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RE: [PrimeNumbers] Gruesome Runs - New Record 18 and 25

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  • Jon Perry
    There are an inifinte number of Gruesome 2 Runs, take 2^p, and 2^p-1 prime. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry
    Message 1 of 12 , Mar 2, 2002
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      There are an inifinte number of Gruesome 2 Runs, take 2^p, and 2^p-1 prime.

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com


      -----Original Message-----
      From: David Cleaver [mailto:wraithx@...]
      Sent: 02 March 2002 08:50
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Gruesome Runs - New Record 18 and 25


      OK, in keeping with my testing the numbers around powers of two, I just
      tried around 128 and 256. At 128 I found a run of 18 which is:

      122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139
      61, 41, 31, 5, 7,127, 2, 43, 13,131, 11, 19, 67, 3, 17,137, 23,139

      And at 256 I found a run of 25 which is:
      the consecutive composites from 248 to 272 (inclusive) and the single
      covering set which is as follows:
      31,83,5,251,7,23,127,17,2,257,43,37,13,29,131,263,11,53,19,89,67,269,3,271,1
      7

      I guess one thing we can conjecture at this point is whether or not
      there is a gruesome run of every integer length >= 1?

      1) A run of 1 is any prime number.
      2) A run of 2 (the only?) is 8,9. The answer to this is up to whether
      or not there are any more a^x - b^y = 1 for a and b prime. (Actually,
      now that I think about it, with inclusion of primes in the sequence,
      Mersenne's fit nicely into this category.)
      3) A run of 3 could be 7,8,9 or 8,9,10.

      Anyway, I would like to hear what the list thinks of the possibility of
      there being a gruesome run of all possible lengths?

      David Cleaver wrote:
      >
      > Mine being:
      >
      > 31,32,33,34,35,36,37,38,39,40,41
      >
      > 31, 2,11,17, 7, 3,37,19,13, 5,41
      >
      > One thing I've noticed is that its best to start a run of these at a
      > power of two [or maybe just before if you're near a Mersenne ;) ] The
      > reason being is that the first element, the 2^k, eliminates the chance
      > that any other succeding number could use 2 as its prime. And with such
      > info, let me look at 64: and yup, I just got a gruesome run of 13,
      > which is:
      >
      > 64,65,66,67,68,69,70,71,72,73,74,75,76
      >
      > 2,13,11,67,17,23, 7,71, 3,73,37, 5,19
      >
      > It took me about 5 minutes with pen and paper to find these two, I'm
      > sure a program could find many more much more quickly. Don't know if
      > I'll write it, I'm going to go rent some movies tonight. Anyway, have
      > fun on your gruesome searches.
      >
      > -David C.
      >
      > Jon Perry wrote:
      > >
      > > Being:
      > >
      > > 16,17,18,19,20,21,22,23
      > >
      > > 2 ,17, 3,19, 5, 7,11,23
      > >
      > > -----Original Message-----
      > >
      > > Owing to the high probabilty that 8,9,10 is the longest gruesome run, I
      have
      > > modified the definition to allow primes.
      > >
      > > So, my new record is:
      > >
      > > 9,10,11,12,13,14
      > >
      > > length 6
      > >
      > > having the single pattern:
      > >
      > > 3,5,11,2,13,7



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    • Phil Carmody
      ... Ah, the infinitude of Mersenne primes, finally proved. Phil ===== -- .sig selecter broken, please ignore.
      Message 2 of 12 , Mar 2, 2002
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        --- Jon Perry <perry@...> wrote:
        > There are an inifinte number of Gruesome 2 Runs, take 2^p, and
        > 2^p-1 prime.

        Ah, the infinitude of Mersenne primes, finally proved.

        Phil

        =====
        --
        .sig selecter broken, please ignore.

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      • Jon Perry
        I was chuffed. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML
        Message 3 of 12 , Mar 2, 2002
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          I was chuffed.

          Jon Perry
          perry@...
          http://www.users.globalnet.co.uk/~perry
          http://www.users.globalnet.co.uk/~perry/maths
          BrainBench MVP for HTML and JavaScript
          http://www.brainbench.com


          -----Original Message-----
          From: Phil Carmody [mailto:thefatphil@...]
          Sent: 02 March 2002 10:55
          To: primenumbers
          Subject: RE: [PrimeNumbers] Gruesome Runs - New Record 18 and 25


          --- Jon Perry <perry@...> wrote:
          > There are an inifinte number of Gruesome 2 Runs, take 2^p, and
          > 2^p-1 prime.

          Ah, the infinitude of Mersenne primes, finally proved.

          Phil

          =====
          --
          .sig selecter broken, please ignore.

          __________________________________________________
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        • Jon Perry
          1: 2 2 2: 2,3 2,3 3: 3,4,5 3,2,5 4: 4,5,6,7 2,5,3,7 5: 7,8,9,10,11 7,2,3, 5,11 6: 9,10,11,12,13,14 3,5,11,2,13,7 7: 16,17,18,19,20,21,22 2 ,17, 3,19, 5, 7,11
          Message 4 of 12 , Mar 2, 2002
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            1:

            2
            2

            2:
            2,3
            2,3

            3:
            3,4,5
            3,2,5

            4:

            4,5,6,7
            2,5,3,7

            5:

            7,8,9,10,11
            7,2,3, 5,11

            6:

            9,10,11,12,13,14
            3,5,11,2,13,7

            7:

            16,17,18,19,20,21,22
            2 ,17, 3,19, 5, 7,11

            8:

            16,17,18,19,20,21,22,23
            2 ,17, 3,19, 5, 7,11,23

            9:

            26,27,28,29,30,31,32,33,34
            13, 3, 7,29, 5,31, 2,11,17

            10:

            31,32,33,34,35,36,37,38,39,40
            31, 2,11,17, 7, 3,37,19,13, 5

            11:

            31,32,33,34,35,36,37,38,39,40,41
            31, 2,11,17, 7, 3,37,19,13, 5,41

            12:

            64,65,66,67,68,69,70,71,72,73,74,75
            2,13,11,67,17,23, 7,71, 3,73,37, 5

            13:

            64,65,66,67,68,69,70,71,72,73,74,75,76
            2,13,11,67,17,23, 7,71, 3,73,37, 5,19


            Jon Perry
            perry@...
            http://www.users.globalnet.co.uk/~perry
            http://www.users.globalnet.co.uk/~perry/maths
            BrainBench MVP for HTML and JavaScript
            http://www.brainbench.com
          • Jon Perry
            1: 2 2 2: 2,3 2,3 3: 3,4,5 3,2,5 4: 4,5,6,7 2,5,3,7 5: 7,8,9,10,11 7,2,3, 5,11 6: 9,10,11,12,13,14 3, 5,11, 2,13, 7 7: 11,12,13,14,15,16,17 11, 3,13, 7, 5,
            Message 5 of 12 , Mar 2, 2002
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              1:
              2
              2

              2:
              2,3
              2,3

              3:
              3,4,5
              3,2,5

              4:
              4,5,6,7
              2,5,3,7

              5:
              7,8,9,10,11
              7,2,3, 5,11

              6:
              9,10,11,12,13,14
              3, 5,11, 2,13, 7

              7:
              11,12,13,14,15,16,17
              11, 3,13, 7, 5, 2,17

              8:
              16,17,18,19,20,21,22,23
              2 ,17, 3,19, 5, 7,11,23

              9:
              26,27,28,29,30,31,32,33,34
              13, 3, 7,29, 5,31, 2,11,17

              ---

              The change from my orignal list is with 7, and I haven't validated beyond 9.

              Jon Perry
              perry@...
              http://www.users.globalnet.co.uk/~perry
              http://www.users.globalnet.co.uk/~perry/maths
              BrainBench MVP for HTML and JavaScript
              http://www.brainbench.com



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            • Jon Perry
              In addition to David Cleaver s conjecture that there exists a grusome run of any length, I would like to add the conjecture that every integer is part of a
              Message 6 of 12 , Mar 2, 2002
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                In addition to David Cleaver's conjecture that there exists a grusome run of
                any length, I would like to add the conjecture that every integer is part of
                a gruesome run.

                This conjecture belies a new definition, which I have termed a 'dire
                straight'. A dire straight is the smallest gruesome run that contains an
                integer.

                This therefore implies the longest gruesome run that contains an integer is
                a 'horrible band'.

                Jon Perry
                perry@...
                http://www.users.globalnet.co.uk/~perry
                http://www.users.globalnet.co.uk/~perry/maths
                BrainBench MVP for HTML and JavaScript
                http://www.brainbench.com
              • Jon Perry
                And a couple more: 1)There exists a grusome run of every length 2)Every integer partakes in a gruesome run 3)No integer has a dire straight length equal to its
                Message 7 of 12 , Mar 2, 2002
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                  And a couple more:

                  1)There exists a grusome run of every length

                  2)Every integer partakes in a gruesome run

                  3)No integer has a dire straight length equal to its horrible band length.

                  4)An integer partakes in gruesome runs of all lengths between its dire
                  straight length and its horrible band length.

                  Jon Perry
                  perry@...
                  http://www.users.globalnet.co.uk/~perry
                  http://www.users.globalnet.co.uk/~perry/maths
                  BrainBench MVP for HTML and JavaScript
                  http://www.brainbench.com


                  -----Original Message-----
                  From: Jon Perry [mailto:perry@...]
                  Sent: 02 March 2002 17:31
                  To: primenumbers
                  Subject: [PrimeNumbers] Gruesome Conjectures


                  In addition to David Cleaver's conjecture that there exists a grusome run of
                  any length, I would like to add the conjecture that every integer is part of
                  a gruesome run.

                  This conjecture belies a new definition, which I have termed a 'dire
                  straight'. A dire straight is the smallest gruesome run that contains an
                  integer.

                  This therefore implies the longest gruesome run that contains an integer is
                  a 'horrible band'.

                  Jon Perry
                  perry@...
                  http://www.users.globalnet.co.uk/~perry
                  http://www.users.globalnet.co.uk/~perry/maths
                  BrainBench MVP for HTML and JavaScript
                  http://www.brainbench.com




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                • djbroadhurst
                  5) Every conceivable combination of ad hoc definitions will be posted eventually.
                  Message 8 of 12 , Mar 2, 2002
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                    5) Every conceivable combination of ad hoc definitions will
                    be posted eventually.
                  • jim_fougeron
                    ... 5b) Each of these combinations will be posted one at a time, on a whim, without any forethought into fully (or even partly) thinking through the possible
                    Message 9 of 12 , Mar 2, 2002
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                      --- In primenumbers@y..., "djbroadhurst" <d.broadhurst@o...> wrote:
                      > 5) Every conceivable combination of ad hoc definitions will
                      > be posted eventually.

                      5b) Each of these combinations will be posted one at a time, on a
                      whim, without any forethought into fully (or even partly) thinking
                      through the possible "set".

                      5c) Each of these singly 1/100th thought out definitions
                      (conjectures) will generally be sent with dozens of additional
                      lines per posting filled in with insignificant items such as
                      overblown .sig files and or the bottom of a top posted prior email
                      (possibly not even relevant to the current "conjecture addition").
                    • djbroadhurst
                      But Jim, just think how Jon outranks you. You are merely a DVP (David valued programmer) whereas Jon is a BrainBench MVP (M valued professional) and
                      Message 10 of 12 , Mar 2, 2002
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                        But Jim, just think how Jon outranks you.
                        You are merely a DVP (David valued programmer)
                        whereas Jon is a "BrainBench" MVP (M valued professional)
                        and presumably M vastly outranks me,
                        your truly grateful [*] user,
                        David
                        [*] http://groups.yahoo.com/group/openpfgw/message/786
                      • Jon Perry
                        M is for Most . Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML
                        Message 11 of 12 , Mar 3, 2002
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                          M is for 'Most'.

                          Jon Perry
                          perry@...
                          http://www.users.globalnet.co.uk/~perry
                          http://www.users.globalnet.co.uk/~perry/maths
                          BrainBench MVP for HTML and JavaScript
                          http://www.brainbench.com


                          -----Original Message-----
                          From: djbroadhurst [mailto:d.broadhurst@...]
                          Sent: 03 March 2002 02:08
                          To: primenumbers@yahoogroups.com
                          Subject: [PrimeNumbers] Re: More Gruesome Conjectures


                          But Jim, just think how Jon outranks you.
                          You are merely a DVP (David valued programmer)
                          whereas Jon is a "BrainBench" MVP (M valued professional)
                          and presumably M vastly outranks me,
                          your truly grateful [*] user,
                          David
                          [*] http://groups.yahoo.com/group/openpfgw/message/786



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