
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;
