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Proceedings of the American Mathematical Society

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


Author: R. J. Cook
Journal: Proc. Amer. Math. Soc. 81 (1981), 33-40
MSC: Primary 10H15
DOI: https://doi.org/10.1090/S0002-9939-1981-0589132-3
MathSciNet review: 589132
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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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DOI: https://doi.org/10.1090/S0002-9939-1981-0589132-3
Keywords: Prime number, density theorem
Article copyright: © Copyright 1981 American Mathematical Society