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

**Authors:** Stephen Marshall

This paper presents a complete proof of the Pell Primes are infinite. 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)!( + ) + +
We use this proof for d = - to
prove the infinitude of Pell 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 Pell Prime Conjecture possible.

**Comments:** 15 Pages.

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### Submission history

[v1] 2017-03-02 16:52:23

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