## Almost prime triples and Chen’s theorem

### Volume 179 / 2017

Acta Arithmetica 179 (2017), 233-250
MSC: Primary 11N25; Secondary 11N36.
DOI: 10.4064/aa8150-1-2017
Published online: 5 June 2017

#### Abstract

It is proved that there exist infinitely many primes $p$ such that $p+2$ and $p+6$ has at most $2$ and at most $14$ prime factors respectively. This result constitutes a refinement upon that of Heath-Brown and Xiannan Li.