
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;
