
theorem
  31 is prime
proof
  now
    31 = 2*15 + 1; hence not 2 divides 31 by NAT_4:9;
    31 = 3*10 + 1; hence not 3 divides 31 by NAT_4:9;
    31 = 5*6 + 1; hence not 5 divides 31 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 31 & n is prime
  holds not n divides 31 by XPRIMET1:6;
  hence thesis by NAT_4:14;
end;
