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单词 FactorialPrime
释义

factorial prime


A factorial primeMathworldPlanetmath is a number that is one less or one more than a factorialMathworldPlanetmath and is also a prime numberMathworldPlanetmath. The first few factorial primes are: 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199 (sequence A088054 in the OEIS). It is conjectured that only for n=3 are both n!-1 and n!+1 both primes.

Factorial primes have a rôle in an argument that 1 is not a prime number. If n is a positive integer and p is a prime number, n!+p is never a prime for p<n, because obviously it will be a multipleMathworldPlanetmath of p, just as n! is. But n!+1, even though it certainly is a multiple of 1, can be a prime, specifically, a factorial prime. (The same is also true if we subtract instead of add).

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更新时间:2025/5/4 22:24:25