
theorem
  647 is prime
proof
  now
    647 = 2*323 + 1; hence not 2 divides 647 by NAT_4:9;
    647 = 3*215 + 2; hence not 3 divides 647 by NAT_4:9;
    647 = 5*129 + 2; hence not 5 divides 647 by NAT_4:9;
    647 = 7*92 + 3; hence not 7 divides 647 by NAT_4:9;
    647 = 11*58 + 9; hence not 11 divides 647 by NAT_4:9;
    647 = 13*49 + 10; hence not 13 divides 647 by NAT_4:9;
    647 = 17*38 + 1; hence not 17 divides 647 by NAT_4:9;
    647 = 19*34 + 1; hence not 19 divides 647 by NAT_4:9;
    647 = 23*28 + 3; hence not 23 divides 647 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 647 & n is prime
  holds not n divides 647 by XPRIMET1:18;
  hence thesis by NAT_4:14;
