Re: Suspicious average timing of isprime() (maybe a bug?!)

[Ilya Zakharevich <nospam-abuse@ilyaz.org>]

On Sat, Sep 21, 2024 at 10:00:24PM +0200, Bill Allombert wrote:
> > THE RESULT:
> > 
> > # Start     Time       Checked primes
> > 1e19    118.700	  457665
> 
> This one make sense.

This is why I did not exclude it. ;―)

> > 2e19    5323.600        449605
> > 4e19    6414.950        443260
> > 8e19    8459.400        437461
> > 1e20    8443.400        434090
> > 2e20    8546.700        427974
> > 4e20    8610.000        422382

Every batch shows a gradual growth with variation of about 1%. 

> > 8e20    16720.000       415756
> > 1e21    16717.400       414056
> > 2e21    17102.800       408566

Likewise here.

> > 4e21    8673.450        401265
> > 8e21    8743.950        396126
> > 1e22    8885.250        393752
> > 2e22    9042.050        389569
> > 4e22    9118.450        384823
> > 8e22    9209.950        379336
> > 1e23    9168.000        377295
> > 2e23    9203.750        372843

Likewise.

> > 4e23    14615.250       368239
> > 8e23    14644.800       363116

I did not check this one in detail…

> So maybe compute the standard deviation for each batchs ?

See above.  Completely negligible variation, then a ∼2x growth/decay
on an interval of width less than twice the width of averaging. 

Hope this helps,
Ilya