
theorem
  457 is prime
proof
  now
    457 = 2*228 + 1; hence not 2 divides 457 by NAT_4:9;
    457 = 3*152 + 1; hence not 3 divides 457 by NAT_4:9;
    457 = 5*91 + 2; hence not 5 divides 457 by NAT_4:9;
    457 = 7*65 + 2; hence not 7 divides 457 by NAT_4:9;
    457 = 11*41 + 6; hence not 11 divides 457 by NAT_4:9;
    457 = 13*35 + 2; hence not 13 divides 457 by NAT_4:9;
    457 = 17*26 + 15; hence not 17 divides 457 by NAT_4:9;
    457 = 19*24 + 1; hence not 19 divides 457 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 457 & n is prime
  holds not n divides 457 by XPRIMET1:16;
  hence thesis by NAT_4:14;
