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.
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