Every sufficiently large odd number is a sum of three primes (Vinogradov 1937). Ramachandra and Sankaranarayanan
(1997) have shown that for sufficiently large 
, the error term is 
. This theorem is closely related to Waring's
prime number conjecture.
Vinogradov's Theorem
See also
Goldbach Conjecture, Schnirelmann's Theorem, Waring's Prime Number ConjectureExplore with Wolfram|Alpha
References
Ramachandra, K. and Sankaranarayanan, A. "Vinogradov's Three Primes Theorem." Math. Student 66, 1-4 and 27-72, 1997.Vaughan, R. C. The Hardy-Littlewood Method. Cambridge, England: Cambridge University Press, 1981.Vinogradov, I. M. The Method of Trigonometrical Sums in the Theory of Numbers (Russian). Trav. Inst. Math. Stekloff 10, 1937.Vinogradov, I. M. The Method of Trigonometrical Sums in the Theory of Numbers (Russian). Trav. Inst. Math. Stekloff 23, 1947.Vinogradov, I. M. The Method of Trigonometrical Sums in the Theory of Numbers. New York: Dover, 2004.Referenced on Wolfram|Alpha
Vinogradov's TheoremCite this as:
Weisstein, Eric W. "Vinogradov's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VinogradovsTheorem.html