9;
9349 = 53*176 + 21; hence not 53 divides 9349 by NAT_4:9;
9349 = 59*158 + 27; hence not 59 divides 9349 by NAT_4:9;
9349 = 61*153 + 16; hence not 61 divides 9349 by NAT_4:9;
9349 = 67*139 + 36; hence not 67 divides 9349 by NAT_4:9;
9349 = 71*131 + 48; hence not 71 divides 9349 by NAT_4:9;
9349 = 73*128 + 5; hence not 73 divides 9349 by NAT_4:9;
9349 = 79*118 + 27; hence not 79 divides 9349 by NAT_4:9;
9349 = 83*112 + 53; hence not 83 divides 9349 by NAT_4:9;
9349 = 89*105 + 4; hence not 89 divides 9349 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9349 & n is prime
holds not n divides 9349 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
9371 is prime
proof
now
9371 = 2*4685 + 1; hence not 2 divides 9371 by NAT_4:9;
9371 = 3*3123 + 2; hence not 3 divides 9371 by NAT_4:9;
9371 = 5*1874 + 1; hence not 5 divides 9371 by NAT_4:9;
9371 = 7*1338 + 5; hence not 7 divides 9371 by NAT_4:9;
9371 = 11*851 + 10; hence not 11 divides 9371 by NAT_4:9;
9371 = 13*720 + 11; hence not 13 divides 9371 by NAT_4:9;
9371 = 17*551 + 4; hence not 17 divides 9371 by NAT_4:9;
9371 = 19*493 + 4; hence not 19 divides 9371 by NAT_4:9;
9371 = 23*407 + 10; hence not 23 divides 9371 by NAT_4:9;
9371 = 29*323 + 4; hence not 29 divides 9371 by NAT_4:9;
9371 = 31*302 + 9; hence not 31 divides 9371 by NAT_4:9;
9371 = 37*253 + 10; hence not 37 divides 9371 by NAT_4:9;
9371 = 41*228 + 23; hence not 41 divides 9371 by NAT_4:9;
9371 = 43*217 + 40; hence not 43 divides 9371 by NAT_4:9;
9371 = 47*199 + 18; hence not 47 divides 9371 by NAT_4:9;
9371 = 53*176 + 43; hence not 53 divides 9371 by NAT_4:9;
9371 = 59*158 + 49; hence not 59 divides 9371 by NAT_4:9;
9371 = 61*153 + 38; hence not 61 divides 9371 by NAT_4:9;
9371 = 67*139 + 58; hence not 67 divides 9371 by NAT_4:9;
9371 = 71*131 + 70; hence not 71 divides 9371 by NAT_4:9;
9371 = 73*128 + 27; hence not 73 divides 9371 by NAT_4:9;
9371 = 79*118 + 49; hence not 79 divides 9371 by NAT_4:9;
9371 = 83*112 + 75; hence not 83 divides 9371 by NAT_4:9;
9371 = 89*105 + 26; hence not 89 divides 9371 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9371 & n is prime
holds not n divides 9371 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9377 is prime
proof
now
9377 = 2*4688 + 1; hence not 2 divides 9377 by NAT_4:9;
9377 = 3*3125 + 2; hence not 3 divides 9377 by NAT_4:9;
9377 = 5*1875 + 2; hence not 5 divides 9377 by NAT_4:9;
9377 = 7*1339 + 4; hence not 7 divides 9377 by NAT_4:9;
9377 = 11*852 + 5; hence not 11 divides 9377 by NAT_4:9;
9377 = 13*721 + 4; hence not 13 divides 9377 by NAT_4:9;
9377 = 17*551 + 10; hence not 17 divides 9377 by NAT_4:9;
9377 = 19*493 + 10; hence not 19 divides 9377 by NAT_4:9;
9377 = 23*407 + 16; hence not 23 divides 9377 by NAT_4:9;
9377 = 29*323 + 10; hence not 29 divides 9377 by NAT_4:9;
9377 = 31*302 + 15; hence not 31 divides 9377 by NAT_4:9;
9377 = 37*253 + 16; hence not 37 divides 9377 by NAT_4:9;
9377 = 41*228 + 29; hence not 41 divides 9377 by NAT_4:9;
9377 = 43*218 + 3; hence not 43 divides 9377 by NAT_4:9;
9377 = 47*199 + 24; hence not 47 divides 9377 by NAT_4:9;
9377 = 53*176 + 49; hence not 53 divides 9377 by NAT_4:9;
9377 = 59*158 + 55; hence not 59 divides 9377 by NAT_4:9;
9377 = 61*153 + 44; hence not 61 divides 9377 by NAT_4:9;
9377 = 67*139 + 64; hence not 67 divides 9377 by NAT_4:9;
9377 = 71*132 + 5; hence not 71 divides 9377 by NAT_4:9;
9377 = 73*128 + 33; hence not 73 divides 9377 by NAT_4:9;
9377 = 79*118 + 55; hence not 79 divides 9377 by NAT_4:9;
9377 = 83*112 + 81; hence not 83 divides 9377 by NAT_4:9;
9377 = 89*105 + 32; hence not 89 divides 9377 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9377 & n is prime
holds not n divides 9377 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9391 is prime
proof
now
9391 = 2*4695 + 1; hence not 2 divides 9391 by NAT_4:9;
9391 = 3*3130 + 1; hence not 3 divides 9391 by NAT_4:9;
9391 = 5*1878 + 1; hence not 5 divides 9391 by NAT_4:9;
9391 = 7*1341 + 4; hence not 7 divides 9391 by NAT_4:9;
9391 = 11*853 + 8; hence not 11 divides 9391 by NAT_4:9;
9391 = 13*722 + 5; hence not 13 divides 9391 by NAT_4:9;
9391 = 17*552 + 7; hence not 17 divides 9391 by NAT_4:9;
9391 = 19*494 + 5; hence not 19 divides 9391 by NAT_4:9;
9391 = 23*408 + 7; hence not 23 divides 9391 by NAT_4:9;
9391 = 29*323 + 24; hence not 29 divides 9391 by NAT_4:9;
9391 = 31*302 + 29; hence not 31 divides 9391 by NAT_4:9;
9391 = 37*253 + 30; hence not 37 divides 9391 by NAT_4:9;
9391 = 41*229 + 2; hence not 41 divides 9391 by NAT_4:9;
9391 = 43*218 + 17; hence not 43 divides 9391 by NAT_4:9;
9391 = 47*199 + 38; hence not 47 divides 9391 by NAT_4:9;
9391 = 53*177 + 10; hence not 53 divides 9391 by NAT_4:9;
9391 = 59*159 + 10; hence not 59 divides 9391 by NAT_4:9;
9391 = 61*153 + 58; hence not 61 divides 9391 by NAT_4:9;
9391 = 67*140 + 11; hence not 67 divides 9391 by NAT_4:9;
9391 = 71*132 + 19; hence not 71 divides 9391 by NAT_4:9;
9391 = 73*128 + 47; hence not 73 divides 9391 by NAT_4:9;
9391 = 79*118 + 69; hence not 79 divides 9391 by NAT_4:9;
9391 = 83*113 + 12; hence not 83 divides 9391 by NAT_4:9;
9391 = 89*105 + 46; hence not 89 divides 9391 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9391 & n is prime
holds not n divides 9391 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9397 is prime
proof
now
9397 = 2*4698 + 1; hence not 2 divides 9397 by NAT_4:9;
9397 = 3*3132 + 1; hence not 3 divides 9397 by NAT_4:9;
9397 = 5*1879 + 2; hence not 5 divides 9397 by NAT_4:9;
9397 = 7*1342 + 3; hence not 7 divides 9397 by NAT_4:9;
9397 = 11*854 + 3; hence not 11 divides 9397 by NAT_4:9;
9397 = 13*722 + 11; hence not 13 divides 9397 by NAT_4:9;
9397 = 17*552 + 13; hence not 17 divides 9397 by NAT_4:9;
9397 = 19*494 + 11; hence not 19 divides 9397 by NAT_4:9;
9397 = 23*408 + 13; hence not 23 divides 9397 by NAT_4:9;
9397 = 29*324 + 1; hence not 29 divides 9397 by NAT_4:9;
9397 = 31*303 + 4; hence not 31 divides 9397 by NAT_4:9;
9397 = 37*253 + 36; hence not 37 divides 9397 by NAT_4:9;
9397 = 41*229 + 8; hence not 41 divides 9397 by NAT_4:9;
9397 = 43*218 + 23; hence not 43 divides 9397 by NAT_4:9;
9397 = 47*199 + 44; hence not 47 divides 9397 by NAT_4:9;
9397 = 53*177 + 16; hence not 53 divides 9397 by NAT_4:9;
9397 = 59*159 + 16; hence not 59 divides 9397 by NAT_4:9;
9397 = 61*154 + 3; hence not 61 divides 9397 by NAT_4:9;
9397 = 67*140 + 17; hence not 67 divides 9397 by NAT_4:9;
9397 = 71*132 + 25; hence not 71 divides 9397 by NAT_4:9;
9397 = 73*128 + 53; hence not 73 divides 9397 by NAT_4:9;
9397 = 79*118 + 75; hence not 79 divides 9397 by NAT_4:9;
9397 = 83*113 + 18; hence not 83 divides 9397 by NAT_4:9;
9397 = 89*105 + 52; hence not 89 divides 9397 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9397 & n is prime
holds not n divides 9397 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9403 is prime
proof
now
9403 = 2*4701 + 1; hence not 2 divides 9403 by NAT_4:9;
9403 = 3*3134 + 1; hence not 3 divides 9403 by NAT_4:9;
9403 = 5*1880 + 3; hence not 5 divides 9403 by NAT_4:9;
9403 = 7*1343 + 2; hence not 7 divides 9403 by NAT_4:9;
9403 = 11*854 + 9; hence not 11 divides 9403 by NAT_4:9;
9403 = 13*723 + 4; hence not 13 divides 9403 by NAT_4:9;
9403 = 17*553 + 2; hence not 17 divides 9403 by NAT_4:9;
9403 = 19*494 + 17; hence not 19 divides 9403 by NAT_4:9;
9403 = 23*408 + 19; hence not 23 divides 9403 by NAT_4:9;
9403 = 29*324 + 7; hence not 29 divides 9403 by NAT_4:9;
9403 = 31*303 + 10; hence not 31 divides 9403 by NAT_4:9;
9403 = 37*254 + 5; hence not 37 divides 9403 by NAT_4:9;
9403 = 41*229 + 14; hence not 41 divides 9403 by NAT_4:9;
9403 = 43*218 + 29; hence not 43 divides 9403 by NAT_4:9;
9403 = 47*200 + 3; hence not 47 divides 9403 by NAT_4:9;
9403 = 53*177 + 22; hence not 53 divides 9403 by NAT_4:9;
9403 = 59*159 + 22; hence not 59 divides 9403 by NAT_4:9;
9403 = 61*154 + 9; hence not 61 divides 9403 by NAT_4:9;
9403 = 67*140 + 23; hence not 67 divides 9403 by NAT_4:9;
9403 = 71*132 + 31; hence not 71 divides 9403 by NAT_4:9;
9403 = 73*128 + 59; hence not 73 divides 9403 by NAT_4:9;
9403 = 79*119 + 2; hence not 79 divides 9403 by NAT_4:9;
9403 = 83*113 + 24; hence not 83 divides 9403 by NAT_4:9;
9403 = 89*105 + 58; hence not 89 divides 9403 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9403 & n is prime
holds not n divides 9403 by XPRIMET1:48;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9413 is prime
proof
now
9413 = 2*4706 + 1; hence not 2 divides 9413 by NAT_4:9;
9413 = 3*3137 + 2; hence not 3 divides 9413 by NAT_4:9;
9413 = 5*1882 + 3; hence not 5 divides 9413 by NAT_4:9;
9413 = 7*1344 + 5; hence not 7 divides 9413 by NAT_4:9;
9413 = 11*855 + 8; hence not 11 divides 9413 by NAT_4:9;
9413 = 13*724 + 1; hence not 13 divides 9413 by NAT_4:9;
9413 = 17*553 + 12; hence not 17 divides 9413 by NAT_4:9;
9413 = 19*495 + 8; hence not 19 divides 9413 by NAT_4:9;
9413 = 23*409 + 6; hence not 23 divides 9413 by NAT_4:9;
9413 = 29*324 + 17; hence not 29 divides 9413 by NAT_4:9;
9413 = 31*303 + 20; hence not 31 divides 9413 by NAT_4:9;
9413 = 37*254 + 15; hence not 37 divides 9413 by NAT_4:9;
9413 = 41*229 + 24; hence not 41 divides 9413 by NAT_4:9;
9413 = 43*218 + 39; hence not 43 divides 9413 by NAT_4:9;
9413 = 47*200 + 13; hence not 47 divides 9413 by NAT_4:9;
9413 = 53*177 + 32; hence not 53 divides 9413 by NAT_4:9;
9413 = 59*159 + 32; hence not 59 divides 9413 by NAT_4:9;
9413 = 61*154 + 19; hence not 61 divides 9413 by NAT_4:9;
9413 = 67*140 + 33; hence not 67 divides 9413 by NAT_4:9;
9413 = 71*132 + 41; hence not 71 divides 9413 by NAT_4:9;
9413 = 73*128 + 69; hence not 73 divides 9413 by NAT_4:9;
9413 = 79*119 + 12; hence not 79 divides 9413 by NAT_4:9;
9413 = 83*113 + 34; hence not 83 divides 9413 by NAT_4:9;
9413 = 89*105 + 68; hence not 89 divides 9413 by NAT_4:9;
9413 = 97*97 + 4; hence not 97 divides 9413 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9413 & n is prime
holds not n divides 9413 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9419 is prime
proof
now
9419 = 2*4709 + 1; hence not 2 divides 9419 by NAT_4:9;
9419 = 3*3139 + 2; hence not 3 divides 9419 by NAT_4:9;
9419 = 5*1883 + 4; hence not 5 divides 9419 by NAT_4:9;
9419 = 7*1345 + 4; hence not 7 divides 9419 by NAT_4:9;
9419 = 11*856 + 3; hence not 11 divides 9419 by NAT_4:9;
9419 = 13*724 + 7; hence not 13 divides 9419 by NAT_4:9;
9419 = 17*554 + 1; hence not 17 divides 9419 by NAT_4:9;
9419 = 19*495 + 14; hence not 19 divides 9419 by NAT_4:9;
9419 = 23*409 + 12; hence not 23 divides 9419 by NAT_4:9;
9419 = 29*324 + 23; hence not 29 divides 9419 by NAT_4:9;
9419 = 31*303 + 26; hence not 31 divides 9419 by NAT_4:9;
9419 = 37*254 + 21; hence not 37 divides 9419 by NAT_4:9;
9419 = 41*229 + 30; hence not 41 divides 9419 by NAT_4:9;
9419 = 43*219 + 2; hence not 43 divides 9419 by NAT_4:9;
9419 = 47*200 + 19; hence not 47 divides 9419 by NAT_4:9;
9419 = 53*177 + 38; hence not 53 divides 9419 by NAT_4:9;
9419 = 59*159 + 38; hence not 59 divides 9419 by NAT_4:9;
9419 = 61*154 + 25; hence not 61 divides 9419 by NAT_4:9;
9419 = 67*140 + 39; hence not 67 divides 9419 by NAT_4:9;
9419 = 71*132 + 47; hence not 71 divides 9419 by NAT_4:9;
9419 = 73*129 + 2; hence not 73 divides 9419 by NAT_4:9;
9419 = 79*119 + 18; hence not 79 divides 9419 by NAT_4:9;
9419 = 83*113 + 40; hence not 83 divides 9419 by NAT_4:9;
9419 = 89*105 + 74; hence not 89 divides 9419 by NAT_4:9;
9419 = 97*97 + 10; hence not 97 divides 9419 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9419 & n is prime
holds not n divides 9419 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9421 is prime
proof
now
9421 = 2*4710 + 1; hence not 2 divides 9421 by NAT_4:9;
9421 = 3*3140 + 1; hence not 3 divides 9421 by NAT_4:9;
9421 = 5*1884 + 1; hence not 5 divides 9421 by NAT_4:9;
9421 = 7*1345 + 6; hence not 7 divides 9421 by NAT_4:9;
9421 = 11*856 + 5; hence not 11 divides 9421 by NAT_4:9;
9421 = 13*724 + 9; hence not 13 divides 9421 by NAT_4:9;
9421 = 17*554 + 3; hence not 17 divides 9421 by NAT_4:9;
9421 = 19*495 + 16; hence not 19 divides 9421 by NAT_4:9;
9421 = 23*409 + 14; hence not 23 divides 9421 by NAT_4:9;
9421 = 29*324 + 25; hence not 29 divides 9421 by NAT_4:9;
9421 = 31*303 + 28; hence not 31 divides 9421 by NAT_4:9;
9421 = 37*254 + 23; hence not 37 divides 9421 by NAT_4:9;
9421 = 41*229 + 32; hence not 41 divides 9421 by NAT_4:9;
9421 = 43*219 + 4; hence not 43 divides 9421 by NAT_4:9;
9421 = 47*200 + 21; hence not 47 divides 9421 by NAT_4:9;
9421 = 53*177 + 40; hence not 53 divides 9421 by NAT_4:9;
9421 = 59*159 + 40; hence not 59 divides 9421 by NAT_4:9;
9421 = 61*154 + 27; hence not 61 divides 9421 by NAT_4:9;
9421 = 67*140 + 41; hence not 67 divides 9421 by NAT_4:9;
9421 = 71*132 + 49; hence not 71 divides 9421 by NAT_4:9;
9421 = 73*129 + 4; hence not 73 divides 9421 by NAT_4:9;
9421 = 79*119 + 20; hence not 79 divides 9421 by NAT_4:9;
9421 = 83*113 + 42; hence not 83 divides 9421 by NAT_4:9;
9421 = 89*105 + 76; hence not 89 divides 9421 by NAT_4:9;
9421 = 97*97 + 12; hence not 97 divides 9421 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9421 & n is prime
holds not n divides 9421 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9431 is prime
proof
now
9431 = 2*4715 + 1; hence not 2 divides 9431 by NAT_4:9;
9431 = 3*3143 + 2; hence not 3 divides 9431 by NAT_4:9;
9431 = 5*1886 + 1; hence not 5 divides 9431 by NAT_4:9;
9431 = 7*1347 + 2; hence not 7 divides 9431 by NAT_4:9;
9431 = 11*857 + 4; hence not 11 divides 9431 by NAT_4:9;
9431 = 13*725 + 6; hence not 13 divides 9431 by NAT_4:9;
9431 = 17*554 + 13; hence not 17 divides 9431 by NAT_4:9;
9431 = 19*496 + 7; hence not 19 divides 9431 by NAT_4:9;
9431 = 23*410 + 1; hence not 23 divides 9431 by NAT_4:9;
9431 = 29*325 + 6; hence not 29 divides 9431 by NAT_4:9;
9431 = 31*304 + 7; hence not 31 divides 9431 by NAT_4:9;
9431 = 37*254 + 33; hence not 37 divides 9431 by NAT_4:9;
9431 = 41*230 + 1; hence not 41 divides 9431 by NAT_4:9;
9431 = 43*219 + 14; hence not 43 divides 9431 by NAT_4:9;
9431 = 47*200 + 31; hence not 47 divides 9431 by NAT_4:9;
9431 = 53*177 + 50; hence not 53 divides 9431 by NAT_4:9;
9431 = 59*159 + 50; hence not 59 divides 9431 by NAT_4:9;
9431 = 61*154 + 37; hence not 61 divides 9431 by NAT_4:9;
9431 = 67*140 + 51; hence not 67 divides 9431 by NAT_4:9;
9431 = 71*132 + 59; hence not 71 divides 9431 by NAT_4:9;
9431 = 73*129 + 14; hence not 73 divides 9431 by NAT_4:9;
9431 = 79*119 + 30; hence not 79 divides 9431 by NAT_4:9;
9431 = 83*113 + 52; hence not 83 divides 9431 by NAT_4:9;
9431 = 89*105 + 86; hence not 89 divides 9431 by NAT_4:9;
9431 = 97*97 + 22; hence not 97 divides 9431 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9431 & n is prime
holds not n divides 9431 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9433 is prime
proof
now
9433 = 2*4716 + 1; hence not 2 divides 9433 by NAT_4:9;
9433 = 3*3144 + 1; hence not 3 divides 9433 by NAT_4:9;
9433 = 5*1886 + 3; hence not 5 divides 9433 by NAT_4:9;
9433 = 7*1347 + 4; hence not 7 divides 9433 by NAT_4:9;
9433 = 11*857 + 6; hence not 11 divides 9433 by NAT_4:9;
9433 = 13*725 + 8; hence not 13 divides 9433 by NAT_4:9;
9433 = 17*554 + 15; hence not 17 divides 9433 by NAT_4:9;
9433 = 19*496 + 9; hence not 19 divides 9433 by NAT_4:9;
9433 = 23*410 + 3; hence not 23 divides 9433 by NAT_4:9;
9433 = 29*325 + 8; hence not 29 divides 9433 by NAT_4:9;
9433 = 31*304 + 9; hence not 31 divides 9433 by NAT_4:9;
9433 = 37*254 + 35; hence not 37 divides 9433 by NAT_4:9;
9433 = 41*230 + 3; hence not 41 divides 9433 by NAT_4:9;
9433 = 43*219 + 16; hence not 43 divides 9433 by NAT_4:9;
9433 = 47*200 + 33; hence not 47 divides 9433 by NAT_4:9;
9433 = 53*177 + 52; hence not 53 divides 9433 by NAT_4:9;
9433 = 59*159 + 52; hence not 59 divides 9433 by NAT_4:9;
9433 = 61*154 + 39; hence not 61 divides 9433 by NAT_4:9;
9433 = 67*140 + 53; hence not 67 divides 9433 by NAT_4:9;
9433 = 71*132 + 61; hence not 71 divides 9433 by NAT_4:9;
9433 = 73*129 + 16; hence not 73 divides 9433 by NAT_4:9;
9433 = 79*119 + 32; hence not 79 divides 9433 by NAT_4:9;
9433 = 83*113 + 54; hence not 83 divides 9433 by NAT_4:9;
9433 = 89*105 + 88; hence not 89 divides 9433 by NAT_4:9;
9433 = 97*97 + 24; hence not 97 divides 9433 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9433 & n is prime
holds not n divides 9433 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9437 is prime
proof
now
9437 = 2*4718 + 1; hence not 2 divides 9437 by NAT_4:9;
9437 = 3*3145 + 2; hence not 3 divides 9437 by NAT_4:9;
9437 = 5*1887 + 2; hence not 5 divides 9437 by NAT_4:9;
9437 = 7*1348 + 1; hence not 7 divides 9437 by NAT_4:9;
9437 = 11*857 + 10; hence not 11 divides 9437 by NAT_4:9;
9437 = 13*725 + 12; hence not 13 divides 9437 by NAT_4:9;
9437 = 17*555 + 2; hence not 17 divides 9437 by NAT_4:9;
9437 = 19*496 + 13; hence not 19 divides 9437 by NAT_4:9;
9437 = 23*410 + 7; hence not 23 divides 9437 by NAT_4:9;
9437 = 29*325 + 12; hence not 29 divides 9437 by NAT_4:9;
9437 = 31*304 + 13; hence not 31 divides 9437 by NAT_4:9;
9437 = 37*255 + 2; hence not 37 divides 9437 by NAT_4:9;
9437 = 41*230 + 7; hence not 41 divides 9437 by NAT_4:9;
9437 = 43*219 + 20; hence not 43 divides 9437 by NAT_4:9;
9437 = 47*200 + 37; hence not 47 divides 9437 by NAT_4:9;
9437 = 53*178 + 3; hence not 53 divides 9437 by NAT_4:9;
9437 = 59*159 + 56; hence not 59 divides 9437 by NAT_4:9;
9437 = 61*154 + 43; hence not 61 divides 9437 by NAT_4:9;
9437 = 67*140 + 57; hence not 67 divides 9437 by NAT_4:9;
9437 = 71*132 + 65; hence not 71 divides 9437 by NAT_4:9;
9437 = 73*129 + 20; hence not 73 divides 9437 by NAT_4:9;
9437 = 79*119 + 36; hence not 79 divides 9437 by NAT_4:9;
9437 = 83*113 + 58; hence not 83 divides 9437 by NAT_4:9;
9437 = 89*106 + 3; hence not 89 divides 9437 by NAT_4:9;
9437 = 97*97 + 28; hence not 97 divides 9437 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9437 & n is prime
holds not n divides 9437 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9439 is prime
proof
now
9439 = 2*4719 + 1; hence not 2 divides 9439 by NAT_4:9;
9439 = 3*3146 + 1; hence not 3 divides 9439 by NAT_4:9;
9439 = 5*1887 + 4; hence not 5 divides 9439 by NAT_4:9;
9439 = 7*1348 + 3; hence not 7 divides 9439 by NAT_4:9;
9439 = 11*858 + 1; hence not 11 divides 9439 by NAT_4:9;
9439 = 13*726 + 1; hence not 13 divides 9439 by NAT_4:9;
9439 = 17*555 + 4; hence not 17 divides 9439 by NAT_4:9;
9439 = 19*496 + 15; hence not 19 divides 9439 by NAT_4:9;
9439 = 23*410 + 9; hence not 23 divides 9439 by NAT_4:9;
9439 = 29*325 + 14; hence not 29 divides 9439 by NAT_4:9;
9439 = 31*304 + 15; hence not 31 divides 9439 by NAT_4:9;
9439 = 37*255 + 4; hence not 37 divides 9439 by NAT_4:9;
9439 = 41*230 + 9; hence not 41 divides 9439 by NAT_4:9;
9439 = 43*219 + 22; hence not 43 divides 9439 by NAT_4:9;
9439 = 47*200 + 39; hence not 47 divides 9439 by NAT_4:9;
9439 = 53*178 + 5; hence not 53 divides 9439 by NAT_4:9;
9439 = 59*159 + 58; hence not 59 divides 9439 by NAT_4:9;
9439 = 61*154 + 45; hence not 61 divides 9439 by NAT_4:9;
9439 = 67*140 + 59; hence not 67 divides 9439 by NAT_4:9;
9439 = 71*132 + 67; hence not 71 divides 9439 by NAT_4:9;
9439 = 73*129 + 22; hence not 73 divides 9439 by NAT_4:9;
9439 = 79*119 + 38; hence not 79 divides 9439 by NAT_4:9;
9439 = 83*113 + 60; hence not 83 divides 9439 by NAT_4:9;
9439 = 89*106 + 5; hence not 89 divides 9439 by NAT_4:9;
9439 = 97*97 + 30; hence not 97 divides 9439 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9439 & n is prime
holds not n divides 9439 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
9461 is prime
proof
now
9461 = 2*4730 + 1; hence not 2 divides 9461 by NAT_4:9;
9461 = 3*3153 + 2; hence not 3 divides 9461 by NAT_4:9;
9461 = 5*1892 + 1; hence not 5 divides 9461 by NAT_4:9;
9461 = 7*1351 + 4; hence not 7 divides 9461 by NAT_4:9;
9461 = 11*860 + 1; hence not 11 divides 9461 by NAT_4:9;
9461 = 13*727 + 10; hence not 13 divides 9461 by NAT_4:9;
9461 = 17*556 + 9; hence not 17 divides 9461 by NAT_4:9;
9461 = 19*497 + 18; hence not 19 divides 9461 by NAT_4:9;
9461 = 23*411 + 8; hence not 23 divides 9461 by NAT_4:9;
9461 = 29*326 + 7; hence not 29 divides 9461 by NAT_4:9;
9461 = 31*305 + 6; hence not 31 divides 9461 by NAT_4:9;
9461 = 37*255 + 26; hence not 37 divides 9461 by NAT_4:9;
9461 = 41*230 + 31; hence not 41 divides 9461 by NAT_4:9;
9461 = 43*220 + 1; hence not 43 divides 9461 by NAT_4:9;
9461 = 47*201 + 14; hence not 47 divides 9461 by NAT_4:9;
9461 = 53*178 + 27; hence not 53 divides 9461 by NAT_4:9;
9461 = 59*160 + 21; hence not 59 divides 9461 by NAT_4:9;
9461 = 61*155 + 6; hence not 61 divides 9461 by NAT_4:9;
9461 = 67*141 + 14; hence not 67 divides 9461 by NAT_4:9;
9461 = 71*133 + 18; hence not 71 divides 9461 by NAT_4:9;
9461 = 73*129 + 44; hence not 73 divides 9461 by NAT_4:9;
9461 = 79*119 + 60; hence not 79 divides 9461 by NAT_4:9;
9461 = 83*113 + 82; hence not 83 divides 9461 by NAT_4:9;
9461 = 89*106 + 27; hence not 89 divides 9461 by NAT_4:9;
9461 = 97*97 + 52; hence not 97 divides 9461 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9461 & n is prime
holds not n divides 9461 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9463 is prime
proof
now
9463 = 2*4731 + 1; hence not 2 divides 9463 by NAT_4:9;
9463 = 3*3154 + 1; hence not 3 divides 9463 by NAT_4:9;
9463 = 5*1892 + 3; hence not 5 divides 9463 by NAT_4:9;
9463 = 7*1351 + 6; hence not 7 divides 9463 by NAT_4:9;
9463 = 11*860 + 3; hence not 11 divides 9463 by NAT_4:9;
9463 = 13*727 + 12; hence not 13 divides 9463 by NAT_4:9;
9463 = 17*556 + 11; hence not 17 divides 9463 by NAT_4:9;
9463 = 19*498 + 1; hence not 19 divides 9463 by NAT_4:9;
9463 = 23*411 + 10; hence not 23 divides 9463 by NAT_4:9;
9463 = 29*326 + 9; hence not 29 divides 9463 by NAT_4:9;
9463 = 31*305 + 8; hence not 31 divides 9463 by NAT_4:9;
9463 = 37*255 + 28; hence not 37 divides 9463 by NAT_4:9;
9463 = 41*230 + 33; hence not 41 divides 9463 by NAT_4:9;
9463 = 43*220 + 3; hence not 43 divides 9463 by NAT_4:9;
9463 = 47*201 + 16; hence not 47 divides 9463 by NAT_4:9;
9463 = 53*178 + 29; hence not 53 divides 9463 by NAT_4:9;
9463 = 59*160 + 23; hence not 59 divides 9463 by NAT_4:9;
9463 = 61*155 + 8; hence not 61 divides 9463 by NAT_4:9;
9463 = 67*141 + 16; hence not 67 divides 9463 by NAT_4:9;
9463 = 71*133 + 20; hence not 71 divides 9463 by NAT_4:9;
9463 = 73*129 + 46; hence not 73 divides 9463 by NAT_4:9;
9463 = 79*119 + 62; hence not 79 divides 9463 by NAT_4:9;
9463 = 83*114 + 1; hence not 83 divides 9463 by NAT_4:9;
9463 = 89*106 + 29; hence not 89 divides 9463 by NAT_4:9;
9463 = 97*97 + 54; hence not 97 divides 9463 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9463 & n is prime
holds not n divides 9463 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9467 is prime
proof
now
9467 = 2*4733 + 1; hence not 2 divides 9467 by NAT_4:9;
9467 = 3*3155 + 2; hence not 3 divides 9467 by NAT_4:9;
9467 = 5*1893 + 2; hence not 5 divides 9467 by NAT_4:9;
9467 = 7*1352 + 3; hence not 7 divides 9467 by NAT_4:9;
9467 = 11*860 + 7; hence not 11 divides 9467 by NAT_4:9;
9467 = 13*728 + 3; hence not 13 divides 9467 by NAT_4:9;
9467 = 17*556 + 15; hence not 17 divides 9467 by NAT_4:9;
9467 = 19*498 + 5; hence not 19 divides 9467 by NAT_4:9;
9467 = 23*411 + 14; hence not 23 divides 9467 by NAT_4:9;
9467 = 29*326 + 13; hence not 29 divides 9467 by NAT_4:9;
9467 = 31*305 + 12; hence not 31 divides 9467 by NAT_4:9;
9467 = 37*255 + 32; hence not 37 divides 9467 by NAT_4:9;
9467 = 41*230 + 37; hence not 41 divides 9467 by NAT_4:9;
9467 = 43*220 + 7; hence not 43 divides 9467 by NAT_4:9;
9467 = 47*201 + 20; hence not 47 divides 9467 by NAT_4:9;
9467 = 53*178 + 33; hence not 53 divides 9467 by NAT_4:9;
9467 = 59*160 + 27; hence not 59 divides 9467 by NAT_4:9;
9467 = 61*155 + 12; hence not 61 divides 9467 by NAT_4:9;
9467 = 67*141 + 20; hence not 67 divides 9467 by NAT_4:9;
9467 = 71*133 + 24; hence not 71 divides 9467 by NAT_4:9;
9467 = 73*129 + 50; hence not 73 divides 9467 by NAT_4:9;
9467 = 79*119 + 66; hence not 79 divides 9467 by NAT_4:9;
9467 = 83*114 + 5; hence not 83 divides 9467 by NAT_4:9;
9467 = 89*106 + 33; hence not 89 divides 9467 by NAT_4:9;
9467 = 97*97 + 58; hence not 97 divides 9467 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9467 & n is prime
holds not n divides 9467 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9473 is prime
proof
now
9473 = 2*4736 + 1; hence not 2 divides 9473 by NAT_4:9;
9473 = 3*3157 + 2; hence not 3 divides 9473 by NAT_4:9;
9473 = 5*1894 + 3; hence not 5 divides 9473 by NAT_4:9;
9473 = 7*1353 + 2; hence not 7 divides 9473 by NAT_4:9;
9473 = 11*861 + 2; hence not 11 divides 9473 by NAT_4:9;
9473 = 13*728 + 9; hence not 13 divides 9473 by NAT_4:9;
9473 = 17*557 + 4; hence not 17 divides 9473 by NAT_4:9;
9473 = 19*498 + 11; hence not 19 divides 9473 by NAT_4:9;
9473 = 23*411 + 20; hence not 23 divides 9473 by NAT_4:9;
9473 = 29*326 + 19; hence not 29 divides 9473 by NAT_4:9;
9473 = 31*305 + 18; hence not 31 divides 9473 by NAT_4:9;
9473 = 37*256 + 1; hence not 37 divides 9473 by NAT_4:9;
9473 = 41*231 + 2; hence not 41 divides 9473 by NAT_4:9;
9473 = 43*220 + 13; hence not 43 divides 9473 by NAT_4:9;
9473 = 47*201 + 26; hence not 47 divides 9473 by NAT_4:9;
9473 = 53*178 + 39; hence not 53 divides 9473 by NAT_4:9;
9473 = 59*160 + 33; hence not 59 divides 9473 by NAT_4:9;
9473 = 61*155 + 18; hence not 61 divides 9473 by NAT_4:9;
9473 = 67*141 + 26; hence not 67 divides 9473 by NAT_4:9;
9473 = 71*133 + 30; hence not 71 divides 9473 by NAT_4:9;
9473 = 73*129 + 56; hence not 73 divides 9473 by NAT_4:9;
9473 = 79*119 + 72; hence not 79 divides 9473 by NAT_4:9;
9473 = 83*114 + 11; hence not 83 divides 9473 by NAT_4:9;
9473 = 89*106 + 39; hence not 89 divides 9473 by NAT_4:9;
9473 = 97*97 + 64; hence not 97 divides 9473 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9473 & n is prime
holds not n divides 9473 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9479 is prime
proof
now
9479 = 2*4739 + 1; hence not 2 divides 9479 by NAT_4:9;
9479 = 3*3159 + 2; hence not 3 divides 9479 by NAT_4:9;
9479 = 5*1895 + 4; hence not 5 divides 9479 by NAT_4:9;
9479 = 7*1354 + 1; hence not 7 divides 9479 by NAT_4:9;
9479 = 11*861 + 8; hence not 11 divides 9479 by NAT_4:9;
9479 = 13*729 + 2; hence not 13 divides 9479 by NAT_4:9;
9479 = 17*557 + 10; hence not 17 divides 9479 by NAT_4:9;
9479 = 19*498 + 17; hence not 19 divides 9479 by NAT_4:9;
9479 = 23*412 + 3; hence not 23 divides 9479 by NAT_4:9;
9479 = 29*326 + 25; hence not 29 divides 9479 by NAT_4:9;
9479 = 31*305 + 24; hence not 31 divides 9479 by NAT_4:9;
9479 = 37*256 + 7; hence not 37 divides 9479 by NAT_4:9;
9479 = 41*231 + 8; hence not 41 divides 9479 by NAT_4:9;
9479 = 43*220 + 19; hence not 43 divides 9479 by NAT_4:9;
9479 = 47*201 + 32; hence not 47 divides 9479 by NAT_4:9;
9479 = 53*178 + 45; hence not 53 divides 9479 by NAT_4:9;
9479 = 59*160 + 39; hence not 59 divides 9479 by NAT_4:9;
9479 = 61*155 + 24; hence not 61 divides 9479 by NAT_4:9;
9479 = 67*141 + 32; hence not 67 divides 9479 by NAT_4:9;
9479 = 71*133 + 36; hence not 71 divides 9479 by NAT_4:9;
9479 = 73*129 + 62; hence not 73 divides 9479 by NAT_4:9;
9479 = 79*119 + 78; hence not 79 divides 9479 by NAT_4:9;
9479 = 83*114 + 17; hence not 83 divides 9479 by NAT_4:9;
9479 = 89*106 + 45; hence not 89 divides 9479 by NAT_4:9;
9479 = 97*97 + 70; hence not 97 divides 9479 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9479 & n is prime
holds not n divides 9479 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9491 is prime
proof
now
9491 = 2*4745 + 1; hence not 2 divides 9491 by NAT_4:9;
9491 = 3*3163 + 2; hence not 3 divides 9491 by NAT_4:9;
9491 = 5*1898 + 1; hence not 5 divides 9491 by NAT_4:9;
9491 = 7*1355 + 6; hence not 7 divides 9491 by NAT_4:9;
9491 = 11*862 + 9; hence not 11 divides 9491 by NAT_4:9;
9491 = 13*730 + 1; hence not 13 divides 9491 by NAT_4:9;
9491 = 17*558 + 5; hence not 17 divides 9491 by NAT_4:9;
9491 = 19*499 + 10; hence not 19 divides 9491 by NAT_4:9;
9491 = 23*412 + 15; hence not 23 divides 9491 by NAT_4:9;
9491 = 29*327 + 8; hence not 29 divides 9491 by NAT_4:9;
9491 = 31*306 + 5; hence not 31 divides 9491 by NAT_4:9;
9491 = 37*256 + 19; hence not 37 divides 9491 by NAT_4:9;
9491 = 41*231 + 20; hence not 41 divides 9491 by NAT_4:9;
9491 = 43*220 + 31; hence not 43 divides 9491 by NAT_4:9;
9491 = 47*201 + 44; hence not 47 divides 9491 by NAT_4:9;
9491 = 53*179 + 4; hence not 53 divides 9491 by NAT_4:9;
9491 = 59*160 + 51; hence not 59 divides 9491 by NAT_4:9;
9491 = 61*155 + 36; hence not 61 divides 9491 by NAT_4:9;
9491 = 67*141 + 44; hence not 67 divides 9491 by NAT_4:9;
9491 = 71*133 + 48; hence not 71 divides 9491 by NAT_4:9;
9491 = 73*130 + 1; hence not 73 divides 9491 by NAT_4:9;
9491 = 79*120 + 11; hence not 79 divides 9491 by NAT_4:9;
9491 = 83*114 + 29; hence not 83 divides 9491 by NAT_4:9;
9491 = 89*106 + 57; hence not 89 divides 9491 by NAT_4:9;
9491 = 97*97 + 82; hence not 97 divides 9491 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9491 & n is prime
holds not n divides 9491 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9497 is prime
proof
now
9497 = 2*4748 + 1; hence not 2 divides 9497 by NAT_4:9;
9497 = 3*3165 + 2; hence not 3 divides 9497 by NAT_4:9;
9497 = 5*1899 + 2; hence not 5 divides 9497 by NAT_4:9;
9497 = 7*1356 + 5; hence not 7 divides 9497 by NAT_4:9;
9497 = 11*863 + 4; hence not 11 divides 9497 by NAT_4:9;
9497 = 13*730 + 7; hence not 13 divides 9497 by NAT_4:9;
9497 = 17*558 + 11; hence not 17 divides 9497 by NAT_4:9;
9497 = 19*499 + 16; hence not 19 divides 9497 by NAT_4:9;
9497 = 23*412 + 21; hence not 23 divides 9497 by NAT_4:9;
9497 = 29*327 + 14; hence not 29 divides 9497 by NAT_4:9;
9497 = 31*306 + 11; hence not 31 divides 9497 by NAT_4:9;
9497 = 37*256 + 25; hence not 37 divides 9497 by NAT_4:9;
9497 = 41*231 + 26; hence not 41 divides 9497 by NAT_4:9;
9497 = 43*220 + 37; hence not 43 divides 9497 by NAT_4:9;
9497 = 47*202 + 3; hence not 47 divides 9497 by NAT_4:9;
9497 = 53*179 + 10; hence not 53 divides 9497 by NAT_4:9;
9497 = 59*160 + 57; hence not 59 divides 9497 by NAT_4:9;
9497 = 61*155 + 42; hence not 61 divides 9497 by NAT_4:9;
9497 = 67*141 + 50; hence not 67 divides 9497 by NAT_4:9;
9497 = 71*133 + 54; hence not 71 divides 9497 by NAT_4:9;
9497 = 73*130 + 7; hence not 73 divides 9497 by NAT_4:9;
9497 = 79*120 + 17; hence not 79 divides 9497 by NAT_4:9;
9497 = 83*114 + 35; hence not 83 divides 9497 by NAT_4:9;
9497 = 89*106 + 63; hence not 89 divides 9497 by NAT_4:9;
9497 = 97*97 + 88; hence not 97 divides 9497 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9497 & n is prime
holds not n divides 9497 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9511 is prime
proof
now
9511 = 2*4755 + 1; hence not 2 divides 9511 by NAT_4:9;
9511 = 3*3170 + 1; hence not 3 divides 9511 by NAT_4:9;
9511 = 5*1902 + 1; hence not 5 divides 9511 by NAT_4:9;
9511 = 7*1358 + 5; hence not 7 divides 9511 by NAT_4:9;
9511 = 11*864 + 7; hence not 11 divides 9511 by NAT_4:9;
9511 = 13*731 + 8; hence not 13 divides 9511 by NAT_4:9;
9511 = 17*559 + 8; hence not 17 divides 9511 by NAT_4:9;
9511 = 19*500 + 11; hence not 19 divides 9511 by NAT_4:9;
9511 = 23*413 + 12; hence not 23 divides 9511 by NAT_4:9;
9511 = 29*327 + 28; hence not 29 divides 9511 by NAT_4:9;
9511 = 31*306 + 25; hence not 31 divides 9511 by NAT_4:9;
9511 = 37*257 + 2; hence not 37 divides 9511 by NAT_4:9;
9511 = 41*231 + 40; hence not 41 divides 9511 by NAT_4:9;
9511 = 43*221 + 8; hence not 43 divides 9511 by NAT_4:9;
9511 = 47*202 + 17; hence not 47 divides 9511 by NAT_4:9;
9511 = 53*179 + 24; hence not 53 divides 9511 by NAT_4:9;
9511 = 59*161 + 12; hence not 59 divides 9511 by NAT_4:9;
9511 = 61*155 + 56; hence not 61 divides 9511 by NAT_4:9;
9511 = 67*141 + 64; hence not 67 divides 9511 by NAT_4:9;
9511 = 71*133 + 68; hence not 71 divides 9511 by NAT_4:9;
9511 = 73*130 + 21; hence not 73 divides 9511 by NAT_4:9;
9511 = 79*120 + 31; hence not 79 divides 9511 by NAT_4:9;
9511 = 83*114 + 49; hence not 83 divides 9511 by NAT_4:9;
9511 = 89*106 + 77; hence not 89 divides 9511 by NAT_4:9;
9511 = 97*98 + 5; hence not 97 divides 9511 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9511 & n is prime
holds not n divides 9511 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9521 is prime
proof
now
9521 = 2*4760 + 1; hence not 2 divides 9521 by NAT_4:9;
9521 = 3*3173 + 2; hence not 3 divides 9521 by NAT_4:9;
9521 = 5*1904 + 1; hence not 5 divides 9521 by NAT_4:9;
9521 = 7*1360 + 1; hence not 7 divides 9521 by NAT_4:9;
9521 = 11*865 + 6; hence not 11 divides 9521 by NAT_4:9;
9521 = 13*732 + 5; hence not 13 divides 9521 by NAT_4:9;
9521 = 17*560 + 1; hence not 17 divides 9521 by NAT_4:9;
9521 = 19*501 + 2; hence not 19 divides 9521 by NAT_4:9;
9521 = 23*413 + 22; hence not 23 divides 9521 by NAT_4:9;
9521 = 29*328 + 9; hence not 29 divides 9521 by NAT_4:9;
9521 = 31*307 + 4; hence not 31 divides 9521 by NAT_4:9;
9521 = 37*257 + 12; hence not 37 divides 9521 by NAT_4:9;
9521 = 41*232 + 9; hence not 41 divides 9521 by NAT_4:9;
9521 = 43*221 + 18; hence not 43 divides 9521 by NAT_4:9;
9521 = 47*202 + 27; hence not 47 divides 9521 by NAT_4:9;
9521 = 53*179 + 34; hence not 53 divides 9521 by NAT_4:9;
9521 = 59*161 + 22; hence not 59 divides 9521 by NAT_4:9;
9521 = 61*156 + 5; hence not 61 divides 9521 by NAT_4:9;
9521 = 67*142 + 7; hence not 67 divides 9521 by NAT_4:9;
9521 = 71*134 + 7; hence not 71 divides 9521 by NAT_4:9;
9521 = 73*130 + 31; hence not 73 divides 9521 by NAT_4:9;
9521 = 79*120 + 41; hence not 79 divides 9521 by NAT_4:9;
9521 = 83*114 + 59; hence not 83 divides 9521 by NAT_4:9;
9521 = 89*106 + 87; hence not 89 divides 9521 by NAT_4:9;
9521 = 97*98 + 15; hence not 97 divides 9521 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9521 & n is prime
holds not n divides 9521 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9533 is prime
proof
now
9533 = 2*4766 + 1; hence not 2 divides 9533 by NAT_4:9;
9533 = 3*3177 + 2; hence not 3 divides 9533 by NAT_4:9;
9533 = 5*1906 + 3; hence not 5 divides 9533 by NAT_4:9;
9533 = 7*1361 + 6; hence not 7 divides 9533 by NAT_4:9;
9533 = 11*866 + 7; hence not 11 divides 9533 by NAT_4:9;
9533 = 13*733 + 4; hence not 13 divides 9533 by NAT_4:9;
9533 = 17*560 + 13; hence not 17 divides 9533 by NAT_4:9;
9533 = 19*501 + 14; hence not 19 divides 9533 by NAT_4:9;
9533 = 23*414 + 11; hence not 23 divides 9533 by NAT_4:9;
9533 = 29*328 + 21; hence not 29 divides 9533 by NAT_4:9;
9533 = 31*307 + 16; hence not 31 divides 9533 by NAT_4:9;
9533 = 37*257 + 24; hence not 37 divides 9533 by NAT_4:9;
9533 = 41*232 + 21; hence not 41 divides 9533 by NAT_4:9;
9533 = 43*221 + 30; hence not 43 divides 9533 by NAT_4:9;
9533 = 47*202 + 39; hence not 47 divides 9533 by NAT_4:9;
9533 = 53*179 + 46; hence not 53 divides 9533 by NAT_4:9;
9533 = 59*161 + 34; hence not 59 divides 9533 by NAT_4:9;
9533 = 61*156 + 17; hence not 61 divides 9533 by NAT_4:9;
9533 = 67*142 + 19; hence not 67 divides 9533 by NAT_4:9;
9533 = 71*134 + 19; hence not 71 divides 9533 by NAT_4:9;
9533 = 73*130 + 43; hence not 73 divides 9533 by NAT_4:9;
9533 = 79*120 + 53; hence not 79 divides 9533 by NAT_4:9;
9533 = 83*114 + 71; hence not 83 divides 9533 by NAT_4:9;
9533 = 89*107 + 10; hence not 89 divides 9533 by NAT_4:9;
9533 = 97*98 + 27; hence not 97 divides 9533 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9533 & n is prime
holds not n divides 9533 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9539 is prime
proof
now
9539 = 2*4769 + 1; hence not 2 divides 9539 by NAT_4:9;
9539 = 3*3179 + 2; hence not 3 divides 9539 by NAT_4:9;
9539 = 5*1907 + 4; hence not 5 divides 9539 by NAT_4:9;
9539 = 7*1362 + 5; hence not 7 divides 9539 by NAT_4:9;
9539 = 11*867 + 2; hence not 11 divides 9539 by NAT_4:9;
9539 = 13*733 + 10; hence not 13 divides 9539 by NAT_4:9;
9539 = 17*561 + 2; hence not 17 divides 9539 by NAT_4:9;
9539 = 19*502 + 1; hence not 19 divides 9539 by NAT_4:9;
9539 = 23*414 + 17; hence not 23 divides 9539 by NAT_4:9;
9539 = 29*328 + 27; hence not 29 divides 9539 by NAT_4:9;
9539 = 31*307 + 22; hence not 31 divides 9539 by NAT_4:9;
9539 = 37*257 + 30; hence not 37 divides 9539 by NAT_4:9;
9539 = 41*232 + 27; hence not 41 divides 9539 by NAT_4:9;
9539 = 43*221 + 36; hence not 43 divides 9539 by NAT_4:9;
9539 = 47*202 + 45; hence not 47 divides 9539 by NAT_4:9;
9539 = 53*179 + 52; hence not 53 divides 9539 by NAT_4:9;
9539 = 59*161 + 40; hence not 59 divides 9539 by NAT_4:9;
9539 = 61*156 + 23; hence not 61 divides 9539 by NAT_4:9;
9539 = 67*142 + 25; hence not 67 divides 9539 by NAT_4:9;
9539 = 71*134 + 25; hence not 71 divides 9539 by NAT_4:9;
9539 = 73*130 + 49; hence not 73 divides 9539 by NAT_4:9;
9539 = 79*120 + 59; hence not 79 divides 9539 by NAT_4:9;
9539 = 83*114 + 77; hence not 83 divides 9539 by NAT_4:9;
9539 = 89*107 + 16; hence not 89 divides 9539 by NAT_4:9;
9539 = 97*98 + 33; hence not 97 divides 9539 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9539 & n is prime
holds not n divides 9539 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9547 is prime
proof
now
9547 = 2*4773 + 1; hence not 2 divides 9547 by NAT_4:9;
9547 = 3*3182 + 1; hence not 3 divides 9547 by NAT_4:9;
9547 = 5*1909 + 2; hence not 5 divides 9547 by NAT_4:9;
9547 = 7*1363 + 6; hence not 7 divides 9547 by NAT_4:9;
9547 = 11*867 + 10; hence not 11 divides 9547 by NAT_4:9;
9547 = 13*734 + 5; hence not 13 divides 9547 by NAT_4:9;
9547 = 17*561 + 10; hence not 17 divides 9547 by NAT_4:9;
9547 = 19*502 + 9; hence not 19 divides 9547 by NAT_4:9;
9547 = 23*415 + 2; hence not 23 divides 9547 by NAT_4:9;
9547 = 29*329 + 6; hence not 29 divides 9547 by NAT_4:9;
9547 = 31*307 + 30; hence not 31 divides 9547 by NAT_4:9;
9547 = 37*258 + 1; hence not 37 divides 9547 by NAT_4:9;
9547 = 41*232 + 35; hence not 41 divides 9547 by NAT_4:9;
9547 = 43*222 + 1; hence not 43 divides 9547 by NAT_4:9;
9547 = 47*203 + 6; hence not 47 divides 9547 by NAT_4:9;
9547 = 53*180 + 7; hence not 53 divides 9547 by NAT_4:9;
9547 = 59*161 + 48; hence not 59 divides 9547 by NAT_4:9;
9547 = 61*156 + 31; hence not 61 divides 9547 by NAT_4:9;
9547 = 67*142 + 33; hence not 67 divides 9547 by NAT_4:9;
9547 = 71*134 + 33; hence not 71 divides 9547 by NAT_4:9;
9547 = 73*130 + 57; hence not 73 divides 9547 by NAT_4:9;
9547 = 79*120 + 67; hence not 79 divides 9547 by NAT_4:9;
9547 = 83*115 + 2; hence not 83 divides 9547 by NAT_4:9;
9547 = 89*107 + 24; hence not 89 divides 9547 by NAT_4:9;
9547 = 97*98 + 41; hence not 97 divides 9547 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9547 & n is prime
holds not n divides 9547 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9551 is prime
proof
now
9551 = 2*4775 + 1; hence not 2 divides 9551 by NAT_4:9;
9551 = 3*3183 + 2; hence not 3 divides 9551 by NAT_4:9;
9551 = 5*1910 + 1; hence not 5 divides 9551 by NAT_4:9;
9551 = 7*1364 + 3; hence not 7 divides 9551 by NAT_4:9;
9551 = 11*868 + 3; hence not 11 divides 9551 by NAT_4:9;
9551 = 13*734 + 9; hence not 13 divides 9551 by NAT_4:9;
9551 = 17*561 + 14; hence not 17 divides 9551 by NAT_4:9;
9551 = 19*502 + 13; hence not 19 divides 9551 by NAT_4:9;
9551 = 23*415 + 6; hence not 23 divides 9551 by NAT_4:9;
9551 = 29*329 + 10; hence not 29 divides 9551 by NAT_4:9;
9551 = 31*308 + 3; hence not 31 divides 9551 by NAT_4:9;
9551 = 37*258 + 5; hence not 37 divides 9551 by NAT_4:9;
9551 = 41*232 + 39; hence not 41 divides 9551 by NAT_4:9;
9551 = 43*222 + 5; hence not 43 divides 9551 by NAT_4:9;
9551 = 47*203 + 10; hence not 47 divides 9551 by NAT_4:9;
9551 = 53*180 + 11; hence not 53 divides 9551 by NAT_4:9;
9551 = 59*161 + 52; hence not 59 divides 9551 by NAT_4:9;
9551 = 61*156 + 35; hence not 61 divides 9551 by NAT_4:9;
9551 = 67*142 + 37; hence not 67 divides 9551 by NAT_4:9;
9551 = 71*134 + 37; hence not 71 divides 9551 by NAT_4:9;
9551 = 73*130 + 61; hence not 73 divides 9551 by NAT_4:9;
9551 = 79*120 + 71; hence not 79 divides 9551 by NAT_4:9;
9551 = 83*115 + 6; hence not 83 divides 9551 by NAT_4:9;
9551 = 89*107 + 28; hence not 89 divides 9551 by NAT_4:9;
9551 = 97*98 + 45; hence not 97 divides 9551 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9551 & n is prime
holds not n divides 9551 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 35
theorem
9587 is prime
proof
now
9587 = 2*4793 + 1; hence not 2 divides 9587 by NAT_4:9;
9587 = 3*3195 + 2; hence not 3 divides 9587 by NAT_4:9;
9587 = 5*1917 + 2; hence not 5 divides 9587 by NAT_4:9;
9587 = 7*1369 + 4; hence not 7 divides 9587 by NAT_4:9;
9587 = 11*871 + 6; hence not 11 divides 9587 by NAT_4:9;
9587 = 13*737 + 6; hence not 13 divides 9587 by NAT_4:9;
9587 = 17*563 + 16; hence not 17 divides 9587 by NAT_4:9;
9587 = 19*504 + 11; hence not 19 divides 9587 by NAT_4:9;
9587 = 23*416 + 19; hence not 23 divides 9587 by NAT_4:9;
9587 = 29*330 + 17; hence not 29 divides 9587 by NAT_4:9;
9587 = 31*309 + 8; hence not 31 divides 9587 by NAT_4:9;
9587 = 37*259 + 4; hence not 37 divides 9587 by NAT_4:9;
9587 = 41*233 + 34; hence not 41 divides 9587 by NAT_4:9;
9587 = 43*222 + 41; hence not 43 divides 9587 by NAT_4:9;
9587 = 47*203 + 46; hence not 47 divides 9587 by NAT_4:9;
9587 = 53*180 + 47; hence not 53 divides 9587 by NAT_4:9;
9587 = 59*162 + 29; hence not 59 divides 9587 by NAT_4:9;
9587 = 61*157 + 10; hence not 61 divides 9587 by NAT_4:9;
9587 = 67*143 + 6; hence not 67 divides 9587 by NAT_4:9;
9587 = 71*135 + 2; hence not 71 divides 9587 by NAT_4:9;
9587 = 73*131 + 24; hence not 73 divides 9587 by NAT_4:9;
9587 = 79*121 + 28; hence not 79 divides 9587 by NAT_4:9;
9587 = 83*115 + 42; hence not 83 divides 9587 by NAT_4:9;
9587 = 89*107 + 64; hence not 89 divides 9587 by NAT_4:9;
9587 = 97*98 + 81; hence not 97 divides 9587 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9587 & n is prime
holds not n divides 9587 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9601 is prime
proof
now
9601 = 2*4800 + 1; hence not 2 divides 9601 by NAT_4:9;
9601 = 3*3200 + 1; hence not 3 divides 9601 by NAT_4:9;
9601 = 5*1920 + 1; hence not 5 divides 9601 by NAT_4:9;
9601 = 7*1371 + 4; hence not 7 divides 9601 by NAT_4:9;
9601 = 11*872 + 9; hence not 11 divides 9601 by NAT_4:9;
9601 = 13*738 + 7; hence not 13 divides 9601 by NAT_4:9;
9601 = 17*564 + 13; hence not 17 divides 9601 by NAT_4:9;
9601 = 19*505 + 6; hence not 19 divides 9601 by NAT_4:9;
9601 = 23*417 + 10; hence not 23 divides 9601 by NAT_4:9;
9601 = 29*331 + 2; hence not 29 divides 9601 by NAT_4:9;
9601 = 31*309 + 22; hence not 31 divides 9601 by NAT_4:9;
9601 = 37*259 + 18; hence not 37 divides 9601 by NAT_4:9;
9601 = 41*234 + 7; hence not 41 divides 9601 by NAT_4:9;
9601 = 43*223 + 12; hence not 43 divides 9601 by NAT_4:9;
9601 = 47*204 + 13; hence not 47 divides 9601 by NAT_4:9;
9601 = 53*181 + 8; hence not 53 divides 9601 by NAT_4:9;
9601 = 59*162 + 43; hence not 59 divides 9601 by NAT_4:9;
9601 = 61*157 + 24; hence not 61 divides 9601 by NAT_4:9;
9601 = 67*143 + 20; hence not 67 divides 9601 by NAT_4:9;
9601 = 71*135 + 16; hence not 71 divides 9601 by NAT_4:9;
9601 = 73*131 + 38; hence not 73 divides 9601 by NAT_4:9;
9601 = 79*121 + 42; hence not 79 divides 9601 by NAT_4:9;
9601 = 83*115 + 56; hence not 83 divides 9601 by NAT_4:9;
9601 = 89*107 + 78; hence not 89 divides 9601 by NAT_4:9;
9601 = 97*98 + 95; hence not 97 divides 9601 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9601 & n is prime
holds not n divides 9601 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9613 is prime
proof
now
9613 = 2*4806 + 1; hence not 2 divides 9613 by NAT_4:9;
9613 = 3*3204 + 1; hence not 3 divides 9613 by NAT_4:9;
9613 = 5*1922 + 3; hence not 5 divides 9613 by NAT_4:9;
9613 = 7*1373 + 2; hence not 7 divides 9613 by NAT_4:9;
9613 = 11*873 + 10; hence not 11 divides 9613 by NAT_4:9;
9613 = 13*739 + 6; hence not 13 divides 9613 by NAT_4:9;
9613 = 17*565 + 8; hence not 17 divides 9613 by NAT_4:9;
9613 = 19*505 + 18; hence not 19 divides 9613 by NAT_4:9;
9613 = 23*417 + 22; hence not 23 divides 9613 by NAT_4:9;
9613 = 29*331 + 14; hence not 29 divides 9613 by NAT_4:9;
9613 = 31*310 + 3; hence not 31 divides 9613 by NAT_4:9;
9613 = 37*259 + 30; hence not 37 divides 9613 by NAT_4:9;
9613 = 41*234 + 19; hence not 41 divides 9613 by NAT_4:9;
9613 = 43*223 + 24; hence not 43 divides 9613 by NAT_4:9;
9613 = 47*204 + 25; hence not 47 divides 9613 by NAT_4:9;
9613 = 53*181 + 20; hence not 53 divides 9613 by NAT_4:9;
9613 = 59*162 + 55; hence not 59 divides 9613 by NAT_4:9;
9613 = 61*157 + 36; hence not 61 divides 9613 by NAT_4:9;
9613 = 67*143 + 32; hence not 67 divides 9613 by NAT_4:9;
9613 = 71*135 + 28; hence not 71 divides 9613 by NAT_4:9;
9613 = 73*131 + 50; hence not 73 divides 9613 by NAT_4:9;
9613 = 79*121 + 54; hence not 79 divides 9613 by NAT_4:9;
9613 = 83*115 + 68; hence not 83 divides 9613 by NAT_4:9;
9613 = 89*108 + 1; hence not 89 divides 9613 by NAT_4:9;
9613 = 97*99 + 10; hence not 97 divides 9613 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9613 & n is prime
holds not n divides 9613 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9619 is prime
proof
now
9619 = 2*4809 + 1; hence not 2 divides 9619 by NAT_4:9;
9619 = 3*3206 + 1; hence not 3 divides 9619 by NAT_4:9;
9619 = 5*1923 + 4; hence not 5 divides 9619 by NAT_4:9;
9619 = 7*1374 + 1; hence not 7 divides 9619 by NAT_4:9;
9619 = 11*874 + 5; hence not 11 divides 9619 by NAT_4:9;
9619 = 13*739 + 12; hence not 13 divides 9619 by NAT_4:9;
9619 = 17*565 + 14; hence not 17 divides 9619 by NAT_4:9;
9619 = 19*506 + 5; hence not 19 divides 9619 by NAT_4:9;
9619 = 23*418 + 5; hence not 23 divides 9619 by NAT_4:9;
9619 = 29*331 + 20; hence not 29 divides 9619 by NAT_4:9;
9619 = 31*310 + 9; hence not 31 divides 9619 by NAT_4:9;
9619 = 37*259 + 36; hence not 37 divides 9619 by NAT_4:9;
9619 = 41*234 + 25; hence not 41 divides 9619 by NAT_4:9;
9619 = 43*223 + 30; hence not 43 divides 9619 by NAT_4:9;
9619 = 47*204 + 31; hence not 47 divides 9619 by NAT_4:9;
9619 = 53*181 + 26; hence not 53 divides 9619 by NAT_4:9;
9619 = 59*163 + 2; hence not 59 divides 9619 by NAT_4:9;
9619 = 61*157 + 42; hence not 61 divides 9619 by NAT_4:9;
9619 = 67*143 + 38; hence not 67 divides 9619 by NAT_4:9;
9619 = 71*135 + 34; hence not 71 divides 9619 by NAT_4:9;
9619 = 73*131 + 56; hence not 73 divides 9619 by NAT_4:9;
9619 = 79*121 + 60; hence not 79 divides 9619 by NAT_4:9;
9619 = 83*115 + 74; hence not 83 divides 9619 by NAT_4:9;
9619 = 89*108 + 7; hence not 89 divides 9619 by NAT_4:9;
9619 = 97*99 + 16; hence not 97 divides 9619 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9619 & n is prime
holds not n divides 9619 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9623 is prime
proof
now
9623 = 2*4811 + 1; hence not 2 divides 9623 by NAT_4:9;
9623 = 3*3207 + 2; hence not 3 divides 9623 by NAT_4:9;
9623 = 5*1924 + 3; hence not 5 divides 9623 by NAT_4:9;
9623 = 7*1374 + 5; hence not 7 divides 9623 by NAT_4:9;
9623 = 11*874 + 9; hence not 11 divides 9623 by NAT_4:9;
9623 = 13*740 + 3; hence not 13 divides 9623 by NAT_4:9;
9623 = 17*566 + 1; hence not 17 divides 9623 by NAT_4:9;
9623 = 19*506 + 9; hence not 19 divides 9623 by NAT_4:9;
9623 = 23*418 + 9; hence not 23 divides 9623 by NAT_4:9;
9623 = 29*331 + 24; hence not 29 divides 9623 by NAT_4:9;
9623 = 31*310 + 13; hence not 31 divides 9623 by NAT_4:9;
9623 = 37*260 + 3; hence not 37 divides 9623 by NAT_4:9;
9623 = 41*234 + 29; hence not 41 divides 9623 by NAT_4:9;
9623 = 43*223 + 34; hence not 43 divides 9623 by NAT_4:9;
9623 = 47*204 + 35; hence not 47 divides 9623 by NAT_4:9;
9623 = 53*181 + 30; hence not 53 divides 9623 by NAT_4:9;
9623 = 59*163 + 6; hence not 59 divides 9623 by NAT_4:9;
9623 = 61*157 + 46; hence not 61 divides 9623 by NAT_4:9;
9623 = 67*143 + 42; hence not 67 divides 9623 by NAT_4:9;
9623 = 71*135 + 38; hence not 71 divides 9623 by NAT_4:9;
9623 = 73*131 + 60; hence not 73 divides 9623 by NAT_4:9;
9623 = 79*121 + 64; hence not 79 divides 9623 by NAT_4:9;
9623 = 83*115 + 78; hence not 83 divides 9623 by NAT_4:9;
9623 = 89*108 + 11; hence not 89 divides 9623 by NAT_4:9;
9623 = 97*99 + 20; hence not 97 divides 9623 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9623 & n is prime
holds not n divides 9623 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9629 is prime
proof
now
9629 = 2*4814 + 1; hence not 2 divides 9629 by NAT_4:9;
9629 = 3*3209 + 2; hence not 3 divides 9629 by NAT_4:9;
9629 = 5*1925 + 4; hence not 5 divides 9629 by NAT_4:9;
9629 = 7*1375 + 4; hence not 7 divides 9629 by NAT_4:9;
9629 = 11*875 + 4; hence not 11 divides 9629 by NAT_4:9;
9629 = 13*740 + 9; hence not 13 divides 9629 by NAT_4:9;
9629 = 17*566 + 7; hence not 17 divides 9629 by NAT_4:9;
9629 = 19*506 + 15; hence not 19 divides 9629 by NAT_4:9;
9629 = 23*418 + 15; hence not 23 divides 9629 by NAT_4:9;
9629 = 29*332 + 1; hence not 29 divides 9629 by NAT_4:9;
9629 = 31*310 + 19; hence not 31 divides 9629 by NAT_4:9;
9629 = 37*260 + 9; hence not 37 divides 9629 by NAT_4:9;
9629 = 41*234 + 35; hence not 41 divides 9629 by NAT_4:9;
9629 = 43*223 + 40; hence not 43 divides 9629 by NAT_4:9;
9629 = 47*204 + 41; hence not 47 divides 9629 by NAT_4:9;
9629 = 53*181 + 36; hence not 53 divides 9629 by NAT_4:9;
9629 = 59*163 + 12; hence not 59 divides 9629 by NAT_4:9;
9629 = 61*157 + 52; hence not 61 divides 9629 by NAT_4:9;
9629 = 67*143 + 48; hence not 67 divides 9629 by NAT_4:9;
9629 = 71*135 + 44; hence not 71 divides 9629 by NAT_4:9;
9629 = 73*131 + 66; hence not 73 divides 9629 by NAT_4:9;
9629 = 79*121 + 70; hence not 79 divides 9629 by NAT_4:9;
9629 = 83*116 + 1; hence not 83 divides 9629 by NAT_4:9;
9629 = 89*108 + 17; hence not 89 divides 9629 by NAT_4:9;
9629 = 97*99 + 26; hence not 97 divides 9629 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9629 & n is prime
holds not n divides 9629 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9631 is prime
proof
now
9631 = 2*4815 + 1; hence not 2 divides 9631 by NAT_4:9;
9631 = 3*3210 + 1; hence not 3 divides 9631 by NAT_4:9;
9631 = 5*1926 + 1; hence not 5 divides 9631 by NAT_4:9;
9631 = 7*1375 + 6; hence not 7 divides 9631 by NAT_4:9;
9631 = 11*875 + 6; hence not 11 divides 9631 by NAT_4:9;
9631 = 13*740 + 11; hence not 13 divides 9631 by NAT_4:9;
9631 = 17*566 + 9; hence not 17 divides 9631 by NAT_4:9;
9631 = 19*506 + 17; hence not 19 divides 9631 by NAT_4:9;
9631 = 23*418 + 17; hence not 23 divides 9631 by NAT_4:9;
9631 = 29*332 + 3; hence not 29 divides 9631 by NAT_4:9;
9631 = 31*310 + 21; hence not 31 divides 9631 by NAT_4:9;
9631 = 37*260 + 11; hence not 37 divides 9631 by NAT_4:9;
9631 = 41*234 + 37; hence not 41 divides 9631 by NAT_4:9;
9631 = 43*223 + 42; hence not 43 divides 9631 by NAT_4:9;
9631 = 47*204 + 43; hence not 47 divides 9631 by NAT_4:9;
9631 = 53*181 + 38; hence not 53 divides 9631 by NAT_4:9;
9631 = 59*163 + 14; hence not 59 divides 9631 by NAT_4:9;
9631 = 61*157 + 54; hence not 61 divides 9631 by NAT_4:9;
9631 = 67*143 + 50; hence not 67 divides 9631 by NAT_4:9;
9631 = 71*135 + 46; hence not 71 divides 9631 by NAT_4:9;
9631 = 73*131 + 68; hence not 73 divides 9631 by NAT_4:9;
9631 = 79*121 + 72; hence not 79 divides 9631 by NAT_4:9;
9631 = 83*116 + 3; hence not 83 divides 9631 by NAT_4:9;
9631 = 89*108 + 19; hence not 89 divides 9631 by NAT_4:9;
9631 = 97*99 + 28; hence not 97 divides 9631 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9631 & n is prime
holds not n divides 9631 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9643 is prime
proof
now
9643 = 2*4821 + 1; hence not 2 divides 9643 by NAT_4:9;
9643 = 3*3214 + 1; hence not 3 divides 9643 by NAT_4:9;
9643 = 5*1928 + 3; hence not 5 divides 9643 by NAT_4:9;
9643 = 7*1377 + 4; hence not 7 divides 9643 by NAT_4:9;
9643 = 11*876 + 7; hence not 11 divides 9643 by NAT_4:9;
9643 = 13*741 + 10; hence not 13 divides 9643 by NAT_4:9;
9643 = 17*567 + 4; hence not 17 divides 9643 by NAT_4:9;
9643 = 19*507 + 10; hence not 19 divides 9643 by NAT_4:9;
9643 = 23*419 + 6; hence not 23 divides 9643 by NAT_4:9;
9643 = 29*332 + 15; hence not 29 divides 9643 by NAT_4:9;
9643 = 31*311 + 2; hence not 31 divides 9643 by NAT_4:9;
9643 = 37*260 + 23; hence not 37 divides 9643 by NAT_4:9;
9643 = 41*235 + 8; hence not 41 divides 9643 by NAT_4:9;
9643 = 43*224 + 11; hence not 43 divides 9643 by NAT_4:9;
9643 = 47*205 + 8; hence not 47 divides 9643 by NAT_4:9;
9643 = 53*181 + 50; hence not 53 divides 9643 by NAT_4:9;
9643 = 59*163 + 26; hence not 59 divides 9643 by NAT_4:9;
9643 = 61*158 + 5; hence not 61 divides 9643 by NAT_4:9;
9643 = 67*143 + 62; hence not 67 divides 9643 by NAT_4:9;
9643 = 71*135 + 58; hence not 71 divides 9643 by NAT_4:9;
9643 = 73*132 + 7; hence not 73 divides 9643 by NAT_4:9;
9643 = 79*122 + 5; hence not 79 divides 9643 by NAT_4:9;
9643 = 83*116 + 15; hence not 83 divides 9643 by NAT_4:9;
9643 = 89*108 + 31; hence not 89 divides 9643 by NAT_4:9;
9643 = 97*99 + 40; hence not 97 divides 9643 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9643 & n is prime
holds not n divides 9643 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9649 is prime
proof
now
9649 = 2*4824 + 1; hence not 2 divides 9649 by NAT_4:9;
9649 = 3*3216 + 1; hence not 3 divides 9649 by NAT_4:9;
9649 = 5*1929 + 4; hence not 5 divides 9649 by NAT_4:9;
9649 = 7*1378 + 3; hence not 7 divides 9649 by NAT_4:9;
9649 = 11*877 + 2; hence not 11 divides 9649 by NAT_4:9;
9649 = 13*742 + 3; hence not 13 divides 9649 by NAT_4:9;
9649 = 17*567 + 10; hence not 17 divides 9649 by NAT_4:9;
9649 = 19*507 + 16; hence not 19 divides 9649 by NAT_4:9;
9649 = 23*419 + 12; hence not 23 divides 9649 by NAT_4:9;
9649 = 29*332 + 21; hence not 29 divides 9649 by NAT_4:9;
9649 = 31*311 + 8; hence not 31 divides 9649 by NAT_4:9;
9649 = 37*260 + 29; hence not 37 divides 9649 by NAT_4:9;
9649 = 41*235 + 14; hence not 41 divides 9649 by NAT_4:9;
9649 = 43*224 + 17; hence not 43 divides 9649 by NAT_4:9;
9649 = 47*205 + 14; hence not 47 divides 9649 by NAT_4:9;
9649 = 53*182 + 3; hence not 53 divides 9649 by NAT_4:9;
9649 = 59*163 + 32; hence not 59 divides 9649 by NAT_4:9;
9649 = 61*158 + 11; hence not 61 divides 9649 by NAT_4:9;
9649 = 67*144 + 1; hence not 67 divides 9649 by NAT_4:9;
9649 = 71*135 + 64; hence not 71 divides 9649 by NAT_4:9;
9649 = 73*132 + 13; hence not 73 divides 9649 by NAT_4:9;
9649 = 79*122 + 11; hence not 79 divides 9649 by NAT_4:9;
9649 = 83*116 + 21; hence not 83 divides 9649 by NAT_4:9;
9649 = 89*108 + 37; hence not 89 divides 9649 by NAT_4:9;
9649 = 97*99 + 46; hence not 97 divides 9649 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9649 & n is prime
holds not n divides 9649 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9661 is prime
proof
now
9661 = 2*4830 + 1; hence not 2 divides 9661 by NAT_4:9;
9661 = 3*3220 + 1; hence not 3 divides 9661 by NAT_4:9;
9661 = 5*1932 + 1; hence not 5 divides 9661 by NAT_4:9;
9661 = 7*1380 + 1; hence not 7 divides 9661 by NAT_4:9;
9661 = 11*878 + 3; hence not 11 divides 9661 by NAT_4:9;
9661 = 13*743 + 2; hence not 13 divides 9661 by NAT_4:9;
9661 = 17*568 + 5; hence not 17 divides 9661 by NAT_4:9;
9661 = 19*508 + 9; hence not 19 divides 9661 by NAT_4:9;
9661 = 23*420 + 1; hence not 23 divides 9661 by NAT_4:9;
9661 = 29*333 + 4; hence not 29 divides 9661 by NAT_4:9;
9661 = 31*311 + 20; hence not 31 divides 9661 by NAT_4:9;
9661 = 37*261 + 4; hence not 37 divides 9661 by NAT_4:9;
9661 = 41*235 + 26; hence not 41 divides 9661 by NAT_4:9;
9661 = 43*224 + 29; hence not 43 divides 9661 by NAT_4:9;
9661 = 47*205 + 26; hence not 47 divides 9661 by NAT_4:9;
9661 = 53*182 + 15; hence not 53 divides 9661 by NAT_4:9;
9661 = 59*163 + 44; hence not 59 divides 9661 by NAT_4:9;
9661 = 61*158 + 23; hence not 61 divides 9661 by NAT_4:9;
9661 = 67*144 + 13; hence not 67 divides 9661 by NAT_4:9;
9661 = 71*136 + 5; hence not 71 divides 9661 by NAT_4:9;
9661 = 73*132 + 25; hence not 73 divides 9661 by NAT_4:9;
9661 = 79*122 + 23; hence not 79 divides 9661 by NAT_4:9;
9661 = 83*116 + 33; hence not 83 divides 9661 by NAT_4:9;
9661 = 89*108 + 49; hence not 89 divides 9661 by NAT_4:9;
9661 = 97*99 + 58; hence not 97 divides 9661 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9661 & n is prime
holds not n divides 9661 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
9677 is prime
proof
now
9677 = 2*4838 + 1; hence not 2 divides 9677 by NAT_4:9;
9677 = 3*3225 + 2; hence not 3 divides 9677 by NAT_4:9;
9677 = 5*1935 + 2; hence not 5 divides 9677 by NAT_4:9;
9677 = 7*1382 + 3; hence not 7 divides 9677 by NAT_4:9;
9677 = 11*879 + 8; hence not 11 divides 9677 by NAT_4:9;
9677 = 13*744 + 5; hence not 13 divides 9677 by NAT_4:9;
9677 = 17*569 + 4; hence not 17 divides 9677 by NAT_4:9;
9677 = 19*509 + 6; hence not 19 divides 9677 by NAT_4:9;
9677 = 23*420 + 17; hence not 23 divides 9677 by NAT_4:9;
9677 = 29*333 + 20; hence not 29 divides 9677 by NAT_4:9;
9677 = 31*312 + 5; hence not 31 divides 9677 by NAT_4:9;
9677 = 37*261 + 20; hence not 37 divides 9677 by NAT_4:9;
9677 = 41*236 + 1; hence not 41 divides 9677 by NAT_4:9;
9677 = 43*225 + 2; hence not 43 divides 9677 by NAT_4:9;
9677 = 47*205 + 42; hence not 47 divides 9677 by NAT_4:9;
9677 = 53*182 + 31; hence not 53 divides 9677 by NAT_4:9;
9677 = 59*164 + 1; hence not 59 divides 9677 by NAT_4:9;
9677 = 61*158 + 39; hence not 61 divides 9677 by NAT_4:9;
9677 = 67*144 + 29; hence not 67 divides 9677 by NAT_4:9;
9677 = 71*136 + 21; hence not 71 divides 9677 by NAT_4:9;
9677 = 73*132 + 41; hence not 73 divides 9677 by NAT_4:9;
9677 = 79*122 + 39; hence not 79 divides 9677 by NAT_4:9;
9677 = 83*116 + 49; hence not 83 divides 9677 by NAT_4:9;
9677 = 89*108 + 65; hence not 89 divides 9677 by NAT_4:9;
9677 = 97*99 + 74; hence not 97 divides 9677 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9677 & n is prime
holds not n divides 9677 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9679 is prime
proof
now
9679 = 2*4839 + 1; hence not 2 divides 9679 by NAT_4:9;
9679 = 3*3226 + 1; hence not 3 divides 9679 by NAT_4:9;
9679 = 5*1935 + 4; hence not 5 divides 9679 by NAT_4:9;
9679 = 7*1382 + 5; hence not 7 divides 9679 by NAT_4:9;
9679 = 11*879 + 10; hence not 11 divides 9679 by NAT_4:9;
9679 = 13*744 + 7; hence not 13 divides 9679 by NAT_4:9;
9679 = 17*569 + 6; hence not 17 divides 9679 by NAT_4:9;
9679 = 19*509 + 8; hence not 19 divides 9679 by NAT_4:9;
9679 = 23*420 + 19; hence not 23 divides 9679 by NAT_4:9;
9679 = 29*333 + 22; hence not 29 divides 9679 by NAT_4:9;
9679 = 31*312 + 7; hence not 31 divides 9679 by NAT_4:9;
9679 = 37*261 + 22; hence not 37 divides 9679 by NAT_4:9;
9679 = 41*236 + 3; hence not 41 divides 9679 by NAT_4:9;
9679 = 43*225 + 4; hence not 43 divides 9679 by NAT_4:9;
9679 = 47*205 + 44; hence not 47 divides 9679 by NAT_4:9;
9679 = 53*182 + 33; hence not 53 divides 9679 by NAT_4:9;
9679 = 59*164 + 3; hence not 59 divides 9679 by NAT_4:9;
9679 = 61*158 + 41; hence not 61 divides 9679 by NAT_4:9;
9679 = 67*144 + 31; hence not 67 divides 9679 by NAT_4:9;
9679 = 71*136 + 23; hence not 71 divides 9679 by NAT_4:9;
9679 = 73*132 + 43; hence not 73 divides 9679 by NAT_4:9;
9679 = 79*122 + 41; hence not 79 divides 9679 by NAT_4:9;
9679 = 83*116 + 51; hence not 83 divides 9679 by NAT_4:9;
9679 = 89*108 + 67; hence not 89 divides 9679 by NAT_4:9;
9679 = 97*99 + 76; hence not 97 divides 9679 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9679 & n is prime
holds not n divides 9679 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9689 is prime
proof
now
9689 = 2*4844 + 1; hence not 2 divides 9689 by NAT_4:9;
9689 = 3*3229 + 2; hence not 3 divides 9689 by NAT_4:9;
9689 = 5*1937 + 4; hence not 5 divides 9689 by NAT_4:9;
9689 = 7*1384 + 1; hence not 7 divides 9689 by NAT_4:9;
9689 = 11*880 + 9; hence not 11 divides 9689 by NAT_4:9;
9689 = 13*745 + 4; hence not 13 divides 9689 by NAT_4:9;
9689 = 17*569 + 16; hence not 17 divides 9689 by NAT_4:9;
9689 = 19*509 + 18; hence not 19 divides 9689 by NAT_4:9;
9689 = 23*421 + 6; hence not 23 divides 9689 by NAT_4:9;
9689 = 29*334 + 3; hence not 29 divides 9689 by NAT_4:9;
9689 = 31*312 + 17; hence not 31 divides 9689 by NAT_4:9;
9689 = 37*261 + 32; hence not 37 divides 9689 by NAT_4:9;
9689 = 41*236 + 13; hence not 41 divides 9689 by NAT_4:9;
9689 = 43*225 + 14; hence not 43 divides 9689 by NAT_4:9;
9689 = 47*206 + 7; hence not 47 divides 9689 by NAT_4:9;
9689 = 53*182 + 43; hence not 53 divides 9689 by NAT_4:9;
9689 = 59*164 + 13; hence not 59 divides 9689 by NAT_4:9;
9689 = 61*158 + 51; hence not 61 divides 9689 by NAT_4:9;
9689 = 67*144 + 41; hence not 67 divides 9689 by NAT_4:9;
9689 = 71*136 + 33; hence not 71 divides 9689 by NAT_4:9;
9689 = 73*132 + 53; hence not 73 divides 9689 by NAT_4:9;
9689 = 79*122 + 51; hence not 79 divides 9689 by NAT_4:9;
9689 = 83*116 + 61; hence not 83 divides 9689 by NAT_4:9;
9689 = 89*108 + 77; hence not 89 divides 9689 by NAT_4:9;
9689 = 97*99 + 86; hence not 97 divides 9689 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9689 & n is prime
holds not n divides 9689 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9697 is prime
proof
now
9697 = 2*4848 + 1; hence not 2 divides 9697 by NAT_4:9;
9697 = 3*3232 + 1; hence not 3 divides 9697 by NAT_4:9;
9697 = 5*1939 + 2; hence not 5 divides 9697 by NAT_4:9;
9697 = 7*1385 + 2; hence not 7 divides 9697 by NAT_4:9;
9697 = 11*881 + 6; hence not 11 divides 9697 by NAT_4:9;
9697 = 13*745 + 12; hence not 13 divides 9697 by NAT_4:9;
9697 = 17*570 + 7; hence not 17 divides 9697 by NAT_4:9;
9697 = 19*510 + 7; hence not 19 divides 9697 by NAT_4:9;
9697 = 23*421 + 14; hence not 23 divides 9697 by NAT_4:9;
9697 = 29*334 + 11; hence not 29 divides 9697 by NAT_4:9;
9697 = 31*312 + 25; hence not 31 divides 9697 by NAT_4:9;
9697 = 37*262 + 3; hence not 37 divides 9697 by NAT_4:9;
9697 = 41*236 + 21; hence not 41 divides 9697 by NAT_4:9;
9697 = 43*225 + 22; hence not 43 divides 9697 by NAT_4:9;
9697 = 47*206 + 15; hence not 47 divides 9697 by NAT_4:9;
9697 = 53*182 + 51; hence not 53 divides 9697 by NAT_4:9;
9697 = 59*164 + 21; hence not 59 divides 9697 by NAT_4:9;
9697 = 61*158 + 59; hence not 61 divides 9697 by NAT_4:9;
9697 = 67*144 + 49; hence not 67 divides 9697 by NAT_4:9;
9697 = 71*136 + 41; hence not 71 divides 9697 by NAT_4:9;
9697 = 73*132 + 61; hence not 73 divides 9697 by NAT_4:9;
9697 = 79*122 + 59; hence not 79 divides 9697 by NAT_4:9;
9697 = 83*116 + 69; hence not 83 divides 9697 by NAT_4:9;
9697 = 89*108 + 85; hence not 89 divides 9697 by NAT_4:9;
9697 = 97*99 + 94; hence not 97 divides 9697 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9697 & n is prime
holds not n divides 9697 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 21
theorem
9719 is prime
proof
now
9719 = 2*4859 + 1; hence not 2 divides 9719 by NAT_4:9;
9719 = 3*3239 + 2; hence not 3 divides 9719 by NAT_4:9;
9719 = 5*1943 + 4; hence not 5 divides 9719 by NAT_4:9;
9719 = 7*1388 + 3; hence not 7 divides 9719 by NAT_4:9;
9719 = 11*883 + 6; hence not 11 divides 9719 by NAT_4:9;
9719 = 13*747 + 8; hence not 13 divides 9719 by NAT_4:9;
9719 = 17*571 + 12; hence not 17 divides 9719 by NAT_4:9;
9719 = 19*511 + 10; hence not 19 divides 9719 by NAT_4:9;
9719 = 23*422 + 13; hence not 23 divides 9719 by NAT_4:9;
9719 = 29*335 + 4; hence not 29 divides 9719 by NAT_4:9;
9719 = 31*313 + 16; hence not 31 divides 9719 by NAT_4:9;
9719 = 37*262 + 25; hence not 37 divides 9719 by NAT_4:9;
9719 = 41*237 + 2; hence not 41 divides 9719 by NAT_4:9;
9719 = 43*226 + 1; hence not 43 divides 9719 by NAT_4:9;
9719 = 47*206 + 37; hence not 47 divides 9719 by NAT_4:9;
9719 = 53*183 + 20; hence not 53 divides 9719 by NAT_4:9;
9719 = 59*164 + 43; hence not 59 divides 9719 by NAT_4:9;
9719 = 61*159 + 20; hence not 61 divides 9719 by NAT_4:9;
9719 = 67*145 + 4; hence not 67 divides 9719 by NAT_4:9;
9719 = 71*136 + 63; hence not 71 divides 9719 by NAT_4:9;
9719 = 73*133 + 10; hence not 73 divides 9719 by NAT_4:9;
9719 = 79*123 + 2; hence not 79 divides 9719 by NAT_4:9;
9719 = 83*117 + 8; hence not 83 divides 9719 by NAT_4:9;
9719 = 89*109 + 18; hence not 89 divides 9719 by NAT_4:9;
9719 = 97*100 + 19; hence not 97 divides 9719 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9719 & n is prime
holds not n divides 9719 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9721 is prime
proof
now
9721 = 2*4860 + 1; hence not 2 divides 9721 by NAT_4:9;
9721 = 3*3240 + 1; hence not 3 divides 9721 by NAT_4:9;
9721 = 5*1944 + 1; hence not 5 divides 9721 by NAT_4:9;
9721 = 7*1388 + 5; hence not 7 divides 9721 by NAT_4:9;
9721 = 11*883 + 8; hence not 11 divides 9721 by NAT_4:9;
9721 = 13*747 + 10; hence not 13 divides 9721 by NAT_4:9;
9721 = 17*571 + 14; hence not 17 divides 9721 by NAT_4:9;
9721 = 19*511 + 12; hence not 19 divides 9721 by NAT_4:9;
9721 = 23*422 + 15; hence not 23 divides 9721 by NAT_4:9;
9721 = 29*335 + 6; hence not 29 divides 9721 by NAT_4:9;
9721 = 31*313 + 18; hence not 31 divides 9721 by NAT_4:9;
9721 = 37*262 + 27; hence not 37 divides 9721 by NAT_4:9;
9721 = 41*237 + 4; hence not 41 divides 9721 by NAT_4:9;
9721 = 43*226 + 3; hence not 43 divides 9721 by NAT_4:9;
9721 = 47*206 + 39; hence not 47 divides 9721 by NAT_4:9;
9721 = 53*183 + 22; hence not 53 divides 9721 by NAT_4:9;
9721 = 59*164 + 45; hence not 59 divides 9721 by NAT_4:9;
9721 = 61*159 + 22; hence not 61 divides 9721 by NAT_4:9;
9721 = 67*145 + 6; hence not 67 divides 9721 by NAT_4:9;
9721 = 71*136 + 65; hence not 71 divides 9721 by NAT_4:9;
9721 = 73*133 + 12; hence not 73 divides 9721 by NAT_4:9;
9721 = 79*123 + 4; hence not 79 divides 9721 by NAT_4:9;
9721 = 83*117 + 10; hence not 83 divides 9721 by NAT_4:9;
9721 = 89*109 + 20; hence not 89 divides 9721 by NAT_4:9;
9721 = 97*100 + 21; hence not 97 divides 9721 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9721 & n is prime
holds not n divides 9721 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9733 is prime
proof
now
9733 = 2*4866 + 1; hence not 2 divides 9733 by NAT_4:9;
9733 = 3*3244 + 1; hence not 3 divides 9733 by NAT_4:9;
9733 = 5*1946 + 3; hence not 5 divides 9733 by NAT_4:9;
9733 = 7*1390 + 3; hence not 7 divides 9733 by NAT_4:9;
9733 = 11*884 + 9; hence not 11 divides 9733 by NAT_4:9;
9733 = 13*748 + 9; hence not 13 divides 9733 by NAT_4:9;
9733 = 17*572 + 9; hence not 17 divides 9733 by NAT_4:9;
9733 = 19*512 + 5; hence not 19 divides 9733 by NAT_4:9;
9733 = 23*423 + 4; hence not 23 divides 9733 by NAT_4:9;
9733 = 29*335 + 18; hence not 29 divides 9733 by NAT_4:9;
9733 = 31*313 + 30; hence not 31 divides 9733 by NAT_4:9;
9733 = 37*263 + 2; hence not 37 divides 9733 by NAT_4:9;
9733 = 41*237 + 16; hence not 41 divides 9733 by NAT_4:9;
9733 = 43*226 + 15; hence not 43 divides 9733 by NAT_4:9;
9733 = 47*207 + 4; hence not 47 divides 9733 by NAT_4:9;
9733 = 53*183 + 34; hence not 53 divides 9733 by NAT_4:9;
9733 = 59*164 + 57; hence not 59 divides 9733 by NAT_4:9;
9733 = 61*159 + 34; hence not 61 divides 9733 by NAT_4:9;
9733 = 67*145 + 18; hence not 67 divides 9733 by NAT_4:9;
9733 = 71*137 + 6; hence not 71 divides 9733 by NAT_4:9;
9733 = 73*133 + 24; hence not 73 divides 9733 by NAT_4:9;
9733 = 79*123 + 16; hence not 79 divides 9733 by NAT_4:9;
9733 = 83*117 + 22; hence not 83 divides 9733 by NAT_4:9;
9733 = 89*109 + 32; hence not 89 divides 9733 by NAT_4:9;
9733 = 97*100 + 33; hence not 97 divides 9733 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9733 & n is prime
holds not n divides 9733 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9739 is prime
proof
now
9739 = 2*4869 + 1; hence not 2 divides 9739 by NAT_4:9;
9739 = 3*3246 + 1; hence not 3 divides 9739 by NAT_4:9;
9739 = 5*1947 + 4; hence not 5 divides 9739 by NAT_4:9;
9739 = 7*1391 + 2; hence not 7 divides 9739 by NAT_4:9;
9739 = 11*885 + 4; hence not 11 divides 9739 by NAT_4:9;
9739 = 13*749 + 2; hence not 13 divides 9739 by NAT_4:9;
9739 = 17*572 + 15; hence not 17 divides 9739 by NAT_4:9;
9739 = 19*512 + 11; hence not 19 divides 9739 by NAT_4:9;
9739 = 23*423 + 10; hence not 23 divides 9739 by NAT_4:9;
9739 = 29*335 + 24; hence not 29 divides 9739 by NAT_4:9;
9739 = 31*314 + 5; hence not 31 divides 9739 by NAT_4:9;
9739 = 37*263 + 8; hence not 37 divides 9739 by NAT_4:9;
9739 = 41*237 + 22; hence not 41 divides 9739 by NAT_4:9;
9739 = 43*226 + 21; hence not 43 divides 9739 by NAT_4:9;
9739 = 47*207 + 10; hence not 47 divides 9739 by NAT_4:9;
9739 = 53*183 + 40; hence not 53 divides 9739 by NAT_4:9;
9739 = 59*165 + 4; hence not 59 divides 9739 by NAT_4:9;
9739 = 61*159 + 40; hence not 61 divides 9739 by NAT_4:9;
9739 = 67*145 + 24; hence not 67 divides 9739 by NAT_4:9;
9739 = 71*137 + 12; hence not 71 divides 9739 by NAT_4:9;
9739 = 73*133 + 30; hence not 73 divides 9739 by NAT_4:9;
9739 = 79*123 + 22; hence not 79 divides 9739 by NAT_4:9;
9739 = 83*117 + 28; hence not 83 divides 9739 by NAT_4:9;
9739 = 89*109 + 38; hence not 89 divides 9739 by NAT_4:9;
9739 = 97*100 + 39; hence not 97 divides 9739 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9739 & n is prime
holds not n divides 9739 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9743 is prime
proof
now
9743 = 2*4871 + 1; hence not 2 divides 9743 by NAT_4:9;
9743 = 3*3247 + 2; hence not 3 divides 9743 by NAT_4:9;
9743 = 5*1948 + 3; hence not 5 divides 9743 by NAT_4:9;
9743 = 7*1391 + 6; hence not 7 divides 9743 by NAT_4:9;
9743 = 11*885 + 8; hence not 11 divides 9743 by NAT_4:9;
9743 = 13*749 + 6; hence not 13 divides 9743 by NAT_4:9;
9743 = 17*573 + 2; hence not 17 divides 9743 by NAT_4:9;
9743 = 19*512 + 15; hence not 19 divides 9743 by NAT_4:9;
9743 = 23*423 + 14; hence not 23 divides 9743 by NAT_4:9;
9743 = 29*335 + 28; hence not 29 divides 9743 by NAT_4:9;
9743 = 31*314 + 9; hence not 31 divides 9743 by NAT_4:9;
9743 = 37*263 + 12; hence not 37 divides 9743 by NAT_4:9;
9743 = 41*237 + 26; hence not 41 divides 9743 by NAT_4:9;
9743 = 43*226 + 25; hence not 43 divides 9743 by NAT_4:9;
9743 = 47*207 + 14; hence not 47 divides 9743 by NAT_4:9;
9743 = 53*183 + 44; hence not 53 divides 9743 by NAT_4:9;
9743 = 59*165 + 8; hence not 59 divides 9743 by NAT_4:9;
9743 = 61*159 + 44; hence not 61 divides 9743 by NAT_4:9;
9743 = 67*145 + 28; hence not 67 divides 9743 by NAT_4:9;
9743 = 71*137 + 16; hence not 71 divides 9743 by NAT_4:9;
9743 = 73*133 + 34; hence not 73 divides 9743 by NAT_4:9;
9743 = 79*123 + 26; hence not 79 divides 9743 by NAT_4:9;
9743 = 83*117 + 32; hence not 83 divides 9743 by NAT_4:9;
9743 = 89*109 + 42; hence not 89 divides 9743 by NAT_4:9;
9743 = 97*100 + 43; hence not 97 divides 9743 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9743 & n is prime
holds not n divides 9743 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9749 is prime
proof
now
9749 = 2*4874 + 1; hence not 2 divides 9749 by NAT_4:9;
9749 = 3*3249 + 2; hence not 3 divides 9749 by NAT_4:9;
9749 = 5*1949 + 4; hence not 5 divides 9749 by NAT_4:9;
9749 = 7*1392 + 5; hence not 7 divides 9749 by NAT_4:9;
9749 = 11*886 + 3; hence not 11 divides 9749 by NAT_4:9;
9749 = 13*749 + 12; hence not 13 divides 9749 by NAT_4:9;
9749 = 17*573 + 8; hence not 17 divides 9749 by NAT_4:9;
9749 = 19*513 + 2; hence not 19 divides 9749 by NAT_4:9;
9749 = 23*423 + 20; hence not 23 divides 9749 by NAT_4:9;
9749 = 29*336 + 5; hence not 29 divides 9749 by NAT_4:9;
9749 = 31*314 + 15; hence not 31 divides 9749 by NAT_4:9;
9749 = 37*263 + 18; hence not 37 divides 9749 by NAT_4:9;
9749 = 41*237 + 32; hence not 41 divides 9749 by NAT_4:9;
9749 = 43*226 + 31; hence not 43 divides 9749 by NAT_4:9;
9749 = 47*207 + 20; hence not 47 divides 9749 by NAT_4:9;
9749 = 53*183 + 50; hence not 53 divides 9749 by NAT_4:9;
9749 = 59*165 + 14; hence not 59 divides 9749 by NAT_4:9;
9749 = 61*159 + 50; hence not 61 divides 9749 by NAT_4:9;
9749 = 67*145 + 34; hence not 67 divides 9749 by NAT_4:9;
9749 = 71*137 + 22; hence not 71 divides 9749 by NAT_4:9;
9749 = 73*133 + 40; hence not 73 divides 9749 by NAT_4:9;
9749 = 79*123 + 32; hence not 79 divides 9749 by NAT_4:9;
9749 = 83*117 + 38; hence not 83 divides 9749 by NAT_4:9;
9749 = 89*109 + 48; hence not 89 divides 9749 by NAT_4:9;
9749 = 97*100 + 49; hence not 97 divides 9749 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9749 & n is prime
holds not n divides 9749 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
9767 is prime
proof
now
9767 = 2*4883 + 1; hence not 2 divides 9767 by NAT_4:9;
9767 = 3*3255 + 2; hence not 3 divides 9767 by NAT_4:9;
9767 = 5*1953 + 2; hence not 5 divides 9767 by NAT_4:9;
9767 = 7*1395 + 2; hence not 7 divides 9767 by NAT_4:9;
9767 = 11*887 + 10; hence not 11 divides 9767 by NAT_4:9;
9767 = 13*751 + 4; hence not 13 divides 9767 by NAT_4:9;
9767 = 17*574 + 9; hence not 17 divides 9767 by NAT_4:9;
9767 = 19*514 + 1; hence not 19 divides 9767 by NAT_4:9;
9767 = 23*424 + 15; hence not 23 divides 9767 by NAT_4:9;
9767 = 29*336 + 23; hence not 29 divides 9767 by NAT_4:9;
9767 = 31*315 + 2; hence not 31 divides 9767 by NAT_4:9;
9767 = 37*263 + 36; hence not 37 divides 9767 by NAT_4:9;
9767 = 41*238 + 9; hence not 41 divides 9767 by NAT_4:9;
9767 = 43*227 + 6; hence not 43 divides 9767 by NAT_4:9;
9767 = 47*207 + 38; hence not 47 divides 9767 by NAT_4:9;
9767 = 53*184 + 15; hence not 53 divides 9767 by NAT_4:9;
9767 = 59*165 + 32; hence not 59 divides 9767 by NAT_4:9;
9767 = 61*160 + 7; hence not 61 divides 9767 by NAT_4:9;
9767 = 67*145 + 52; hence not 67 divides 9767 by NAT_4:9;
9767 = 71*137 + 40; hence not 71 divides 9767 by NAT_4:9;
9767 = 73*133 + 58; hence not 73 divides 9767 by NAT_4:9;
9767 = 79*123 + 50; hence not 79 divides 9767 by NAT_4:9;
9767 = 83*117 + 56; hence not 83 divides 9767 by NAT_4:9;
9767 = 89*109 + 66; hence not 89 divides 9767 by NAT_4:9;
9767 = 97*100 + 67; hence not 97 divides 9767 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9767 & n is prime
holds not n divides 9767 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9769 is prime
proof
now
9769 = 2*4884 + 1; hence not 2 divides 9769 by NAT_4:9;
9769 = 3*3256 + 1; hence not 3 divides 9769 by NAT_4:9;
9769 = 5*1953 + 4; hence not 5 divides 9769 by NAT_4:9;
9769 = 7*1395 + 4; hence not 7 divides 9769 by NAT_4:9;
9769 = 11*888 + 1; hence not 11 divides 9769 by NAT_4:9;
9769 = 13*751 + 6; hence not 13 divides 9769 by NAT_4:9;
9769 = 17*574 + 11; hence not 17 divides 9769 by NAT_4:9;
9769 = 19*514 + 3; hence not 19 divides 9769 by NAT_4:9;
9769 = 23*424 + 17; hence not 23 divides 9769 by NAT_4:9;
9769 = 29*336 + 25; hence not 29 divides 9769 by NAT_4:9;
9769 = 31*315 + 4; hence not 31 divides 9769 by NAT_4:9;
9769 = 37*264 + 1; hence not 37 divides 9769 by NAT_4:9;
9769 = 41*238 + 11; hence not 41 divides 9769 by NAT_4:9;
9769 = 43*227 + 8; hence not 43 divides 9769 by NAT_4:9;
9769 = 47*207 + 40; hence not 47 divides 9769 by NAT_4:9;
9769 = 53*184 + 17; hence not 53 divides 9769 by NAT_4:9;
9769 = 59*165 + 34; hence not 59 divides 9769 by NAT_4:9;
9769 = 61*160 + 9; hence not 61 divides 9769 by NAT_4:9;
9769 = 67*145 + 54; hence not 67 divides 9769 by NAT_4:9;
9769 = 71*137 + 42; hence not 71 divides 9769 by NAT_4:9;
9769 = 73*133 + 60; hence not 73 divides 9769 by NAT_4:9;
9769 = 79*123 + 52; hence not 79 divides 9769 by NAT_4:9;
9769 = 83*117 + 58; hence not 83 divides 9769 by NAT_4:9;
9769 = 89*109 + 68; hence not 89 divides 9769 by NAT_4:9;
9769 = 97*100 + 69; hence not 97 divides 9769 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9769 & n is prime
holds not n divides 9769 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9781 is prime
proof
now
9781 = 2*4890 + 1; hence not 2 divides 9781 by NAT_4:9;
9781 = 3*3260 + 1; hence not 3 divides 9781 by NAT_4:9;
9781 = 5*1956 + 1; hence not 5 divides 9781 by NAT_4:9;
9781 = 7*1397 + 2; hence not 7 divides 9781 by NAT_4:9;
9781 = 11*889 + 2; hence not 11 divides 9781 by NAT_4:9;
9781 = 13*752 + 5; hence not 13 divides 9781 by NAT_4:9;
9781 = 17*575 + 6; hence not 17 divides 9781 by NAT_4:9;
9781 = 19*514 + 15; hence not 19 divides 9781 by NAT_4:9;
9781 = 23*425 + 6; hence not 23 divides 9781 by NAT_4:9;
9781 = 29*337 + 8; hence not 29 divides 9781 by NAT_4:9;
9781 = 31*315 + 16; hence not 31 divides 9781 by NAT_4:9;
9781 = 37*264 + 13; hence not 37 divides 9781 by NAT_4:9;
9781 = 41*238 + 23; hence not 41 divides 9781 by NAT_4:9;
9781 = 43*227 + 20; hence not 43 divides 9781 by NAT_4:9;
9781 = 47*208 + 5; hence not 47 divides 9781 by NAT_4:9;
9781 = 53*184 + 29; hence not 53 divides 9781 by NAT_4:9;
9781 = 59*165 + 46; hence not 59 divides 9781 by NAT_4:9;
9781 = 61*160 + 21; hence not 61 divides 9781 by NAT_4:9;
9781 = 67*145 + 66; hence not 67 divides 9781 by NAT_4:9;
9781 = 71*137 + 54; hence not 71 divides 9781 by NAT_4:9;
9781 = 73*133 + 72; hence not 73 divides 9781 by NAT_4:9;
9781 = 79*123 + 64; hence not 79 divides 9781 by NAT_4:9;
9781 = 83*117 + 70; hence not 83 divides 9781 by NAT_4:9;
9781 = 89*109 + 80; hence not 89 divides 9781 by NAT_4:9;
9781 = 97*100 + 81; hence not 97 divides 9781 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9781 & n is prime
holds not n divides 9781 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9787 is prime
proof
now
9787 = 2*4893 + 1; hence not 2 divides 9787 by NAT_4:9;
9787 = 3*3262 + 1; hence not 3 divides 9787 by NAT_4:9;
9787 = 5*1957 + 2; hence not 5 divides 9787 by NAT_4:9;
9787 = 7*1398 + 1; hence not 7 divides 9787 by NAT_4:9;
9787 = 11*889 + 8; hence not 11 divides 9787 by NAT_4:9;
9787 = 13*752 + 11; hence not 13 divides 9787 by NAT_4:9;
9787 = 17*575 + 12; hence not 17 divides 9787 by NAT_4:9;
9787 = 19*515 + 2; hence not 19 divides 9787 by NAT_4:9;
9787 = 23*425 + 12; hence not 23 divides 9787 by NAT_4:9;
9787 = 29*337 + 14; hence not 29 divides 9787 by NAT_4:9;
9787 = 31*315 + 22; hence not 31 divides 9787 by NAT_4:9;
9787 = 37*264 + 19; hence not 37 divides 9787 by NAT_4:9;
9787 = 41*238 + 29; hence not 41 divides 9787 by NAT_4:9;
9787 = 43*227 + 26; hence not 43 divides 9787 by NAT_4:9;
9787 = 47*208 + 11; hence not 47 divides 9787 by NAT_4:9;
9787 = 53*184 + 35; hence not 53 divides 9787 by NAT_4:9;
9787 = 59*165 + 52; hence not 59 divides 9787 by NAT_4:9;
9787 = 61*160 + 27; hence not 61 divides 9787 by NAT_4:9;
9787 = 67*146 + 5; hence not 67 divides 9787 by NAT_4:9;
9787 = 71*137 + 60; hence not 71 divides 9787 by NAT_4:9;
9787 = 73*134 + 5; hence not 73 divides 9787 by NAT_4:9;
9787 = 79*123 + 70; hence not 79 divides 9787 by NAT_4:9;
9787 = 83*117 + 76; hence not 83 divides 9787 by NAT_4:9;
9787 = 89*109 + 86; hence not 89 divides 9787 by NAT_4:9;
9787 = 97*100 + 87; hence not 97 divides 9787 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9787 & n is prime
holds not n divides 9787 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9791 is prime
proof
now
9791 = 2*4895 + 1; hence not 2 divides 9791 by NAT_4:9;
9791 = 3*3263 + 2; hence not 3 divides 9791 by NAT_4:9;
9791 = 5*1958 + 1; hence not 5 divides 9791 by NAT_4:9;
9791 = 7*1398 + 5; hence not 7 divides 9791 by NAT_4:9;
9791 = 11*890 + 1; hence not 11 divides 9791 by NAT_4:9;
9791 = 13*753 + 2; hence not 13 divides 9791 by NAT_4:9;
9791 = 17*575 + 16; hence not 17 divides 9791 by NAT_4:9;
9791 = 19*515 + 6; hence not 19 divides 9791 by NAT_4:9;
9791 = 23*425 + 16; hence not 23 divides 9791 by NAT_4:9;
9791 = 29*337 + 18; hence not 29 divides 9791 by NAT_4:9;
9791 = 31*315 + 26; hence not 31 divides 9791 by NAT_4:9;
9791 = 37*264 + 23; hence not 37 divides 9791 by NAT_4:9;
9791 = 41*238 + 33; hence not 41 divides 9791 by NAT_4:9;
9791 = 43*227 + 30; hence not 43 divides 9791 by NAT_4:9;
9791 = 47*208 + 15; hence not 47 divides 9791 by NAT_4:9;
9791 = 53*184 + 39; hence not 53 divides 9791 by NAT_4:9;
9791 = 59*165 + 56; hence not 59 divides 9791 by NAT_4:9;
9791 = 61*160 + 31; hence not 61 divides 9791 by NAT_4:9;
9791 = 67*146 + 9; hence not 67 divides 9791 by NAT_4:9;
9791 = 71*137 + 64; hence not 71 divides 9791 by NAT_4:9;
9791 = 73*134 + 9; hence not 73 divides 9791 by NAT_4:9;
9791 = 79*123 + 74; hence not 79 divides 9791 by NAT_4:9;
9791 = 83*117 + 80; hence not 83 divides 9791 by NAT_4:9;
9791 = 89*110 + 1; hence not 89 divides 9791 by NAT_4:9;
9791 = 97*100 + 91; hence not 97 divides 9791 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9791 & n is prime
holds not n divides 9791 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9803 is prime
proof
now
9803 = 2*4901 + 1; hence not 2 divides 9803 by NAT_4:9;
9803 = 3*3267 + 2; hence not 3 divides 9803 by NAT_4:9;
9803 = 5*1960 + 3; hence not 5 divides 9803 by NAT_4:9;
9803 = 7*1400 + 3; hence not 7 divides 9803 by NAT_4:9;
9803 = 11*891 + 2; hence not 11 divides 9803 by NAT_4:9;
9803 = 13*754 + 1; hence not 13 divides 9803 by NAT_4:9;
9803 = 17*576 + 11; hence not 17 divides 9803 by NAT_4:9;
9803 = 19*515 + 18; hence not 19 divides 9803 by NAT_4:9;
9803 = 23*426 + 5; hence not 23 divides 9803 by NAT_4:9;
9803 = 29*338 + 1; hence not 29 divides 9803 by NAT_4:9;
9803 = 31*316 + 7; hence not 31 divides 9803 by NAT_4:9;
9803 = 37*264 + 35; hence not 37 divides 9803 by NAT_4:9;
9803 = 41*239 + 4; hence not 41 divides 9803 by NAT_4:9;
9803 = 43*227 + 42; hence not 43 divides 9803 by NAT_4:9;
9803 = 47*208 + 27; hence not 47 divides 9803 by NAT_4:9;
9803 = 53*184 + 51; hence not 53 divides 9803 by NAT_4:9;
9803 = 59*166 + 9; hence not 59 divides 9803 by NAT_4:9;
9803 = 61*160 + 43; hence not 61 divides 9803 by NAT_4:9;
9803 = 67*146 + 21; hence not 67 divides 9803 by NAT_4:9;
9803 = 71*138 + 5; hence not 71 divides 9803 by NAT_4:9;
9803 = 73*134 + 21; hence not 73 divides 9803 by NAT_4:9;
9803 = 79*124 + 7; hence not 79 divides 9803 by NAT_4:9;
9803 = 83*118 + 9; hence not 83 divides 9803 by NAT_4:9;
9803 = 89*110 + 13; hence not 89 divides 9803 by NAT_4:9;
9803 = 97*101 + 6; hence not 97 divides 9803 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9803 & n is prime
holds not n divides 9803 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9811 is prime
proof
now
9811 = 2*4905 + 1; hence not 2 divides 9811 by NAT_4:9;
9811 = 3*3270 + 1; hence not 3 divides 9811 by NAT_4:9;
9811 = 5*1962 + 1; hence not 5 divides 9811 by NAT_4:9;
9811 = 7*1401 + 4; hence not 7 divides 9811 by NAT_4:9;
9811 = 11*891 + 10; hence not 11 divides 9811 by NAT_4:9;
9811 = 13*754 + 9; hence not 13 divides 9811 by NAT_4:9;
9811 = 17*577 + 2; hence not 17 divides 9811 by NAT_4:9;
9811 = 19*516 + 7; hence not 19 divides 9811 by NAT_4:9;
9811 = 23*426 + 13; hence not 23 divides 9811 by NAT_4:9;
9811 = 29*338 + 9; hence not 29 divides 9811 by NAT_4:9;
9811 = 31*316 + 15; hence not 31 divides 9811 by NAT_4:9;
9811 = 37*265 + 6; hence not 37 divides 9811 by NAT_4:9;
9811 = 41*239 + 12; hence not 41 divides 9811 by NAT_4:9;
9811 = 43*228 + 7; hence not 43 divides 9811 by NAT_4:9;
9811 = 47*208 + 35; hence not 47 divides 9811 by NAT_4:9;
9811 = 53*185 + 6; hence not 53 divides 9811 by NAT_4:9;
9811 = 59*166 + 17; hence not 59 divides 9811 by NAT_4:9;
9811 = 61*160 + 51; hence not 61 divides 9811 by NAT_4:9;
9811 = 67*146 + 29; hence not 67 divides 9811 by NAT_4:9;
9811 = 71*138 + 13; hence not 71 divides 9811 by NAT_4:9;
9811 = 73*134 + 29; hence not 73 divides 9811 by NAT_4:9;
9811 = 79*124 + 15; hence not 79 divides 9811 by NAT_4:9;
9811 = 83*118 + 17; hence not 83 divides 9811 by NAT_4:9;
9811 = 89*110 + 21; hence not 89 divides 9811 by NAT_4:9;
9811 = 97*101 + 14; hence not 97 divides 9811 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9811 & n is prime
holds not n divides 9811 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9817 is prime
proof
now
9817 = 2*4908 + 1; hence not 2 divides 9817 by NAT_4:9;
9817 = 3*3272 + 1; hence not 3 divides 9817 by NAT_4:9;
9817 = 5*1963 + 2; hence not 5 divides 9817 by NAT_4:9;
9817 = 7*1402 + 3; hence not 7 divides 9817 by NAT_4:9;
9817 = 11*892 + 5; hence not 11 divides 9817 by NAT_4:9;
9817 = 13*755 + 2; hence not 13 divides 9817 by NAT_4:9;
9817 = 17*577 + 8; hence not 17 divides 9817 by NAT_4:9;
9817 = 19*516 + 13; hence not 19 divides 9817 by NAT_4:9;
9817 = 23*426 + 19; hence not 23 divides 9817 by NAT_4:9;
9817 = 29*338 + 15; hence not 29 divides 9817 by NAT_4:9;
9817 = 31*316 + 21; hence not 31 divides 9817 by NAT_4:9;
9817 = 37*265 + 12; hence not 37 divides 9817 by NAT_4:9;
9817 = 41*239 + 18; hence not 41 divides 9817 by NAT_4:9;
9817 = 43*228 + 13; hence not 43 divides 9817 by NAT_4:9;
9817 = 47*208 + 41; hence not 47 divides 9817 by NAT_4:9;
9817 = 53*185 + 12; hence not 53 divides 9817 by NAT_4:9;
9817 = 59*166 + 23; hence not 59 divides 9817 by NAT_4:9;
9817 = 61*160 + 57; hence not 61 divides 9817 by NAT_4:9;
9817 = 67*146 + 35; hence not 67 divides 9817 by NAT_4:9;
9817 = 71*138 + 19; hence not 71 divides 9817 by NAT_4:9;
9817 = 73*134 + 35; hence not 73 divides 9817 by NAT_4:9;
9817 = 79*124 + 21; hence not 79 divides 9817 by NAT_4:9;
9817 = 83*118 + 23; hence not 83 divides 9817 by NAT_4:9;
9817 = 89*110 + 27; hence not 89 divides 9817 by NAT_4:9;
9817 = 97*101 + 20; hence not 97 divides 9817 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9817 & n is prime
holds not n divides 9817 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9829 is prime
proof
now
9829 = 2*4914 + 1; hence not 2 divides 9829 by NAT_4:9;
9829 = 3*3276 + 1; hence not 3 divides 9829 by NAT_4:9;
9829 = 5*1965 + 4; hence not 5 divides 9829 by NAT_4:9;
9829 = 7*1404 + 1; hence not 7 divides 9829 by NAT_4:9;
9829 = 11*893 + 6; hence not 11 divides 9829 by NAT_4:9;
9829 = 13*756 + 1; hence not 13 divides 9829 by NAT_4:9;
9829 = 17*578 + 3; hence not 17 divides 9829 by NAT_4:9;
9829 = 19*517 + 6; hence not 19 divides 9829 by NAT_4:9;
9829 = 23*427 + 8; hence not 23 divides 9829 by NAT_4:9;
9829 = 29*338 + 27; hence not 29 divides 9829 by NAT_4:9;
9829 = 31*317 + 2; hence not 31 divides 9829 by NAT_4:9;
9829 = 37*265 + 24; hence not 37 divides 9829 by NAT_4:9;
9829 = 41*239 + 30; hence not 41 divides 9829 by NAT_4:9;
9829 = 43*228 + 25; hence not 43 divides 9829 by NAT_4:9;
9829 = 47*209 + 6; hence not 47 divides 9829 by NAT_4:9;
9829 = 53*185 + 24; hence not 53 divides 9829 by NAT_4:9;
9829 = 59*166 + 35; hence not 59 divides 9829 by NAT_4:9;
9829 = 61*161 + 8; hence not 61 divides 9829 by NAT_4:9;
9829 = 67*146 + 47; hence not 67 divides 9829 by NAT_4:9;
9829 = 71*138 + 31; hence not 71 divides 9829 by NAT_4:9;
9829 = 73*134 + 47; hence not 73 divides 9829 by NAT_4:9;
9829 = 79*124 + 33; hence not 79 divides 9829 by NAT_4:9;
9829 = 83*118 + 35; hence not 83 divides 9829 by NAT_4:9;
9829 = 89*110 + 39; hence not 89 divides 9829 by NAT_4:9;
9829 = 97*101 + 32; hence not 97 divides 9829 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9829 & n is prime
holds not n divides 9829 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9833 is prime
proof
now
9833 = 2*4916 + 1; hence not 2 divides 9833 by NAT_4:9;
9833 = 3*3277 + 2; hence not 3 divides 9833 by NAT_4:9;
9833 = 5*1966 + 3; hence not 5 divides 9833 by NAT_4:9;
9833 = 7*1404 + 5; hence not 7 divides 9833 by NAT_4:9;
9833 = 11*893 + 10; hence not 11 divides 9833 by NAT_4:9;
9833 = 13*756 + 5; hence not 13 divides 9833 by NAT_4:9;
9833 = 17*578 + 7; hence not 17 divides 9833 by NAT_4:9;
9833 = 19*517 + 10; hence not 19 divides 9833 by NAT_4:9;
9833 = 23*427 + 12; hence not 23 divides 9833 by NAT_4:9;
9833 = 29*339 + 2; hence not 29 divides 9833 by NAT_4:9;
9833 = 31*317 + 6; hence not 31 divides 9833 by NAT_4:9;
9833 = 37*265 + 28; hence not 37 divides 9833 by NAT_4:9;
9833 = 41*239 + 34; hence not 41 divides 9833 by NAT_4:9;
9833 = 43*228 + 29; hence not 43 divides 9833 by NAT_4:9;
9833 = 47*209 + 10; hence not 47 divides 9833 by NAT_4:9;
9833 = 53*185 + 28; hence not 53 divides 9833 by NAT_4:9;
9833 = 59*166 + 39; hence not 59 divides 9833 by NAT_4:9;
9833 = 61*161 + 12; hence not 61 divides 9833 by NAT_4:9;
9833 = 67*146 + 51; hence not 67 divides 9833 by NAT_4:9;
9833 = 71*138 + 35; hence not 71 divides 9833 by NAT_4:9;
9833 = 73*134 + 51; hence not 73 divides 9833 by NAT_4:9;
9833 = 79*124 + 37; hence not 79 divides 9833 by NAT_4:9;
9833 = 83*118 + 39; hence not 83 divides 9833 by NAT_4:9;
9833 = 89*110 + 43; hence not 89 divides 9833 by NAT_4:9;
9833 = 97*101 + 36; hence not 97 divides 9833 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9833 & n is prime
holds not n divides 9833 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9839 is prime
proof
now
9839 = 2*4919 + 1; hence not 2 divides 9839 by NAT_4:9;
9839 = 3*3279 + 2; hence not 3 divides 9839 by NAT_4:9;
9839 = 5*1967 + 4; hence not 5 divides 9839 by NAT_4:9;
9839 = 7*1405 + 4; hence not 7 divides 9839 by NAT_4:9;
9839 = 11*894 + 5; hence not 11 divides 9839 by NAT_4:9;
9839 = 13*756 + 11; hence not 13 divides 9839 by NAT_4:9;
9839 = 17*578 + 13; hence not 17 divides 9839 by NAT_4:9;
9839 = 19*517 + 16; hence not 19 divides 9839 by NAT_4:9;
9839 = 23*427 + 18; hence not 23 divides 9839 by NAT_4:9;
9839 = 29*339 + 8; hence not 29 divides 9839 by NAT_4:9;
9839 = 31*317 + 12; hence not 31 divides 9839 by NAT_4:9;
9839 = 37*265 + 34; hence not 37 divides 9839 by NAT_4:9;
9839 = 41*239 + 40; hence not 41 divides 9839 by NAT_4:9;
9839 = 43*228 + 35; hence not 43 divides 9839 by NAT_4:9;
9839 = 47*209 + 16; hence not 47 divides 9839 by NAT_4:9;
9839 = 53*185 + 34; hence not 53 divides 9839 by NAT_4:9;
9839 = 59*166 + 45; hence not 59 divides 9839 by NAT_4:9;
9839 = 61*161 + 18; hence not 61 divides 9839 by NAT_4:9;
9839 = 67*146 + 57; hence not 67 divides 9839 by NAT_4:9;
9839 = 71*138 + 41; hence not 71 divides 9839 by NAT_4:9;
9839 = 73*134 + 57; hence not 73 divides 9839 by NAT_4:9;
9839 = 79*124 + 43; hence not 79 divides 9839 by NAT_4:9;
9839 = 83*118 + 45; hence not 83 divides 9839 by NAT_4:9;
9839 = 89*110 + 49; hence not 89 divides 9839 by NAT_4:9;
9839 = 97*101 + 42; hence not 97 divides 9839 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9839 & n is prime
holds not n divides 9839 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9851 is prime
proof
now
9851 = 2*4925 + 1; hence not 2 divides 9851 by NAT_4:9;
9851 = 3*3283 + 2; hence not 3 divides 9851 by NAT_4:9;
9851 = 5*1970 + 1; hence not 5 divides 9851 by NAT_4:9;
9851 = 7*1407 + 2; hence not 7 divides 9851 by NAT_4:9;
9851 = 11*895 + 6; hence not 11 divides 9851 by NAT_4:9;
9851 = 13*757 + 10; hence not 13 divides 9851 by NAT_4:9;
9851 = 17*579 + 8; hence not 17 divides 9851 by NAT_4:9;
9851 = 19*518 + 9; hence not 19 divides 9851 by NAT_4:9;
9851 = 23*428 + 7; hence not 23 divides 9851 by NAT_4:9;
9851 = 29*339 + 20; hence not 29 divides 9851 by NAT_4:9;
9851 = 31*317 + 24; hence not 31 divides 9851 by NAT_4:9;
9851 = 37*266 + 9; hence not 37 divides 9851 by NAT_4:9;
9851 = 41*240 + 11; hence not 41 divides 9851 by NAT_4:9;
9851 = 43*229 + 4; hence not 43 divides 9851 by NAT_4:9;
9851 = 47*209 + 28; hence not 47 divides 9851 by NAT_4:9;
9851 = 53*185 + 46; hence not 53 divides 9851 by NAT_4:9;
9851 = 59*166 + 57; hence not 59 divides 9851 by NAT_4:9;
9851 = 61*161 + 30; hence not 61 divides 9851 by NAT_4:9;
9851 = 67*147 + 2; hence not 67 divides 9851 by NAT_4:9;
9851 = 71*138 + 53; hence not 71 divides 9851 by NAT_4:9;
9851 = 73*134 + 69; hence not 73 divides 9851 by NAT_4:9;
9851 = 79*124 + 55; hence not 79 divides 9851 by NAT_4:9;
9851 = 83*118 + 57; hence not 83 divides 9851 by NAT_4:9;
9851 = 89*110 + 61; hence not 89 divides 9851 by NAT_4:9;
9851 = 97*101 + 54; hence not 97 divides 9851 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9851 & n is prime
holds not n divides 9851 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9857 is prime
proof
now
9857 = 2*4928 + 1; hence not 2 divides 9857 by NAT_4:9;
9857 = 3*3285 + 2; hence not 3 divides 9857 by NAT_4:9;
9857 = 5*1971 + 2; hence not 5 divides 9857 by NAT_4:9;
9857 = 7*1408 + 1; hence not 7 divides 9857 by NAT_4:9;
9857 = 11*896 + 1; hence not 11 divides 9857 by NAT_4:9;
9857 = 13*758 + 3; hence not 13 divides 9857 by NAT_4:9;
9857 = 17*579 + 14; hence not 17 divides 9857 by NAT_4:9;
9857 = 19*518 + 15; hence not 19 divides 9857 by NAT_4:9;
9857 = 23*428 + 13; hence not 23 divides 9857 by NAT_4:9;
9857 = 29*339 + 26; hence not 29 divides 9857 by NAT_4:9;
9857 = 31*317 + 30; hence not 31 divides 9857 by NAT_4:9;
9857 = 37*266 + 15; hence not 37 divides 9857 by NAT_4:9;
9857 = 41*240 + 17; hence not 41 divides 9857 by NAT_4:9;
9857 = 43*229 + 10; hence not 43 divides 9857 by NAT_4:9;
9857 = 47*209 + 34; hence not 47 divides 9857 by NAT_4:9;
9857 = 53*185 + 52; hence not 53 divides 9857 by NAT_4:9;
9857 = 59*167 + 4; hence not 59 divides 9857 by NAT_4:9;
9857 = 61*161 + 36; hence not 61 divides 9857 by NAT_4:9;
9857 = 67*147 + 8; hence not 67 divides 9857 by NAT_4:9;
9857 = 71*138 + 59; hence not 71 divides 9857 by NAT_4:9;
9857 = 73*135 + 2; hence not 73 divides 9857 by NAT_4:9;
9857 = 79*124 + 61; hence not 79 divides 9857 by NAT_4:9;
9857 = 83*118 + 63; hence not 83 divides 9857 by NAT_4:9;
9857 = 89*110 + 67; hence not 89 divides 9857 by NAT_4:9;
9857 = 97*101 + 60; hence not 97 divides 9857 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9857 & n is prime
holds not n divides 9857 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9859 is prime
proof
now
9859 = 2*4929 + 1; hence not 2 divides 9859 by NAT_4:9;
9859 = 3*3286 + 1; hence not 3 divides 9859 by NAT_4:9;
9859 = 5*1971 + 4; hence not 5 divides 9859 by NAT_4:9;
9859 = 7*1408 + 3; hence not 7 divides 9859 by NAT_4:9;
9859 = 11*896 + 3; hence not 11 divides 9859 by NAT_4:9;
9859 = 13*758 + 5; hence not 13 divides 9859 by NAT_4:9;
9859 = 17*579 + 16; hence not 17 divides 9859 by NAT_4:9;
9859 = 19*518 + 17; hence not 19 divides 9859 by NAT_4:9;
9859 = 23*428 + 15; hence not 23 divides 9859 by NAT_4:9;
9859 = 29*339 + 28; hence not 29 divides 9859 by NAT_4:9;
9859 = 31*318 + 1; hence not 31 divides 9859 by NAT_4:9;
9859 = 37*266 + 17; hence not 37 divides 9859 by NAT_4:9;
9859 = 41*240 + 19; hence not 41 divides 9859 by NAT_4:9;
9859 = 43*229 + 12; hence not 43 divides 9859 by NAT_4:9;
9859 = 47*209 + 36; hence not 47 divides 9859 by NAT_4:9;
9859 = 53*186 + 1; hence not 53 divides 9859 by NAT_4:9;
9859 = 59*167 + 6; hence not 59 divides 9859 by NAT_4:9;
9859 = 61*161 + 38; hence not 61 divides 9859 by NAT_4:9;
9859 = 67*147 + 10; hence not 67 divides 9859 by NAT_4:9;
9859 = 71*138 + 61; hence not 71 divides 9859 by NAT_4:9;
9859 = 73*135 + 4; hence not 73 divides 9859 by NAT_4:9;
9859 = 79*124 + 63; hence not 79 divides 9859 by NAT_4:9;
9859 = 83*118 + 65; hence not 83 divides 9859 by NAT_4:9;
9859 = 89*110 + 69; hence not 89 divides 9859 by NAT_4:9;
9859 = 97*101 + 62; hence not 97 divides 9859 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9859 & n is prime
holds not n divides 9859 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9871 is prime
proof
now
9871 = 2*4935 + 1; hence not 2 divides 9871 by NAT_4:9;
9871 = 3*3290 + 1; hence not 3 divides 9871 by NAT_4:9;
9871 = 5*1974 + 1; hence not 5 divides 9871 by NAT_4:9;
9871 = 7*1410 + 1; hence not 7 divides 9871 by NAT_4:9;
9871 = 11*897 + 4; hence not 11 divides 9871 by NAT_4:9;
9871 = 13*759 + 4; hence not 13 divides 9871 by NAT_4:9;
9871 = 17*580 + 11; hence not 17 divides 9871 by NAT_4:9;
9871 = 19*519 + 10; hence not 19 divides 9871 by NAT_4:9;
9871 = 23*429 + 4; hence not 23 divides 9871 by NAT_4:9;
9871 = 29*340 + 11; hence not 29 divides 9871 by NAT_4:9;
9871 = 31*318 + 13; hence not 31 divides 9871 by NAT_4:9;
9871 = 37*266 + 29; hence not 37 divides 9871 by NAT_4:9;
9871 = 41*240 + 31; hence not 41 divides 9871 by NAT_4:9;
9871 = 43*229 + 24; hence not 43 divides 9871 by NAT_4:9;
9871 = 47*210 + 1; hence not 47 divides 9871 by NAT_4:9;
9871 = 53*186 + 13; hence not 53 divides 9871 by NAT_4:9;
9871 = 59*167 + 18; hence not 59 divides 9871 by NAT_4:9;
9871 = 61*161 + 50; hence not 61 divides 9871 by NAT_4:9;
9871 = 67*147 + 22; hence not 67 divides 9871 by NAT_4:9;
9871 = 71*139 + 2; hence not 71 divides 9871 by NAT_4:9;
9871 = 73*135 + 16; hence not 73 divides 9871 by NAT_4:9;
9871 = 79*124 + 75; hence not 79 divides 9871 by NAT_4:9;
9871 = 83*118 + 77; hence not 83 divides 9871 by NAT_4:9;
9871 = 89*110 + 81; hence not 89 divides 9871 by NAT_4:9;
9871 = 97*101 + 74; hence not 97 divides 9871 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9871 & n is prime
holds not n divides 9871 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 11
theorem
9883 is prime
proof
now
9883 = 2*4941 + 1; hence not 2 divides 9883 by NAT_4:9;
9883 = 3*3294 + 1; hence not 3 divides 9883 by NAT_4:9;
9883 = 5*1976 + 3; hence not 5 divides 9883 by NAT_4:9;
9883 = 7*1411 + 6; hence not 7 divides 9883 by NAT_4:9;
9883 = 11*898 + 5; hence not 11 divides 9883 by NAT_4:9;
9883 = 13*760 + 3; hence not 13 divides 9883 by NAT_4:9;
9883 = 17*581 + 6; hence not 17 divides 9883 by NAT_4:9;
9883 = 19*520 + 3; hence not 19 divides 9883 by NAT_4:9;
9883 = 23*429 + 16; hence not 23 divides 9883 by NAT_4:9;
9883 = 29*340 + 23; hence not 29 divides 9883 by NAT_4:9;
9883 = 31*318 + 25; hence not 31 divides 9883 by NAT_4:9;
9883 = 37*267 + 4; hence not 37 divides 9883 by NAT_4:9;
9883 = 41*241 + 2; hence not 41 divides 9883 by NAT_4:9;
9883 = 43*229 + 36; hence not 43 divides 9883 by NAT_4:9;
9883 = 47*210 + 13; hence not 47 divides 9883 by NAT_4:9;
9883 = 53*186 + 25; hence not 53 divides 9883 by NAT_4:9;
9883 = 59*167 + 30; hence not 59 divides 9883 by NAT_4:9;
9883 = 61*162 + 1; hence not 61 divides 9883 by NAT_4:9;
9883 = 67*147 + 34; hence not 67 divides 9883 by NAT_4:9;
9883 = 71*139 + 14; hence not 71 divides 9883 by NAT_4:9;
9883 = 73*135 + 28; hence not 73 divides 9883 by NAT_4:9;
9883 = 79*125 + 8; hence not 79 divides 9883 by NAT_4:9;
9883 = 83*119 + 6; hence not 83 divides 9883 by NAT_4:9;
9883 = 89*111 + 4; hence not 89 divides 9883 by NAT_4:9;
9883 = 97*101 + 86; hence not 97 divides 9883 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9883 & n is prime
holds not n divides 9883 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 3
theorem
9887 is prime
proof
now
9887 = 2*4943 + 1; hence not 2 divides 9887 by NAT_4:9;
9887 = 3*3295 + 2; hence not 3 divides 9887 by NAT_4:9;
9887 = 5*1977 + 2; hence not 5 divides 9887 by NAT_4:9;
9887 = 7*1412 + 3; hence not 7 divides 9887 by NAT_4:9;
9887 = 11*898 + 9; hence not 11 divides 9887 by NAT_4:9;
9887 = 13*760 + 7; hence not 13 divides 9887 by NAT_4:9;
9887 = 17*581 + 10; hence not 17 divides 9887 by NAT_4:9;
9887 = 19*520 + 7; hence not 19 divides 9887 by NAT_4:9;
9887 = 23*429 + 20; hence not 23 divides 9887 by NAT_4:9;
9887 = 29*340 + 27; hence not 29 divides 9887 by NAT_4:9;
9887 = 31*318 + 29; hence not 31 divides 9887 by NAT_4:9;
9887 = 37*267 + 8; hence not 37 divides 9887 by NAT_4:9;
9887 = 41*241 + 6; hence not 41 divides 9887 by NAT_4:9;
9887 = 43*229 + 40; hence not 43 divides 9887 by NAT_4:9;
9887 = 47*210 + 17; hence not 47 divides 9887 by NAT_4:9;
9887 = 53*186 + 29; hence not 53 divides 9887 by NAT_4:9;
9887 = 59*167 + 34; hence not 59 divides 9887 by NAT_4:9;
9887 = 61*162 + 5; hence not 61 divides 9887 by NAT_4:9;
9887 = 67*147 + 38; hence not 67 divides 9887 by NAT_4:9;
9887 = 71*139 + 18; hence not 71 divides 9887 by NAT_4:9;
9887 = 73*135 + 32; hence not 73 divides 9887 by NAT_4:9;
9887 = 79*125 + 12; hence not 79 divides 9887 by NAT_4:9;
9887 = 83*119 + 10; hence not 83 divides 9887 by NAT_4:9;
9887 = 89*111 + 8; hence not 89 divides 9887 by NAT_4:9;
9887 = 97*101 + 90; hence not 97 divides 9887 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9887 & n is prime
holds not n divides 9887 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 13
theorem
9901 is prime
proof
now
9901 = 2*4950 + 1; hence not 2 divides 9901 by NAT_4:9;
9901 = 3*3300 + 1; hence not 3 divides 9901 by NAT_4:9;
9901 = 5*1980 + 1; hence not 5 divides 9901 by NAT_4:9;
9901 = 7*1414 + 3; hence not 7 divides 9901 by NAT_4:9;
9901 = 11*900 + 1; hence not 11 divides 9901 by NAT_4:9;
9901 = 13*761 + 8; hence not 13 divides 9901 by NAT_4:9;
9901 = 17*582 + 7; hence not 17 divides 9901 by NAT_4:9;
9901 = 19*521 + 2; hence not 19 divides 9901 by NAT_4:9;
9901 = 23*430 + 11; hence not 23 divides 9901 by NAT_4:9;
9901 = 29*341 + 12; hence not 29 divides 9901 by NAT_4:9;
9901 = 31*319 + 12; hence not 31 divides 9901 by NAT_4:9;
9901 = 37*267 + 22; hence not 37 divides 9901 by NAT_4:9;
9901 = 41*241 + 20; hence not 41 divides 9901 by NAT_4:9;
9901 = 43*230 + 11; hence not 43 divides 9901 by NAT_4:9;
9901 = 47*210 + 31; hence not 47 divides 9901 by NAT_4:9;
9901 = 53*186 + 43; hence not 53 divides 9901 by NAT_4:9;
9901 = 59*167 + 48; hence not 59 divides 9901 by NAT_4:9;
9901 = 61*162 + 19; hence not 61 divides 9901 by NAT_4:9;
9901 = 67*147 + 52; hence not 67 divides 9901 by NAT_4:9;
9901 = 71*139 + 32; hence not 71 divides 9901 by NAT_4:9;
9901 = 73*135 + 46; hence not 73 divides 9901 by NAT_4:9;
9901 = 79*125 + 26; hence not 79 divides 9901 by NAT_4:9;
9901 = 83*119 + 24; hence not 83 divides 9901 by NAT_4:9;
9901 = 89*111 + 22; hence not 89 divides 9901 by NAT_4:9;
9901 = 97*102 + 7; hence not 97 divides 9901 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9901 & n is prime
holds not n divides 9901 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9907 is prime
proof
now
9907 = 2*4953 + 1; hence not 2 divides 9907 by NAT_4:9;
9907 = 3*3302 + 1; hence not 3 divides 9907 by NAT_4:9;
9907 = 5*1981 + 2; hence not 5 divides 9907 by NAT_4:9;
9907 = 7*1415 + 2; hence not 7 divides 9907 by NAT_4:9;
9907 = 11*900 + 7; hence not 11 divides 9907 by NAT_4:9;
9907 = 13*762 + 1; hence not 13 divides 9907 by NAT_4:9;
9907 = 17*582 + 13; hence not 17 divides 9907 by NAT_4:9;
9907 = 19*521 + 8; hence not 19 divides 9907 by NAT_4:9;
9907 = 23*430 + 17; hence not 23 divides 9907 by NAT_4:9;
9907 = 29*341 + 18; hence not 29 divides 9907 by NAT_4:9;
9907 = 31*319 + 18; hence not 31 divides 9907 by NAT_4:9;
9907 = 37*267 + 28; hence not 37 divides 9907 by NAT_4:9;
9907 = 41*241 + 26; hence not 41 divides 9907 by NAT_4:9;
9907 = 43*230 + 17; hence not 43 divides 9907 by NAT_4:9;
9907 = 47*210 + 37; hence not 47 divides 9907 by NAT_4:9;
9907 = 53*186 + 49; hence not 53 divides 9907 by NAT_4:9;
9907 = 59*167 + 54; hence not 59 divides 9907 by NAT_4:9;
9907 = 61*162 + 25; hence not 61 divides 9907 by NAT_4:9;
9907 = 67*147 + 58; hence not 67 divides 9907 by NAT_4:9;
9907 = 71*139 + 38; hence not 71 divides 9907 by NAT_4:9;
9907 = 73*135 + 52; hence not 73 divides 9907 by NAT_4:9;
9907 = 79*125 + 32; hence not 79 divides 9907 by NAT_4:9;
9907 = 83*119 + 30; hence not 83 divides 9907 by NAT_4:9;
9907 = 89*111 + 28; hence not 89 divides 9907 by NAT_4:9;
9907 = 97*102 + 13; hence not 97 divides 9907 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9907 & n is prime
holds not n divides 9907 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 15
theorem
9923 is prime
proof
now
9923 = 2*4961 + 1; hence not 2 divides 9923 by NAT_4:9;
9923 = 3*3307 + 2; hence not 3 divides 9923 by NAT_4:9;
9923 = 5*1984 + 3; hence not 5 divides 9923 by NAT_4:9;
9923 = 7*1417 + 4; hence not 7 divides 9923 by NAT_4:9;
9923 = 11*902 + 1; hence not 11 divides 9923 by NAT_4:9;
9923 = 13*763 + 4; hence not 13 divides 9923 by NAT_4:9;
9923 = 17*583 + 12; hence not 17 divides 9923 by NAT_4:9;
9923 = 19*522 + 5; hence not 19 divides 9923 by NAT_4:9;
9923 = 23*431 + 10; hence not 23 divides 9923 by NAT_4:9;
9923 = 29*342 + 5; hence not 29 divides 9923 by NAT_4:9;
9923 = 31*320 + 3; hence not 31 divides 9923 by NAT_4:9;
9923 = 37*268 + 7; hence not 37 divides 9923 by NAT_4:9;
9923 = 41*242 + 1; hence not 41 divides 9923 by NAT_4:9;
9923 = 43*230 + 33; hence not 43 divides 9923 by NAT_4:9;
9923 = 47*211 + 6; hence not 47 divides 9923 by NAT_4:9;
9923 = 53*187 + 12; hence not 53 divides 9923 by NAT_4:9;
9923 = 59*168 + 11; hence not 59 divides 9923 by NAT_4:9;
9923 = 61*162 + 41; hence not 61 divides 9923 by NAT_4:9;
9923 = 67*148 + 7; hence not 67 divides 9923 by NAT_4:9;
9923 = 71*139 + 54; hence not 71 divides 9923 by NAT_4:9;
9923 = 73*135 + 68; hence not 73 divides 9923 by NAT_4:9;
9923 = 79*125 + 48; hence not 79 divides 9923 by NAT_4:9;
9923 = 83*119 + 46; hence not 83 divides 9923 by NAT_4:9;
9923 = 89*111 + 44; hence not 89 divides 9923 by NAT_4:9;
9923 = 97*102 + 29; hence not 97 divides 9923 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9923 & n is prime
holds not n divides 9923 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9929 is prime
proof
now
9929 = 2*4964 + 1; hence not 2 divides 9929 by NAT_4:9;
9929 = 3*3309 + 2; hence not 3 divides 9929 by NAT_4:9;
9929 = 5*1985 + 4; hence not 5 divides 9929 by NAT_4:9;
9929 = 7*1418 + 3; hence not 7 divides 9929 by NAT_4:9;
9929 = 11*902 + 7; hence not 11 divides 9929 by NAT_4:9;
9929 = 13*763 + 10; hence not 13 divides 9929 by NAT_4:9;
9929 = 17*584 + 1; hence not 17 divides 9929 by NAT_4:9;
9929 = 19*522 + 11; hence not 19 divides 9929 by NAT_4:9;
9929 = 23*431 + 16; hence not 23 divides 9929 by NAT_4:9;
9929 = 29*342 + 11; hence not 29 divides 9929 by NAT_4:9;
9929 = 31*320 + 9; hence not 31 divides 9929 by NAT_4:9;
9929 = 37*268 + 13; hence not 37 divides 9929 by NAT_4:9;
9929 = 41*242 + 7; hence not 41 divides 9929 by NAT_4:9;
9929 = 43*230 + 39; hence not 43 divides 9929 by NAT_4:9;
9929 = 47*211 + 12; hence not 47 divides 9929 by NAT_4:9;
9929 = 53*187 + 18; hence not 53 divides 9929 by NAT_4:9;
9929 = 59*168 + 17; hence not 59 divides 9929 by NAT_4:9;
9929 = 61*162 + 47; hence not 61 divides 9929 by NAT_4:9;
9929 = 67*148 + 13; hence not 67 divides 9929 by NAT_4:9;
9929 = 71*139 + 60; hence not 71 divides 9929 by NAT_4:9;
9929 = 73*136 + 1; hence not 73 divides 9929 by NAT_4:9;
9929 = 79*125 + 54; hence not 79 divides 9929 by NAT_4:9;
9929 = 83*119 + 52; hence not 83 divides 9929 by NAT_4:9;
9929 = 89*111 + 50; hence not 89 divides 9929 by NAT_4:9;
9929 = 97*102 + 35; hence not 97 divides 9929 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9929 & n is prime
holds not n divides 9929 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT
theorem
9931 is prime
proof
now
9931 = 2*4965 + 1; hence not 2 divides 9931 by NAT_4:9;
9931 = 3*3310 + 1; hence not 3 divides 9931 by NAT_4:9;
9931 = 5*1986 + 1; hence not 5 divides 9931 by NAT_4:9;
9931 = 7*1418 + 5; hence not 7 divides 9931 by NAT_4:9;
9931 = 11*902 + 9; hence not 11 divides 9931 by NAT_4:9;
9931 = 13*763 + 12; hence not 13 divides 9931 by NAT_4:9;
9931 = 17*584 + 3; hence not 17 divides 9931 by NAT_4:9;
9931 = 19*522 + 13; hence not 19 divides 9931 by NAT_4:9;
9931 = 23*431 + 18; hence not 23 divides 9931 by NAT_4:9;
9931 = 29*342 + 13; hence not 29 divides 9931 by NAT_4:9;
9931 = 31*320 + 11; hence not 31 divides 9931 by NAT_4:9;
9931 = 37*268 + 15; hence not 37 divides 9931 by NAT_4:9;
9931 = 41*242 + 9; hence not 41 divides 9931 by NAT_4:9;
9931 = 43*230 + 41; hence not 43 divides 9931 by NAT_4:9;
9931 = 47*211 + 14; hence not 47 divides 9931 by NAT_4:9;
9931 = 53*187 + 20; hence not 53 divides 9931 by NAT_4:9;
9931 = 59*168 + 19; hence not 59 divides 9931 by NAT_4:9;
9931 = 61*162 + 49; hence not 61 divides 9931 by NAT_4:9;
9931 = 67*148 + 15; hence not 67 divides 9931 by NAT_4:9;
9931 = 71*139 + 62; hence not 71 divides 9931 by NAT_4:9;
9931 = 73*136 + 3; hence not 73 divides 9931 by NAT_4:9;
9931 = 79*125 + 56; hence not 79 divides 9931 by NAT_4:9;
9931 = 83*119 + 54; hence not 83 divides 9931 by NAT_4:9;
9931 = 89*111 + 52; hence not 89 divides 9931 by NAT_4:9;
9931 = 97*102 + 37; hence not 97 divides 9931 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9931 & n is prime
holds not n divides 9931 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 9
theorem
9941 is prime
proof
now
9941 = 2*4970 + 1; hence not 2 divides 9941 by NAT_4:9;
9941 = 3*3313 + 2; hence not 3 divides 9941 by NAT_4:9;
9941 = 5*1988 + 1; hence not 5 divides 9941 by NAT_4:9;
9941 = 7*1420 + 1; hence not 7 divides 9941 by NAT_4:9;
9941 = 11*903 + 8; hence not 11 divides 9941 by NAT_4:9;
9941 = 13*764 + 9; hence not 13 divides 9941 by NAT_4:9;
9941 = 17*584 + 13; hence not 17 divides 9941 by NAT_4:9;
9941 = 19*523 + 4; hence not 19 divides 9941 by NAT_4:9;
9941 = 23*432 + 5; hence not 23 divides 9941 by NAT_4:9;
9941 = 29*342 + 23; hence not 29 divides 9941 by NAT_4:9;
9941 = 31*320 + 21; hence not 31 divides 9941 by NAT_4:9;
9941 = 37*268 + 25; hence not 37 divides 9941 by NAT_4:9;
9941 = 41*242 + 19; hence not 41 divides 9941 by NAT_4:9;
9941 = 43*231 + 8; hence not 43 divides 9941 by NAT_4:9;
9941 = 47*211 + 24; hence not 47 divides 9941 by NAT_4:9;
9941 = 53*187 + 30; hence not 53 divides 9941 by NAT_4:9;
9941 = 59*168 + 29; hence not 59 divides 9941 by NAT_4:9;
9941 = 61*162 + 59; hence not 61 divides 9941 by NAT_4:9;
9941 = 67*148 + 25; hence not 67 divides 9941 by NAT_4:9;
9941 = 71*140 + 1; hence not 71 divides 9941 by NAT_4:9;
9941 = 73*136 + 13; hence not 73 divides 9941 by NAT_4:9;
9941 = 79*125 + 66; hence not 79 divides 9941 by NAT_4:9;
9941 = 83*119 + 64; hence not 83 divides 9941 by NAT_4:9;
9941 = 89*111 + 62; hence not 89 divides 9941 by NAT_4:9;
9941 = 97*102 + 47; hence not 97 divides 9941 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9941 & n is prime
holds not n divides 9941 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 7
theorem
9949 is prime
proof
now
9949 = 2*4974 + 1; hence not 2 divides 9949 by NAT_4:9;
9949 = 3*3316 + 1; hence not 3 divides 9949 by NAT_4:9;
9949 = 5*1989 + 4; hence not 5 divides 9949 by NAT_4:9;
9949 = 7*1421 + 2; hence not 7 divides 9949 by NAT_4:9;
9949 = 11*904 + 5; hence not 11 divides 9949 by NAT_4:9;
9949 = 13*765 + 4; hence not 13 divides 9949 by NAT_4:9;
9949 = 17*585 + 4; hence not 17 divides 9949 by NAT_4:9;
9949 = 19*523 + 12; hence not 19 divides 9949 by NAT_4:9;
9949 = 23*432 + 13; hence not 23 divides 9949 by NAT_4:9;
9949 = 29*343 + 2; hence not 29 divides 9949 by NAT_4:9;
9949 = 31*320 + 29; hence not 31 divides 9949 by NAT_4:9;
9949 = 37*268 + 33; hence not 37 divides 9949 by NAT_4:9;
9949 = 41*242 + 27; hence not 41 divides 9949 by NAT_4:9;
9949 = 43*231 + 16; hence not 43 divides 9949 by NAT_4:9;
9949 = 47*211 + 32; hence not 47 divides 9949 by NAT_4:9;
9949 = 53*187 + 38; hence not 53 divides 9949 by NAT_4:9;
9949 = 59*168 + 37; hence not 59 divides 9949 by NAT_4:9;
9949 = 61*163 + 6; hence not 61 divides 9949 by NAT_4:9;
9949 = 67*148 + 33; hence not 67 divides 9949 by NAT_4:9;
9949 = 71*140 + 9; hence not 71 divides 9949 by NAT_4:9;
9949 = 73*136 + 21; hence not 73 divides 9949 by NAT_4:9;
9949 = 79*125 + 74; hence not 79 divides 9949 by NAT_4:9;
9949 = 83*119 + 72; hence not 83 divides 9949 by NAT_4:9;
9949 = 89*111 + 70; hence not 89 divides 9949 by NAT_4:9;
9949 = 97*102 + 55; hence not 97 divides 9949 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9949 & n is prime
holds not n divides 9949 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 17
theorem
9967 is prime
proof
now
9967 = 2*4983 + 1; hence not 2 divides 9967 by NAT_4:9;
9967 = 3*3322 + 1; hence not 3 divides 9967 by NAT_4:9;
9967 = 5*1993 + 2; hence not 5 divides 9967 by NAT_4:9;
9967 = 7*1423 + 6; hence not 7 divides 9967 by NAT_4:9;
9967 = 11*906 + 1; hence not 11 divides 9967 by NAT_4:9;
9967 = 13*766 + 9; hence not 13 divides 9967 by NAT_4:9;
9967 = 17*586 + 5; hence not 17 divides 9967 by NAT_4:9;
9967 = 19*524 + 11; hence not 19 divides 9967 by NAT_4:9;
9967 = 23*433 + 8; hence not 23 divides 9967 by NAT_4:9;
9967 = 29*343 + 20; hence not 29 divides 9967 by NAT_4:9;
9967 = 31*321 + 16; hence not 31 divides 9967 by NAT_4:9;
9967 = 37*269 + 14; hence not 37 divides 9967 by NAT_4:9;
9967 = 41*243 + 4; hence not 41 divides 9967 by NAT_4:9;
9967 = 43*231 + 34; hence not 43 divides 9967 by NAT_4:9;
9967 = 47*212 + 3; hence not 47 divides 9967 by NAT_4:9;
9967 = 53*188 + 3; hence not 53 divides 9967 by NAT_4:9;
9967 = 59*168 + 55; hence not 59 divides 9967 by NAT_4:9;
9967 = 61*163 + 24; hence not 61 divides 9967 by NAT_4:9;
9967 = 67*148 + 51; hence not 67 divides 9967 by NAT_4:9;
9967 = 71*140 + 27; hence not 71 divides 9967 by NAT_4:9;
9967 = 73*136 + 39; hence not 73 divides 9967 by NAT_4:9;
9967 = 79*126 + 13; hence not 79 divides 9967 by NAT_4:9;
9967 = 83*120 + 7; hence not 83 divides 9967 by NAT_4:9;
9967 = 89*111 + 88; hence not 89 divides 9967 by NAT_4:9;
9967 = 97*102 + 73; hence not 97 divides 9967 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9967 & n is prime
holds not n divides 9967 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;
::$CT 5
theorem
9973 is prime
proof
now
9973 = 2*4986 + 1; hence not 2 divides 9973 by NAT_4:9;
9973 = 3*3324 + 1; hence not 3 divides 9973 by NAT_4:9;
9973 = 5*1994 + 3; hence not 5 divides 9973 by NAT_4:9;
9973 = 7*1424 + 5; hence not 7 divides 9973 by NAT_4:9;
9973 = 11*906 + 7; hence not 11 divides 9973 by NAT_4:9;
9973 = 13*767 + 2; hence not 13 divides 9973 by NAT_4:9;
9973 = 17*586 + 11; hence not 17 divides 9973 by NAT_4:9;
9973 = 19*524 + 17; hence not 19 divides 9973 by NAT_4:9;
9973 = 23*433 + 14; hence not 23 divides 9973 by NAT_4:9;
9973 = 29*343 + 26; hence not 29 divides 9973 by NAT_4:9;
9973 = 31*321 + 22; hence not 31 divides 9973 by NAT_4:9;
9973 = 37*269 + 20; hence not 37 divides 9973 by NAT_4:9;
9973 = 41*243 + 10; hence not 41 divides 9973 by NAT_4:9;
9973 = 43*231 + 40; hence not 43 divides 9973 by NAT_4:9;
9973 = 47*212 + 9; hence not 47 divides 9973 by NAT_4:9;
9973 = 53*188 + 9; hence not 53 divides 9973 by NAT_4:9;
9973 = 59*169 + 2; hence not 59 divides 9973 by NAT_4:9;
9973 = 61*163 + 30; hence not 61 divides 9973 by NAT_4:9;
9973 = 67*148 + 57; hence not 67 divides 9973 by NAT_4:9;
9973 = 71*140 + 33; hence not 71 divides 9973 by NAT_4:9;
9973 = 73*136 + 45; hence not 73 divides 9973 by NAT_4:9;
9973 = 79*126 + 19; hence not 79 divides 9973 by NAT_4:9;
9973 = 83*120 + 13; hence not 83 divides 9973 by NAT_4:9;
9973 = 89*112 + 5; hence not 89 divides 9973 by NAT_4:9;
9973 = 97*102 + 79; hence not 97 divides 9973 by NAT_4:9;
end;
then for n being Element of NAT st 1 < n & n*n <= 9973 & n is prime
holds not n divides 9973 by XPRIMET1:50;
hence thesis by NAT_4:14;
end;