Re: reasonable number size limit for working with with PARI/GP? (googol is fine, googolplex is not)

[American Citizen <website.reader3@gmail.com>]

Hermann:

This really depends upon the capabilities of your computer, particularly 
system RAM.

I have 32 gigs on my HP Z420 workstation with 6 Xeon processors running 
3.4 Gigahertz or so.

I would suggest looking at the "htop" linux command and take a look at 
how much system ram is being used up by your program.

This will give you a better idea on what's feasible for your systems.

Or you can use the simple linux command: %ps -o %mem pid where pid is 
the pid # of the executing GP-Pari program

I believe GP-Pari will allow you to run external bash commands and pipe 
the input back into GP-Pari

Randall

On 11/29/23 04:14, hermann@stamm-wilbrandt.de wrote:
> What is a reasonable number size limit for working with with PARI/GP?
> Working with 11.9million decimal digit numbers is no problem, even sub 
> second:
> https://github.com/Hermann-SW/RSA_numbers_factored/blob/main/pari/sqrtm1.11887192_digit.largest_known_1mod4_prime.gp 
>
>
> hermann@7600x:~/RSA_numbers_factored/pari$ gp -q < 
> sqrtm1.11887192_digit.largest_known_1mod4_prime.gp
> 11887192-digit prime p (39488395 bits)
> [M,V] = halfgcd(sqrtm1, p)
>   ***   last result computed in 183 ms.
> [x,y] = [V[2], M[2,1]]
>   ***   last result computed in 0 ms.
> sqrtm1 = lift(Mod(x, p)/y)
>   ***   last result computed in 391 ms.
> done, all asserts OK
> hermann@7600x:~/RSA_numbers_factored/pari$
>
>
> But googolplex is too much ...
> https://en.wikipedia.org/wiki/Googolplex
>
> hermann@7600x:~$ gp --version
>                                             GP/PARI CALCULATOR Version 
> 2.15.4 (released)
>                                     amd64 running linux 
> (x86-64/GMP-6.2.1 kernel) 64-bit version
>                               compiled: Aug 21 2023, gcc version 
> 11.4.0 (Ubuntu 11.4.0-1ubuntu1~22.04)
>                                                       threading 
> engine: single
>                                           (readline v8.1 disabled, 
> extended help enabled)
> hermann@7600x:~$ gp -q
> ? googol=10^100;
> ? googolplex=10^googol;
>   ***   at top-level: googolplex=10^googol
>   ***                              ^-------
>   *** _^_: overflow in lg().
>   ***   Break loop: type 'break' to go back to GP prompt
> break>
>
>
> ? #digits(googol-1)
> 100
> ? ##
>   ***   last result computed in 0 ms.
> ?
>
>
> Regards,
>
> Hermann.