
theorem
  257 is prime
proof
  now
    257 = 2*128 + 1; hence not 2 divides 257 by NAT_4:9;
    257 = 3*85 + 2; hence not 3 divides 257 by NAT_4:9;
    257 = 5*51 + 2; hence not 5 divides 257 by NAT_4:9;
    257 = 7*36 + 5; hence not 7 divides 257 by NAT_4:9;
    257 = 11*23 + 4; hence not 11 divides 257 by NAT_4:9;
    257 = 13*19 + 10; hence not 13 divides 257 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 257 & n is prime
  holds not n divides 257 by XPRIMET1:12;
  hence thesis by NAT_4:14;
