What is the best known upper bound for the number of twin primes? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T00:46:49Z http://mathoverflow.net/feeds/question/34719 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34719/what-is-the-best-known-upper-bound-for-the-number-of-twin-primes What is the best known upper bound for the number of twin primes? Mark Lewko 2010-08-06T02:10:49Z 2010-08-10T11:36:54Z <p>A quantitative form of the twin prime conjecture asserts that the the number of twin primes less than $n$ is asymptotically equal to <code>$2\, C\, n/ \ln^2(n)$</code> where $C$ is the so-called twin prime constant. A variety of sieve methods (originating with Brun) can be used show that the number of twin primes less than $n$ is at most <code>$A\, n/ \ln^2 (n)$</code> for some constant <code>$A&gt;2C$</code>. My question is: What is the smallest known value of $A$? I'd also be interested in learning what the best known constants are for the prime k-tuple conjecture?</p> http://mathoverflow.net/questions/34719/what-is-the-best-known-upper-bound-for-the-number-of-twin-primes/34723#34723 Answer by Gerry Myerson for What is the best known upper bound for the number of twin primes? Gerry Myerson 2010-08-06T02:58:05Z 2010-08-06T02:58:05Z <p>J Wu, Chen's double sieve, Goldbach's conjecture, and the twin prime problem, Acta Arith 114 (2004) 215-273, MR 2005e:11128, bounds the number of twin primes above by $2aCx/\log^2x$, with $C=\prod p(p-2)/(p-1)^2$, and $a=3.3996$; I don't know whether there have been any improvements. </p> http://mathoverflow.net/questions/34719/what-is-the-best-known-upper-bound-for-the-number-of-twin-primes/35011#35011 Answer by Hashem sazegar for What is the best known upper bound for the number of twin primes? Hashem sazegar 2010-08-09T15:05:29Z 2010-08-10T11:36:54Z <p>you can also see this : numbers.computation.free.fr/Constants/Primes/… </p>