This article investigates the existence of infinitely many primes defined by a specific floor function involving irrationals, suggesting a positive outcome.
This article aims to investigate whether there exist infinitely many primes p such that α₁p^c₁+α₂p^c₂+β is also a prime for almost all irrationals α₁>0 and α₂>0 (in the sense of Lebesgue measure). Our result provides an affirmative answer to this question by utilizing elementary and analytic methods, especially the division trick and estimates of exponential sums.
No takes yet. Share an insight, caveat, or question.
Y. Song (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: