Goldbach numbers in short interval (Ⅱ)

摘要

Suppose that B is a sufficiently large positive constant, ε is a sufficiently small positive constant and N is sufficiently large. In this paper, it has been mainly proved that (ⅰ) if A = N~(7/78+ ε), then the even numbers in (N, N+A), except for O (Alog ~(-B)N) values, are all Goldbach numbers; (ⅱ) there is at least one Goldbach number, in (N, N+N~(23/546+ε)).