- 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] - 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 - --- 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 - 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/>

[Non-text portions of this message have been removed]

> 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

>

>

>

- --- In primenumbers@yahoogroups.com, Devaraj Kandadai wrote:

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

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.

>

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

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