An asymptotic upper bound on prime gaps

André LeClair

Published 2015-06-10Version 1

The Cram\'er-Granville conjecture is an upper bound on prime gaps, $p_{n+1} - p_n < c \, \log^2 p_n$ for some constant $c\geq 1$. Using a formula of Selberg, we demonstrate the validity of the conjecture in the limit of large $n$ with $c=1$.