# Goldbach's conjecture

- kind: problem
- status: open
- year: 1742
- authors: Christian Goldbach in a letter to Euler

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

It has been checked by computer up to $4 \times 10^{18}$. The weak version, about odd numbers and three primes, was proved in 2013. The binary version resists because two primes give too little room for the averaging arguments that work with three. Chen Jingrun came closest in 1973: every large even number is a prime plus a number with at most two prime factors.

Posed 1742, Christian Goldbach in a letter to Euler.

## What would settle it

Lean statement in formal-conjectures

## Related problems

- Progress here drew on [Weak Goldbach conjecture](/wiki/Problem:weak-goldbach.md), whose resolution the original curation lists as unlocking it; the argument for the link has not been written yet.

## Sources

- [Wikipedia: Goldbach's conjecture](https://en.wikipedia.org/wiki/Goldbach%27s_conjecture)

[Number theory](/wiki/Space:number-theory.md) · [Mathematics](/wiki/Continent:mathematics.md)

## Relations

- uses [weak-goldbach](/wiki/Problem:weak-goldbach.md) — Progress here drew on Weak Goldbach conjecture, whose resolution the original curation lists as unlocking it; the argument for the link has not been written yet.

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