Loading ...
Sorry, an error occurred while loading the content.

Re: Nth Index of a Prime

Expand Messages
  • pbtoau
    Hi, If by Nth index you mean pi(x) then: pi(123571113171923) = 3933667972530 pi(231917131175321) = 7237459689186 pi(1235711131175321) = 36647548937934
    Message 1 of 6 , Jun 30, 2010
    • 0 Attachment
      Hi,

      If by Nth index you mean pi(x) then:

      pi(123571113171923) = 3933667972530
      pi(231917131175321) = 7237459689186
      pi(1235711131175321) = 36647548937934
      pi(1357911131197531) = 40159216312772

      The next one is too big for my implementation and I do not think anyone knows pi(R23) for sure. I could provide good approximations.

      - David

      --- In primenumbers@yahoogroups.com, Ali Adams <alipoland@...> wrote:
      >
      > Peace to all,
      >
      > Can someone please tell me what is the best way to find the Nth index of the following not so large prime numbers?
      >
      > 12345678910987654321 (from 1 to 10 and back)
      >
      > 1357911131197531 (odds from 1 to 13 and back)
      >
      > 1235711131175321 (primes from 1 to 13 and back)
      >
      > 123571113171923 (primes from 1 to 23)
      >
      > 231917131175321 (primes from 23 to 1)
      >
      > and
      >
      > 11111111111111111111111 (23 ones)
      >
      > Thank you all.
      >
      > Ali Adams
      > God > infinity
      > www.heliwave.com
      >
      >
      >
      >
      >
      >
      >
      > [Non-text portions of this message have been removed]
      >
    • djbroadhurst
      ... How did you compute pi(x) with x 10^15, please, David? Andrew Booker s programme hosted at http://primes.utm.edu/nthprime/ is restricted to pi(x) with x
      Message 2 of 6 , Jul 13 6:56 AM
      • 0 Attachment
        --- In primenumbers@yahoogroups.com,
        David Baugh <PbtoAu@...> wrote:

        > pi(1357911131197531) = 40159216312772
        > The next one is too big for my implementation

        How did you compute pi(x) with x > 10^15, please, David?

        Andrew Booker's programme hosted at
        http://primes.utm.edu/nthprime/
        is restricted to pi(x) with x < 3*10^13.

        For those with dollars to burn, Mma seems
        able to compute pi(x) with x < 8*10^13:
        http://mathworld.wolfram.com/PrimeCountingFunction.html

        It seems that you have an implementation that
        comfortably copes with x > 10^15.

        Might you consider making your code available to
        Chris Caldwell, for on-line use at the Prime Pages,
        as Andrew generously did with his? If the data tables
        are too big or the CPUtime too onerous for such on-line use,
        might you kindly provide a source that others may compile?

        Best regards

        David Broadhurst
      • Jens Kruse Andersen
        ... I don t know what David Baugh uses but there is something better. At http://mersenneforum.org/showthread.php?t=13210 I wrote: Two years ago I searched for
        Message 3 of 6 , Jul 13 9:01 AM
        • 0 Attachment
          David Broadhurst wrote:
          > David Baugh <PbtoAu@...> wrote:
          >
          >> pi(1357911131197531) = 40159216312772
          >> The next one is too big for my implementation
          >
          > How did you compute pi(x) with x > 10^15, please, David?

          I don't know what David Baugh uses but there is something better.
          At http://mersenneforum.org/showthread.php?t=13210 I wrote:

          "Two years ago I searched for a good pi(x) program, found an old mention
          of Christian Bau and dug up a link to http://www.cbau.freeserve.co.uk
          The link was and still is dead but the Wayback Machine has archived
          versions up to 2005 at
          http://web.archive.org/web/*/http://www.cbau.freeserve.co.uk.

          There is C++ source by Christian Bau for the Extended Meissel-Lehmer
          algorithm. It works to 2^64 and my test runs agree with published counts
          by Tomás Oliveira e Silva. I have used the program for a few projects
          such as http://primes.utm.edu/curios/includes/puzzio.php. The archive has
          Version 0.92, 25/Sep/2003. The site speaks of unfinished work in
          progress and mentions future improved versions but I have not found that."

          It takes 1 minute for the program to compute pi(1357911131197531) on
          one core of a 2.4 GHz Core 2 Duo. The value agrees with David Baugh.

          --
          Jens Kruse Andersen
        • djbroadhurst
          ... Thanks, Jens! web.archive.org/web/20040125140056/http://www.cbau.freeserve.co.uk/ ... which seems to permit personal use. David
          Message 4 of 6 , Jul 13 9:36 AM
          • 0 Attachment
            --- In primenumbers@yahoogroups.com,
            "Jens Kruse Andersen" <jens.k.a@...> wrote:

            > Two years ago I searched for a good pi(x) program,
            > found an old mention of Christian Bau and dug up a link to
            > http://www.cbau.freeserve.co.uk [broken URL]

            Thanks, Jens!

            web.archive.org/web/20040125140056/http://www.cbau.freeserve.co.uk/

            seems to be an appropriate archived URL. "PrimeCount.cp" says:

            > This code is unfinished work in progress. For this reason,
            > you may download this code and use it on the computer that
            > you used for downloading, but any further distribution is
            > strictly prohibited.

            which seems to permit personal use.

            David
          • pbtoau
            Looks like Bau s code goes twice as high as Baugh s code and I don t have source code. The code the community needs is that developed by Tomás Oliveira e
            Message 5 of 6 , Jul 14 12:20 PM
            • 0 Attachment
              Looks like Bau's code goes twice as high as Baugh's code and I don't have source code. The code the community needs is that developed by Tomás Oliveira e Silva. His can go to at least 10^23. I have asked, but I guess not nicely enough.

              - David

              --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
              >
              >
              >
              > --- In primenumbers@yahoogroups.com,
              > David Baugh <PbtoAu@> wrote:
              >
              > > pi(1357911131197531) = 40159216312772
              > > The next one is too big for my implementation
              >
              > How did you compute pi(x) with x > 10^15, please, David?
              >
              > Andrew Booker's programme hosted at
              > http://primes.utm.edu/nthprime/
              > is restricted to pi(x) with x < 3*10^13.
              >
              > For those with dollars to burn, Mma seems
              > able to compute pi(x) with x < 8*10^13:
              > http://mathworld.wolfram.com/PrimeCountingFunction.html
              >
              > It seems that you have an implementation that
              > comfortably copes with x > 10^15.
              >
              > Might you consider making your code available to
              > Chris Caldwell, for on-line use at the Prime Pages,
              > as Andrew generously did with his? If the data tables
              > are too big or the CPUtime too onerous for such on-line use,
              > might you kindly provide a source that others may compile?
              >
              > Best regards
              >
              > David Broadhurst
              >
            Your message has been successfully submitted and would be delivered to recipients shortly.