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3019 digit Ap7

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  • kraDen
    Hi All, 234043271+N*481789017*7001#+1 (0
    Message 1 of 15 , Feb 9, 2012
      Hi All,

      234043271+N*481789017*7001#+1 (0 < N < 6) describes a 3019 digit ap7 of primes

      Haven't finished processing the 4543646 prps (N=1,000,000,000-3,000,000,000)
      extending all ap4s up (and most down - I should have started at N>1,000,000,000) yet so don't have final stats.
      Got a bit lucky as I had only found 83 ap6s when the ap7 popped up.
      I have already listed the 52 ap6s that have term 6 < 2,600,000,000

      cheers
      Ken

      p.s. While hunting I also found the following ap4 which I found interesting
      2834722253+N*7001#+1 (0 < N < 3)
      which describes a 3019 digit ap4 of primes with difference 7001#

      Primality testing 234043271*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 2
      Running N-1 test using base 3
      Calling Brillhart-Lehmer-Selfridge with factored part 33.40%
      234043271*7001#+1 is prime! (3.4101s+0.0025s)
      Primality testing 715832288*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 7057
      Calling Brillhart-Lehmer-Selfridge with factored part 33.37%
      715832288*7001#+1 is prime! (3.1254s+0.0020s)
      Primality testing 1197621305*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 7
      Calling Brillhart-Lehmer-Selfridge with factored part 33.46%
      1197621305*7001#+1 is prime! (3.0342s+0.0020s)
      Primality testing 1679410322*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 2
      Calling Brillhart-Lehmer-Selfridge with factored part 33.42%
      1679410322*7001#+1 is prime! (3.0399s+0.0019s)
      Primality testing 2161199339*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 11
      Calling Brillhart-Lehmer-Selfridge with factored part 33.37%
      2161199339*7001#+1 is prime! (3.0163s+0.0020s)
      Primality testing 2642988356*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 7019
      Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
      2642988356*7001#+1 is prime! (3.1304s+0.0020s)
      Primality testing 3124777373*7001#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 19
      Calling Brillhart-Lehmer-Selfridge with factored part 33.38%
      3124777373*7001#+1 is prime! (3.0224s+0.0020s)
    • paulunderwooduk
      ... Congratulations Ken. You made 3rd on the merit table for APs: http://primes.utm.edu/top20/page.php?id=14 Paul
      Message 2 of 15 , Feb 9, 2012
        --- In primeform@yahoogroups.com, "kraDen" <kradenken@...> wrote:
        >
        > Hi All,
        >
        > 234043271+N*481789017*7001#+1 (0 < N < 6) describes a 3019 digit ap7 of primes
        >
        > Haven't finished processing the 4543646 prps (N=1,000,000,000-3,000,000,000)
        > extending all ap4s up (and most down - I should have started at N>1,000,000,000) yet so don't have final stats.
        > Got a bit lucky as I had only found 83 ap6s when the ap7 popped up.
        > I have already listed the 52 ap6s that have term 6 < 2,600,000,000
        >
        > cheers
        > Ken
        >
        > p.s. While hunting I also found the following ap4 which I found interesting
        > 2834722253+N*7001#+1 (0 < N < 3)
        > which describes a 3019 digit ap4 of primes with difference 7001#
        Congratulations Ken. You made 3rd on the merit table for APs:
        http://primes.utm.edu/top20/page.php?id=14

        Paul
      • djbroadhurst
        ... Big Congrats! A rating of 50.65... appears if one hovers a mouse over 3019 in the third line of the second table of
        Message 3 of 15 , Feb 9, 2012
          --- In primeform@yahoogroups.com,
          "kraDen" <kradenken@...> wrote:

          > 234043271+N*481789017*7001#+1 (0 < N < 6)
          > describes a 3019 digit ap7 of primes

          Big Congrats!

          A rating of 50.65... appears if one hovers a mouse
          over "3019" in the third line of the second table of
          http://primes.utm.edu/top20/page.php?id=14

          I believe that Phil regards such hiding of data
          as improper use of HTML, since at least 3 mice
          are well known to be blind :-)

          David
        • Jens
          ... Big congratulations! It should have parentheses: (234043271+N*481789017)*7001#+1 http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. It is
          Message 4 of 15 , Feb 9, 2012
            Ken wrote:
            > 234043271+N*481789017*7001#+1 (0 < N < 6) describes
            > a 3019 digit ap7 of primes

            Big congratulations!
            It should have parentheses: (234043271+N*481789017)*7001#+1
            http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.
            It is also listed as AP6 record.

            > p.s. While hunting I also found the following ap4 which I found interesting
            > 2834722253+N*7001#+1 (0 < N < 3)
            > which describes a 3019 digit ap4 of primes with difference 7001#

            Interesting indeed!
            It should also have parentheses: (2834722253+N)*7001#+1
            It is above the 2835-digit record for 4 simultaneous primes at
            http://users.cybercity.dk/~dsl522332/math/simultprime.htm
            but my rules do not allow AP's with such a large primorial difference.
            There has to be limits on AP differences but they may seem a little arbitrary.

            --
            Jens Kruse Andersen
          • djbroadhurst
            ... Jens now lists (987502724 + 41489812*n)*7001#+1 as previous AP6 record-holder. Ken might like to tell us a more precise history of the AP6 record, in the
            Message 5 of 15 , Feb 9, 2012
              --- In primeform@yahoogroups.com,
              "Jens" <jens.k.a@...> wrote:

              > It is also listed as AP6 record.

              Jens now lists
              (987502724 + 41489812*n)*7001#+1
              as previous AP6 record-holder.

              Ken might like to tell us a more precise history
              of the AP6 record, in the light of having posted
              66 larger primes in the 180 days since Jens
              previously edited the AP6 history.

              > Used 0.2774 second(s) to find 66 primes matching the
              > selection criteria: Comment includes '\\(6,d'.
              > Maximum age =180 days. Number of primes to find 200.
              > Query required 0.188 seconds.

              I imagine that Ken was careful to ensure that the maximum
              possible of those 66 stood as record holders at the Prime Pages,
              albeit briefly. He might also agree that Jens may be excused
              from recording the true history.

              Best wishes to both,

              David
            • djbroadhurst
              ... Here are some historical notes on visually challenged mice: http://www.rhymes.org.uk/three_blind_mice.htm and a politically corrected version:
              Message 6 of 15 , Feb 9, 2012
                --- In primeform@yahoogroups.com,
                "djbroadhurst" <d.broadhurst@...> wrote:

                > A rating of 50.65... appears if one hovers a mouse
                > over "3019" in the third line of the second table of
                > http://primes.utm.edu/top20/page.php?id=14
                >
                > I believe that Phil regards such hiding of data
                > as improper use of HTML, since at least 3 mice
                > are well known to be blind :-)

                Note also that hovering mice are not so hot at spelling:
                > weigth 50.6538138337352

                Here are some historical notes on visually challenged mice:
                http://www.rhymes.org.uk/three_blind_mice.htm
                and a politically corrected version:
                http://www.re-quest.net/reading/rhymes/three-blind-mice/index.htm

                David
              • Jens
                ... Nothing gets by you. ... My page is updated manually. 66 updates would have been a pain. -- Jens Kruse Andersen
                Message 7 of 15 , Feb 9, 2012
                  David wrote:
                  > Jens now lists
                  > (987502724 + 41489812*n)*7001#+1
                  > as previous AP6 record-holder.
                  >
                  > Ken might like to tell us a more precise history
                  > of the AP6 record, in the light of having posted
                  > 66 larger primes in the 180 days since Jens
                  > previously edited the AP6 history.

                  Nothing gets by you.
                  Ken asked me about marginal improvements in 2011. I replied:
                  > The former record was from 2010 and it's nice to have the
                  > right record year so I updated
                  > http://users.cybercity.dk/~dsl522332/math/aprecords.htm.
                  > But if you find many more of the same size and with the
                  > same programs this year then I don't think they all have
                  > to be listed. You can post the largest when you stop the
                  > search or if you get at least one more digit in the
                  > largest of the primes.

                  My page is updated manually. 66 updates would have been a pain.

                  --
                  Jens Kruse Andersen
                • kraDen
                  ... There will be more. I ve only listed Ap6s with N up to 2,600,000,000. I plan on processing prps for N = 1,000,000,000 to 3,400,000,0000 and extending all
                  Message 8 of 15 , Feb 9, 2012
                    --- In primeform@yahoogroups.com, "Jens" <jens.k.a@...> wrote:
                    >
                    > David wrote:
                    > > Jens now lists
                    > > (987502724 + 41489812*n)*7001#+1
                    > > as previous AP6 record-holder.
                    > >
                    > > Ken might like to tell us a more precise history
                    > > of the AP6 record, in the light of having posted
                    > > 66 larger primes in the 180 days since Jens
                    > > previously edited the AP6 history.
                    >
                    > Nothing gets by you.
                    > Ken asked me about marginal improvements in 2011. I replied:
                    > > The former record was from 2010 and it's nice to have the
                    > > right record year so I updated
                    > > http://users.cybercity.dk/~dsl522332/math/aprecords.htm.
                    > > But if you find many more of the same size and with the
                    > > same programs this year then I don't think they all have
                    > > to be listed. You can post the largest when you stop the
                    > > search or if you get at least one more digit in the
                    > > largest of the primes.
                    >
                    > My page is updated manually. 66 updates would have been a pain.

                    There will be more.
                    I've only listed Ap6s with N up to 2,600,000,000.
                    I plan on processing prps for N = 1,000,000,000 to 3,400,000,0000 and extending all Ap4s.
                    I will let you know the largest Ap6 when I've finished.
                    btw. Only 50 updates would have been necessary, as not all the primes larger that the previous listing are the 6th in the progression ;-)
                    cheers
                    Ken
                    > --
                    > Jens Kruse Andersen
                    >
                  • djbroadhurst
                    ... They also may not be so hot at computing. The prime-page mice seem to use the low-precision values of Table 3 of
                    Message 9 of 15 , Feb 13, 2012
                      --- In primeform@yahoogroups.com,
                      "djbroadhurst" <d.broadhurst@...> wrote:

                      > Note also that hovering mice are not so hot at spelling:
                      > > weigth 50.6538138337352

                      They also may not be so hot at computing.

                      The prime-page mice seem to use the
                      low-precision values of Table 3 of

                      http://www.ams.org/journals/mcom/1979-33-148/S0025-5718-1979-0537981-9/S0025-5718-1979-0537981-9.pdf

                      These may be computed to 20 digits and extended to AP26,
                      in less than a second:

                      [3, 1.3203236316937391479]
                      [4, 2.8582485957192204324]
                      [5, 4.1511808632374157572]
                      [6, 10.131794949996079844]
                      [7, 17.298612311584888606]
                      [8, 53.971948300129652396]
                      [9, 148.55162866378537116]
                      [10, 336.03432674923186553]
                      [11, 511.42228205899585597]
                      [12, 1312.3197112986432675]
                      [13, 2364.5989633059275071]
                      [14, 7820.6000302445688588]
                      [15, 22938.908632325426846]
                      [16, 55651.462553499144397]
                      [17, 91555.111226144195593]
                      [18, 256474.85985417425475]
                      [19, 510992.01030920904417]
                      [20, 1900972.5848741822648]
                      [21, 6423764.3135147211453]
                      [22, 18606666.174071255441]
                      [23, 38734732.676678709886]
                      [24, 153217016.95730047461]
                      [25, 568632503.54733746258]
                      [26, 1941938594.6964590121]
                      255 ms

                      David
                    • djbroadhurst
                      ... David
                      Message 10 of 15 , Feb 13, 2012
                        --- In primeform@yahoogroups.com,
                        "djbroadhurst" <d.broadhurst@...> wrote:

                        > Note also that hovering mice are not so hot at spelling:
                        > > weigth 50.6538138337352
                        > They also may not be so hot at computing.

                        But they are fast learners:

                        > weight 50.6538134778804

                        David
                      • Mark Rodenkirch
                        With a GPU based app, I wonder how much faster one could discover record APs? --Mark ... [Non-text portions of this message have been removed]
                        Message 11 of 15 , Feb 13, 2012
                          With a GPU based app, I wonder how much faster one could discover record APs?

                          --Mark

                          On Feb 13, 2012, at 6:13 PM, djbroadhurst wrote:
                          > --- In primeform@yahoogroups.com,
                          > "djbroadhurst" <d.broadhurst@...> wrote:
                          >
                          > > Note also that hovering mice are not so hot at spelling:
                          > > > weigth 50.6538138337352
                          > > They also may not be so hot at computing.
                          >
                          > But they are fast learners:
                          >
                          > > weight 50.6538134778804
                          >
                          > David


                          [Non-text portions of this message have been removed]
                        • kraDen
                          ... Don t think I haven t been trying. I haven t managed to get CUDA to work on my machine yet (Though I do have a card that supports it) With short APs how
                          Message 12 of 15 , Feb 13, 2012
                            --- In primeform@yahoogroups.com, Mark Rodenkirch <mgrogue@...> wrote:
                            >
                            > With a GPU based app, I wonder how much faster one could discover record APs?

                            Don't think I haven't been trying.
                            I haven't managed to get CUDA to work on my machine yet (Though I do have a card that supports it)

                            With short APs how much faster it would be it depends how much faster the GPU can find prps as getting a large number of prps to search takes the majority of the time. Once you have the prps finding APs, among them or by extension is "comparatively" quick.

                            I've also tried to implement an ap search in assembler but couldn't find a "free" assembler that allowed for large enough bit maps to make it worthwhile.

                            Ken

                            >
                            > --Mark
                            >
                            > On Feb 13, 2012, at 6:13 PM, djbroadhurst wrote:
                            > > --- In primeform@yahoogroups.com,
                            > > "djbroadhurst" <d.broadhurst@> wrote:
                            > >
                            > > > Note also that hovering mice are not so hot at spelling:
                            > > > > weigth 50.6538138337352
                            > > > They also may not be so hot at computing.
                            > >
                            > > But they are fast learners:
                            > >
                            > > > weight 50.6538134778804
                            > >
                            > > David
                            >
                            >
                            > [Non-text portions of this message have been removed]
                            >
                          • djbroadhurst
                            ... Mark s original question was apposite. At large FFT sizes, I was amazed by a statistic, on http://primes.utm.edu/primes/page.php?id=104592 Just look at
                            Message 13 of 15 , Feb 14, 2012
                              --- In primeform@yahoogroups.com,
                              "kraDen" <kradenken@...> wrote:

                              > > With a GPU based app, I wonder how much faster one
                              > > could discover record APs?
                              > Don't think I haven't been trying.
                              > I haven't managed to get CUDA to work on my machine yet
                              > (Though I do have a card that supports it)

                              Mark's original question was apposite.

                              At large FFT sizes, I was amazed by a statistic, on
                              http://primes.utm.edu/primes/page.php?id=104592

                              Just look at this:
                              http://www.primegrid.com/forum_thread.php?id=4068
                              > The prime is 1,528,413 digits long...
                              > This GPU took about 1 hour 30 minutes to probable prime
                              > (PRP) test with GenefCUDA.

                              Law of unintended consequences:
                              unthinking gameboys have more cycles than
                              they can possibly know how sensibly to use.

                              Congrats to PrimeGrid for tapping into this
                              resource, for GFN primes, in the first instance.

                              Watch this space, for other prime-forms?

                              David
                            • Lélio
                              ... The discovery was made by *Carlos Loureiro* of Portugal using an NVIDIA GeForce GTX 550 Ti in an Intel Core i5-2500K @ 3.30GHz system with 4GB RAM, running
                              Message 14 of 15 , Feb 14, 2012
                                > In [PrimeForm] 2012/2/14 djbroadhurst d.broadhurst@... said:

                                > Just look at this:
                                > http://www.primegrid.com/forum_thread.php?id=4068
                                > The prime is 1,528,413 digits long...
                                > This GPU took about 1 hour 30 minutes to probable prime
                                > (PRP) test with GenefCUDA.
                                The discovery was made by *Carlos Loureiro* of Portugal using an NVIDIA
                                GeForce GTX 550 Ti in an Intel Core i5-2500K @ 3.30GHz system with 4GB RAM,
                                running Windows 7 Ultimate x64. This GPU took about 1 hour 30 minutes to
                                probable prime (PRP) test with GenefCUDA.

                                Except for the game card, my system resembles Carlos'.
                                Even our native languages are the same.
                                So I'd better learn what's inside a GeForce GTX 550 Ti very fast.

                                Lélio




                                >
                                >


                                [Non-text portions of this message have been removed]
                              • mgrogue@wi.rr.com
                                ... I don t know how easy it would be to use the cudaFFT library to do a PRP test. I was thinking that sieving should be able to go much deeper, thus reducing
                                Message 15 of 15 , Feb 14, 2012
                                  ---- djbroadhurst <d.broadhurst@...> wrote:
                                  >
                                  >
                                  > --- In primeform@yahoogroups.com,
                                  > "kraDen" <kradenken@...> wrote:
                                  >
                                  > > > With a GPU based app, I wonder how much faster one
                                  > > > could discover record APs?
                                  > > Don't think I haven't been trying.
                                  > > I haven't managed to get CUDA to work on my machine yet
                                  > > (Though I do have a card that supports it)
                                  >
                                  > Mark's original question was apposite.
                                  >
                                  > At large FFT sizes, I was amazed by a statistic, on
                                  > http://primes.utm.edu/primes/page.php?id=104592
                                  >
                                  > Just look at this:
                                  > http://www.primegrid.com/forum_thread.php?id=4068
                                  > > The prime is 1,528,413 digits long...
                                  > > This GPU took about 1 hour 30 minutes to probable prime
                                  > > (PRP) test with GenefCUDA.

                                  I don't know how easy it would be to use the cudaFFT library to do a PRP test. I was thinking that sieving should be able to go much deeper, thus reducing the number of PRP tests one needs to do to discover a new AP.

                                  --Mark
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