阶乘素数是和某个阶乘相邻的素数，即它是某个阶乘的增一或减一。

最小的几个阶乘素数为： 2(0!+1或1!+1), 3(2!+1), 5(3!-1), 7(3!+1), 23(4!-1), 719(6!-1), 5039(7!-1), 39916801(11!+1), 479001599(12!-1), 87178291199(14!-1), ...（OEIS中的数列A088054）

使n!+1是素数的n有： 0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, 110059, 150209, ...（OEIS中的数列A002981）

A factorial prime is a prime number that is one less or one more than a factorial (all factorials > 1 are even). The first few factorial primes are:

n! − 1 is prime for (sequence A002982 in OEIS):

n! + 1 is prime for (sequence A002981 in OEIS):

No other factorial primes are known as of August 2015.