
theorem
  269 is prime
proof
  now
    269 = 2*134 + 1; hence not 2 divides 269 by NAT_4:9;
    269 = 3*89 + 2; hence not 3 divides 269 by NAT_4:9;
    269 = 5*53 + 4; hence not 5 divides 269 by NAT_4:9;
    269 = 7*38 + 3; hence not 7 divides 269 by NAT_4:9;
    269 = 11*24 + 5; hence not 11 divides 269 by NAT_4:9;
    269 = 13*20 + 9; hence not 13 divides 269 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 269 & n is prime
  holds not n divides 269 by XPRIMET1:12;
  hence thesis by NAT_4:14;
