Bahar Uğurdoğan

Multiplicity Constants for Rough Numbers in Prime Gaps

Let $p_n$ be the $n$th prime and $g_n=p_{n+1}-p_n$. Following Gafni and Tao, an integer $m$ with $p_n<m<p_{n+1}$ is rough for the gap if its least prime factor is at least $g_n$; let $M_n$ be the number of such integers. Gafni and Tao proved that the number of $n$ with $X\le p_n\le 2X$ and $M_n=0$ is $O(X/\log^2 X)$, a...