English

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

Number Theory 2017-07-20 v1

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.

Keywords

Cite

@article{arxiv.1707.06014,
  title  = {Primes of the form n^2+n+p have density 1},
  author = {Ivan Blanco-Chacon and Gary McGuire and Oisin Robinson},
  journal= {arXiv preprint arXiv:1707.06014},
  year   = {2017}
}