Can someone please explain this better then the OG?

153. Does the integer k have a factor p such that 1>p>k?
(1) k>4!
(2) 13! + 2 <= k <= 13! + 13

I understand that (1) is not sufficient.
With (2), how can you be sure that k is not a prime number between 13!+2 and 13! + 13?

Thanks!