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Goldbach's conjecture states that every even integer which is greater than 2 can be expressed as the sum of two prime numbers.
There is not "the" conjecture: there are several. The oldest and probably best known unsolved conjecture in number theory is the Goldbach conjecture. According to it every even integer greater than two can be expressed as the sum of two prime numbers.
Hypothesis
Because mathematics is a axiomatic system so that every new statement remains a conjecture until it is proved.
The Poincaré Conjecture.