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arXiv · 1802.10327

Short intervals containing a prescribed number of primes

Daniele Mastrostefano
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Abstract

We prove that for every nonnegative integer $m$ there exists an $\varepsilon>0$ such that if $\lambda\in (0,\varepsilon]$ and $x$ is sufficiently large in terms of $m$, then the number of positive integers $n\leq x$ for which the interval $[n,n+\lambda\log n]$ contains exactly $m$ primes is at least a constant times $x/\log x.$ This improves a result of T. Freiberg, when $\lambda$ is small.

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Daniele Mastrostefano. 2018-02-28. Short intervals containing a prescribed number of primes. https://arxiv.org/abs/1802.10327

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