Goldbach's conjecture
Prove that every even integer greater than 2 is the sum of two primes. For example and .
Posed by Christian Goldbach, in correspondence with Leonhard Euler, 1742
History and references
Still open as of 2026.
Goldbach raised the question in a letter to Euler in June 1742, and the statement about even numbers appears in Euler's reply later that month. It has been verified by computer for every even number up to . In the late 1930s it was shown that almost all even numbers are sums of two primes, meaning the exceptions, if any, have density zero. The weak version, that every odd number greater than 5 is a sum of three primes, was proved by Harald Helfgott in 2013. The strong version does not follow from the weak one and remains open.
References
Solutions 0
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