On Erdős constant

Abstract

In 1944, P. Erdős \cite{1} proved that if $n$ is a large highly composite number (HCN) and $n_1$ is the next HCN, then $$n<n_1<n+n(\log n{)}^{-c},$$ where $c>0$ is a constant. In this paper, using numerical results by D. A. Corneth, we show that most likely $c<1.$

3 pages