
theorem
  433 is prime
proof
  now
    433 = 2*216 + 1; hence not 2 divides 433 by NAT_4:9;
    433 = 3*144 + 1; hence not 3 divides 433 by NAT_4:9;
    433 = 5*86 + 3; hence not 5 divides 433 by NAT_4:9;
    433 = 7*61 + 6; hence not 7 divides 433 by NAT_4:9;
    433 = 11*39 + 4; hence not 11 divides 433 by NAT_4:9;
    433 = 13*33 + 4; hence not 13 divides 433 by NAT_4:9;
    433 = 17*25 + 8; hence not 17 divides 433 by NAT_4:9;
    433 = 19*22 + 15; hence not 19 divides 433 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 433 & n is prime
  holds not n divides 433 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
