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Re: Prime sequence teaser!

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  • djbroadhurst
    ... Suggestion: Strip my Sophies ... and then the residual part of his diseased brain :-) resides in ... of Cunningham base-2 [pmain901] David (refusing to
    Message 1 of 29 , May 29 1:00 PM
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      Marcel:

      > except 11113. I failed

      Suggestion: Strip my Sophies

      > 7 23 47 167 263 359 383 479 503 719 839
      > 863 887 983 1319 1367 1439 1487 1823

      from Phil's perversity:

      > 23, 47, 431, 167, 263, 359, 383, 479,
      > 503, 719, ...
      > 839 863 887 11113 983 1319 1367 1439
      > 1487 8831

      and then the residual part of
      his diseased brain :-)
      resides in

      > 43 431.9719.2099863

      > 463 11113.3407681.448747600991881.239932071009857681156251129.
      > 385606580062688087218266143.P62

      > 883 8831.63577.258777491057348926546569104663.P228

      of Cunningham base-2 [pmain901]

      David (refusing to ORDER:-)
    • djbroadhurst
      ... And even then the setter can return and say: you got the right answer for a different reason, perhaps. Frankly, I opted out, on the grounds that such
      Message 2 of 29 , May 29 3:26 PM
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        Marcel:
        > Each time I try to solve a puzzle, I believe
        > that the key is to find _the_
        > interesting property which justifies the
        > puzzle :-)
        And even then the setter can return and say:
        you got the right answer for a different reason,
        perhaps.
        Frankly, I opted out, on the grounds that
        such things are not to be encouraged.
        David
      • djbroadhurst
        PS: I hope you appreciate, dear Marcel, that Phil will probably slap your hand for suggesting that he ever said that 193949641=3863*50207 was part of his ...
        Message 3 of 29 , May 29 4:19 PM
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          PS: I hope you appreciate, dear Marcel, that Phil
          will probably slap your hand for suggesting
          that he ever said that
          193949641=3863*50207
          was part of his
          > Prime sequence teaser!
          ..^^^^^
          When he asked, "what comes next"
          he probably meant: find the next composite.
          Sorry about that, but I thought you
          should learn of it from a friend
          rather than from the teaser himself...
          David
        • djbroadhurst
          For the truly perverse: 174143*2263847 193949641 = 3863*50207 However I wish it to be recorded that this true statement is in no way to be construed as a
          Message 4 of 29 , May 29 4:41 PM
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            For the truly perverse:

            174143*2263847 > 193949641 = 3863*50207

            However I wish it to be recorded that
            this true statement is in no way to
            be construed as a response to Phil's postings;
            rather I offer it in deference to Marcel's
            great igenuity, which far exceeded mine.

            David
          • Phil Carmody
            ... The sequence was _generated_ by primes, I never promised it contained only primes. Maybe the fact that I owned up to it including the number 193949641
            Message 5 of 29 , May 29 4:43 PM
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              --- djbroadhurst <d.broadhurst@...> wrote:
              > PS: I hope you appreciate, dear Marcel, that Phil
              > will probably slap your hand for suggesting
              > that he ever said that
              > 193949641=3863*50207
              > was part of his
              > > Prime sequence teaser!
              > ..^^^^^
              > When he asked, "what comes next"
              > he probably meant: find the next composite.
              > Sorry about that, but I thought you
              > should learn of it from a friend
              > rather than from the teaser himself...

              The sequence was _generated_ by primes, I never promised it contained
              only primes. Maybe the fact that I owned up to it including the
              number 193949641 would have been enough of a clue that it wasn't
              entirely prime in its contents, But maybe not.
              How should I know, I'm merely the generator! Erm... Sue me?

              Phil

              =====
              --
              "One cannot delete the Web browser from KDE without
              losing the ability to manage files on the user's own
              hard disk." - Prof. Stuart E Madnick, MIT.
              So called "expert" witness for Microsoft. 2002/05/02

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            • djbroadhurst
              ... It is quite sufficient to shame you. David :-)
              Message 6 of 29 , May 29 4:48 PM
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                Phil:
                > Sue me?
                It is quite sufficient to shame you.
                David :-)
              • Phil Carmody
                ... The simple script was: $ calc p=1;while(p 1)print g;} i.e. you re spot on. Well done. I m reading mail in
                Message 7 of 29 , May 29 4:51 PM
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                  --- Marcel Martin <znz@...> wrote:
                  >
                  > In short, the sequence is constituded of the gcd's
                  > (2^p_i-1,3^p_i-1).

                  The 'simple script' was:

                  $ calc
                  'p=1;while(p<999){p=nextprime(p);g=gcd(2^p-1,3^p-1);if(g>1)print g;}'

                  i.e. you're spot on.

                  Well done.
                  I'm reading mail in reverse, but s far you're the first to have
                  described it in the terms that I vieed it in. Which makes you a
                  winner, if there is such a thing. :-|

                  > As far as I am concerned, it is impossible to find such result.
                  > Each
                  > time I try to solve a puzzle, I believe that the key is to find
                  > _the_
                  > interesting property which justifies the puzzle :-)
                  >
                  > >Bonus question:
                  > >What comes next in this subsequence of the above?
                  > > 193949641, ...
                  >
                  > 4007,

                  Hmmm, those looked a little prime to me.

                  Anyone got any composites that are in the sequence?

                  Of course, if you obeyed orders, then the answer is p s.t. Order(2,
                  mod p) = Order(3, mod p). So a coincidence isn't impossible. One
                  composite was interesting, but I never found a second...

                  Phil

                  =====
                  --
                  "One cannot delete the Web browser from KDE without
                  losing the ability to manage files on the user's own
                  hard disk." - Prof. Stuart E Madnick, MIT.
                  So called "expert" witness for Microsoft. 2002/05/02

                  __________________________________________________
                  Do You Yahoo!?
                  Yahoo! - Official partner of 2002 FIFA World Cup
                  http://fifaworldcup.yahoo.com
                • Phil Carmody
                  ... Now that I ve released the answer I have no problem re-posing the question without the obfuscation. The initial sequence I posed was the non-1 values for
                  Message 8 of 29 , May 29 5:02 PM
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                    --- Insall <montez@...> wrote:
                    > Phil wrote: ``And I am genuinely interested in the answer to the
                    > bonus
                    > question - I've not found the answer myself.''
                    >
                    > I am a newbie. Would you mind repeating for me the ``bonus
                    > question''?

                    Now that I've released the answer I have no problem re-posing the
                    question without the obfuscation.

                    The initial sequence I posed was the non-1 values for gcd(2^p-1,
                    3^p-2) for prime p. I calculated about something like 5000 terms, and
                    many of them were 1. Some, the ones I posted as the original
                    sequence, were not 1, and were prime. However _one_ term was a
                    composite. That was the 'bonus' sequence.

                    What is the next composite value of gcd(2^p-1,3^p-1)?
                    Genuinely, I don't know.

                    Phil


                    =====
                    --
                    "One cannot delete the Web browser from KDE without
                    losing the ability to manage files on the user's own
                    hard disk." - Prof. Stuart E Madnick, MIT.
                    So called "expert" witness for Microsoft. 2002/05/02

                    __________________________________________________
                    Do You Yahoo!?
                    Yahoo! - Official partner of 2002 FIFA World Cup
                    http://fifaworldcup.yahoo.com
                  • djbroadhurst
                    It get s even more boring: 213407*2774279
                    Message 9 of 29 , May 29 5:09 PM
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                      It get's even more boring:
                      213407*2774279
                    • Phil Carmody
                      ... 3^p-1, that is And yes, I deny any inginuity in coming up with the sequence, and ascribe all whatevers to whomever. Phil ===== -- One cannot delete the
                      Message 10 of 29 , May 29 5:13 PM
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                        --- Phil Carmody <thefatphil@...> wrote:
                        >
                        > --- Insall <montez@...> wrote:
                        > > Phil wrote: ``And I am genuinely interested in the answer to the
                        > > bonus
                        > > question - I've not found the answer myself.''
                        > >
                        > > I am a newbie. Would you mind repeating for me the ``bonus
                        > > question''?
                        >
                        > Now that I've released the answer I have no problem re-posing the
                        > question without the obfuscation.
                        >
                        > The initial sequence I posed was the non-1 values for gcd(2^p-1,
                        > 3^p-2) for prime p. I calculated about something like 5000 terms,

                        3^p-1, that is

                        And yes, I deny any inginuity in coming up with the sequence, and
                        ascribe all whatevers to whomever.

                        Phil

                        =====
                        --
                        "One cannot delete the Web browser from KDE without
                        losing the ability to manage files on the user's own
                        hard disk." - Prof. Stuart E Madnick, MIT.
                        So called "expert" witness for Microsoft. 2002/05/02

                        __________________________________________________
                        Do You Yahoo!?
                        Yahoo! - Official partner of 2002 FIFA World Cup
                        http://fifaworldcup.yahoo.com
                      • djbroadhurst
                        ... gcd(2^1931-1,3^1931-1) trivially factors as: 3863*50207 gcd(2^87071-1,3^87071-1) has factors: 174143*2263847 gcd(2^106703-1,3^106703-1) has factors:
                        Message 11 of 29 , May 30 8:00 AM
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                          > Anyone got any composites that are in the sequence?
                          gcd(2^1931-1,3^1931-1) trivially factors as: 3863*50207
                          gcd(2^87071-1,3^87071-1) has factors: 174143*2263847
                          gcd(2^106703-1,3^106703-1) has factors: 213407*2774279
                          gcd(2^215863-1,3^215863-1) has factors: 2158631*5180713
                          gcd(2^305219-1,3^305219-1) has factors: 610439*29911463
                          gcd(2^327779-1,3^327779-1) has factors: 655559*16388951
                          gcd(2^453983-1,3^453983-1) has factors: 907967*10895593
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