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Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states:

Every even integer greater than 2 can be expressed as the sum of two primes.

The conjecture has been shown to hold up through 4 × 1018, but remains unproven.

Further reading

Goldbach's original letter to Euler in 1742.

Note that Goldbach's weak conjecture (a.k.a Goldbach's odd conjecture)

Every odd number greater than 7 can be expressed as the sum of three odd primes

is generally accepted to have been finally proved in 2013, by Harald Helfgott

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