Number Theory


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.

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Submission history

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

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