
theorem
  227 is prime
proof
  now
    227 = 2*113 + 1; hence not 2 divides 227 by NAT_4:9;
    227 = 3*75 + 2; hence not 3 divides 227 by NAT_4:9;
    227 = 5*45 + 2; hence not 5 divides 227 by NAT_4:9;
    227 = 7*32 + 3; hence not 7 divides 227 by NAT_4:9;
    227 = 11*20 + 7; hence not 11 divides 227 by NAT_4:9;
    227 = 13*17 + 6; hence not 13 divides 227 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 227 & n is prime
  holds not n divides 227 by XPRIMET1:12;
  hence thesis by NAT_4:14;
