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arXiv · 1906.09555

The Differences Between Consecutive Primes. V

D. R. Heath-Brown
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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 $\varepsilon>0$. This improves a result of Matomäki, in which the exponent was $2/3$.

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D. R. Heath-Brown. 2019-06-23. The Differences Between Consecutive Primes. V. https://arxiv.org/abs/1906.09555

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