
theorem
  467 is prime
proof
  now
    467 = 2*233 + 1; hence not 2 divides 467 by NAT_4:9;
    467 = 3*155 + 2; hence not 3 divides 467 by NAT_4:9;
    467 = 5*93 + 2; hence not 5 divides 467 by NAT_4:9;
    467 = 7*66 + 5; hence not 7 divides 467 by NAT_4:9;
    467 = 11*42 + 5; hence not 11 divides 467 by NAT_4:9;
    467 = 13*35 + 12; hence not 13 divides 467 by NAT_4:9;
    467 = 17*27 + 8; hence not 17 divides 467 by NAT_4:9;
    467 = 19*24 + 11; hence not 19 divides 467 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 467 & n is prime
  holds not n divides 467 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
