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Research Article | Open Access

On primes of the form $⌊ α p^{c} + β ⌋$ for almost all $α$

Yanbo Song(

)

Department of Mathematics, School of Information Engineering, Xi'an University, Xi'an 710065, China

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Abstract

In this paper, we prove that for almost all irrational numbers $α > 0$ (in the sense of Lebesgue measure), there exist infinitely many primes $p$ in a Beatty sequence such that $⌊ α p^{c} + β ⌋$ is also a prime, where $c \in (1, \frac{150}{119})$ .

Keywords

prime number Goldbach conjecture twin prime conjecture Selberg's sieve method generalized Piatetski-Shapiro sequence Beatty sequence

CLC number: 11P32, 11L07

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AIMS Mathematics

Volume 11 Issue 6,
June 2026

Pages 15912-15925

DOI: 10.3934/math.2026655

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Cite this article:

Song Y. On primes of the form

⌊ α p^{c} + β ⌋

for almost all

α

. AIMS Mathematics, 2026, 11(6): 15912-15925. https://doi.org/10.3934/math.2026655

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Received: 24 February 2026

Revised: 27 May 2026

Accepted: 01 June 2026

Published: 15 June 2026

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)

On primes of the form ⌊ α p c + β ⌋ for almost all α

Abstract

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On primes of the form $⌊ α p^{c} + β ⌋$ for almost all $α$