Goldbach Conjecture

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Conjecture

Every even integer greater than $2$ is the sum of two primes.


Marginal Conjecture

Every integer greater than $5$ can be written as the sum of three primes.


Hilbert $23$

This problem is no. $8b$ in the Hilbert $23$.


Also see


Source of Name

This entry was named for Christian Goldbach.


Historical Note

Christian Goldbach actually proposed what is now known as Goldbach's Marginal Conjecture in $1742$ in a letter to Leonhard Paul Euler. Euler then proposed this stronger conjecture.

It has been checked by computer for numbers up to at least $10^{18}$.

Partial results are given by Chen's Theorem and Vinogradov's Theorem.


Sources