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Re: Carmichael Numbers

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  • Lélio Ribeiro de Paula
    ... Sorry for the typo in my previous answer The 5th Carmichael number, namely 2821, has not one but TWO Mersenne factors. Also the factor 127 occurs in 25 of
    Message 1 of 11 , Apr 2, 2009
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      --- In primenumbers@yahoogroups.com, Devaraj Kandadai <dkandadai@...> wrote:
      >
      > All the factors of a Carmichael Number cannot be Mersenne.
      >
      > You are hereby invited to prove/disprove the above.
      >

      Sorry for the typo in my previous answer

      The 5th Carmichael number, namely 2821, has not one but TWO Mersenne factors.

      Also the factor 127 occurs in 25 of the first 646 Carmichael numbers.

      Lélio
    • David Broadhurst
      ... Analyzing all 1401644 Carmichael numbers less than 10^18, one finds the following tallies of divisors that are Mersenne primes: 3: 1967 7: 133381 31:
      Message 2 of 11 , Apr 3, 2009
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        --- In primenumbers@yahoogroups.com,
        Lélio Ribeiro de Paula <lelio73@...> wrote:

        > the factor 127 occurs in 25 of the
        > first 646 Carmichael numbers.

        Analyzing all 1401644 Carmichael numbers less
        than 10^18, one finds the following tallies
        of divisors that are Mersenne primes:

        3: 1967
        7: 133381
        31: 242813
        127: 109199
        8191: 5044
        131071: 8
        524287: 4

        Perhaps, when A.K.Devaraj wrote

        > All the factors of a Carmichael Number cannot be Mersenne

        he intended to claim that

        no Carmichael number is a product of Mersenne primes

        which is a more tenable conjecture than the one that
        Lélio reasonably parsed from A.K.'s poorly worded formulation.

        David
      • Devaraj Kandadai
        I am inclined to believe that this is a corollary of the Devaraj-Pomernce-Maxal Thoerem (see www.crorepatibaniye.com/failurefunctions). A.K. Devaraj ...
        Message 3 of 11 , Apr 3, 2009
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          I am inclined to believe that this is a corollary of the
          Devaraj-Pomernce-Maxal Thoerem (see
          www.crorepatibaniye.com/failurefunctions).
          A.K. Devaraj

          On Thu, Apr 2, 2009 at 4:37 PM, Devaraj Kandadai <dkandadai@...>wrote:

          > My conjecture pertaining to Carmichael Numbers was proved by Pomerance
          > and Maxal(see www.crorepatibaniye.com/failurefunctions). Another
          > conjecture:
          >
          > All the factors of a Carmichael Number cannot be Mersenne.
          >
          > You are hereby invited to prove/disprove the above.
          >
          > A.K.Devaraj
          >


          [Non-text portions of this message have been removed]
        • Maximilian Hasler
          It seems impossible to access http://www.crorepatibaniye.com/. The last update seen by web.archive of /any/ page on that site dates back to Nov.2007. The
          Message 4 of 11 , Apr 3, 2009
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            It seems impossible to access http://www.crorepatibaniye.com/.
            The last update seen by web.archive of /any/ page on that site dates back to Nov.2007.
            The latest version of your "theorem" which I can access via web.archive is
            http://web.archive.org/web/20070111140456/http://www.crorepatibaniye.com/failurefunctions/conjecture2.asp
            which has been *disproved*: sequence
            http://www.research.att.com/~njas/sequences/A104017
            lists the first three lines of counter-examples.

            Given the moderate number of Mersenne primes we know and the rate at which this knowledge increases, you are quite safe from a counter-example against your new Conjecture (re-stated as: "the prime factors of a Carmichael Number cannot all be Mersenne").

            Maximilian

            --- In primenumbers@yahoogroups.com, Devaraj Kandadai <dkandadai@...> wrote:
            >
            > I am inclined to believe that this is a corollary of the
            > Devaraj-Pomernce-Maxal Thoerem (see
            > www.crorepatibaniye.com/failurefunctions).
            > A.K. Devaraj
            >
            > On Thu, Apr 2, 2009 at 4:37 PM, Devaraj Kandadai <dkandadai@...>wrote:
            >
            > > My conjecture pertaining to Carmichael Numbers was proved by Pomerance
            > > and Maxal(see www.crorepatibaniye.com/failurefunctions). Another
            > > conjecture:
            > >
            > > All the factors of a Carmichael Number cannot be Mersenne.
            > >
            > > You are hereby invited to prove/disprove the above.
            > >
            > > A.K.Devaraj
          • David Broadhurst
            ... How many mistakes can be packed into 7 words? 1) Deveraj has no Thoerem. 2) Devaraj has no theorem, either. 3) Pomerance (not Pomernce) and 4) Alekseyev
            Message 5 of 11 , Apr 4, 2009
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              --- In primenumbers@yahoogroups.com,
              Devaraj Kandadai <dkandadai@...> wrote:

              > corollary of the Devaraj-Pomernce-Maxal Thoerem

              How many mistakes can be packed into 7 words?

              1) Deveraj has no Thoerem.
              2) Devaraj has no theorem, either.
              3) Pomerance (not Pomernce) and
              4) Alekseyev (not Maxal) showed that
              5) merely half of a conjecture by Deveraj holds,
              6) while the other half is patently false
              7) and hence can have no corollary.

              Any advance on 7 mistakes?

              David
            • Devaraj Kandadai
              Dear Maxmilian, Let me clarify; A 104016 is the sequence of Devaraj Numbers which are also Carmichael Numbers and A 104017 is that of Devaraj Numbers which
              Message 6 of 11 , Apr 4, 2009
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                Dear Maxmilian,
                Let me clarify;
                A 104016 is the sequence of Devaraj Numbers
                which are also Carmichael
                Numbers and A 104017 is that of Devaraj Numbers which are NOT CNs. Both
                display a property of
                Let me clarify; A 104016 represents Devaraj numbers which are CNs and
                A104017 represents DNs which are not CNs. best illustrated by following
                numerical examples

                Let us take 561, the smallest CN.

                561=3*11*17;
                My conjecture about this is that 2*560/10*16 is
                an integer ( and so it is =7).

                Now let us take the smallest in the seq A 104017 viz 11305=5*7*17*19

                My conjecture: 4*11304*11304/6*16*18 is an integer and so it is.

                As regards my site if it is not accessible I wd be only too happy to send
                the relevant file as an attachment/

                Trust I have made myself clear.
                A.K.Devaraj

                On Sat, Apr 4, 2009 at 11:34 AM, Maximilian Hasler <
                maximilian.hasler@...> wrote:

                > It seems impossible to access http://www.crorepatibaniye.com/.<http://www.crorepatibaniye.com/>
                > The last update seen by web.archive of /any/ page on that site dates back
                > to Nov.2007.
                > The latest version of your "theorem" which I can access via web.archive is
                >
                > http://web.archive.org/web/20070111140456/http://www.crorepatibaniye.com/failurefunctions/conjecture2.asp
                > which has been *disproved*: sequence
                > http://www.research.att.com/~njas/sequences/A104017
                > lists the first three lines of counter-examples.
                >
                > Given the moderate number of Mersenne primes we know and the rate at which
                > this knowledge increases, you are quite safe from a counter-example against
                > your new Conjecture (re-stated as: "the prime factors of a Carmichael Number
                > cannot all be Mersenne").
                >
                > Maximilian
                >
                > --- In primenumbers@yahoogroups.com <primenumbers%40yahoogroups.com>,
                > Devaraj Kandadai <dkandadai@...> wrote:
                > >
                > > I am inclined to believe that this is a corollary of the
                > > Devaraj-Pomernce-Maxal Thoerem (see
                > > www.crorepatibaniye.com/failurefunctions).
                > > A.K. Devaraj
                > >
                > > On Thu, Apr 2, 2009 at 4:37 PM, Devaraj Kandadai <dkandadai@...>wrote:
                > >
                > > > My conjecture pertaining to Carmichael Numbers was proved by Pomerance
                > > > and Maxal(see www.crorepatibaniye.com/failurefunctions). Another
                > > > conjecture:
                > > >
                > > > All the factors of a Carmichael Number cannot be Mersenne.
                > > >
                > > > You are hereby invited to prove/disprove the above.
                > > >
                > > > A.K.Devaraj
                >
                >
                >


                [Non-text portions of this message have been removed]
              • Maximilian Hasler
                ... As far as I understood, the D-numbers are /defined/ as those for which this is an integer; your conjecture says that this is a CN, but it isn t. Maximilian
                Message 7 of 11 , Apr 5, 2009
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                  --- In primenumbers@yahoogroups.com, Devaraj Kandadai wrote:

                  > Now let us take the smallest in the seq A 104017 viz 11305=5*7*17*19
                  >
                  > My conjecture: 4*11304*11304/6*16*18 is an integer and so it is.

                  As far as I understood, the D-numbers are /defined/ as those for which this is an integer; your conjecture says that this is a CN, but it isn't.

                  Maximilian

                  PS: the posts 2e4 and 2e4-1 are empty since you cannot send attachments. But we have the Pomerance-Alekseyev proof at http://www.mersenneforum.org/showpost.php?p=55271
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