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Re: AP25

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  • jarek372000
    I am not sure what was the exact CPU power used, as Raanan was distributing the program among his computers, and also the number and kind of computers he had
    Message 1 of 7 , May 17, 2008
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      I am not sure what was the exact CPU power used, as Raanan was
      distributing the program among his computers, and also the number and
      kind of computers he had access to, varied. However, I understand you
      are asking what order of magnitude of CPU takes to find such a result.

      I think we weren't either particularly lucky or unlucky. Data gathered
      during the search indicates that it was about time to expect the first
      AP25.

      The search was in a natural way divided into many independent
      segments, each taking about 3 minutes on Athlon 64, it would take some
      10 times more on a 32-bit computer, otherwise it depends on the
      particular processor. Probably no RAM is used, processor cache should
      be enough. I think Raanan went through less than 10,000,000 such
      segments before finding the AP25 - this would be somewhat lower if we
      targeted AP25 from the start since we would have scheduled the search
      differently.

      To hunt AP26, the program could be speed up by a factor of 2, at the
      cost of missing about one third of AP25's on the way of current
      search, but with no loss of AP26's. I think that one would have to go
      through something like 500,000,000 segments without finding AP26, to
      be eligible to complain on bad luck.

      So we are talkig about at least 1000 CPU years of 64-bit computers to
      honestly expect an AP26.

      Now, I am not a professional programmer. I have written a C-code which
      can be run on a single computer, and in consequence it can be run on a
      local network with a proper script. I have no ability to make a
      distibuted project on the network. If someone is interested in running
      a wide distributed search, I can provide the code. Program segments
      are numbered, so in principle you can distribute the search ranges by
      sending out to everyone a New Year postcard once a year with the
      assigned range for the next year. Or with a few hundred million of
      computers you can find AP26 in a few minutes (provided you can
      distribute the numbers of segments).

      Jarek

      --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:
      >
      > --- On Sat, 5/17/08, jarek372000 <Jaroslaw.Wroblewski@...> wrote:
      > > This morning the first known AP25 has been discovered:
      > >
      > > 6171054912832631 + 366384*23#*n, for n=0 to 24
      > > (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008)
      > >
      > > My contribution was the search program, while Raanan
      > > provided the computer power.
      >
      > Wow! A marvelous find. I think a lot of people here have been
      crossing their fingers for you over the last few months as the AP24s
      have been coming in, I certainly have.
      >
      > What kind of CPU power was behind the task? Does your program
      sensibly distribute? I'd certainly be willing to stick a CPU or two on
      a distributed project that was pushing for an AP26. However, my fear
      is that the bandwidth/comms issues might be cause Amdahl's law to
      frown at such a task.
      >
      > Phil
      >
    • Paul Schmidt
      Jarek, I might be interested in helping to set up a distributed system. Since each segment is independent, this shouldn t take anything fancy. I am a
      Message 2 of 7 , May 17, 2008
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        Jarek,

        I might be interested in helping to set up a distributed system. Since each
        segment is independent, this shouldn't take anything fancy. I am a professional
        web programmer and could manage this as a web project in a database. That
        way people could easily request segments and get them assigned.

        Is your program just source at this point? Or do you have a stand alone exe?
        Someone else might be able to put together an windows version.

        I have also looked at PrimeGrid and this is probably the best way to distribute
        the project. Does anyone here have experience on that system?

        Paul


        ----- Original Message -----
        From: jarek372000
        To: primenumbers@yahoogroups.com
        Sent: Saturday, May 17, 2008 5:45 AM
        Subject: [PrimeNumbers] Re: AP25


        I am not sure what was the exact CPU power used, as Raanan was
        distributing the program among his computers, and also the number and
        kind of computers he had access to, varied. However, I understand you
        are asking what order of magnitude of CPU takes to find such a result.

        I think we weren't either particularly lucky or unlucky. Data gathered
        during the search indicates that it was about time to expect the first
        AP25.

        The search was in a natural way divided into many independent
        segments, each taking about 3 minutes on Athlon 64, it would take some
        10 times more on a 32-bit computer, otherwise it depends on the
        particular processor. Probably no RAM is used, processor cache should
        be enough. I think Raanan went through less than 10,000,000 such
        segments before finding the AP25 - this would be somewhat lower if we
        targeted AP25 from the start since we would have scheduled the search
        differently.

        To hunt AP26, the program could be speed up by a factor of 2, at the
        cost of missing about one third of AP25's on the way of current
        search, but with no loss of AP26's. I think that one would have to go
        through something like 500,000,000 segments without finding AP26, to
        be eligible to complain on bad luck.

        So we are talkig about at least 1000 CPU years of 64-bit computers to
        honestly expect an AP26.

        Now, I am not a professional programmer. I have written a C-code which
        can be run on a single computer, and in consequence it can be run on a
        local network with a proper script. I have no ability to make a
        distibuted project on the network. If someone is interested in running
        a wide distributed search, I can provide the code. Program segments
        are numbered, so in principle you can distribute the search ranges by
        sending out to everyone a New Year postcard once a year with the
        assigned range for the next year. Or with a few hundred million of
        computers you can find AP26 in a few minutes (provided you can
        distribute the numbers of segments).

        Jarek

        --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:
        >
        > --- On Sat, 5/17/08, jarek372000 <Jaroslaw.Wroblewski@...> wrote:
        > > This morning the first known AP25 has been discovered:
        > >
        > > 6171054912832631 + 366384*23#*n, for n=0 to 24
        > > (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008)
        > >
        > > My contribution was the search program, while Raanan
        > > provided the computer power.
        >
        > Wow! A marvelous find. I think a lot of people here have been
        crossing their fingers for you over the last few months as the AP24s
        have been coming in, I certainly have.
        >
        > What kind of CPU power was behind the task? Does your program
        sensibly distribute? I'd certainly be willing to stick a CPU or two on
        a distributed project that was pushing for an AP26. However, my fear
        is that the bandwidth/comms issues might be cause Amdahl's law to
        frown at such a task.
        >
        > Phil
        >





        [Non-text portions of this message have been removed]
      • Jens Kruse Andersen
        ... Huge congratulations! This is a very impressive and well deserved feat. http://hjem.get2net.dk/jka/math/aprecords.htm is updated. As the only known AP25 it
        Message 3 of 7 , May 17, 2008
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          Jarek wrote:
          > This morning the first known AP25 has been discovered:
          >
          > 6171054912832631 + 366384*23#*n, for n=0 to 24
          > (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008)
          >
          > My contribution was the search program, while Raanan provided the
          > computer power.

          Huge congratulations!
          This is a very impressive and well deserved feat.
          http://hjem.get2net.dk/jka/math/aprecords.htm is updated.
          As the only known AP25 it gets 5 records: Longest known AP, largest
          known AP25, and smallest known difference, start and end for an AP25.
          Getting 5 records for one AP may sound like a lot but it's much more
          than 5 times as hard as most of the other records.

          --
          Jens Kruse Andersen
        • Chris Caldwell
          ... I agree! Decided to change my 2006 banner notes about the last Mersenne to this AP on my main page primes.utm.edu/ and primes.utm.edu/largest.html ...
          Message 4 of 7 , May 17, 2008
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            Jens Kruse Andersen wrote:
            > Huge congratulations!
            > This is a very impressive and well deserved feat.
            > http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

            I agree! Decided to change my 2006 banner notes about the last
            Mersenne to this AP on my "main" page primes.utm.edu/
            and primes.utm.edu/largest.html

            > Getting 5 records for one AP may sound like a lot but it's
            > much more than 5 times as hard as most of the other records.

            We know they exist with arbitrary length, but 25 seems a long
            way from infinity doesn't it?

            CC
          • Jens Kruse Andersen
            ... Nice. I see it s already in Prime Curios!: http://primes.utm.edu/curios/page.php/6171054912832631.html This can also be updated:
            Message 5 of 7 , May 17, 2008
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              Chris Caldwell wrote:

              > I agree! Decided to change my 2006 banner notes about the last
              > Mersenne to this AP on my "main" page primes.utm.edu/
              > and primes.utm.edu/largest.html

              Nice. I see it's already in Prime Curios!:
              http://primes.utm.edu/curios/page.php/6171054912832631.html
              This can also be updated:
              http://primes.utm.edu/glossary/page.php?sort=ArithmeticSequence

              > We know they exist with arbitrary length, but 25 seems a long
              > way from infinity doesn't it?

              Yes it does. I made a similar "but" when Jarek's earlier record was
              mentioned on Wikipedia's main page in 2007 with the text:
              "Did you know...
              ...that existence of arbitrarily many primes in arithmetic progression was
              proven in 2004, but it took 75 computers to find an example with 24 primes?"

              It's archived at
              http://en.wikipedia.org/w/index.php?title=Template:Did_you_know&oldid=138995374
              (People are not supposed to know the "Did you know" facts)

              I have updated http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression

              --
              Jens Kruse Andersen
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