On 10/1/06, Nacho <[EMAIL PROTECTED]> wrote: > For example, the software Mathematica implements the function > PrimePi[n], and the help says: > > "PrimePi use sparse caching and sieving. For large a, the > Lagarias-Miller-Odlyzko algorithm for PrimePi is used, based on > asymptotic estimates of the density of primes." > > It works with an n up to about 8*10^13 and it is very fast.
A quote from SeqFan maillist: ****** Originally Posted by Ralf Stephan > I used Mathematica, which fortunately has some sophisticated pi(x) routines > built-in. The implementation notes say that the Lagarias-Miller-Odlyzko > algorithm (an improvement on the Meissel-Lehmer Algorithm that I once knew I once was interested in that and digged up some references but the implementation was well over my head... http://www.ams.org/journal-getitem?pii=S0025-5718-96-00674-6 http://citeseer.nj.nec.com/8559.html http://numbers.computation.free.fr/Constants/constants.html and Marc Deléglise habilitation On the Lagarias-Odlyzko algorithm: http://www.math.uiuc.edu/~galway/SlidesETC/thesis-slides-98.pdf http://www.math.uiuc.edu/~galway/SlidesETC/thesis-slides-98.ps.gz ralf ****** _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
