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arXiv · 1804.07659

A heuristic study of the distribution of primes in short and not-so-short intervals

Miguel-Angel Sanchis-Lozano
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Abstract

A numerical study on the distributions of primes in short intervals of length $h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$ but $h \ll N$, providing support to the Montgomery and Soundararajan conjecture on the variance of the prime distribution at this scale.

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Miguel-Angel Sanchis-Lozano. 2018-04-20. A heuristic study of the distribution of primes in short and not-so-short intervals. https://arxiv.org/abs/1804.07659

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