Primes of the form n^2+n+p have density 1

Ivan Blanco-Chacon; Gary McGuire; Oisin Robinson

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arXiv · 1707.06014

Primes of the form n^2+n+p have density 1

Ivan Blanco-Chacon·Gary McGuire·Oisin Robinson

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Abstract

We consider the representation of primes as a sum of a prime and twice a triangular number. We prove that a subset of the primes having density 1 is expressible in this form. We conjecture that every odd prime number is expressible as a sum of a twin prime and twice a triangular number. We show that this conjecture implies the existence of infinitely many twin primes.

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Ivan Blanco-Chacon, Gary McGuire, Oisin Robinson. 2017-07-19. Primes of the form n^2+n+p have density 1. https://arxiv.org/abs/1707.06014

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