Explicit Chen's theorem

TL;DR

This paper proves that all sufficiently large even numbers can be expressed as the sum of a prime and a number with at most two prime factors, advancing understanding of additive number theory.

Contribution

It establishes an explicit version of Chen's theorem for even numbers greater than a double exponential threshold.

Findings

Every even number > exp exp 36 is representable as prime + product of ≤2 primes

Provides explicit bounds for Chen's theorem

Advances the explicit understanding of Goldbach-type problems

Abstract

We show that every even number $>\exp\exp 36$ can be represented as the sum of a prime and a product of at most two primes.