PARI/GP timings for operations on biggest known 41,024,320 decimal digit prime

[hermann@stamm-wilbrandt.de]

Recently new biggest known prime (41,024,320 decimal digits) M_52 was 
found.

It turned out that for all Mersenne primes but M_1, -3 is a quadratic 
residue.
Therefore there are integers x,y with M_52=x^2+3*y^2.

The whole computation took 8.01 days with 1580% CPU (AMD 7950X) LLR 
software
(patched to write out "sqrt(Mod(-3,p))") based on gwnum library:
https://gist.github.com/Hermann-SW/1aa0859f90bf2423b0d0a2ebc7f3eb2c

Computation of x,y from sqrt(Mod(-3,p)) took 17 seconds with:
[M,V]=halfgcd(lift(s),p);

Leftmost 60 characters of gist GP script:

hermann@7950x:~/llr405src/linux64llr$ cut -b-60 
M_52.is.x^2_plus_3_times_y^2.gp
p=2^136279841-1;
##
x=4624919986798384683510429678492757870361922596523736044043
##
y=-471803447302992039086168784360506296339127284694422433463
##
p==x^2+3*y^2
##
hermann@7950x:~/llr405src/linux64llr$


Computing p is fast (6ms), storing (20MB) numbers into variables x,y 
takes
1.1 seconds each, validation of equation takes 357ms only:

hermann@7950x:~/llr405src/linux64llr$ gp -q < 
M_52.is.x^2_plus_3_times_y^2.gp
  ***   last result computed in 6 ms.
  ***   last result computed in 1,106 ms.
  ***   last result computed in 1,051 ms.
1
  ***   last result computed in 357 ms.
hermann@7950x:~/llr405src/linux64llr$


Regards,

Hermann.