Chen's double sieve, Goldbach's conjecture and the twin prime problem, 2

TL;DR

This paper establishes a new lower bound for the number of representations of even integers as a sum of a prime and an integer with at most two prime factors, contributing to the understanding of Goldbach's conjecture and related problems.

Contribution

It provides a novel lower bound for D_{1,2}(N), advancing the analytical methods related to Goldbach's conjecture and the twin prime problem.

Findings

New lower bound for D_{1,2}(N) established

Improves understanding of representations involving primes and semi-primes

Contributes to Goldbach's conjecture research

Abstract

For every even integer N, denote by D_{1,2}(N) the number of representations of N as a sum of a prime and an integer having at most two prime factors. In this paper, we give a new lower bound for D_{1,2}(N).