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Base 13 Generalized Woodall Prime (finally!)

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  • mgrogue
    An amazing discovery over at PrimeGrid: http://www.primegrid.com/download/gw13-563528.pdf
    Message 1 of 16 , Dec 9, 2009
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      An amazing discovery over at PrimeGrid:

      http://www.primegrid.com/download/gw13-563528.pdf
    • djbroadhurst
      ... Congratulations to all concerned, including Mark and George, whose remake of OpenPFGW presumably enabled this notable discovery. PrimeMogul s verifier has
      Message 2 of 16 , Dec 9, 2009
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        --- In primenumbers@yahoogroups.com,
        "mgrogue" <mgrogue@...> wrote:

        > http://www.primegrid.com/download/gw13-563528.pdf

        Congratulations to all concerned, including Mark and
        George, whose remake of OpenPFGW presumably enabled
        this notable discovery.

        PrimeMogul's verifier has already been running for
        34 hours and will, very probably, credit a prime to
        http://primes.utm.edu/bios/code.php?code=p262
        real soon.

        David
      • Mark Rodenkirch
        ... It would have been found with the PFGW 1.x, but it would have taken longer. It is likely that many users would have used phrot. Even so, it might have
        Message 3 of 16 , Dec 10, 2009
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          On Dec 9, 2009, at 9:05 PM, djbroadhurst wrote:

          > --- In primenumbers@yahoogroups.com,
          > "mgrogue" <mgrogue@...> wrote:
          >
          > > http://www.primegrid.com/download/gw13-563528.pdf
          >
          > Congratulations to all concerned, including Mark and
          > George, whose remake of OpenPFGW presumably enabled
          > this notable discovery.
          >
          > PrimeMogul's verifier has already been running for
          > 34 hours and will, very probably, credit a prime to
          > http://primes.utm.edu/bios/code.php?code=p262
          > real soon.
          >
          > David

          It would have been found with the PFGW 1.x, but it would have taken
          longer. It is likely that many users would have used phrot. Even so,
          it might have taken another year before this one was found.

          My thanks go to PrimeGrid and Lennart for hosting PRPNet. Congrats to
          Lennart for the lucky find. I had done a lot more tests, but he was
          at the right place at the right time.

          --Mark

          [Non-text portions of this message have been removed]
        • djbroadhurst
          ... I m happy to report that OpenPFGW discovered and proved that ... At 512775 digits, it seems to occupy second place in the neither base-2 nor GF league,
          Message 4 of 16 , Feb 13, 2010
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            --- In primenumbers@yahoogroups.com,
            "mgrogue" <mgrogue@...> wrote:

            > An amazing discovery over at PrimeGrid:
            > http://www.primegrid.com/download/gw13-563528.pdf

            I'm happy to report that OpenPFGW discovered and proved that

            > 2*3^1074726+1 is 3-PRP!
            > 2*3^1074726+1 is prime!

            At 512775 digits, it seems to occupy second place in the
            "neither base-2 nor GF" league, though it lags a fair way
            behind the redoubtable
            http://primes.utm.edu/primes/page.php?id=91121
            that Mark was referring to.

            It may take a while to verify at the Prime Pages, since the
            current OpenPFGW needed to work its way through 7 witnesses

            > Running N-1 test using base 2
            > Running N-1 test using base 3
            > Running N-1 test using base 17
            > Running N-1 test using base 23
            > Running N-1 test using base 29
            > Running N-1 test using base 31
            > Running N-1 test using base 41

            before the GCD was as required.

            With thanks to George Woltman and Mark Rodenkirch,
            for refurbishing OpenPFGW so thoroughly, and to
            Steven Harvey, for a port to linux,

            David Broadhurst, 13 February 2010
          • jpyah2001
            Nice result!! I shall verify it using LLR 3.8.0 Congratulations to you and to OpenPFGW developpers! Jean
            Message 5 of 16 , Feb 13, 2010
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              Nice result!!

              I shall verify it using LLR 3.8.0

              Congratulations to you and to OpenPFGW developpers!
              Jean

              --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
              >
              >
              >
              > --- In primenumbers@yahoogroups.com,
              > "mgrogue" <mgrogue@> wrote:
              >
              > > An amazing discovery over at PrimeGrid:
              > > http://www.primegrid.com/download/gw13-563528.pdf
              >
              > I'm happy to report that OpenPFGW discovered and proved that
              >
              > > 2*3^1074726+1 is 3-PRP!
              > > 2*3^1074726+1 is prime!
              >
              > At 512775 digits, it seems to occupy second place in the
              > "neither base-2 nor GF" league, though it lags a fair way
              > behind the redoubtable
              > http://primes.utm.edu/primes/page.php?id=91121
              > that Mark was referring to.
              >
              > It may take a while to verify at the Prime Pages, since the
              > current OpenPFGW needed to work its way through 7 witnesses
              >
              > > Running N-1 test using base 2
              > > Running N-1 test using base 3
              > > Running N-1 test using base 17
              > > Running N-1 test using base 23
              > > Running N-1 test using base 29
              > > Running N-1 test using base 31
              > > Running N-1 test using base 41
              >
              > before the GCD was as required.
              >
              > With thanks to George Woltman and Mark Rodenkirch,
              > for refurbishing OpenPFGW so thoroughly, and to
              > Steven Harvey, for a port to linux,
              >
              > David Broadhurst, 13 February 2010
              >
            • djbroadhurst
              ... Thanks, Jean. I had been hoping for just such a mega-trit prime. David, pp SCRUB, Society for the Comfort and Relief of Underprivileged Bases
              Message 6 of 16 , Feb 13, 2010
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                --- In primenumbers@yahoogroups.com,
                "jpyah2001" <jpenne@...> wrote:

                > Nice result!!
                > I shall verify it using LLR 3.8.0
                > Congratulations to you and to OpenPFGW developpers!
                > Jean

                Thanks, Jean. I had been hoping for just such a "mega-trit" prime.

                David, pp SCRUB,
                Society for the Comfort and Relief of Underprivileged Bases
                http://primes.utm.edu/primes/page.php?id=91746#comments
              • djbroadhurst
                ... Update: a second mega-trit has popped up as 3-PRP, just nearby. Seems like a lucky weekend, as long as OpenPFGW is behaving. The N-1 BLS test is now in
                Message 7 of 16 , Feb 13, 2010
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                  --- In primenumbers@yahoogroups.com,
                  "djbroadhurst" <d.broadhurst@...> wrote:

                  > Thanks, Jean. I had been hoping for just such a "mega-trit" prime.

                  Update: a second mega-trit has popped up as 3-PRP, just nearby.

                  Seems like a lucky weekend, as long as OpenPFGW is behaving.
                  The N-1 BLS test is now in progress, locally.
                  Maybe it will take less than 7 witnesses, this time.

                  David, pp SCRUB,
                  Society for the Comfort and Relief of Underprivileged Bases
                • djbroadhurst
                  ... One witness seemed to be enough this time: Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^1086112+1 is
                  Message 8 of 16 , Feb 13, 2010
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                    --- In primenumbers@yahoogroups.com,
                    "djbroadhurst" <d.broadhurst@...> wrote:

                    > Seems like a lucky weekend, as long as OpenPFGW is behaving.
                    > The N-1 BLS test is now in progress, locally.
                    > Maybe it will take less than 7 witnesses, this time.

                    One witness seemed to be enough this time:

                    Running N-1 test using base 2
                    Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
                    2*3^1086112+1 is prime! (4856.6481s+0.0729s)

                    But I would rest easier if Jean can confirm it with LLR.
                    It was a bit weird getting two in two days:
                    http://primes.utm.edu/primes/page.php?id=91751#comments

                    David, pp SCRUB,
                    Society for the Comfort and Relief of Underprivileged Bases
                  • Mark Rodenkirch
                    ... Two in such a short time. Great finds, David! --Mark [Non-text portions of this message have been removed]
                    Message 9 of 16 , Feb 13, 2010
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                      On Feb 13, 2010, at 5:30 PM, djbroadhurst wrote:

                      > --- In primenumbers@yahoogroups.com,
                      > "djbroadhurst" <d.broadhurst@...> wrote:
                      >
                      > Running N-1 test using base 2
                      > Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
                      > 2*3^1086112+1 is prime! (4856.6481s+0.0729s)
                      >
                      > But I would rest easier if Jean can confirm it with LLR.
                      > It was a bit weird getting two in two days:
                      > http://primes.utm.edu/primes/page.php?id=91751#comments
                      >
                      > David, pp SCRUB,
                      > Society for the Comfort and Relief of Underprivileged Bases

                      Two in such a short time. Great finds, David!

                      --Mark

                      [Non-text portions of this message have been removed]
                    • jpyah2001
                      What a beautiful double success !! I tested the first this night : ~/llr380src/linuxllr $ ./llr -d -q 2*3^1074726+1 Base prime factor(s) taken : 3 Starting
                      Message 10 of 16 , Feb 13, 2010
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                        What a beautiful double success !!

                        I tested the first this night :

                        ~/llr380src/linuxllr $ ./llr -d -q"2*3^1074726+1"
                        Base prime factor(s) taken : 3
                        Starting N-1 prime test of 2*3^1074726+1
                        2*3^1074726+1 may be prime, trying to compute gcd's
                        2*3^1074726+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 7320.190 sec.
                        Restarting N-1 prime test of 2*3^1074726+1
                        2*3^1074726+1 may be prime, trying to compute gcd's
                        5^((N-1)/3)-1 is coprime to N!
                        2*3^1074726+1 is prime! Time : 8911.548 sec.

                        It seems I was a bit more lucky than OpenPFGW while finding a primitive root base... Do you know a mean not to be submitted only to luck about this search?

                        I shall now verify the second (mainly to test the young new LLR, I am confident it is prime!)

                        Many congratulations, and Best Regards,
                        Jean

                        --- In primenumbers@yahoogroups.com, Mark Rodenkirch <mgrogue@...> wrote:
                        >
                        >
                        > On Feb 13, 2010, at 5:30 PM, djbroadhurst wrote:
                        >
                        > > --- In primenumbers@yahoogroups.com,
                        > > "djbroadhurst" <d.broadhurst@> wrote:
                        > >
                        > > Running N-1 test using base 2
                        > > Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
                        > > 2*3^1086112+1 is prime! (4856.6481s+0.0729s)
                        > >
                        > > But I would rest easier if Jean can confirm it with LLR.
                        > > It was a bit weird getting two in two days:
                        > > http://primes.utm.edu/primes/page.php?id=91751#comments
                        > >
                        > > David, pp SCRUB,
                        > > Society for the Comfort and Relief of Underprivileged Bases
                        >
                        > Two in such a short time. Great finds, David!
                        >
                        > --Mark
                        >
                        > [Non-text portions of this message have been removed]
                        >
                      • djbroadhurst
                        ... Thank you, kindly, dear Sir. I am much relieved. ... It was the second that made me worry: too much of a good thing , I said to myself, with my usual
                        Message 11 of 16 , Feb 14, 2010
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                          --- In primenumbers@yahoogroups.com,
                          "jpyah2001" <jpenne@...> wrote:

                          > 2*3^1074726+1 is prime! Time : 8911.548 sec.

                          Thank you, kindly, dear Sir. I am much relieved.

                          > I shall now verify the second (mainly to test the young
                          > new LLR, I am confident it is prime!)

                          It was the second that made me worry:
                          "too much of a good thing", I said to myself,
                          with my usual skepticism.

                          So another test by "young new LLR" would be
                          much appreciated, even though it does now
                          look as if it indeed may succeed.

                          As ever, I rely on the existence of a variety
                          of software, with dedicated and generous authors
                          and maintainers, to keep us free of needless error.

                          David
                        • jpyah2001
                          It is prime, indeed!! ./llr -d -q 2*3^1086112+1 Base prime factor(s) taken : 3 Starting N-1 prime test of 2*3^1086112+1 2*3^1086112+1 may be prime, trying to
                          Message 12 of 16 , Feb 14, 2010
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                            It is prime, indeed!!

                            ./llr -d -q"2*3^1086112+1"
                            Base prime factor(s) taken : 3
                            Starting N-1 prime test of 2*3^1086112+1
                            2*3^1086112+1 may be prime, trying to compute gcd's
                            3^((N-1)/3)-1 is coprime to N!
                            2*3^1086112+1 is prime! Time : 7392.541 sec.

                            Bravo!
                            Jean

                            --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
                            >
                            >
                            >
                            > --- In primenumbers@yahoogroups.com,
                            > "jpyah2001" <jpenne@> wrote:
                            >
                            > > 2*3^1074726+1 is prime! Time : 8911.548 sec.
                            >
                            > Thank you, kindly, dear Sir. I am much relieved.
                            >
                            > > I shall now verify the second (mainly to test the young
                            > > new LLR, I am confident it is prime!)
                            >
                            > It was the second that made me worry:
                            > "too much of a good thing", I said to myself,
                            > with my usual skepticism.
                            >
                            > So another test by "young new LLR" would be
                            > much appreciated, even though it does now
                            > look as if it indeed may succeed.
                            >
                            > As ever, I rely on the existence of a variety
                            > of software, with dedicated and generous authors
                            > and maintainers, to keep us free of needless error.
                            >
                            > David
                            >
                          • djbroadhurst
                            ... Here s a third, according to OpenPFGW: Primality testing 2*3^1175232+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test
                            Message 13 of 16 , Feb 22, 2010
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                              --- In primenumbers@yahoogroups.com,
                              "jpyah2001" <jpenne@...> wrote:

                              > 2*3^1086112+1 is prime! Time : 7392.541 sec.

                              Here's a third, according to OpenPFGW:

                              Primality testing 2*3^1175232+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 100.00%
                              2*3^1175232+1 is prime! (12689.9371s+0.0402s)

                              David
                            • djbroadhurst
                              ... I am trying to learn to count in Telefol, which uses base 27. http://en.wikipedia.org/wiki/Telefol_language ... The first 27 positive integers are
                              Message 14 of 16 , Feb 26, 2010
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                                --- In primenumbers@yahoogroups.com,
                                "djbroadhurst" <d.broadhurst@...> wrote:

                                > 2*3^1175232+1 is prime! (12689.9371s+0.0402s)

                                I am trying to learn to count in Telefol, which uses base 27.

                                http://en.wikipedia.org/wiki/Telefol_language
                                > Telefol is a language spoken by the Telefol people in Papua
                                > New Guinea, notable for possessing a base-27 numeral system.

                                The first 27 positive integers are signalled like this:

                                01--05: left small finger to left thumb
                                06--10: left wrist, ulna, elbow, humerus, shoulder
                                11--13: left side of neck, left ear, left eye
                                14--14: nose
                                15--17: right eye, right ear, right side of neck
                                18--22: right shoulder, humerus, elbow, ulna, wrist
                                24--27: right thumb to right small finger

                                If we then adopt place value, the right small finger also
                                serves as our zero, in base 27. So you have more than
                                333,333 exercises on that finger, to signal one of the three
                                known mega-trit primes. Now it so happens that I have a
                                severe Dupuytren contracture of my right small finger, so my
                                position of Secretary of SCRUB has now become quite
                                challenging.

                                David, pp SCRUB
                                Society for the Comfort and Relief of Underprivileged Bases,
                                Main Office: Telefomin District, Sandaun Province, Papua New Guinea
                              • djbroadhurst
                                ... SCRUB wishes to apologize to speakers of Hewa, Oksapmin, Orokolo, Sanio and Tifal, for having previously omitted to mention that they also count in base
                                Message 15 of 16 , Feb 26, 2010
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                                  --- In primenumbers@yahoogroups.com,
                                  "djbroadhurst" <d.broadhurst@...> wrote:

                                  > I am trying to learn to count in Telefol, which uses base 27.

                                  SCRUB wishes to apologize to speakers of Hewa, Oksapmin,
                                  Orokolo, Sanio and Tifal, for having previously omitted
                                  to mention that they also count in base 27, as shown here:
                                  http://www.uog.ac.pg/glec/counting_sys/t-coutning_sys/t-counting_sys.htm

                                  David, pp SCRUB
                                  Society for the Comfort and Relief of Underprivileged Bases
                                • jpyah2001
                                  Many congrats for this third success! But, this time LLR needed one more restart... ... Base prime factor(s) taken : 3 Starting N-1 prime test of 2*3^1175232+1
                                  Message 16 of 16 , Mar 1, 2010
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                                    Many congrats for this third success!

                                    But, this time LLR needed one more restart...

                                    >cllr -d -a68 -q"2*3^1175232+1"
                                    Base prime factor(s) taken : 3
                                    Starting N-1 prime test of 2*3^1175232+1
                                    Using all-complex FFT length 96K, a = 3
                                    2*3^1175232+1 may be prime, trying to compute gcd's
                                    2*3^1175232+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 8983.686 sec.
                                    Restarting N-1 prime test of 2*3^1175232+1
                                    Using all-complex FFT length 96K, a = 5
                                    2*3^1175232+1 may be prime, trying to compute gcd's
                                    5^((N-1)/3)-1 is coprime to N!
                                    2*3^1175232+1 is prime! Time : 8834.941 sec.

                                    Best Regards,
                                    Jean

                                    --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
                                    >
                                    >
                                    >
                                    > --- In primenumbers@yahoogroups.com,
                                    > "jpyah2001" <jpenne@> wrote:
                                    >
                                    > > 2*3^1086112+1 is prime! Time : 7392.541 sec.
                                    >
                                    > Here's a third, according to OpenPFGW:
                                    >
                                    > Primality testing 2*3^1175232+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 100.00%
                                    > 2*3^1175232+1 is prime! (12689.9371s+0.0402s)
                                    >
                                    > David
                                    >
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