Schnirelmann's theorem on Goldbach's conjecture

Statement

There exists a constant $s_{0}$ such that every positive integer is the sum of at most $s_{0}$ primes.

Related facts and conjectures

• Goldbach's conjecture: This would imply that $s_{0}=3$.
• Weak Goldbach's conjecture: This would imply that $s_{0}=3$. This is known to follow from the generalized Riemann hypothesis.
• Vinogradov's theorem on Goldbach's conjecture
• Chen's theorem

Facts used

1. Mann's theorem