factor_add_primes logic

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

Dear pari-dev,

using default(factor_add_primes,1) causes factor() to add large prime 
factors found in factorizations, but only if the number to be factored 
(after trial division) is not prime.

In my opinion, there should be an option to make factor() add ALL big 
primes found in factorizations, even if I do factor(nextprime(2^100)). 
This could be done with a new value for the default, say 
default(factor_add_primes,2).

To motivate this, I see the following uses for factor_add_primes:
1) Continuing an interrupted (CTRL-C) factorization. Current behaviour 
works.
2) Repeatedly doing the same factorization during a computation: say I 
need to compute znorder(Mod(a,n)) for several a's with n fixed and I am 
too lazy/stupid to give the factorization of n as an argument.  Also 
here, current behaviour works.
3) Doing different factorizations but where the same prime factors occur 
multiple times.  Say P is a point on an elliptic curve and I want to 
factor the denominator of [n]P where n varies.  Here the current 
behaviour is not optimal, it would be better to add every large prime 
factor of the factorizations (even if the number-to-be-factored was prime).

I would like to add that for uses 1) and 2) it would actually suffice to 
add all but the largest prime factors of factorizations: if n has k 
different large prime factors, only add k-1 of them.  This would also be 
consistent with the current behaviour for "factoring" primes, where no 
prime is added.


What do you think?

Cheers,
Jeroen