
theorem
  109 is prime
proof
  now
    109 = 2*54 + 1; hence not 2 divides 109 by NAT_4:9;
    109 = 3*36 + 1; hence not 3 divides 109 by NAT_4:9;
    109 = 5*21 + 4; hence not 5 divides 109 by NAT_4:9;
    109 = 7*15 + 4; hence not 7 divides 109 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 109 & n is prime
  holds not n divides 109 by XPRIMET1:8;
  hence thesis by NAT_4:14;
