It is a well-known conjecture that the number of of twin primes below $n$ is asymptotically equal to 
`\[2C_2 \frac{n}{(\log n)^2}\]` with $C_2 = 0.66...$ (the value of a certain infinite product). 
See eg this wikipedia page http://en.wikipedia.org/wiki/Twin_prime that also mentions Brun's upper bound which is perhaps what you refer to.