
theorem
  101 is prime
proof
  now
    101 = 2*50 + 1; hence not 2 divides 101 by NAT_4:9;
    101 = 3*33 + 2; hence not 3 divides 101 by NAT_4:9;
    101 = 5*20 + 1; hence not 5 divides 101 by NAT_4:9;
    101 = 7*14 + 3; hence not 7 divides 101 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 101 & n is prime
  holds not n divides 101 by XPRIMET1:8;
  hence thesis by NAT_4:14;
