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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.

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