On Chen's theorem (II)

Abstract

Let N be a sufficiently large even integer and S ( N ) denote the number of solutions of the equation N = p + P 2 , where p denotes a prime and P 2 denotes an almost-prime with at most two prime factors. In this paper we obtain S ( N ) > 0.867 C ( N ) N log 2 N , where C ( N ) = ∏ p > 2 ( 1 − 1 ( p − 1 ) 2 ) ∏ p | N p > 2 p − 1 p − 2 , and thus improved the previous result S ( N ) > 0.836 C ( N ) N log 2 N due to J. Wu.