I was looking at an article about factorial primes, and I noticed that both $n!+1$ and $n!-1$ were not prime. (As in, there are no numbers $n$ such that both $n!+1$ and $n!-1$ are prime). I think that for any $n$, both $n!+1$ and $n!-1$ cannot be prime. Is this an easy thing to prove? If so, how? Would Wilson's theorem be applicable in some way?
This is just a conjecture that I am asking out of curiosity. I would love some thoughts on how one might approach such a problem as this one.
from Hot Weekly Questions - Mathematics Stack Exchange
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