
theorem
  661 is prime
proof
  now
    661 = 2*330 + 1; hence not 2 divides 661 by NAT_4:9;
    661 = 3*220 + 1; hence not 3 divides 661 by NAT_4:9;
    661 = 5*132 + 1; hence not 5 divides 661 by NAT_4:9;
    661 = 7*94 + 3; hence not 7 divides 661 by NAT_4:9;
    661 = 11*60 + 1; hence not 11 divides 661 by NAT_4:9;
    661 = 13*50 + 11; hence not 13 divides 661 by NAT_4:9;
    661 = 17*38 + 15; hence not 17 divides 661 by NAT_4:9;
    661 = 19*34 + 15; hence not 19 divides 661 by NAT_4:9;
    661 = 23*28 + 17; hence not 23 divides 661 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 661 & n is prime
  holds not n divides 661 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
