A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for n = 1, 2, 3, 4, 6, 7, 11, 12, 14) 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 (see prime gap).