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Almost prime triples and Chen’s theorem

Volume 179 / 2017

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


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.


  • Yingchun CaiDepartment of Mathematics
    Tongji University
    Shanghai 200092, P.R. China

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