How long a ZetaZero calculation takes?

Questions
1

Hello folks,
I have been waiting Mathematica 11.2 to perform following summation for two days:

ZetaZeroSum.png

Is this normal and if it so how long the calculation will take?

PS. I haven’t used Mathematica for years, so there may be some silly mistake I’ve done.

2

Mikael,

you should post your code as code and not an image.

I would do the numerical before the Im[] but it is only a minor speedup. This will help:

AbsoluteTiming[ParallelSum[Im[N[ZetaZero[i]]], {i, 1, 10000}]]

it takes 32 seconds on my machine with 8 kernels which means you would need 100 times that to get to a million or 3200 seconds (about an hour)…

Regards,

Neil

3

Hi Mikael.

If you want the answer, you have to wait few hours for computations.

ZetaZero function is the bottleneck, I tried five different ways to speed up, but your code is the fastest.

Maybe this helps.

Regards Mariusz

4

Hello Neil and Mauriusz,

thank you for advice and sorry for the image. I just wanted to ensure that it looks correct, but in the future I’ll post code.

Yes, it took more than 48 hours on my machine to get the result: 10.4471 if someone is interested. Only one kernel was used, although there were two Mathematica kernels available according to the Windows Task manager.

Regards,
Mikael

5

Two in the task manager really means one computational kernel. You should go into the menu and look at kernel status. You need to turn them on explicitly to use them. As a measure of your machine speed I’d restart mma and post the speed to do 10,000. Then try it in parallel.