The Differences Between Consecutive Primes. V

Abstract

We show that \[\sum_{\substack{p_n\le x\\ p_{n+1}-p_n\ge\sqrt{p_n}}}(p_{n+1}-p_n)\ll_{\varepsilon} x^{3/5+\varepsilon}\] for any fixed $\epsilon >0$. This improves a result of Matomäki, in which the exponent was $2/3$.