Chen's theorem on Goldbach's conjecture

Statement

Chen's theorem on Goldbach's conjecture states that every sufficiently large even integer can be expressed either as the sum of two primes, or as the sum of a prime and a semiprime (i.e., a number that is a product of two distinct primes).

Relation with other facts/conjectures

Stronger facts

• Cai's theorem on Goldbach's conjecture: Every sufficiently large even integer $N$ can be written as the sum of a prime less than or equal to $N^{0.95}$ and a number with at most two prime factors.

Other related facts

• Chen's theorem on prime gaps: For every positive even integer $h$, there exist infinitely many pairs $(p,p+h)$ such that $p$ is a prime number and $p+h$ is either a prime or a semiprime.