On Chen's theorem, Goldbach's conjecture and almost prime twins

Let N denotes a sufficiently large even integer, we define D1,2(N) as the same as those in previous articles about Chen's theorem. In this paper, we show that D1,2(N) 1.253 C(N) N/(log N)², improving previous record of Wu about $40%$. We also get similar results on twin prime problem and additive representations of integers. An important step in the proof is the application of a theorem of Lichtman.