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arXiv · 2311.18701

Arbitrarily long strings of consecutive primes in special sets

Sai Sanjeev Balakrishnan·Félix Houde·Vahagn Hovhannisyan·Maryna Manskova·Yiqing Wang
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Abstract

Let $F(x)$ be a function of the form $ \sum_{i=1}^r d_i x^{ρ_i}$ where $d_1,\ldots,d_r\in\mathbb{R}$, $0 \leq ρ_1 < \ldots < ρ_r,$ $ρ_r \not\in \mathbb{Z},ρ_i \in \mathbb{R}$ for $ 1 \leq i \leq r$ and $d_r\not=0$. We prove that sets of the form $\{ n \in \mathbb{N}: \{ F(n) \} \in U \}$ for any non-empty open set $U \subset [0,1)$ contain arbitrarily long strings of consecutive primes.

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Sai Sanjeev Balakrishnan, Félix Houde, Vahagn Hovhannisyan, Maryna Manskova, Yiqing Wang. 2025-08-22. Arbitrarily long strings of consecutive primes in special sets. https://arxiv.org/abs/2311.18701

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