Chen's primes and ternary Goldbach problem

TL;DR

This paper proves that sufficiently large odd integers divisible by 3 can be expressed as the sum of two Chen's primes and a third prime with limited prime factors, advancing understanding of the ternary Goldbach problem.

Contribution

It establishes a new representation result involving Chen's primes and primes with restricted prime factors for large odd integers divisible by 3.

Findings

Existence of such prime representations for large odd integers divisible by 3

Bound on the number of prime factors of p_3+2

Extension of Goldbach-type results involving Chen's primes

Abstract

We prove that there exists a k_0>0 such that every sufficiently large odd integer n with 3\mid n can be represented as p_1+p_2+p_3, where p_1,p_2 are Chen's primes and p_3 is a prime with p_3+2 has at most k_0 prime factors.