On the proximity of large primes
Number Theory
2017-11-17 v1
Abstract
By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis , we show that there are infinitely many pairs of primes the base expansion of which differ in at most two digits. Likewise, for any fixed integer there are infinitely many pairs of primes, the first digits of which are the same. In another direction, we show that, there is a constant depending on such that for infinitely many integers there are at least primes which differ from by at most one base digit.
Cite
@article{arxiv.1711.05793,
title = {On the proximity of large primes},
author = {Minjia Shi and Florian Luca and Patrick Solé},
journal= {arXiv preprint arXiv:1711.05793},
year = {2017}
}