Weak Goldbach conjecture

Name

This conjecture is variously known as the weak Goldbach's conjecture, the odd Goldbach's conjecture, and the ternary Goldbach's conjecture.

Statement

The conjecture states that every odd integer greater than $7$ can be expressed as the sum of three odd primes.

Relation with other conjectures and facts

Stronger conjectures

• Goldbach's conjecture: This states that every even integer greater than $2$ is a sum of two primes.

Weaker conjectures and facts

• Vinogradov's theorem: This states that every sufficiently large odd integer is a sum of three odd primes. Chaohua's strengthening of Vinogradov's theorem further allows us to pick the three primes to be roughly equal.
• Schnirelmann's theorem on Goldbach's conjecture: This states that every even integer greater than $2$ is a sum of at most $300,000$ primes.