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arXiv · 1506.03042

Upper bounds for prime gaps related to Firoozbakht's conjecture

Alexei Kourbatov
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Abstract

We study two kinds of conjectural bounds for the prime gap after the k-th prime $p_k$: (A) $p_{k+1} < (p_k)^{1+1/k}$ and (B) $p_{k+1}-p_k < \log^2 p_k - \log p_k - b$ for $k>9$. The upper bound (A) is equivalent to Firoozbakht's conjecture. We prove that (A) implies (B) with $b=1$; on the other hand, (B) with $b=1.17$ implies (A). We also give other sufficient conditions for (A) that have the form (B) with $b\to1$ as $k\to\infty$.

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Alexei Kourbatov. 2015-06-09. Upper bounds for prime gaps related to Firoozbakht's conjecture. https://arxiv.org/abs/1506.03042

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