On the Representation of Large Even Integers as Sums of Two Almost Primes. Ii

Abstract

In a previous paper [3] the writer has given with Miss A. Togashi an elementary proof for the fact that every sufficiently large even integer is representable as a sum of two almost primes, each of which has at most three prime factors, a result first obtained by A. I. Vinogradov. On the other hand, we are able to prove by a rather transcendental method that every large even integer is representable as a sum of a prime and an almost prime composed of at most four prime factors (see [4]). The aim in the present paper is to show that a somewhat weaker result than this can be obtained by an elementary argument. We shall prove the following1)Theorem.