
theorem
  443 is prime
proof
  now
    443 = 2*221 + 1; hence not 2 divides 443 by NAT_4:9;
    443 = 3*147 + 2; hence not 3 divides 443 by NAT_4:9;
    443 = 5*88 + 3; hence not 5 divides 443 by NAT_4:9;
    443 = 7*63 + 2; hence not 7 divides 443 by NAT_4:9;
    443 = 11*40 + 3; hence not 11 divides 443 by NAT_4:9;
    443 = 13*34 + 1; hence not 13 divides 443 by NAT_4:9;
    443 = 17*26 + 1; hence not 17 divides 443 by NAT_4:9;
    443 = 19*23 + 6; hence not 19 divides 443 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 443 & n is prime
  holds not n divides 443 by XPRIMET1:16;
  hence thesis by NAT_4:14;
