Estimating the Twin prime constant

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On this website:

http://numbers.computation.free.fr/Constants/Primes/twin.html

it says: "This last constant occurs in some asymptotic estimations involving primes and it's interesting to observe that it may be estimated using properties of the Riemann Zeta function to thousand of digits (Sebah computed it to more than 5000 digits)."

Can someone explain how you can use the Riemann zeta function to estimate the digits of the twin prime constant?