Vinogradov-Goldbach theorem

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A theorem on the representation of all sufficiently large odd numbers by a sum of three prime numbers. It is a consequence of the asymptotic formula for the number $I(N)$ of solutions of the equation


in prime numbers, demonstrated by I.M. Vinogradov in 1937:


where $N$ is odd, $r=\log N$ and


Cf. Vinogradov method; Goldbach problem.


[1] I.M. Vinogradov, "Selected works" , Springer (1985) (Translated from Russian)
[2] L.-K. Hua, "Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie" , Enzyklopaedie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen , 1 : 2 (1959) (Heft 13, Teil 1)
How to Cite This Entry:
Vinogradov-Goldbach theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.A. Karatsuba (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article