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 Conjecture## Explore 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 Theorem## Cite this as:

Weisstein, Eric W. "Vinogradov's Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/VinogradovsTheorem.html