Goldbach's conjecture

Statement

Each even integer $n > 2$ is the sum of two prime numbers.

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.