Goldbach's conjecture

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.