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CC15, CC16, SP16

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  • 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 1 of 21 , May 28 7:24 PM
      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 2 of 21 , May 29 1:23 PM
        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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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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