Re: Improving primecert(n, 0)

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Dec 22, 2021 at 08:56:47PM -0700, bobbaillie@frii.com wrote:
> The primecert(n, 0) function generates prime certificates (prime proofs)
> and is very useful!

Thanks!
 
> However, I have noticed two limitations, at least on Windows:
> 1) it uses only one core no matter how many the machine has.

You need to use the parallel version of PARI/GP.

You can try this
<https://pari.math.u-bordeaux.fr/pub/pari/windows/Pari64-2-13-3-pthread.exe>

But for PARI, if you want fast parallelism on Windows, you need to use
the Windows subsystem for Linux, see
<https://pari.math.u-bordeaux.fr/PDF/PARIwithWindows.pdf>

> 2) the amount of memory it needs seems to increase as the square of the
> number of digits.
> Empirically: if T is the number of digits in Thousands, the number of
> gigabytes of RAM needed will be about T^2. So, a 7000 digit number would
> need about 49 GB of RAM.

The master branch has some improvements, memory-wise.

I am working on a branch with better parallelism and better memory
usage for large numbers, but it is slower for small number.
We used it to compute the certificate for fibonacci(148091) (about 30000
digits).

Cheers,
Bill