Almost prime triples and Chen's Theorem

TL;DR

This paper proves the existence of infinitely many primes where both p+2 and p+6 have a limited number of prime factors, refining Chen's theorem on primes and almost primes.

Contribution

It introduces a new result showing infinitely many primes with both p+2 and p+6 having bounded prime divisors, extending Chen's theorem.

Findings

Infinitely many primes p with p+2 having at most two prime factors

p+6 also has a bounded number of prime divisors for these primes

Refinement of Chen's theorem on primes and almost primes

Abstract

We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen.