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

**Authors:** Stephen Marshall

This paper presents a complete proof of the Cullen 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:
See paper for this equation, as the text in this abstract does not support the mathematical format for this equation.
We use this proof for d = P2 + 1 to prove the infinitude of Cullen 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 Cullen Prime Conjecture possible.

**Comments:** 7 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-02-21 16:20:17

**Unique-IP document downloads:** 20 times

**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.*

*
*