On Chen's theorem (II)

Let N   be a sufficiently large even integer and S(N)S(N) denote the number of solutions of the equationN=p+P2,N=p+P2, where p   denotes a prime and P2P2 denotes an almost-prime with at most two prime factors. In this paper we obtainS(N)>0.867C(N)Nlog2N, whereC(N)=∏p>2(1−1(p−1)2)∏p|Np>2p−1p−2, and thus improved the previous resultS(N)>0.836C(N)Nlog2N due to J. Wu.