阶乘素数

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

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減一。

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

使n!-1是素数的n有: 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, 147855, ...OEIS中的数列A002982

阶乘素数有趣之處是它們有時表示了一連串的連續合數的開始或終結。例如質數12!-1 = 479 001 599後一個質數為479 001 629,中間有30個合數。

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