A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even).
[1] The first 10 factorial primes (for n = 1, 2, 3, 4, 6, 7, 11, 12, 14) are (sequence A088054 in the OEIS): n!
− 1 is prime for (sequence A002982 in the OEIS): n!
+ 1 is prime for (sequence A002981 in the OEIS): No other factorial primes are known as of December 2024[update].
± 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 (see prime gap).