Re: moebius function

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Chris De Corte [2015-02-17 04:34]:
> Your moebius function seems to do calculations for very high
> figures.But your prime function seems to only go for low figures.

prime(n) uses a naive O~(n) algorithm (see ??prime), whereas moebius() calls
factor / factorint which use subexponential algorithms in exp O~(log n)^(1/2).

> Is your moebius then reliable?

It is to the extent factor() is: there is a remote possibility  that a
composite > 2^64 is incorrectly considered as prime (??factor).
[No example is known at present]

Use

  default(factor_proven, 1)

to get rid of this possibility (or set factor_proven = 1 in your gprc).
This will slow down a little the arithmetic kernel, but it may be
tolerable, or even negligible, in your application ( at worst 
O(log n)^logloglog(n) extra cost when needing to factor the integer n )

In any case, moebius() will remain much faster than prime() :-)

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
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