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 rĂ´le 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).

Title factorial prime
Canonical name FactorialPrime
Date of creation 2013-03-22 16:19:19
Last modified on 2013-03-22 16:19:19
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41
Classification msc 05A10
Classification msc 11B65