Vinogradov's Theorem/Corollary 1

Corollary to Vinogradov's Theorem
Let:
 * $\displaystyle r \left({N}\right) = \sum_{p_1 + p_2 + p_3 = N} 1$

where $p_1, p_2, p_3$ are prime.

Then for sufficiently large odd integers $N$:


 * $\displaystyle r \left({N}\right) = \mathfrak S \left({N}\right) \frac {N^2} {2 \left({\log N}\right)^3} \left({1 + \mathcal O \left({\frac{\log \log N} {\log N}}\right)}\right)$

where $\mathcal O$ denotes big O-notation.