Michael J. Mossinghoff

Frangible prime gaps

A prime gap $(p_n, p_{n+1})$ is \textit{frangible} if the smallest prime divisor of every integer $m$ with $p_n<m<p_{n+1}$ is strictly less than the size of the gap, $p_{n+1}-p_n$. Gafni and Tao recently proved that the number of frangible gaps up to $X$ is $\ll X/\log^2 X$, answering a question of Erd\H{o}s. They also...