Loading ...
Sorry, an error occurred while loading the content.

symmetrical primes

Expand Messages
  • Mark Underwood
    Hi all, Six primes are symmetrically arranged around the number 12: 5, 7, 11, (12) 13, 17, 19. Six primes are also symmtrically arranged around the number 15:
    Message 1 of 13 , Mar 11, 2006
    • 0 Attachment
      Hi all,

      Six primes are symmetrically arranged around the number 12:
      5, 7, 11, (12) 13, 17, 19.

      Six primes are also symmtrically arranged around the number 15:
      7, 11, 13, (15) 17, 19, 23.

      Ten primes are symmetrically arranged around the number 30:
      13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47.

      Twelve primes are symmetrically arranged around the number 165:
      137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193.

      I looked up to 100,000 primes there are six cases of twelve primes
      symmetrically arranged around a central number. Found nothing higher.
      When is the first case of a symmetrical grouping of more than twelve
      primes?

      Mark
    • Alan McFarlane
      First case of 4 primes: 5 7 (9) 11 13 First case of 6 primes: 7 11 13 (15) 17 19 23 First case of 8 primes: 17 19 23 29 (30) 31 37 41 43 First case of 10
      Message 2 of 13 , Mar 12, 2006
      • 0 Attachment
        First case of 4 primes:
        5 7 (9) 11 13

        First case of 6 primes:
        7 11 13 (15) 17 19 23

        First case of 8 primes:
        17 19 23 29 (30) 31 37 41 43

        First case of 10 primes:
        139 149 151 157 163 (165) 167 173 179 181 191

        First case of 12 primes:
        55787 55793 55799 55807 55813 55817 (55818) 55819 55823 55829 55837
        55843 55849

        First case of 14 primes:
        8021749 8021753 8021759 8021771 8021789 8021791 8021801 (8021811)
        8021821 8021831 8021833 8021851 8021863 8021869 8021873

        First case of 16 primes:
        1071065111 1071065123 1071065129 1071065137 1071065141 1071065153
        1071065167 1071065179 (1071065190) 1071065201 1071065213 1071065227
        1071065239 1071065243 1071065251 1071065257 1071065269

        First case of 18 primes:
        1613902553 1613902561 1613902567 1613902573 1613902601 1613902621
        1613902627 1613902643 1613902649 (1613902650) 1613902651 1613902657
        1613902673 1613902679 1613902699 1613902727 1613902733 1613902739
        1613902747


        I can easily do up 2^64-59 for you as well
        --
        Alan McFarlane



        Mark Underwood wrote:
        > Hi all,
        >
        > Six primes are symmetrically arranged around the number 12:
        > 5, 7, 11, (12) 13, 17, 19.
        >
        > Six primes are also symmtrically arranged around the number 15:
        > 7, 11, 13, (15) 17, 19, 23.
        >
        > Ten primes are symmetrically arranged around the number 30:
        > 13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47.
        >
        > Twelve primes are symmetrically arranged around the number 165:
        > 137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193.
        >
        > I looked up to 100,000 primes there are six cases of twelve primes
        > symmetrically arranged around a central number. Found nothing higher.
        > When is the first case of a symmetrical grouping of more than twelve
        > primes?
        >
        > Mark
        >
        >
        >
        >
        >
        >
        >
        > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        > The Prime Pages : http://www.primepages.org/
        >
        >
        > Yahoo! Groups Links
        >
        >
        >
        >
        >
        >
        >
      • mikeoakes2@aol.com
        ... A pretty idea, Mark! For primes up to 2*10^9, here are the first occurrences of your patterns, as output by my Pascal program:- count=2: 3, (4) 5, count=4:
        Message 3 of 13 , Mar 12, 2006
        • 0 Attachment
          In an email dated Sun, 12 3 2006 4:43:42 am GMT, "Mark Underwood" <mark.underwood@...> writes:

          >Six primes are symmetrically arranged around the number 12:
          >5, 7, 11, (12) 13, 17, 19.
          >
          >Six primes are also symmtrically arranged around the number 15:
          >7, 11, 13, (15) 17, 19, 23.
          >
          >Ten primes are symmetrically arranged around the number 30:
          >13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47.
          >
          >Twelve primes are symmetrically arranged around the number 165:
          >137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193.
          >
          >I looked up to 100,000 primes there are six cases of twelve primes
          >symmetrically arranged around a central number. Found nothing higher.
          >When is the first case of a symmetrical grouping of more than twelve
          >primes?
          >

          A pretty idea, Mark!

          For primes up to 2*10^9, here are the first occurrences of your patterns, as output by my Pascal program:-

          count=2:
          3, (4) 5,
          count=4:
          5, 7, (9) 11, 13,
          count=6:
          5, 7, 11, (12) 13, 17, 19,
          count=10:
          13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47,
          count=12:
          137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193,
          count=14:
          8021749, 8021753, 8021759, 8021771, 8021789, 8021791, 8021801, (8021811) 8021821, 8021831, 8021833, 8021851, 8021863, 8021869, 8021873,
          count=16:
          1071065111, 1071065123, 1071065129, 1071065137, 1071065141, 1071065153, 1071065167, 1071065179, (1071065190) 1071065201, 1071065213, 1071065227, 1071065239, 1071065243, 1071065251, 1071065257, 1071065269,
          count=18:
          1613902553, 1613902561, 1613902567, 1613902573, 1613902601, 1613902621, 1613902627, 1613902643, 1613902649, (1613902650) 1613902651, 1613902657, 1613902673, 1613902679, 1613902699, 1613902727, 1613902733, 1613902739, 1613902747,

          [At 2.08GHz, 3 mins to compute all the primes, 2 secs to find all the patterns.]

          -Mike Oakes
        • Phil Carmody
          From: Mark Underwood ... A great puzzle Mark! Shame I misread it - I was trying to stick a prime in the middle... Some
          Message 4 of 13 , Mar 12, 2006
          • 0 Attachment
            From: "Mark Underwood" <mark.underwood@...>
            > Hi all,
            >
            > Six primes are symmetrically arranged around the number 12:
            > 5, 7, 11, (12) 13, 17, 19.
            >
            > Six primes are also symmtrically arranged around the number 15:
            > 7, 11, 13, (15) 17, 19, 23.
            >
            > Ten primes are symmetrically arranged around the number 30:
            > 13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47.
            >
            > Twelve primes are symmetrically arranged around the number 165:
            > 137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193.
            >
            > I looked up to 100,000 primes there are six cases of twelve primes
            > symmetrically arranged around a central number. Found nothing higher.
            > When is the first case of a symmetrical grouping of more than twelve
            > primes?


            A great puzzle Mark!

            Shame I misread it - I was trying to stick a prime in the middle...

            Some examples:

            6 primes symmetrically arranged around a central prime
            683747 683759 683777 683783 683789 683807 683819
            . +12 +18 +6 +6 +18 +12

            8 primes symmetrically arranged around a central prime
            98303867 98303873 98303897 98303903 98303927 98303951 98303957 98303981
            98303987
            . +6 +24 +6 +24 +24 +6 +24 +6

            10 primes symmetrically arranged around a central prime
            60335249851 +6
            60335249857 +12
            60335249869 +12
            60335249881 +60
            60335249941 +18
            60335249959 +18
            60335249977 +60
            60335250037 +12
            60335250049 +12
            60335250061 +6
            60335250067

            12 - well, that's a job for Jens :-)


            Quiz question:
            Why are my minimal examples so much larger than Mark's examples?

            I have the answer. It's quite elementary, but still took 30 seconds of head
            scratching before I worked it out. Award yourself a Carmody-approved pat on the
            back if you work it out more quickly.

            Yes, I appreciate this does not answer your original question :-P

            Phil

            () ASCII ribbon campaign () Hopeless ribbon campaign
            /\ against HTML mail /\ against gratuitous bloodshed

            [stolen with permission from Daniel B. Cristofani]

            __________________________________________________
            Do You Yahoo!?
            Tired of spam? Yahoo! Mail has the best spam protection around
            http://mail.yahoo.com
          • thefatphil
            ... Easily? Do you realise how big 2^64 is? The above length-18 case may only be 4 GHz seconds of computation using a naive algorithm, and going 2^33 times
            Message 5 of 13 , Mar 12, 2006
            • 0 Attachment
              --- In primenumbers@yahoogroups.com, Alan McFarlane
              <alan.mcfarlane@...> wrote:
              > First case of 18 primes:
              > 1613902553 1613902561 1613902567 1613902573 1613902601 1613902621
              > 1613902627 1613902643 1613902649 (1613902650) 1613902651 1613902657
              > 1613902673 1613902679 1613902699 1613902727 1613902733 1613902739
              > 1613902747
              >
              >
              > I can easily do up 2^64-59 for you as well

              Easily? Do you realise how big 2^64 is?

              The above length-18 case may only be 4 GHz seconds of computation
              using a naive algorithm, and going 2^33 times further would imply
              about 2GHz millennia.

              Phil
            • Alan McFarlane
              Hmm, I noticed that... I have, however, successfully completed an exhaustive search up to 10^12 and not found any occurences of 20 primes in symetrical
              Message 6 of 13 , Mar 12, 2006
              • 0 Attachment
                Hmm, I noticed that...

                I have, however, successfully completed an exhaustive search up to 10^12
                and not found any occurences of 20 primes in symetrical sequence.

                I'll keep it running for a while, but I may have to resort to running it
                on my farm for a week or so :)


                thefatphil wrote:
                > --- In primenumbers@yahoogroups.com, Alan McFarlane
                > <alan.mcfarlane@...> wrote:
                >> First case of 18 primes:
                >> 1613902553 1613902561 1613902567 1613902573 1613902601 1613902621
                >> 1613902627 1613902643 1613902649 (1613902650) 1613902651 1613902657
                >> 1613902673 1613902679 1613902699 1613902727 1613902733 1613902739
                >> 1613902747
                >>
                >>
                >> I can easily do up 2^64-59 for you as well
                >
                > Easily? Do you realise how big 2^64 is?
                >
                > The above length-18 case may only be 4 GHz seconds of computation
                > using a naive algorithm, and going 2^33 times further would imply
                > about 2GHz millennia.
                >
                > Phil
                >
                >
                >
                >
                >
                >
                > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                > The Prime Pages : http://www.primepages.org/
                >
                >
                > Yahoo! Groups Links
                >
                >
                >
                >
                >
                >
                >
              • Phil Carmody
                ... Confirmed. (2^40, rather than 10^12) Quoth a 2GHz Athlon (sharing with a nice PIES process): bash-3.1$ time ./symprimeven real 101m15.817s user 84m27.830s
                Message 7 of 13 , Mar 12, 2006
                • 0 Attachment
                  --- Alan McFarlane <alan.mcfarlane@...> wrote:
                  > Hmm, I noticed that...
                  >
                  > I have, however, successfully completed an exhaustive search up to 10^12
                  > and not found any occurences of 20 primes in symetrical sequence.

                  Confirmed. (2^40, rather than 10^12)

                  Quoth a 2GHz Athlon (sharing with a nice PIES process):

                  bash-3.1$ time ./symprimeven

                  real 101m15.817s
                  user 84m27.830s
                  sys 0m2.550s

                  > I'll keep it running for a while, but I may have to resort to running it
                  > on my farm for a week or so :)

                  I think it is worth trying to find such a cluster, and also that it's not worth
                  competing, and definitely worth cooperating. So you have dibbs on the task (if
                  you have a farm, that only makes sense -- I only have a herb garden!). If my
                  code's faster than yours, you can have it freely. However, as I hinted, my
                  code's not very clever.

                  I was thinking of a branchless FSM-like approach optimisation, but decided to
                  not bother in the end. However, if you want to try to work on optimising the
                  task, I can join you in a brainstorm.

                  Phil

                  () ASCII ribbon campaign () Hopeless ribbon campaign
                  /\ against HTML mail /\ against gratuitous bloodshed

                  [stolen with permission from Daniel B. Cristofani]

                  __________________________________________________
                  Do You Yahoo!?
                  Tired of spam? Yahoo! Mail has the best spam protection around
                  http://mail.yahoo.com
                • Alan McFarlane
                  I m just in the process of writing an optimized version (ANSI C to start with), but in the interim, why don t we allocate blocks of data to work on. Say a
                  Message 8 of 13 , Mar 12, 2006
                  • 0 Attachment
                    I'm just in the process of writing an optimized version (ANSI C to start
                    with), but in the interim, why don't we allocate blocks of data to work on.

                    Say a block size of 2^40? Seems a reasonable size to me - it's fairly
                    easy for most machines to do, but is still meaty enough to be interesting.

                    Block 1 : (0 * 2^40) .. (1 * 2^40) - completed (18 digits found) [AM/PC]
                    Block 2 : (1 * 2^40) .. (2 * 2^40)
                    Block 3 : (2 * 2^40) .. (3 * 2^40)
                    Block 4 : (3 * 2^40) .. (4 * 2^40)
                    Block 5 : (4 * 2^40) .. (5 * 2^40)

                    ...

                    etc

                    If you agree with this, reserve a block or two, I'll do the same, and
                    see just where we can get to.

                    BTW, we will need to have a small overlap just in case a sequence is on
                    a block boundary. It might be an idea to start, say, 100 primes before
                    the block and end 100 primes after.

                    --
                    Alan



                    Phil Carmody wrote:
                    > --- Alan McFarlane <alan.mcfarlane@...> wrote:
                    >> Hmm, I noticed that...
                    >>
                    >> I have, however, successfully completed an exhaustive search up to 10^12
                    >> and not found any occurences of 20 primes in symetrical sequence.
                    >
                    > Confirmed. (2^40, rather than 10^12)
                    >
                    > Quoth a 2GHz Athlon (sharing with a nice PIES process):
                    >
                    > bash-3.1$ time ./symprimeven
                    >
                    > real 101m15.817s
                    > user 84m27.830s
                    > sys 0m2.550s
                    >
                    >> I'll keep it running for a while, but I may have to resort to running it
                    >> on my farm for a week or so :)
                    >
                    > I think it is worth trying to find such a cluster, and also that it's not worth
                    > competing, and definitely worth cooperating. So you have dibbs on the task (if
                    > you have a farm, that only makes sense -- I only have a herb garden!). If my
                    > code's faster than yours, you can have it freely. However, as I hinted, my
                    > code's not very clever.
                    >
                    > I was thinking of a branchless FSM-like approach optimisation, but decided to
                    > not bother in the end. However, if you want to try to work on optimising the
                    > task, I can join you in a brainstorm.
                    >
                    > Phil
                    >
                    > () ASCII ribbon campaign () Hopeless ribbon campaign
                    > /\ against HTML mail /\ against gratuitous bloodshed
                    >
                    > [stolen with permission from Daniel B. Cristofani]
                    >
                    > __________________________________________________
                    > Do You Yahoo!?
                    > Tired of spam? Yahoo! Mail has the best spam protection around
                    > http://mail.yahoo.com
                    >
                  • Phil Carmody
                    [note - I ve changed my primenumbers settings from daily digest to individual mails, so do not need an expedited copy sent directly to me any more.] ... If
                    Message 9 of 13 , Mar 12, 2006
                    • 0 Attachment
                      [note - I've changed my primenumbers settings from daily digest to individual
                      mails, so do not need an expedited copy sent directly to me any more.]

                      --- Alan McFarlane <alan.mcfarlane@...> wrote:
                      > I'm just in the process of writing an optimized version (ANSI C to start

                      If your C is not fast enough and you're tempted to go into assembler, then
                      you're not writing fast enough C! (Not always true, of course, but I am
                      notoriously pro-C.)

                      > with), but in the interim, why don't we allocate blocks of data to work on.
                      > Say a block size of 2^40? Seems a reasonable size to me - it's fairly
                      > easy for most machines to do, but is still meaty enough to be interesting.

                      That does make some sense. I'll look at optimising my code too, and decide how
                      much I want to bite off. I'd normally have my machines running PRP-ing for Les
                      GeneFermiers, but can certainly put aside a few hours. Maybe more on a "spare"
                      ancient machine (a crime against primality!) that I've not powered up for a
                      while.

                      > If you agree with this, reserve a block or two, I'll do the same, and
                      > see just where we can get to.

                      The more efficient code should be run. I'll put another 168 GHz minutes
                      onto a chunk:

                      Block 1 : (0 * 2^40) .. (1 * 2^40) - completed (18 digits found) [AM/PC]
                      Block 2 : (1 * 2^40) .. (2 * 2^40) - reserved PC
                      Block 3 : (2 * 2^40) .. (3 * 2^40)
                      Block 4 : (3 * 2^40) .. (4 * 2^40)
                      Block 5 : (4 * 2^40) .. (5 * 2^40)

                      If you tell me my code's faster, I'll grab a few more. If you tell me yours is
                      faster, I'll only look at my new routine, and put my machine back onto LG.

                      > BTW, we will need to have a small overlap just in case a sequence is on
                      > a block boundary. It might be an idea to start, say, 100 primes before
                      > the block and end 100 primes after.

                      Yup, that makes sense. Or at least 20 primes does.
                      I'll do 0x<N>fffffff000 to 0x<N+2>0000000fff .

                      Phil

                      () ASCII ribbon campaign () Hopeless ribbon campaign
                      /\ against HTML mail /\ against gratuitous bloodshed

                      [stolen with permission from Daniel B. Cristofani]

                      __________________________________________________
                      Do You Yahoo!?
                      Tired of spam? Yahoo! Mail has the best spam protection around
                      http://mail.yahoo.com
                    • Phil Carmody
                      ... Looks like you stopped to soon first time - the whole block took 2hrs on the 2GHz Athlon. 1797595815167 1797595815157 +10 1797595815133 +24 1797595815109
                      Message 10 of 13 , Mar 12, 2006
                      • 0 Attachment
                        --- Alan McFarlane <alan.mcfarlane@...> wrote:
                        > I'll test my code on Block #3
                        >
                        > Block 1 : (0 * 240) .. (1 * 240) - completed (18 digits found) [AM/PC]
                        > Block 2 : (1 * 240) .. (2 * 240) - reserved PC
                        > Block 3 : (2 * 240) .. (3 * 240) - reserved AM

                        Looks like you stopped to soon first time - the whole block took 2hrs on the
                        2GHz Athlon.


                        1797595815167
                        1797595815157 +10
                        1797595815133 +24
                        1797595815109 +24
                        1797595815091 +18
                        1797595815089 +2
                        1797595815079 +10
                        1797595815053 +26
                        1797595815019 +34
                        1797595815017 +2
                        1797595815013 +4
                        1797595815011 +2
                        1797595814977 +34
                        1797595814951 +26
                        1797595814941 +10
                        1797595814939 +2
                        1797595814921 +18
                        1797595814897 +24
                        1797595814873 +24
                        1797595814863 +10

                        Phil

                        () ASCII ribbon campaign () Hopeless ribbon campaign
                        /\ against HTML mail /\ against gratuitous bloodshed

                        [stolen with permission from Daniel B. Cristofani]

                        __________________________________________________
                        Do You Yahoo!?
                        Tired of spam? Yahoo! Mail has the best spam protection around
                        http://mail.yahoo.com
                      • Alan McFarlane
                        Good one Phil, well spotted! I admit to making a couple of minor blunders in my code, but I ve rewritten it now - hopefully it works. I m working on block #3,
                        Message 11 of 13 , Mar 12, 2006
                        • 0 Attachment
                          Good one Phil, well spotted!

                          I admit to making a couple of minor blunders in my code, but I've
                          rewritten it now - hopefully it works.

                          I'm working on block #3, current results as follows:

                          C:\Documents and Settings\Alan\My Documents\Work in Progress\ssop>ssop 3
                          [2006-03-12 22:22:57] Initializing
                          [2006-03-12 22:22:57] Processing block #3 (2199023255552-3298534948863)
                          [2006-03-12 22:22:57] Found a sequence of 2 primes starting at
                          2199023255579 with offsets from 2199023255598 of plus and minus
                          [2006-03-12 22:22:57] 19
                          [2006-03-12 22:22:57] Found a sequence of 4 primes starting at
                          2199023256557 with offsets from 2199023256585 of plus and minus
                          [2006-03-12 22:22:57] 16 28
                          [2006-03-12 22:22:57] Found a sequence of 6 primes starting at
                          2199023258429 with offsets from 2199023258454 of plus and minus
                          [2006-03-12 22:22:57] 5 23 25
                          [2006-03-12 22:22:57] Found a sequence of 8 primes starting at
                          2199023370119 with offsets from 2199023370141 of plus and minus
                          [2006-03-12 22:22:57] 2 8 20 22
                          [2006-03-12 22:22:58] Found a sequence of 10 primes starting at
                          2199027144263 with offsets from 2199027144381 of plus and minus
                          [2006-03-12 22:22:58] 62 70 82 92 118
                          [2006-03-12 22:23:06] Found a sequence of 12 primes starting at
                          2199128142049 with offsets from 2199128142126 of plus and minus
                          [2006-03-12 22:23:06] 17 35 53 67 73 77
                          [2006-03-12 22:26:31] Found a sequence of 14 primes starting at
                          2201711786839 with offsets from 2201711786988 of plus and minus
                          [2006-03-12 22:26:31] 5 41 71 95 125 145 149
                          [2006-03-12 22:28:06] Found a sequence of 16 primes starting at
                          2202939530537 with offsets from 2202939530610 of plus and minus
                          [2006-03-12 22:28:06] 1 41 43 47 53 59 67 73
                          [2006-03-12 23:24:00] ...

                          I don't know when it will finish, as I'm testing for sequences up to 80
                          in length, but hopefully it should be in another couple of hours or so.

                          This is a slow machine - AMD Athlon 1.25 GHz, but I'm not running
                          anything else too heavy on it. (ssop is getting around 90% of processor
                          time allocated to it).



                          Phil Carmody wrote:
                          > --- Alan McFarlane <alan.mcfarlane@...> wrote:
                          >> I'll test my code on Block #3
                          >>
                          >> Block 1 : (0 * 240) .. (1 * 240) - completed (18 digits found) [AM/PC]
                          >> Block 2 : (1 * 240) .. (2 * 240) - reserved PC
                          >> Block 3 : (2 * 240) .. (3 * 240) - reserved AM
                          >
                          > Looks like you stopped to soon first time - the whole block took 2hrs on the
                          > 2GHz Athlon.
                          >
                          >
                          > 1797595815167
                          > 1797595815157 +10
                          > 1797595815133 +24
                          > 1797595815109 +24
                          > 1797595815091 +18
                          > 1797595815089 +2
                          > 1797595815079 +10
                          > 1797595815053 +26
                          > 1797595815019 +34
                          > 1797595815017 +2
                          > 1797595815013 +4
                          > 1797595815011 +2
                          > 1797595814977 +34
                          > 1797595814951 +26
                          > 1797595814941 +10
                          > 1797595814939 +2
                          > 1797595814921 +18
                          > 1797595814897 +24
                          > 1797595814873 +24
                          > 1797595814863 +10
                          >
                          > Phil
                          >
                          > () ASCII ribbon campaign () Hopeless ribbon campaign
                          > /\ against HTML mail /\ against gratuitous bloodshed
                          >
                          > [stolen with permission from Daniel B. Cristofani]
                          >
                          > __________________________________________________
                          > Do You Yahoo!?
                          > Tired of spam? Yahoo! Mail has the best spam protection around
                          > http://mail.yahoo.com
                          >
                        • Mark Underwood
                          Great going you guys, a symmetrical 20 cluster is found. Phil, I noticed that your central number - 1797595815015 - is very factor rich (containing all primes
                          Message 12 of 13 , Mar 12, 2006
                          • 0 Attachment
                            Great going you guys, a symmetrical 20 cluster is found. Phil, I
                            noticed that your central number - 1797595815015 - is very factor
                            rich (containing all primes from 3 to 17).

                            I did some head scratching as well as to why first occurances of
                            cluster sizes are so much larger with a prime as the centre number.
                            Although it me much longer than 30 seconds to get it, I still gave
                            myself a pat on the back. :)

                            Another puzzle is on the way.

                            Mark


                            --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>
                            wrote:
                            >
                            > --- Alan McFarlane <alan.mcfarlane@...> wrote:
                            > > I'll test my code on Block #3
                            > >
                            > > Block 1 : (0 * 240) .. (1 * 240) - completed (18 digits found)
                            [AM/PC]
                            > > Block 2 : (1 * 240) .. (2 * 240) - reserved PC
                            > > Block 3 : (2 * 240) .. (3 * 240) - reserved AM
                            >
                            > Looks like you stopped to soon first time - the whole block took
                            2hrs on the
                            > 2GHz Athlon.
                            >
                            >
                            > 1797595815167
                            > 1797595815157 +10
                            > 1797595815133 +24
                            > 1797595815109 +24
                            > 1797595815091 +18
                            > 1797595815089 +2
                            > 1797595815079 +10
                            > 1797595815053 +26
                            > 1797595815019 +34
                            > 1797595815017 +2
                            > 1797595815013 +4
                            > 1797595815011 +2
                            > 1797595814977 +34
                            > 1797595814951 +26
                            > 1797595814941 +10
                            > 1797595814939 +2
                            > 1797595814921 +18
                            > 1797595814897 +24
                            > 1797595814873 +24
                            > 1797595814863 +10
                            >
                            > Phil
                            >
                            > () ASCII ribbon campaign () Hopeless ribbon campaign
                            > /\ against HTML mail /\ against gratuitous bloodshed
                            >
                            > [stolen with permission from Daniel B. Cristofani]
                            >
                            > __________________________________________________
                            > Do You Yahoo!?
                            > Tired of spam? Yahoo! Mail has the best spam protection around
                            > http://mail.yahoo.com
                            >
                          • Jens Kruse Andersen
                            ... I didn t like the fast growth of the minimal solution so I searched a non-minimal instead: Find 7 simultaneous primes in a specific chosen pattern with 6
                            Message 13 of 13 , Mar 20, 2006
                            • 0 Attachment
                              Phil Carmody wrote:

                              > 6 primes symmetrically arranged around a central prime
                              > 683747 683759 683777 683783 683789 683807 683819
                              > . +12 +18 +6 +6 +18 +12
                              >
                              > 8 primes symmetrically arranged around a central prime
                              > 98303867 98303873 98303897 98303903 98303927 98303951 98303957 98303981
                              > 98303987
                              > . +6 +24 +6 +24 +24 +6 +24 +6
                              >
                              > 10 primes symmetrically arranged around a central prime
                              > 60335249851 +6
                              > 60335249857 +12
                              > 60335249869 +12
                              > 60335249881 +60
                              > 60335249941 +18
                              > 60335249959 +18
                              > 60335249977 +60
                              > 60335250037 +12
                              > 60335250049 +12
                              > 60335250061 +6
                              > 60335250067
                              >
                              > 12 - well, that's a job for Jens :-)

                              I didn't like the fast growth of the minimal solution so
                              I searched a non-minimal instead:
                              Find 7 simultaneous primes in a specific chosen pattern
                              with 6 symmetric around the center.
                              Then see how far the symmetri extends.

                              After 338 cases with 10 symmetric, a 12 finally appeared:
                              3391781771953843 +/- 6, 24, 36, 66, 120, 126.

                              In Phil's notation:
                              3391781771953717 +6
                              3391781771953723 +54
                              3391781771953777 +30
                              3391781771953807 +12
                              3391781771953819 +18
                              3391781771953837 +6
                              3391781771953843 +6
                              3391781771953849 +18
                              3391781771953867 +12
                              3391781771953879 +30
                              3391781771953909 +54
                              3391781771953963 +6
                              3391781771953969

                              Prp testing by the GMP library and primality proving by PARI/GP.

                              --
                              Jens Kruse Andersen
                            Your message has been successfully submitted and would be delivered to recipients shortly.