Schnirelmann's constant

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In mathematics, Schnirelmann's constant, named for Lev Schnirelmann is the lowest number C such that every integer greater than 1 can be expressed as a sum of at most C prime numbers. Schnirelmann's theorem shows that Schnirelmann's constant indeed exists.

Olivier Ramaré^[1] showed in 1995 that Schnirelmann's constant is at most 7, improving the earlier upper bound 19 by Hans Riesel and R. C. Vaughan.

Schnirelmann's constant is at least 3, and the truth of both Goldbach's weak conjecture and Goldbach's strong conjecture would imply that this is the constant's actual value.