Chen's theorem

It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes.

The theorem was first stated by Chinese mathematician Chen Jingrun in 1966,[1] with further details of the proof in 1973.

[3] Chen's theorem is a significant step towards Goldbach's conjecture, and a celebrated application of sieve methods.

Chen's theorem represents the strengthening of a previous result due to Alfréd Rényi, who in 1947 had shown there exists a finite K such that any even number can be written as the sum of a prime number and the product of at most K primes.

Ying Chun Cai proved the following in 2002:[6] In 2025, Daniel R. Johnston, Matteo Bordignon, and Valeriia Starichkova provided an explicit version of Chen's theorem:[7] which refined upon an earlier result by Tomohiro Yamada[8].

assuming the Generalized Riemann hypothesis (GRH) for Dirichlet L-functions.

In 2019, Huixi Li gave a version of Chen's theorem for odd numbers.