The Khinchin constant has been computed with 10⁶ 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 n8/3.

Last updated: Tuesday, 11-Oct-2016 10:42:39 CEST