
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;
