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arXiv · 1310.1323

On Legendre's, Brocard's, Andrica's, and Oppermann's Conjectures

Germán Paz
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Abstract

Let $n\in\mathbb{Z}^+$. Is it true that every sequence of $n$ consecutive integers greater than $n^2$ and smaller than $(n+1)^2$ contains at least one prime number? In this paper we show that this is actually the case for every $n \leq 1,193,806,023$. In addition, we prove that a positive answer to the previous question for all $n$ would imply Legendre's, Brocard's, Andrica's, and Oppermann's conjectures, as well as the assumption that for every $n$ there is always a prime number in the interval $[n,n+2\lfloor\sqrt{n}\rfloor-1]$.

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Germán Paz. 2014-04-02. On Legendre's, Brocard's, Andrica's, and Oppermann's Conjectures. https://arxiv.org/abs/1310.1323

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