#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 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.
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Ticket URL: <http://trac.sagemath.org/ticket/16878#comment:37>
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