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), ...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,