We are using flint:
if mpz_fits_slong_p(n.value):
....
n_factor(&f, mpz_get_ui(n.value), proof)
where n_factor is defined in sage.libs.flint.ulong_extras.
David
On Wed, Jun 18, 2014 at 4:28 AM, John Cremona <john.crem...@gmail.com>
wrote:
> I noticed an announcement on the flint-dev list which led me to try
> this, and indeed we have the bug:
>
> sage: n=2007193456621
> sage: n.is_prime()
> False
> sage: n.factor() # !!!!!!!!!!
> 2007193456621
> sage: pari(n).factor()
> [1001797, 1; 2003593, 1]
> sage: n == 1001797 * 2003593
> True
>
> See flint-dev for more details, but this seems serious enough to
> report here too. I do not understand why Sage fails to factor n since
> the documentation says that pari is the default, and pari can factor
> this n (as above), however:
>
> sage: n.factor(algorithm='pari')
> 2007193456621
>
> but
>
> sage: from sage.rings.factorint import factor_using_pari
> sage: factor_using_pari(n)
> [(1001797, 1), (2003593, 1)]
>
> so something is going wrong before pari is getting called, perhaps a
> primality test?
>
> John
>
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