# Million digits of K0!

% Remco Bloemen % 2009-12-29, last updated 2014-03-04

## The million digit round

remco@server ~KhinchinK0-1M \$ time ..khinchin
How many thousand decimals of K0 would you like today? 1000
Accuracy is 3322 kilobit, 1000 thousand decimals.
Calculating 1660999 terms of the summation Σ (ζ(2n)-1)n Σ ±1k
Terms need to be 3322022 bits accurate
Using von Staudt-Clausen until n = 120498
Using only bitshifting from n = 1047982
Calculating table of small primes… 21311 primes found.
Power table requires K = 14112 items.
Power table requires 3322037 bits sum accuracy.
Calculating power table… 100% (in 629283 ms)
Approximate size: 5723160 kB
Factor required 3442520 bits of accuracy
Calculating factor = (4π²)^(SCN)   (2 SCN!)…
Calculating S2(SCN) = Σ ±1k
Initialising summation variables…
Summing the von Staudt-Clausen terms… 100% (in 144669539.373 ms)
Summing the powtable terms… 100% (in 74445950.490 ms)
K0 is written to K0.txt

real    3665m34.260s
user    3660m33.890s
sys     4m23.356s


## The verification round

How many thousand decimals of K0 would you like today? 1100
This might take a few days, but I'll try.
Accuracy is 3654 kilobit, 1100 thousand decimals.
Calculating 1827099 terms of the summation Σ (ζ(2n)-1)n Σ ±1k
Terms need to be 3654222 bits accurate
Using von Staudt-Clausen until n = 131361
Using only bitshifting from n = 1152779
Calculating table of small primes… 23056 primes found.
Power table requires K = 15384 items.
Power table requires 3654237 bits sum accuracy.
Calculating power table… 100% (in 797610 ms)
Approximate size: 6862871 kB
Factor required 3785583 bits of accuracy
Calculating factor = (4π²)^(SCN)   (2 SCN!)…
Calculating S2(SCN) = Σ ±1k
Initialising summation variables…
Summing the von Staudt-Clausen terms… 100% (in 198981058.192 ms)
Summing the powtable terms… 100% (in 95374658.929 ms)
K0 is written to K0.txt

real    4923m7.264s
user    4922m10.648s
sys     0m0.957s Remco Bloemen
Math & Engineering
https://2π.com