Factorial prime
A factorial prime is a prime number that is one less or one more than a factorial.
The first 10 factorial primes are :
n! − 1 is prime for :
n! + 1 is prime for :
No other factorial primes are known.
When both n! + 1 and n! − 1 are composite, there must be at least 2n + 1 consecutive composite numbers around n!, since besides n! ± 1 and n! itself, also, each number of form n! ± k is divisible by k for 2 ≤ k ≤ n. However, the necessary length of this gap is asymptotically smaller than the average composite run for integers of similar size.