---
tag: 063JNBSMJ0
kind: conjecture
name: Goldbach's conjecture
aliases: [strong-goldbach-conjecture]
msc: [11P32]
sources:
  - url: https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
    locator: lead section
same_as:
  wikidata: Q485520
  wikipedia: Goldbach's conjecture
---

## Statement

Each even integer $n > 2$ is the sum of two [[prime numbers|0SN0MAEKYX]].

## Remarks

For example, $4 = 2 + 2$, $28 = 5 + 23 = 11 + 17$ and $100 = 3 + 97$.
The weak Goldbach conjecture says that each odd integer $n > 5$ is the sum of three primes. Harald Helfgott proved it in 2013.
The conjecture is open. A distributed computer search checked it for each even $n \le 4 \cdot 10^{18}$.

## History

Goldbach stated a form of the conjecture in a letter to Euler in 1742.

## Explanations

### L1 human

Take an even number larger than $2$. The conjecture says that you can always split it into two primes.
For example, $18 = 7 + 11$. Nobody has found an even number that fails, but nobody has a proof.