
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;
