Schnirelmann Density - Schnirelmann's Theorem

In 1930 Schnirelmann used these ideas in conjunction with the Brun sieve to prove Schnirelmann's theorem, that any natural number greater than one can be written as the sum of not more than C prime numbers, where C is an effectively computable constant: Schnirelmann obtained C < 800000. Schnirelmann's constant is the lowest number C with this property.

Olivier Ramaré showed in (Ramaré 1995) that Schnirelmann's constant is at most 7, improving the earlier upper bound of 19 obtained by Hans Riesel and R. C. Vaughan.

Schnirelmann's constant is at least 3; Goldbach's conjecture implies that this is the constant's actual value.