MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A quantitative form of the twin prime conjecture asserts that the the number of twin primes less than $n$ is asymptotically equal to $2\, C\, n/ \ln^2(n)$ 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 $A\, n/ \ln^2 (n) $ for some constant $A>2C$. 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?

share|cite|improve this question
up vote 13 down vote accepted

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.

share|cite|improve this answer
I have checked Math Reviews for papers and reviews that cite Wu's paper. As far as I can tell from the reviews, there is no claim of an improvement on Wu's result. – Gerry Myerson Aug 9 '10 at 23:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.