Ayla Gafni

Affiliation: University of Mississippi

Title Of Talk: Rough numbers between consecutive primes

URLS:
https://arxiv.org/abs/2508.06463

Abstract: Erd\H{o}s problem \#682 conjectures that almost every prime gap contains a rough number whose smallest prime factor is at least the size of the gap. We confirm this conjecture and give upper bounds for the size of the exceptional set of gaps. Further, we establish precise asymptotics for the exceptional set, under the assumption of the Hardy-Littlewood prime tuples conjecture. This is joint work with Terence Tao.

WARNING: This page contains MATH-JAX

Last update made Tue Mar 10 21:28:03 CDT 2026.
Please report problems to: fgarvan@ufl.edu