Chen's Theorem with Small Primes

Abstract

Let N be a sufficiently large even integer. In this paper it is proved that the equation $$ \begin{array}{*{20}c} {{N = p + P_{2} ,}} & {{p \leqslant N^{{0.95}} ,}} \\ \end{array} $$ is solvable, where p denotes a prime and P 2 denotes an almost prime with at most two prime factors.