Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Re: Carmichael Numbers

Expand Messages
  • 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 1 of 11 , Apr 4, 2009
    • 0 Attachment
      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 2 of 11 , Apr 5, 2009
      • 0 Attachment
        --- 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
      Your message has been successfully submitted and would be delivered to recipients shortly.