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Gruesome Runs - New Record 18 and 25

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  • David Cleaver
    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:
    Message 1 of 12 , Mar 2 12:49 AM
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      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:
      31,83,5,251,7,23,127,17,2,257,43,37,13,29,131,263,11,53,19,89,67,269,3,271,17

      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
    • 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 2 of 12 , Mar 2 1:03 AM
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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 3 of 12 , Mar 2 2:55 AM
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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 4 of 12 , Mar 2 3:44 AM
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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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            Yahoo! Sports - sign up for Fantasy Baseball
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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 5 of 12 , Mar 2 3:50 AM
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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 6 of 12 , Mar 2 6:18 AM
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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



                Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
              • 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 7 of 12 , Mar 2 9:31 AM
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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 8 of 12 , Mar 2 12:32 PM
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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




                    Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
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                  • djbroadhurst
                    5) Every conceivable combination of ad hoc definitions will be posted eventually.
                    Message 9 of 12 , Mar 2 3:17 PM
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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 10 of 12 , Mar 2 4:42 PM
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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 11 of 12 , Mar 2 6:07 PM
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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 12 of 12 , Mar 3 2:37 AM
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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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