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Re: Carmichael Numbers

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  • 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 1 of 11 , Apr 3 10:33 PM
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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 2 of 11 , Apr 3 11:04 PM
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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 3 of 11 , Apr 4 4:07 AM
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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 4 of 11 , Apr 4 10:14 PM
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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 5 of 11 , Apr 5 6:53 AM
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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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