English

On the gap between primes

Number Theory 2022-08-02 v9

Abstract

It is proven that there are infinitely prime pairs whose difference is no greater than 84. In proving that result, a new sieve weight is constructed. The new idea is to construct the largest sieve support which admits the use of the Bombieri-Vinogradov theorem.

Keywords

Cite

@article{arxiv.2109.03681,
  title  = {On the gap between primes},
  author = {Chunlei Liu},
  journal= {arXiv preprint arXiv:2109.03681},
  year   = {2022}
}

Comments

It is pointed to the author by Terence Tao that the sieve support lacks of downward closeness, and hence the proof is invalid

R2 v1 2026-06-24T05:47:30.148Z