
theorem
  97 is prime
proof
  now
    97 = 2*48 + 1; hence not 2 divides 97 by NAT_4:9;
    97 = 3*32 + 1; hence not 3 divides 97 by NAT_4:9;
    97 = 5*19 + 2; hence not 5 divides 97 by NAT_4:9;
    97 = 7*13 + 6; hence not 7 divides 97 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 97 & n is prime
  holds not n divides 97 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
