View source for 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

$$p_1+p_2+p_3=N$$

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

$$I(N)=\frac{N^2}{2r^3}S(N)+O\left(\frac{N^2}{r^{3.5-\epsilon}}\right),$$

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

$$S(N)=\prod_p\left(1+\frac{1}{(p-1)^3}\right)\prod_{p|N}\left(1-\frac{1}{p^2-3p+3}\right)>0.6.$$

Cf. [[Vinogradov method|Vinogradov method]]; [[Goldbach problem|Goldbach problem]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  I.M. Vinogradov,   "Selected works" , Springer  (1985)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  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)</TD></TR></table>