Re: Re: PrimePi and limit of argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg78128] Re: [mg78087] Re: [mg77911] PrimePi and limit of argument*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 23 Jun 2007 07:15:53 -0400 (EDT)*References*: <7566193.1182423757619.JavaMail.root@m35> <200706221049.GAA16611@smc.vnet.net>

That's not quite right: in the case of solving polynomial equations in terms of radicals there is a mathematical limitation, in the other case there is a limitation of the particualr implementation. The value of PrimePi[10^15] is well known, in fact it is: 29844570422669 In Mathemaitca you can get a pretty good approximation by evaluating: Round[LogIntegral[10^15]] 29844571475288 Andrzej Kozlowski On 22 Jun 2007, at 19:49, DrMajorBob wrote: > 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 >

**References**:**Re: PrimePi and limit of argument***From:*DrMajorBob <drmajorbob@bigfoot.com>