An explicit version of Chen's theorem assuming the Generalized Riemann Hypothesis

TL;DR

This paper proves that, assuming the Generalized Riemann Hypothesis, every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime factors, providing an explicit version of Chen's theorem.

Contribution

It provides an explicit bound under the GRH for representing large even numbers as a sum of a prime and a semi-prime, strengthening Chen's theorem.

Findings

Every even number greater than exp(exp(15.85)) can be written as prime plus semi-prime under GRH.

The result makes Chen's theorem explicit with a concrete bound.

Supports the validity of Chen's theorem assuming GRH for large numbers.

Abstract

We prove that assuming the Generalized Riemann Hypothesis every even integer larger than $\exp(\exp(15.85))$ can be written as the sum of a prime number and a number that has at most two prime factors.