
theorem
  509 is prime
proof
  now
    509 = 2*254 + 1; hence not 2 divides 509 by NAT_4:9;
    509 = 3*169 + 2; hence not 3 divides 509 by NAT_4:9;
    509 = 5*101 + 4; hence not 5 divides 509 by NAT_4:9;
    509 = 7*72 + 5; hence not 7 divides 509 by NAT_4:9;
    509 = 11*46 + 3; hence not 11 divides 509 by NAT_4:9;
    509 = 13*39 + 2; hence not 13 divides 509 by NAT_4:9;
    509 = 17*29 + 16; hence not 17 divides 509 by NAT_4:9;
    509 = 19*26 + 15; hence not 19 divides 509 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 509 & n is prime
  holds not n divides 509 by XPRIMET1:16;
  hence thesis by NAT_4:14;
