The Khinchin constant has been computed with $10^6$ decimal digits
using the formula (see Wikipedia)
\[ \log(K_0)=\frac{1}{\log(2)}\sum_{n=1}^{\infty} \frac{\zeta(2n)-1}{n}
\sum_{k=1}^{2n-1} \frac{(-1)^{k+1}}{k} \]
using PARI. In a single processor the computation took 17272 minutes
(near 12 days).
For large values of the number of decimal digits $n$ the CPU time
behaves, approximately, as $n^{8/3}$.