Re: PrimePi and limit of argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg78087] Re: [mg77911] PrimePi and limit of argument*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Fri, 22 Jun 2007 06:49:05 -0400 (EDT)*References*: <7566193.1182423757619.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

If you decide to compute PrimePi[100] by hand, you might take a piece of paper and write down the primes up to 97, then count them. If you try the same method for PrimePi[10^15], you'll need a bigger piece of paper. But you'll need a lot MORE than a bigger piece of paper -- you'll need a smarter algorithm, or you'll never live long enough. And that's what Mathematica is telling you; the PrimePi method has an upper ceiling, independent of how big your machine might be. You may as well demand a general solution in radicals for 7th-degree polynomials. 7 isn't a large number, but even so, it can't be done... even if your machine is bigger than the universe. Bobby On Tue, 19 Jun 2007 05:47:55 -0500, Robert Pigeon <robert.pigeon at videotron.ca> wrote: > Hello all, > > I was playing around with the function PrimePi[] and trying different > arguments. When I tried PrimePi[10^15] I got the error message saying > that > the argument is too large for this implementation. I know that it is a > large > number.! When I use 10^14 as the argument I get an answer, it takes a > while > but I get an answer. > > I tried this on a PC running Vista Home Premium 64-bit with Mathematica > 6. > Then I tried the same thing under Windows XP 32-bit. There was no > difference, I got an answer for 10^14 and same error message with 10^15. > > > My question is: I thought that with a 64-bit computer I could use larger > numbers.! Maybe I am misunderstanding something here, so please help me > understand J > > > Thanks, > > > Robert > > > Robert Pigeon > > -- DrMajorBob at bigfoot.com

**Follow-Ups**:**Re: Re: PrimePi and limit of argument***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>