Re: foursquares.gp

[hermann@stamm-wilbrandt.de]

On 2023-11-19 00:28, hermann@stamm-wilbrandt.de wrote:
> Bill did develop and tuned foursquares.gp based on this thread:
> https://pari.math.u-bordeaux.fr/archives/pari-users-2310/msg00003.html
>
> You can find foursquares.gp in contributed GP scripts section:
> https://pari.math.u-bordeaux.fr/Scripts/
> https://pari.math.u-bordeaux.fr/Scripts/foursquares.gp
Just saw (interesting) discussion
"Fermat's 12th composite part as sum of two squares"
in "mersenneforum.org->Fun Stuff->Puzzles":
https://mersenneforum.org/showthread.php?t=29344

F_12 (2^2^12+1) has 6 known factors, and the composite part has 1133 
decimal digits.
Alpertron used his calculator to provide one sum of two squares 
representation.

I cloned his repo, and that computation took less than 0.1s.
I tried to make it compute another sum of two squares [for factoring the 
composite part ;-)].
But fsquares returned sum of three squares next, again in less than a 
second.

So the code for determining sum of (up to 4) squares was perhaps just 
lucky to find two squares:
https://mersenneforum.org/showthread.php?p=651405#post651405


I did run PARI/GP twosquares() on composite part and aborted after 81min 
on AMD 7950X CPU.

foursquares(n) returns result in 136ms, threesquares(n) in 259ms for 
composite n.


Regards,

Hermann.