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

Re: [PrimeNumbers] SoB finds 10th prime!

Expand Messages
  • Jack Brennen
    ... I can t seem to find any real numbers on how far the remaining 7 k values have been tested. The SoB pages seem to indicate that all of them have been
    Message 1 of 8 , May 5, 2007
      Phil Carmody wrote:
      > --- Paul Underwood <paulunderwood@...> wrote:
      >> Congrats to Konstantin Agafonov and Seventeen or Bust for finding the
      >> Sierpinski problem prime 19249*2^13018586+1 which has 3.9 million digits!
      >
      > Jack, or someone, any model for when the next one's due,
      > assuming a sperical homogeneous Poisson?
      >

      I can't seem to find any "real" numbers on how far the remaining 7
      k values have been tested. The SoB pages seem to indicate that all
      of them have been tested to n=10^7, but that can't be an accurate
      accounting.

      However, if we assume that n=10^7 is accurate for each of them,
      there would be about a 50% chance of finding a prime for one of
      the 7 candidate k values with n < 14675000.

      That's the good news.

      The bad news is that in order to have a 50% chance of resolving
      the Sierpinski conjecture, you'd need to search for all
      n < 2965000000000. (2.965*10^12)

      That's an improvement over the last numbers I remember putting
      together, which would have given somewhere around a 40% chance of
      resolving the Sierpinski conjecture by that limit...

      http://tech.groups.yahoo.com/group/primenumbers/message/10258

      Still, even a single test in the n > 10^12 range is beyond our
      reasonable capabilities today -- we're just not ready to do
      modular arithmetic on terabit numbers.


      Also, the chance to resolve the conjecture before n = 10^9 has
      risen to 3.98% from the previous 2.45%.


      I think a lot of this improvement in the outlook (modest as it
      is) is due to the fact that this latest k value (19249) was
      one of the three "toughest" k values to crack of the original
      seventeen (one of the three lowest Proth weights). Only the
      k values of 22699 and 67607 (both still uncracked) have lower
      Proth weights.


      Jack
    • Jean Penné
      Many congrats to the discoverer and all participants for this outstanding result!! However, I have two questions about it : 1) If I am not wrong, the record
      Message 2 of 8 , May 5, 2007
        Many congrats to the discoverer and all participants for this
        outstanding result!!

        However, I have two questions about it :

        1) If I am not wrong, the record has been posted to SoB on March 26 ;
        why is it not yet posted to the top 5000 database ?

        2) What is/are the proving program(s)?

        Woul you excuse my curiosity...

        Jean
      • Phil Carmody
        ... That s quite optmistic. Maybe the one just found was that one! ... Remind me to never ignorantly cross you, Jack ;-) ... We re most of the way there.
        Message 3 of 8 , May 6, 2007
          --- Jack Brennen <jb@...> wrote:
          > Phil Carmody wrote:
          > > Jack, or someone, any model for when the next one's due,
          > > assuming a sperical homogeneous Poisson?
          >
          > I can't seem to find any "real" numbers on how far the remaining 7
          > k values have been tested. The SoB pages seem to indicate that all
          > of them have been tested to n=10^7, but that can't be an accurate
          > accounting.
          >
          > However, if we assume that n=10^7 is accurate for each of them,
          > there would be about a 50% chance of finding a prime for one of
          > the 7 candidate k values with n < 14675000.
          >
          > That's the good news.

          That's quite optmistic. Maybe the one just found was that one!

          > The bad news is that in order to have a 50% chance of resolving
          > the Sierpinski conjecture, you'd need to search for all
          > n < 2965000000000. (2.965*10^12)
          >
          > That's an improvement over the last numbers I remember putting
          > together, which would have given somewhere around a 40% chance of
          > resolving the Sierpinski conjecture by that limit...
          >
          > http://tech.groups.yahoo.com/group/primenumbers/message/10258

          Remind me to never ignorantly cross you, Jack ;-)

          > Still, even a single test in the n > 10^12 range is beyond our
          > reasonable capabilities today -- we're just not ready to do
          > modular arithmetic on terabit numbers.

          We're most of the way there. Compared with those flipping iron rings at least.
          Doing it 10^12 times I think will be a harder target.

          > Also, the chance to resolve the conjecture before n = 10^9 has
          > risen to 3.98% from the previous 2.45%.

          Impressive.

          > I think a lot of this improvement in the outlook (modest as it
          > is) is due to the fact that this latest k value (19249) was
          > one of the three "toughest" k values to crack of the original
          > seventeen (one of the three lowest Proth weights). Only the
          > k values of 22699 and 67607 (both still uncracked) have lower
          > Proth weights.

          Ah probably the single most pervasive snippet of utter wrongness
          I've seen various people throw around on their project fora is
          that getting rid of the dense ones is best. Of course, that's
          the worse possible situation, you want to get rid of the most
          difficult numbers sooner rather than later. I've tried telling
          them that, but most just didn't seem to grok the concept.

          Thanks for the quick numerics, as always, Jack.

          Phil

          () ASCII ribbon campaign () Hopeless ribbon campaign
          /\ against HTML mail /\ against gratuitous bloodshed

          [stolen with permission from Daniel B. Cristofani]

          __________________________________________________
          Do You Yahoo!?
          Tired of spam? Yahoo! Mail has the best spam protection around
          http://mail.yahoo.com
        • Jack Brennen
          ... First, I realize reading this that I m being way too precise. With the unknown depth of search, and the inaccuracy of the Proth weight values, I should
          Message 4 of 8 , May 6, 2007
            Phil Carmody wrote:
            >>
            >> However, if we assume that n=10^7 is accurate for each of them,
            >> there would be about a 50% chance of finding a prime for one of
            >> the 7 candidate k values with n < 14675000.
            >>
            >> That's the good news.
            >
            > That's quite optmistic. Maybe the one just found was that one!

            First, I realize reading this that I'm being way too precise. With
            the unknown depth of search, and the inaccuracy of the Proth weight
            values, I should probably have just said n < 15_000_000.

            In any case, with the remaining 7 k values, if they've been
            completely searched up to n < A, we're about 50% to find another
            prime with n < 1.5*A. A very quick justification which is very
            close to being mathematically "correct":

            The remaining 7 k values should produce an aggregate total of about
            1.25 primes per "octave" (A < n < 2*A), and the distribution should
            be very Poisson-like.

            To get a 50% chance of a hit in a Poisson distribution, we need an
            expectation of log(2) primes. That requires 0.55 octaves, or
            A < n < 1.47*A.

            >
            > Remind me to never ignorantly cross you, Jack ;-)

            If you read the forum link where Louie originally trashed my math,
            he admitted very quickly afterward that he did make a mistake and
            that I was probably "in the ballpark"...

            >
            >> Still, even a single test in the n > 10^12 range is beyond our
            >> reasonable capabilities today -- we're just not ready to do
            >> modular arithmetic on terabit numbers.
            >
            > We're most of the way there. Compared with those flipping iron rings at least.
            > Doing it 10^12 times I think will be a harder target.

            Keeping even a single terabit number in high-speed RAM is far out of
            the capability of the vast majority of computers in existence -- that's
            my point. Clearly we have the capability to build such hardware, but
            the whole point of SoB and other cooperative computing projects is to
            use inexpensive commonly available PC-like devices, and they're still
            many years away from being able to hold even a single terabit number
            in RAM.

            >
            > Ah probably the single most pervasive snippet of utter wrongness
            > I've seen various people throw around on their project fora is
            > that getting rid of the dense ones is best. Of course, that's
            > the worse possible situation, you want to get rid of the most
            > difficult numbers sooner rather than later. I've tried telling
            > them that, but most just didn't seem to grok the concept.
            >

            To put things in perspective, the toughest two k values have an
            aggregate expectation of 0.15 primes per octave. In very rough
            numbers, that means an expectation to find 1 prime between these
            two k values as we push n from 10^7 to 10^9 (about 6.6 octaves).
            And note of course that 1 prime between those two k values won't
            resolve the conjecture.
          • Jean Penné
            Now I see the responses to my two questions! Hurrah for Seveteen or Bust!! Jean
            Message 5 of 8 , May 8, 2007
              Now I see the responses to my two questions!

              Hurrah for Seveteen or Bust!!

              Jean

              --- In primenumbers@yahoogroups.com, Jean Penné <jpenne@...> wrote:
              >
              > Many congrats to the discoverer and all participants for this
              > outstanding result!!
              >
              > However, I have two questions about it :
              >
              > 1) If I am not wrong, the record has been posted to SoB on March 26 ;
              > why is it not yet posted to the top 5000 database ?
              >
              > 2) What is/are the proving program(s)?
              >
              > Woul you excuse my curiosity...
              >
              > Jean
              >
            Your message has been successfully submitted and would be delivered to recipients shortly.