
theorem
  251 is prime
proof
  now
    251 = 2*125 + 1; hence not 2 divides 251 by NAT_4:9;
    251 = 3*83 + 2; hence not 3 divides 251 by NAT_4:9;
    251 = 5*50 + 1; hence not 5 divides 251 by NAT_4:9;
    251 = 7*35 + 6; hence not 7 divides 251 by NAT_4:9;
    251 = 11*22 + 9; hence not 11 divides 251 by NAT_4:9;
    251 = 13*19 + 4; hence not 13 divides 251 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 251 & n is prime
  holds not n divides 251 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
