Jeroen Demeyer on Mon, 23 Mar 2009 12:28:55 +0100

```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.
```
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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).
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To motivate this, I see the following uses for factor_add_primes:
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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).
```
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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

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