
theorem
  641 is prime
proof
  now
    641 = 2*320 + 1; hence not 2 divides 641 by NAT_4:9;
    641 = 3*213 + 2; hence not 3 divides 641 by NAT_4:9;
    641 = 5*128 + 1; hence not 5 divides 641 by NAT_4:9;
    641 = 7*91 + 4; hence not 7 divides 641 by NAT_4:9;
    641 = 11*58 + 3; hence not 11 divides 641 by NAT_4:9;
    641 = 13*49 + 4; hence not 13 divides 641 by NAT_4:9;
    641 = 17*37 + 12; hence not 17 divides 641 by NAT_4:9;
    641 = 19*33 + 14; hence not 19 divides 641 by NAT_4:9;
    641 = 23*27 + 20; hence not 23 divides 641 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 641 & n is prime
  holds not n divides 641 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
