Goldbach conjecture
Number theory
The conjecture that every even integer greater than 2 is a sum of two primes. The two primes need not be distinct, as in 4 = 2 + 2.
What is usually left out
This is the binary or strong form and is open. The weak form — every odd number greater than 5 is a sum of three primes — was proved by Helfgott in 2013. Strong Goldbach implies weak Goldbach, so the harder statement remains the open one.
Related terms
In the atlas
- Goldbach conjecture — Number theory, open
- Goldbach's weak conjecture — Number theory, solved