In 2013, he released two papers claiming a proof of Goldbach's weak conjecture.

Goldbach's weak conjecture also follows from the generalized Riemann hypothesis.

See also Goldbach's weak conjecture.

The Lemoine conjecture is similar to but stronger than Goldbach's weak conjecture.

It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a representation for all odd integers greater than five.

The truth of Ramaré's result for all sufficiently large even numbers is a consequence of Vinogradov's theorem, whereas the full result follows from Goldbach's weak conjecture.

This means in particular that any sufficiently large odd integer can be written as a sum of three primes, thus showing Goldbach's weak conjecture for all but finitely many cases.

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that:

In 1997, Deshouillers, Effinger, te Riele and Zinoviev published a result showing that the generalized Riemann hypothesis implies Goldbach's weak conjecture for all numbers.

Vinogradov's theorem proves Goldbach's weak conjecture for sufficiently large n. Deshouillers, Effinger, te Riele and Zinoviev conditionally proved the weak conjecture under the GRH.