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arXiv · 2608.27323

On Piatetski-Shapiro primes from almost primes

Yuhua Zhao·Jinjiang Li·Linji Long·Min Zhang
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Abstract

Denote by $\mathcal{P}_r$ an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this manuscript, it is established that, for any fixed $0.98353<\gamma<1$, there exist infinitely many primes of the form $p=[n^{1/\gamma}]$, where $n$ is an almost-prime $\mathcal{P}_7$. This result constitutes an improvement upon the previous result of Baker, Banks, Guo and Yeager [1], who showed that there exist infinitely many primes $p$ such that $p=[n^{1/\gamma}]$ with $n\in\mathcal{P}_8$ for $\gamma$ near to one.

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Yuhua Zhao, Jinjiang Li, Linji Long, Min Zhang. 2026-08-27. On Piatetski-Shapiro primes from almost primes. https://arxiv.org/abs/2608.27323

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