Schnirelmann's Theorem

There exists a Positive Integer $s$ such that every sufficiently large Integer is the sum of at most $s$ Primes. It follows that there exists a Positive Integer $s_0\geq s$ such that every Integer $>1$ is a sum of at most $s_0$ Primes, where $s_0$ is the Schnirelmann Constant. The best current estimate is $s_0=19$.

See also Prime Number, Schnirelmann Density, Waring's Problem

References

Khinchin, A. Y. ``The Landau-Schnirelmann Hypothesis and Mann's Theorem.'' Ch. 2 in Three Pearls of Number Theory. New York: Dover, pp. 18-36, 1998.