There exists a Positive Integer such that every sufficiently large Integer is the sum of at most Primes. It follows that there exists a Positive Integer such that every Integer is a sum of at most Primes, where is the Schnirelmann Constant. The best current estimate is .
See also Prime Number, Schnirelmann Density, Waring's Problem
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.