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arXiv · 2607.04283

Improving on the Brun-Titchmarsh Theorem

Olvier Ramaré·Jan Christoph Schlage-Puchta
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Abstract

We prove that the number of primes in an interval of length $N$ is at most $2N/(\log N+3.53)$ when $N$ is large enough. This is obtained through a sieving process which can be seen as a hybrid between the large sieve and the Selberg sieve, and draws on what we call "local models". This paper has been published in {\sc Acta Arithmetica, 2008, vol. 131, nb. 4, pages 351--366}.

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Olvier Ramaré, Jan Christoph Schlage-Puchta. 2026-07-05. Improving on the Brun-Titchmarsh Theorem. https://doi.org/10.4064/aa131-4-4

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