#16878: faster is_prime
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Vincent | Reviewers: Jeroen Demeyer,
Delecroix, Jeroen Demeyer | Vincent Delecroix
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16878 | e6f88c5f9adef669ede74e3c161e19fe37203276
Dependencies: #15767 | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:37 jdemeyer]:
> In `is_pseudoprime_small_power`, the fixed exponent bound of 1024 is
clearly not acceptable.
>
> The PARI implementation of `isprimepower()` is as follows: first do
trial division by small primes up to 100. If we do not find a divisor,
then find out if the number is a perfect power. This is now a lot cheaper
since the exponent can be at most `log(n)/log(p)`, where `n` is the number
to check and `p` the smallest prime that we didn't check in the trial
division.
>
> But overall, I would prefer PARI to add a new function
`ispseudoprimepower()` such that Sage can interface it.
Me too. I saw that you already submit the question
[http://pari.math.u-bordeaux.fr/archives/pari-dev-1409/msg00011.html]...
On the other hand, we need a reasonable fix in order to get this ticket
in.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16878#comment:38>
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