## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 79 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*