hermann on Wed, 29 Nov 2023 13:14:52 +0100


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


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.