Re: Re: PrimePi and limit of argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg78141] Re: [mg78087] Re: [mg77911] PrimePi and limit of argument*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Sat, 23 Jun 2007 07:22:33 -0400 (EDT)*Organization*: Deep Space Corps of Engineers*References*: <7566193.1182423757619.JavaMail.root@m35> <200706221049.GAA16611@smc.vnet.net> <25396560.1182560007011.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

My point was that increasing the address space -- like getting a bigger piece of paper -- doesn't solve every big problem, as if by magic. "Look! I can calculate 500 factorial! So I can solve equations in that many unknowns, too, right? I can find the 500 factorial-th prime, right?" Well... no. Sorry. Mathematica will, for the most part, solve the same problems on a 64-bit machine as it does on a 32-bit machine. It won't run out of memory as often, perhaps, but the algorithms don't suddenly change. Bobby On Fri, 22 Jun 2007 19:40:56 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > *This message was transferred with a trial version of CommuniGate(tm) > Pro* > 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 >> > > -- DrMajorBob at bigfoot.com

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