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New Prime Found

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  • b2lee2003
    Later today, hopefully, we at Riesel Sieve will announce the finding of yet another prime. Weighing in at 661786 digits, it won t be the largest for our
    Message 1 of 9 , May 23, 2006
      Later today, hopefully, we at Riesel Sieve will announce the finding
      of yet another prime. Weighing in at 661786 digits, it won't be the
      largest for our project but a wonderful accomplishment none the less.
      We are currently running a double check and will report it to Prime
      Pages upon completion. So, I guess this is a warning to Chris
      Caldwell also. VERY soon we will be killing your verification system
      with a large prime:)

      This will be the second 600k+ digit prime found in the month of May
      this year for Riesel Sieve. As many know, I'm a firm believer in
      numbers of a restricted form producing primes that seem to 'bunch'
      together. Hopefully we will get yet another prime in before we hit
      another 100+ day stretch of primeless search.

      Lee Stephens
      Riesel Sieve
    • Paul Leyland
      ... If you believe that results of such searches occur at essentially random intervals, this bunching behaviour is exactly what you should expect. Read up on
      Message 2 of 9 , May 23, 2006
        On Tue, 2006-05-23 at 15:55, b2lee2003 wrote:

        > this year for Riesel Sieve. As many know, I'm a firm believer in
        > numbers of a restricted form producing primes that seem to 'bunch'
        > together. Hopefully we will get yet another prime in before we hit
        > another 100+ day stretch of primeless search.

        If you believe that results of such searches occur at essentially random
        intervals, this bunching behaviour is exactly what you should expect.
        Read up on "Poisson statistics".


        Paul



        [Non-text portions of this message have been removed]
      • Phil Carmody
        ... Islands , they were once called. Some have mistakenly genuinely believed that they can be predicted. That was basically a re-working of the law of
        Message 3 of 9 , May 23, 2006
          --- Paul Leyland <paul@...> wrote:
          > On Tue, 2006-05-23 at 15:55, b2lee2003 wrote:
          > > this year for Riesel Sieve. As many know, I'm a firm believer in
          > > numbers of a restricted form producing primes that seem to 'bunch'
          > > together. Hopefully we will get yet another prime in before we hit
          > > another 100+ day stretch of primeless search.

          "Islands", they were once called. Some have mistakenly genuinely
          believed that they can be predicted. That was basically a re-working
          of the "law of averages", which is basically assumes that things like
          roulette tables, dice, or primes, have a memory. However, as Paul says:

          > If you believe that results of such searches occur at essentially random
          > intervals, this bunching behaviour is exactly what you should expect.
          > Read up on "Poisson statistics".

          A great starter is to queue for a ride on the paradoxical Poisson bus:

          http://groups.yahoo.com/group/primenumbers/message/10356

          (Which looks at the gaps rather than the hits themselves, but the maths
          is the same.)

          Phil, part of the Paul-Phil-prime-posting-partnership

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        • jbrennen
          ... Well put, Phil. ;^) Another interesting (and nonintuitive) fact about Poisson distributions... Consider that bus stop which receives an average of one
          Message 4 of 9 , May 24, 2006
            --- Phil Carmody wrote:
            > A great starter is to queue for a ride on the paradoxical Poisson
            > bus:
            >
            > http://groups.yahoo.com/group/primenumbers/message/10356

            Well put, Phil. ;^)

            Another interesting (and nonintuitive) fact about Poisson
            distributions... Consider that bus stop which receives
            an average of one bus per hour with Poisson distribution.
            If you sample the gaps between buses over an extended period,
            and round the result off to the nearest minute, what will be
            the most-often-seen gap? Answer below...












































            The most often seen gap (when samples are rounded to the nearest
            minute): 1 minute. Nowhere near the "intuitive" answer of
            60 minutes.

            That's a powerful argument for the existence of "prime islands"
            and also a powerful argument against being able to predict them
            (since they occur naturally as the result of a totally random
            process).
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