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21577[PrimeNumbers] Re: Nth Index of a Prime

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  • Jens Kruse Andersen
    Jul 13 9:01 AM
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      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
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