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.gphermann@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 --versionGP/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.