
theorem
  479 is prime
proof
  now
    479 = 2*239 + 1; hence not 2 divides 479 by NAT_4:9;
    479 = 3*159 + 2; hence not 3 divides 479 by NAT_4:9;
    479 = 5*95 + 4; hence not 5 divides 479 by NAT_4:9;
    479 = 7*68 + 3; hence not 7 divides 479 by NAT_4:9;
    479 = 11*43 + 6; hence not 11 divides 479 by NAT_4:9;
    479 = 13*36 + 11; hence not 13 divides 479 by NAT_4:9;
    479 = 17*28 + 3; hence not 17 divides 479 by NAT_4:9;
    479 = 19*25 + 4; hence not 19 divides 479 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 479 & n is prime
  holds not n divides 479 by XPRIMET1:16;
  hence thesis by NAT_4:14;
