Geodesic
On the Goldbaсh-numbers
Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 4-8

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In this paper proved asymptotic formula $$ R(n)=\sum\limits_{n=p_1+p_2}\ln p_1\ln p_2=2n\prod\limits_{p>2}\frac{p(p-2)}{(p-1)^2}\prod\limits_{\genfrac{}{}{0pt}{}{p\setminus n}{ p>2}}\frac{p-1}{p-2}+O(n^{1-2\delta}) $$ for all even $n\leq N,$ with the exception can of at most $E(N)$ values of $n$. Here $N$ is sufficiently large natural number, $p_1$, $p_2$, $p_3$ — are prime numbers, $\delta$ ($0\delta1$) is small positive constant. In prove used of Generalized Rieman Hypothesis. 
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     author = {I. A. Allakov},
     title = {On the {Goldba{\cyrs}h-numbers}},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a0/}
}
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I. A. Allakov. On the Goldbaсh-numbers. Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 4-8. http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a0/