Let $N$ denote a sufficiently large even integer. In this paper itis proved that for $0.941 \leq \theta \leq 1$, the equation$$N=p+P_2,\hspace{10mm} p\leq N^{\theta}$$is solvable, where $p$ is a prime and $P_2$ is an almost prime withat most two prime factors. The range $0.941 \leq \theta \leq 1$ extended the previous one $0.945 \leq \theta \leq 1$.
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