
theorem
  463 is prime
proof
  now
    463 = 2*231 + 1; hence not 2 divides 463 by NAT_4:9;
    463 = 3*154 + 1; hence not 3 divides 463 by NAT_4:9;
    463 = 5*92 + 3; hence not 5 divides 463 by NAT_4:9;
    463 = 7*66 + 1; hence not 7 divides 463 by NAT_4:9;
    463 = 11*42 + 1; hence not 11 divides 463 by NAT_4:9;
    463 = 13*35 + 8; hence not 13 divides 463 by NAT_4:9;
    463 = 17*27 + 4; hence not 17 divides 463 by NAT_4:9;
    463 = 19*24 + 7; hence not 19 divides 463 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 463 & n is prime
  holds not n divides 463 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
