
theorem
  499 is prime
proof
  now
    499 = 2*249 + 1; hence not 2 divides 499 by NAT_4:9;
    499 = 3*166 + 1; hence not 3 divides 499 by NAT_4:9;
    499 = 5*99 + 4; hence not 5 divides 499 by NAT_4:9;
    499 = 7*71 + 2; hence not 7 divides 499 by NAT_4:9;
    499 = 11*45 + 4; hence not 11 divides 499 by NAT_4:9;
    499 = 13*38 + 5; hence not 13 divides 499 by NAT_4:9;
    499 = 17*29 + 6; hence not 17 divides 499 by NAT_4:9;
    499 = 19*26 + 5; hence not 19 divides 499 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 499 & n is prime
  holds not n divides 499 by XPRIMET1:16;
  hence thesis by NAT_4:14;
