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I know that there is a result from J Wu that the number of twin primes less than a given magnitude $N$ does not exceed $$\frac{2aCN}{\log^2{N}}$$ Where $C=\prod \frac{p(p-2)}{(p-1)^2}$ and $a$ is something like $3.4$. Is this a direct result of the Selberg Sieve, or is there additional knowledge on the distribution of Twin Primes used?

Alexander Botros
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    http://mathoverflow.net/questions/58535/work-down-on-the-upper-bound-of-the-twin-primes http://mathoverflow.net/questions/34719/what-is-the-best-known-upper-bound-for-the-number-of-twin-primes Wu's paper is http://hal.archives-ouvertes.fr/hal-00145781/en/ See also (for Goldbach) http://journals.impan.pl/cgi-bin/doi?aa131-4-5 PS: Comments have annoyance, when you press Enter. – v08ltu Jul 08 '13 at 23:58

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