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Christian Goldbach
Christian Goldbach (1690–1764) was a Prussian jurist and amateur mathematician, secretary of the St Petersburg Academy of Sciences, best known for the Goldbach conjecture posed to Euler in 1742.
Goldbach's conjecture
Goldbach's conjecture, the strong Goldbach conjecture, says every even number greater than 2 is the sum of two primes; proposed in 1742, it remains unproved.
Goldbach's weak conjecture
Goldbach's weak conjecture, also called the ternary Goldbach conjecture, states every odd integer greater than 5 is a sum of three primes; Helfgott proved it in 2013.
Twin prime
Twin primes, or prime pairs, are pairs of primes differing by exactly 2, like (3, 5) and (5, 7); whether infinitely many exist is an open conjecture.