
theorem
  659 is prime
proof
  now
    659 = 2*329 + 1; hence not 2 divides 659 by NAT_4:9;
    659 = 3*219 + 2; hence not 3 divides 659 by NAT_4:9;
    659 = 5*131 + 4; hence not 5 divides 659 by NAT_4:9;
    659 = 7*94 + 1; hence not 7 divides 659 by NAT_4:9;
    659 = 11*59 + 10; hence not 11 divides 659 by NAT_4:9;
    659 = 13*50 + 9; hence not 13 divides 659 by NAT_4:9;
    659 = 17*38 + 13; hence not 17 divides 659 by NAT_4:9;
    659 = 19*34 + 13; hence not 19 divides 659 by NAT_4:9;
    659 = 23*28 + 15; hence not 23 divides 659 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 659 & n is prime
  holds not n divides 659 by XPRIMET1:18;
  hence thesis by NAT_4:14;
