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阶乘素数

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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, 288465, 308084, ...(OEIS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, 208003, ...(OEIS数列A002982

阶乘素数有趣之处是它们有时表示了一连串的连续合数的开始或终结。例如素数12!-1 = 479 001 599后一个素数为479 001 629,中间有30个合数。

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阶乘素数
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