An upper bound for the sum of large differences between prime numbers

Cook, R. J.

doi:10.1090/S0002-9939-1981-0589132-3

An upper bound for the sum of large differences between prime numbers
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by R. J. Cook PDF

Proc. Amer. Math. Soc. 81 (1981), 33-40 Request permission

Abstract:

Let ${p_n}$ denote the $n$th prime number, ${d_n} = {p_{n + 1}} - {p_n}$. We estimate the sum $\Sigma {d_n}$ taken over ${p_n} \leqslant x,{d_n} > {x^\mu }$ where $1/6 < \mu < 5/9$.

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