In this paper, we prove that for almost all irrational numbers $ \alpha > 0 $ (in the sense of Lebesgue measure), there exist infinitely many primes $ p $ in a Beatty sequence such that $ \lfloor\alpha p^c+\beta\rfloor $ is also a prime, where $ c\in(1, \frac{150}{119}) $.
Citation: Yanbo Song. On primes of the form $ \lfloor\alpha p^c+\beta\rfloor $ for almost all $ \alpha $[J]. AIMS Mathematics, 2026, 11(6): 15912-15925. doi: 10.3934/math.2026655
In this paper, we prove that for almost all irrational numbers $ \alpha > 0 $ (in the sense of Lebesgue measure), there exist infinitely many primes $ p $ in a Beatty sequence such that $ \lfloor\alpha p^c+\beta\rfloor $ is also a prime, where $ c\in(1, \frac{150}{119}) $.
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Yanbo Song. On primes of the form $ \lfloor\alpha p^c+\beta\rfloor $ for almost all $ \alpha $[J]. AIMS Mathematics, 2026, 11(6): 15912-15925. doi: 10.3934/math.2026655
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