PrimePi
Usage Message: PrimePi[x] gives the number of primes less than or equal to x. Attributes[PrimePi] = {Listable, Protected}
Notes: PrimePi and Prime
use sparse caching and sieving for n less than about 10^8. For large n the Lagarias-Miller-Odlyzko algorithm is used for PrimePi, based on asymptotic estimates of the density of primes, and is inverted to give Prime[n].
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/PrimePi.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/PrimePi.html
Questions or comments? Send email to support@wolfram.com.
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