## Elementary Proof that an Infinite Number of Factorial Primes Exist

**Authors:** Stephen Marshall

This paper presents a complete proof of the Factorial Primes are infinite, even though only 16 of them have been found as of 21 Feb 2017. We use a proof found in Reference 1, that if p > 1 and d > 0 are integers, that p and p+ d are both primes if and only if for integer m:
m = (p-1)!( 1/p + ((-1)^d(d!))/(p+d)) + 1/p + 1/(p+d)
We use this proof for d = n(n!) to prove the infinitude of Factorial prime numbers.
The author would like to give many thanks to the authors of 1001 Problems in Classical Number Theory, Jean-Marie De Koninck and Armel Mercier, 2004, Exercise Number 161 (see Reference 1). The proof provided in Exercise 6 is the key to making this paper on the Factorial Prime possible.

**Comments:** 7 Pages.

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### Submission history

[v1] 2017-02-23 14:27:23

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