On the Connection Between the Goldbach Conjecture and the Elliott-Halberstam Conjecture

Abstract

In this paper we prove that the binary Goldbach conjecture for sufficiently large even integers would follow under the assumptions of both the Elliott-Halberstam conjecture and a variant of the Elliott-Halberstam conjecture twisted by the Mobius function, provided that the sum of their level of distributions exceeds 1. This continues the work of Pan [10]. An analogous result for the twin prime conjecture is obtained by Ram Murty and Vatwani [13].