
theorem
  503 is prime
proof
  now
    503 = 2*251 + 1; hence not 2 divides 503 by NAT_4:9;
    503 = 3*167 + 2; hence not 3 divides 503 by NAT_4:9;
    503 = 5*100 + 3; hence not 5 divides 503 by NAT_4:9;
    503 = 7*71 + 6; hence not 7 divides 503 by NAT_4:9;
    503 = 11*45 + 8; hence not 11 divides 503 by NAT_4:9;
    503 = 13*38 + 9; hence not 13 divides 503 by NAT_4:9;
    503 = 17*29 + 10; hence not 17 divides 503 by NAT_4:9;
    503 = 19*26 + 9; hence not 19 divides 503 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 503 & n is prime
  holds not n divides 503 by XPRIMET1:16;
  hence thesis by NAT_4:14;
