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.
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