English

Almost primes and primes that are sums of two squares plus one

Number Theory 2025-02-28 v2

Abstract

In this paper, we obtain a lower bound for the number of primes pxp\leq x such that p1p-1 is a sum of two squares and p+2p+2 has a bounded number of prime factors. The proof uses the vector sieve framework, involving a semi-linear sieve and a linear sieve.

Keywords

Cite

@article{arxiv.2501.16723,
  title  = {Almost primes and primes that are sums of two squares plus one},
  author = {Kunjakanan Nath and Likun Xie},
  journal= {arXiv preprint arXiv:2501.16723},
  year   = {2025}
}

Comments

Fixed a few typos; a small necessary numerical calculations fix in the proof of Theorem 1.1 was applied