Editing Goldbach's conjecture (section)


{{Short description|Even integers as sums of two primes}}

{{Infobox mathematical statement
| name = Goldbach's conjecture
| image = File:Letter Goldbach-Euler.jpg
| caption = Letter from Goldbach to Euler dated 07&nbsp;June 1742 ([[Latin]]-[[German language|German]])<ref>''Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle'' (Band 1), St.-Pétersbourg 1843, [https://books.google.com/books?id=OGMSAAAAIAAJ&pg=PA125 pp. 125–129].</ref>
| field = [[Number theory]]
| conjectured by = [[Christian Goldbach]]
| conjecture date = 1742
| open problem = Yes
| first proof by = 
| first proof date = 
| implied by = 
| consequences = [[Goldbach's weak conjecture]]
}}

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

The conjecture has been shown to hold for all integers less than {{val|4e18}} but remains unproven despite considerable effort.