On Primes of the Form $ \lfloor\alpha_{1}p^{c_{1}}+\alpha_{2}p^{c_{2}}+\beta\rfloor $

This article aims to investigate whether there exist infinitely many primes $ p $ such that $ \lfloor\alpha_{1}p^{c_{1}}+\alpha_{2}p^{c_{2}}+\beta\rfloor $ is also a prime for almost all irrationals $ \alpha_{1}>0 $ and $ \alpha_{2}>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.