Re: Carmichael Numbers

Expand Messages
• ... 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
• 0 Attachment
>
> 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
• ... 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
• 0 Attachment
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
• 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
• 0 Attachment
I am inclined to believe that this is a corollary of the
Devaraj-Pomernce-Maxal Thoerem (see
www.crorepatibaniye.com/failurefunctions).
A.K. Devaraj

> 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]
• 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
• 0 Attachment
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.
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

>
> 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
• ... 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
• 0 Attachment

> 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.

David
• 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
• 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;
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.
>
> 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
>
> >
> > 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]
• ... 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
• 0 Attachment