Re: Why does factorint() take 128ms for 1853 decimal digit prime, while isprime() takes 16:45min/2min cpu/real time?

On 2026-02-24 14:46, Karim Belabas wrote:
>> But I should have learned about it myself easily with "??factorint".
> 
> Maybe I'm missing something but this seems to be easy to find:
> 
> 14:38) gp > ??factorint
> factorint(x,{flag = 0}):
> 
>    Factors  the  integer n into a product of pseudoprimes  (see 
> ispseudoprime),
> [...]
> the  divisors  are  by  default not proven primes if they are larger 
> than 2^64,
> they only failed the BPSW compositeness test (see ispseudoprime).   Use 
> isprime
> on  the  result  if  you  want  to guarantee primality or set the 
> factor_proven
> default  to 1.
> [...]
> 
> 
> N.B. I don't recommend setting that default outside validating a 
> specific
> computation (then unsetting it again). It may slow down gp considerably
> in ways which are hard to predict or mitigate for users.
> 
> Cheers,
> 
>     K.B.
> 
You are right, easy to find, and that was what I tried to say with my 
last posting.

Regards,

Hermann.