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AP25

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  • jarek372000
    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
    Message 1 of 7 , May 16, 2008
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      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.

      Jarek
    • Phil Carmody
      ... 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
      Message 2 of 7 , May 17, 2008
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        --- 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
      • 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 3 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 4 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 5 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 6 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 7 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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