TITLE: Are there infinitely many primes of the form $n!+1$?
QUESTION [6 upvotes]: For some numbers $n!+1$ is prime, but all such numbers are not prime. For example, $5!+1 = 11\times 11$. The question is this:
Are there infinitely many primes of the form $n!+1$?

REPLY [3 votes]: Please see answers to another related question here (Is n!+1 often a prime?).
There you can learn:

what factorial primes are, and how many are known to us at the present moment
some probability heuristics about existence and frequency of factorial primes
some collaborative computation efforts to find more factorial primes

Hope this would help.