I'm not sure if these have been looked into extensively (they probably have, I just have a hard time finding them), but I was just wondering about a couple conjectures I thought up and tested by hand for a bit. Matlab can't run it for very long. Let me know if anyone finds a contradiction or if there are any links to more information about these. [itex]\forall[/itex]n[itex]\epsilon[/itex]integers, n is not prime (n! is not prime) [itex]\forall[/itex]n[itex]\epsilon[/itex]integers, n is not prime ((n!+1) is not prime) Also I'm new to proofs and this method of formatting, I'm just playing around with these for fun so let me know if I have my notation wrong. I couldn't find the correct capital Z that stands for integers. Also should I say n is composite or should I say n is not prime? Does it matter?