#13516: prime_powers doesn't work with start very well
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Reporter: kcrisman | Owner: was
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.4
Component: number theory | Resolution:
Keywords: beginner | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by was):
I would prefer to leave 1 as a prime power because it is listed in
Sloane's tables as a prime power: http://oeis.org/A000961
There he says "Since 1 = p^0 does not have a well defined prime base p, it
is sometimes not regarded as a prime power.", which might be where your
misgivings come from.
If by "prime power" one thinks of "power of a prime", the only question
is in what set are we considering the prime powers. If we take the
natural numbers, then the number 1 is definitely a power of a prime.
If by "prime power" one thinks "power of a specific canonical prime", then
1 is not such a thing.
In this case, the best thing to do is stick with what is there (to avoid
introducing bugs in other people's code!) and clearly document/define what
a prime power is in Sage.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13516#comment:6>
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