
theorem
  229 is prime
proof
  now
    229 = 2*114 + 1; hence not 2 divides 229 by NAT_4:9;
    229 = 3*76 + 1; hence not 3 divides 229 by NAT_4:9;
    229 = 5*45 + 4; hence not 5 divides 229 by NAT_4:9;
    229 = 7*32 + 5; hence not 7 divides 229 by NAT_4:9;
    229 = 11*20 + 9; hence not 11 divides 229 by NAT_4:9;
    229 = 13*17 + 8; hence not 13 divides 229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 229 & n is prime
  holds not n divides 229 by XPRIMET1:12;
  hence thesis by NAT_4:14;
