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Re: P(x) question?

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  • djbroadhurst
    ... This method http://www.dtc.umn.edu/~odlyzko/doc/arch/meissel.lehmer.pdf require O(x^(2/3)) operations and O(x^(1/3)) bits of storage. ...
    Message 1 of 5 , Sep 11, 2011
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      --- In primenumbers@yahoogroups.com,
      "techno.buddhist" <yahoo@...> wrote:

      > Other than Riemann Hypothesis is no other way
      > to calculate 'exact' P(x)?

      This method
      http://www.dtc.umn.edu/~odlyzko/doc/arch/meissel.lehmer.pdf
      require O(x^(2/3)) operations and O(x^(1/3)) bits of storage.

      > If there was such a method then somebody could do the
      > opposite of Riemann and work from the solution by adding
      > waves to get to x/Li(x)?

      http://www.dtc.umn.edu/~odlyzko/doc/zeta.html
      contains relevant papers

      David
    • kenzi_x
      One of the problems, I think, that you might bump into is that many of the interesting combinatorial prime counting algorithms out there (like the method
      Message 2 of 5 , Sep 12, 2011
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        One of the problems, I think, that you might bump into is that many of the interesting combinatorial prime counting algorithms out there (like the method djbroadhurst linked to) don't seem to have any obvious connection to the logarithmic integral, so it's hard to know where you would add the error terms back in.

        In addition to dj's links, if you're really interested in playing around with this approach, one set of ideas you might take a look at is this:

        http://www.icecreambreakfast.com/primecount/logintegral.html

        (warning: I just wrote this up last week, so consider this un-peer-reviewed, suspect, and possibly self-aggrandizing) It actually has some reasonable raw material for an attempt at what you're talking about, I think.

        Nathan McKenzie

        --- In primenumbers@yahoogroups.com, "techno.buddhist" <yahoo@...> wrote:
        >
        > Hi all,
        >
        > Newbie with a newbie question here. Other than Riemann Hypothesis is no other way to calculate 'exact' P(x)?
        >
        > If there was such a method then somebody could do the opposite of Riemann and work from the solution by adding waves to get to x/Li(x)?
        >
        > In other words prove RH by downgrading the exact result to meet the PNT estimate of x/Li(x)?
        >
        > Thanks
        >
        > TechnoBuddhist
        >
      • Mathieu Therrien
        Hello, I was wondering if it is possible to get a list of all  multiples
        Message 3 of 5 , Sep 13, 2011
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          Hello, I was wondering if it is possible to get a list of all  multiples < Cte


          under the form: a / a^2 / b / b*a / b^2 /.... < Cte  very easily, or do this kind of computations gets messy quickly?



          ________________________________
          From: djbroadhurst <d.broadhurst@...>
          To: primenumbers@yahoogroups.com
          Sent: Sunday, September 11, 2011 6:30:11 AM
          Subject: [PrimeNumbers] Re: P(x) question?


           


          --- In primenumbers@yahoogroups.com,
          "techno.buddhist" <yahoo@...> wrote:

          > Other than Riemann Hypothesis is no other way
          > to calculate 'exact' P(x)?

          This method
          http://www.dtc.umn.edu/~odlyzko/doc/arch/meissel.lehmer.pdf
          require O(x^(2/3)) operations and O(x^(1/3)) bits of storage.

          > If there was such a method then somebody could do the
          > opposite of Riemann and work from the solution by adding
          > waves to get to x/Li(x)?

          http://www.dtc.umn.edu/~odlyzko/doc/zeta.html
          contains relevant papers

          David




          [Non-text portions of this message have been removed]
        • techno.buddhist
          I looked at your work, I got mesmerised by the eye candy for a while(I build the odd website now and again and the flash apps really caught my attention). If
          Message 4 of 5 , Sep 14, 2011
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            I looked at your work, I got mesmerised by the eye candy for a while(I build the odd website now and again and the flash apps really caught my attention). If the flash apps are your work, well done, very nice!

            Took me a while before I got it(my head obviously wasn't in the zone) but the basic gist is what interested me anyway. Using integration to approximate is an interesting approach. I'll see if it can be used in my work.

            Thanks, very informative!

            TechnoBuddhist


            --- In primenumbers@yahoogroups.com, "kenzi_x" <nathan@...> wrote:
            >
            > One of the problems, I think, that you might bump into is that many of the interesting combinatorial prime counting algorithms out there (like the method djbroadhurst linked to) don't seem to have any obvious connection to the logarithmic integral, so it's hard to know where you would add the error terms back in.
            >
            > In addition to dj's links, if you're really interested in playing around with this approach, one set of ideas you might take a look at is this:
            >
            > http://www.icecreambreakfast.com/primecount/logintegral.html
            >
            > (warning: I just wrote this up last week, so consider this un-peer-reviewed, suspect, and possibly self-aggrandizing) It actually has some reasonable raw material for an attempt at what you're talking about, I think.
            >
            > Nathan McKenzie
            >
            > --- In primenumbers@yahoogroups.com, "techno.buddhist" <yahoo@> wrote:
            > >
            > > Hi all,
            > >
            > > Newbie with a newbie question here. Other than Riemann Hypothesis is no other way to calculate 'exact' P(x)?
            > >
            > > If there was such a method then somebody could do the opposite of Riemann and work from the solution by adding waves to get to x/Li(x)?
            > >
            > > In other words prove RH by downgrading the exact result to meet the PNT estimate of x/Li(x)?
            > >
            > > Thanks
            > >
            > > TechnoBuddhist
            > >
            >
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