An effective version of the Bombieri–Vinogradov theorem, and applications to Chen’s theorem and to sums of primes and powers of two

摘要

In this paper we give an effective version of the Bombieri–Vinogradov theorem of Bombieri, Friedlander, and Iwaniec. As applications, we refine Chen’s theorem on primes with difference h for h ≤ x 1/56, with a consequence on integers of the form p + 2 k .