Goldbach's conjecture

Goldbach's conjecture
Letter from Goldbach to Euler dated 07 June 1742 (Latin-German)
FieldNumber theory
Conjectured byChristian Goldbach
Conjectured in1742
Open problemYes
ConsequencesGoldbach's weak conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.

The conjecture has been shown to hold for all integers less than 4×1018 but remains unproven despite considerable effort.

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