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CC 2nd kind

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  • jarek372000
    Here are a few things I have done about 2nd kind Cunningham Chains. 1. I have determined that the known solution 3203000719597029781 is the only start of a 2nd
    Message 1 of 21 , May 25, 2008
      Here are a few things I have done about 2nd kind Cunningham Chains.

      1. I have determined that the known solution
      3203000719597029781
      is the only start of a 2nd kind CC16 below
      67280843307747189120=6.278*10^19.
      The search required about 70 hours CPU (3 hours real time using many
      computers).

      2. By a selective search I have found the following new solutions:

      CC14, 2nd kind: 20299226100350079536373721 (26 digits)

      CC15, 2nd kind: 13029362719535767707961 (23 digits)
      CC15, 2nd kind: 11270578849664703769201 (23 digits)
      CC15, 2nd kind: 7339063830988412866201 (22 digits)

      CC16, 2nd kind: 15745040405007366603151 (23 digits)
      CC16, 2nd kind: 2447621166480001151641 (22 digits)

      Jarek
    • Jens Kruse Andersen
      ... Congratulations! If you use just some of the cpu power from AP hunting on Cunningham chains then I guess you could dominate the record tables.
      Message 2 of 21 , May 26, 2008
        Jarek wrote:
        > 3203000719597029781
        > is the only start of a 2nd kind CC16 below
        > 67280843307747189120=6.278*10^19.

        > CC14, 2nd kind: 20299226100350079536373721 (26 digits)
        > CC15, 2nd kind: 13029362719535767707961 (23 digits)
        > CC16, 2nd kind: 15745040405007366603151 (23 digits)

        Congratulations! If you use just some of the cpu power from
        AP hunting on Cunningham chains then I guess you could
        dominate the record tables.

        http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm
        will be updated when Dirk Augustin has updated the source.

        --
        Jens Kruse Andersen
      • jarek372000
        ... Thanks. After about one day of running my program on 27 computers at Mathematical Institute of Wroclaw University, I think I know what it is capable of.
        Message 3 of 21 , May 26, 2008
          --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
          <jens.k.a@...> wrote:

          > Congratulations! If you use just some of the cpu power from
          > AP hunting on Cunningham chains then I guess you could
          > dominate the record tables.

          Thanks. After about one day of running my program on 27 computers at
          Mathematical Institute of Wroclaw University, I think I know what it
          is capable of.

          CC13 record of 39 digits is safe, as far as my methods are concerned.
          My sieving is fairly efficient, but very shallow (it ends at 3-digit
          primes and there is no way to extend it further). It would be insane
          to try for a record well over 30 digits.

          Likewise AP17 and AP18 records, you can take CC14 back, Jens :-) If
          you add a few digits to it, I am unlikely to think of trying to
          recapture it :-)

          I feel pretty comfortable with longer chains. My feeling is that CC17
          is just a matter of time. The real challenge is CC18, but I think that
          with CPU power comparable to used in AP25 search it is worth trying.

          Jarek
        • jarek372000
          I have just found a new high: CC15, 2nd kind: 105998574608115401372161 (24 digits) Jarek
          Message 4 of 21 , May 26, 2008
            I have just found a new high:

            CC15, 2nd kind: 105998574608115401372161 (24 digits)

            Jarek
          • jarek372000
            I got it! CC17, 1st kind: 2759832934171386593519 (22 digits) This is the only one CC16+ 1st kind I have found so far. I have found 4 new CC16 2nd kind and
            Message 5 of 21 , May 26, 2008
              I got it!

              CC17, 1st kind: 2759832934171386593519 (22 digits)

              This is the only one CC16+ 1st kind I have found so far.
              I have found 4 new CC16 2nd kind and rediscovered the old one.

              Current records divided by 10^20 are as follows:

              CC15 1st: 119.93 (Alm/Andersen 2004)
              CC15 2nd: 1059.98 (JW 2008)

              CC16 1st: 55.19 (part of CC17)
              CC16 2nd: 157.45 (JW 2008)

              CC17 1st: 27.59 (JW 2008)

              16 Simultaneous Primes Record is
              Tuplet (Andersen 2004) and it would
              require CC16: 800.96 to beat.

              17 Simultaneous Primes Record is
              Tuplet (Waldvogel/Leikauf 2000) and it would
              require CC17: 111.15 to beat.

              Jarek
            • Jens Kruse Andersen
              ... Big congratulations! 11 years after the first CC16 (of the 2nd kind), a new length record! -- Jens Kruse Andersen
              Message 6 of 21 , May 26, 2008
                Jarek wrote:
                > CC17, 1st kind: 2759832934171386593519 (22 digits)

                Big congratulations!
                11 years after the first CC16 (of the 2nd kind), a new length record!

                --
                Jens Kruse Andersen
              • jarek372000
                I have found the following Cunningham Chains of length 15: CC15, 1st kind: 196426752643710966405599 (24 digits) CC15, 2nd kind: 188024012029458846281041 (24
                Message 7 of 21 , May 28, 2008
                  I have found the following Cunningham Chains of length 15:

                  CC15, 1st kind: 196426752643710966405599 (24 digits)
                  CC15, 2nd kind: 188024012029458846281041 (24 digits)

                  They become largest known CC15.

                  Jarek
                • jarek372000
                  I have found the following improvements of the 1st kind of Cunningham Chains: New largest known CC15: CC15, 1st kind: 662311489517467124375039 (24 digits) New
                  Message 8 of 21 , May 28, 2008
                    I have found the following improvements of the 1st kind of Cunningham
                    Chains:

                    New largest known CC15:
                    CC15, 1st kind: 662311489517467124375039 (24 digits)

                    New largest known CC16:
                    CC16, 1st kind: 91304653283578934559359 (23 digits)
                    It has 8th term
                    11686995620298103623598079 (26 digits)
                    which, if I am not mistaken, should be enough for a tiny improvement
                    of The Largest Known 16 Simultaneous Primes record.

                    Jarek
                  • Jens Kruse Andersen
                    ... Congratulations. Yes, it s just large enough for a new record at http://hjem.get2net.dk/jka/math/simultprime.htm -- Jens Kruse Andersen
                    Message 9 of 21 , May 29, 2008
                      Jarek wrote:
                      > CC16, 1st kind: 91304653283578934559359 (23 digits)
                      > It has 8th term
                      > 11686995620298103623598079 (26 digits)
                      > which, if I am not mistaken, should be enough for a tiny improvement
                      > of The Largest Known 16 Simultaneous Primes record.

                      Congratulations. Yes, it's just large enough for a new record at
                      http://hjem.get2net.dk/jka/math/simultprime.htm

                      --
                      Jens Kruse Andersen
                    • Dirk Augustin
                      ... Wow, very impressive. Congratulations, Jarek, for setting a new mark by discovering the first CC17 ever! I will update the CC record list as soon as
                      Message 10 of 21 , Jun 3, 2008
                        --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
                        <jens.k.a@...> wrote:
                        >
                        > Jarek wrote:
                        > > CC17, 1st kind: 2759832934171386593519 (22 digits)
                        >
                        > Big congratulations!
                        > 11 years after the first CC16 (of the 2nd kind), a new length record!
                        >
                        > --
                        > Jens Kruse Andersen
                        >

                        Wow, very impressive.

                        Congratulations, Jarek, for setting a new mark by discovering the first
                        CC17 ever!

                        I will update the CC record list as soon as possible.
                      • Jaroslaw.Wroblewski@math.uni.wroc.pl
                        Yestyerday I have found 2 new CC17: CC17 2nd kind: 40244844789379926979141 CC17 2nd kind: 127806074555607670094731 Both were verified by Jens yesterday (I am
                        Message 11 of 21 , Jun 5, 2008
                          Yestyerday I have found 2 new CC17:
                          CC17 2nd kind: 40244844789379926979141
                          CC17 2nd kind: 127806074555607670094731

                          Both were verified by Jens yesterday (I am on a short vacation with a
                          mobile phone internet access only).

                          Today I worked out a way to verify them myself and (I hope) to post them.

                          I have also found the largest known CC15:
                          CC15 2nd kind: 2817673877915370357723841

                          Jarek
                        • Jens Kruse Andersen
                          ... Congratulations again! The middle prime in the larger CC17 makes it the largest known case of both 16 and 17 simultaneous primes. The smaller CC17 was
                          Message 12 of 21 , Jun 6, 2008
                            Jarek wrote:
                            > Yestyerday I have found 2 new CC17:
                            > CC17 2nd kind: 40244844789379926979141
                            > CC17 2nd kind: 127806074555607670094731
                            >
                            > Both were verified by Jens yesterday (I am on a short vacation
                            > with a mobile phone internet access only).

                            Congratulations again!
                            The middle prime in the larger CC17 makes it the largest known
                            case of both 16 and 17 simultaneous primes.
                            The smaller CC17 was found and posted a few hours earlier so
                            I included it in the record history at
                            http://hjem.get2net.dk/jka/math/simultprime.htm#history17

                            > I have also found the largest known CC15:
                            > CC15 2nd kind: 2817673877915370357723841

                            And I have found the largest known CC14:
                            CC14 2nd kind: 2337673907855670908145009878491

                            --
                            Jens Kruse Andersen
                          • Dirk Augustin
                            Hi Jarek, congrats, very nice finds again! BTW, did you use any additional (public) programs for sieving/prp- /primetest beside your own programs? I need to
                            Message 13 of 21 , Jun 6, 2008
                              Hi Jarek,
                              congrats, very nice finds again!

                              BTW, did you use any additional (public) programs for sieving/prp-
                              /primetest beside your own programs?

                              I need to know this for the update of the CC record list where I
                              normally list all used programs.

                              Regards,
                              Dirk


                              --- In primenumbers@yahoogroups.com, Jaroslaw.Wroblewski@... wrote:
                              >
                              > Yestyerday I have found 2 new CC17:
                              > CC17 2nd kind: 40244844789379926979141
                              > CC17 2nd kind: 127806074555607670094731
                              >
                              > Both were verified by Jens yesterday (I am on a short vacation with
                              a
                              > mobile phone internet access only).
                              >
                              > Today I worked out a way to verify them myself and (I hope) to post
                              them.
                              >
                              > I have also found the largest known CC15:
                              > CC15 2nd kind: 2817673877915370357723841
                              >
                              > Jarek
                              >
                            • jarek372000
                              Today I have discovered new largest CC16 (also new 16 Simultaneous Primes record): CC16, 2nd kind: 258296136493222766530021 (24 digits) It is a tiny
                              Message 14 of 21 , Jun 8, 2008
                                Today I have discovered new largest CC16 (also new 16 Simultaneous
                                Primes record):

                                CC16, 2nd kind: 258296136493222766530021 (24 digits)

                                It is a tiny improvement of the previous best 255... (also 24 digits)
                                being a part of a CC17.

                                All my Cunningham Chains search, which has already been going for
                                about two weeks, is conducted by my own program written in C and run
                                on 28 64-bit computers at Mathematical Institute of Wroclaw University.
                                Primality check inside the program is performed by calling GMP function
                                mpz_probab_prime_p

                                The sieving algorithm is of my own design and implemented by
                                using basic C operations only, with very little memory (probably
                                processor's cache is enough on most computers).

                                Jarek
                              • jarek372000
                                I have just discovered: CC17, 2nd kind: 1302312696655394336638441 (25 digits) CC15, 2nd kind: 5830768257311375388822241 (25 digits) I have given up searching
                                Message 15 of 21 , Jun 10, 2008
                                  I have just discovered:

                                  CC17, 2nd kind: 1302312696655394336638441 (25 digits)
                                  CC15, 2nd kind: 5830768257311375388822241 (25 digits)

                                  I have given up searching for CC17 and wanted to improve the largest
                                  known CC16, so I have shifted my search to larger numbers this
                                  morning, which wouldn't be a smart thing to do if I intended to hunt
                                  for another CC17. After 9.5 hours of 28 computers work, the above were
                                  the only 2 CC's longer than 14. Given the data collected during this
                                  9.5 hour search I think I deserved to find 3 CC15's and a half of
                                  CC16. I was counting on a CC16 by tomorrow morning, but a CC17 today
                                  is a very nice surprise :-)

                                  Jarek
                                • jarek372000
                                  I have discovered: CC16, 2nd kind: 20193491108493165642344881 (26 digits) CC15, 2nd kind: 71838292723844326926417601 (26 digits) Jarek
                                  Message 16 of 21 , Jun 11, 2008
                                    I have discovered:

                                    CC16, 2nd kind: 20193491108493165642344881 (26 digits)
                                    CC15, 2nd kind: 71838292723844326926417601 (26 digits)

                                    Jarek
                                  • Dirk Augustin
                                    ... Congratulations for improving the CC15 and CC16 records by another digit! Finally I managed to update the record list in the Files section. Jens Kruse
                                    Message 17 of 21 , Jun 13, 2008
                                      --- In primenumbers@yahoogroups.com, "jarek372000"
                                      <Jaroslaw.Wroblewski@...> wrote:
                                      >
                                      > I have discovered:
                                      >
                                      > CC16, 2nd kind: 20193491108493165642344881 (26 digits)
                                      > CC15, 2nd kind: 71838292723844326926417601 (26 digits)
                                      >
                                      > Jarek
                                      >

                                      Congratulations for improving the CC15 and CC16 records by another
                                      digit!

                                      Finally I managed to update the record list in the Files section. Jens
                                      Kruse Andersen will update the corresponding web page.

                                      Regards,
                                      Dirk
                                    • jaroslaw.wroblewski@gmail.com
                                      Thanks. Currently I am hunting for a 31 digit CC15 (2nd kind). After 40 hours of 29 computers work I have 2 CC14: CC14, 2nd kind:
                                      Message 18 of 21 , Jun 13, 2008
                                        Thanks.

                                        Currently I am hunting for a 31 digit CC15 (2nd kind). After 40 hours
                                        of 29 computers work I have 2 CC14:

                                        CC14, 2nd kind: 2354904873485081880414653783011 (31 digits)
                                        CC14, 2nd kind: 756623498046318886601149174501 (30 digits)

                                        and 21 CC13 in 30-32 digits, with the top 3 being:

                                        CC13, 2nd kind: 71893041796676884721115682595521 (32 digits)
                                        CC13, 2nd kind: 71183625845277875816974563041281 (32 digits)
                                        CC13, 2nd kind: 61769341861507223234745310908481 (32 digits)

                                        Jarek

                                        2008/6/14, Dirk Augustin <Dirk_Augustin@...>:
                                        > --- In primenumbers@yahoogroups.com, "jarek372000"
                                        > <Jaroslaw.Wroblewski@...> wrote:
                                        >>
                                        >> I have discovered:
                                        >>
                                        >> CC16, 2nd kind: 20193491108493165642344881 (26 digits)
                                        >> CC15, 2nd kind: 71838292723844326926417601 (26 digits)
                                        >>
                                        >> Jarek
                                        >>
                                        >
                                        > Congratulations for improving the CC15 and CC16 records by another
                                        > digit!
                                        >
                                        > Finally I managed to update the record list in the Files section. Jens
                                        > Kruse Andersen will update the corresponding web page.
                                        >
                                        > Regards,
                                        > Dirk
                                        >
                                        >
                                        >
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                                      • jarek372000
                                        After over 9 days of 30 computers work I have discovered: CC16, 2nd kind: 2368823992523350998418445521 (28 digits) It has 30 digit 8th term:
                                        Message 19 of 21 , Jun 26, 2008
                                          After over 9 days of 30 computers work I have discovered:

                                          CC16, 2nd kind: 2368823992523350998418445521 (28 digits)

                                          It has 30 digit 8th term:

                                          303209471042988927797561026561

                                          which is responsible for 16 Simultaneous Primes score.

                                          I am resending this message as the previous one seems to have been
                                          corrupted. My apologies if you get it twice.

                                          Jarek
                                        • Jens Kruse Andersen
                                          ... Congratulations on your sixth improvement of this record in a month: http://hjem.get2net.dk/jka/math/simultprime.htm#history16 -- Jens Kruse Andersen
                                          Message 20 of 21 , Jun 26, 2008
                                            Jarek wrote:
                                            > CC16, 2nd kind: 2368823992523350998418445521 (28 digits)
                                            >
                                            > It has 30 digit 8th term:
                                            >
                                            > 303209471042988927797561026561
                                            >
                                            > which is responsible for 16 Simultaneous Primes score.

                                            Congratulations on your sixth improvement of this record in a month:
                                            http://hjem.get2net.dk/jka/math/simultprime.htm#history16

                                            --
                                            Jens Kruse Andersen
                                          • Jaroslaw Wroblewski
                                            I have found a new record for 15 Largest Known Simultaneous Primes: CC15 (1st kind, 41 digit first term): 27353790674175627273118204975428644651730*2^n-1,
                                            Message 21 of 21 , Apr 24, 2014
                                              I have found a new record for 15 Largest Known Simultaneous Primes:

                                              CC15 (1st kind, 41 digit first term):
                                              27353790674175627273118204975428644651730*2^n-1, n=0..14
                                              (Apr 25, 2014, Jaroslaw Wroblewski)
                                              43 digit 8-th term 3501285206294480290959130236854866515421439

                                              I applied a litlle trick, namely created and used polynomial
                                              P(x) = 86730930*x^2,
                                              which has nice property of having over-average density of Cunningham Chains
                                              P(x)*2^n-1

                                              The above Cunningham Chain is obtained for
                                              x=17759132926784169, so it can also be written as

                                              86730930*17759132926784169^2 * 2^n - 1, n=0..14

                                              The search was very lucky (only one CC13 and the above CC15 was found)
                                              and short (2 hours of 60 threads).

                                              Jarek
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