- First, Caldwell (if that means me) made no such "conjecture." Folks are too lose with that word. Why I put the opinion "probably not" on that page some years ago, I have no clue now myself. The reference I linked to that page suggests the opposite (also carefully not stated as a conjecture) which seems to suggest I intended "probably."

-----Original Message-----

From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On Behalf Of WarrenS

Sent: Tuesday, March 26, 2013 1:40 PM

To: primenumbers@yahoogroups.com

Subject: [PrimeNumbers] Caldwell conjectured #Wieferich primes = finite?

What is the reasoning behind this conjecture?

(Wikipedia says Caldwell conjectured this.)

------------------------------------

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Yahoo! Groups Links - --- On Wed, 3/27/13, Chris Caldwell <caldwell@...> wrote:
> First, Caldwell (if that means me)

And if we're being loose with the word, and accepting that there's an enormous, and unmeasurable, level of doubt in such statements, then it's not uncommon to come up with paradoxical conclusions.

> made no such "conjecture." Folks are too lose with

> that word. Why I put the opinion "probably not" on

> that page some years ago, I have no clue now myself.

> The reference I linked to that page suggests the opposite

> (also carefully not stated as a conjecture) which seems to

> suggest I intended "probably."

Let's look also at the another set with the same expected density, but even fewer are known - the $620 pseudoprimes. A conjecture about the density of those grossly overestimate the number that we've actually found - none. What are the chances of there being so few? The heuristics are simple, but the heuristics are naive. The data is simple, but the data is unassailably true.

It's not a big leap to say "one of the assumptions behind the heuristic must be wrong". Probably.

Which of course if different from a statement that the tally of such objects is finite - it only takes a small factor to make something infinite become pointlessly sparse.

Phil

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[stolen with permission from Daniel B. Cristofani] - --- In primenumbers@yahoogroups.com,

Chris Caldwell <caldwell@...> wrote:

> First, Caldwell (if that means me) made no such "conjecture."

Indeed. It was an "obiter dictum", now changed in

> Folks are too lose with that word.

http://primes.utm.edu/glossary/xpage/WieferichPrime.html

to the converse remark. Neither then nor now should Warren,

or others, seek to elevate it to a "conjecture" by Chris.

I have found Warren's contributions fruitful enough to set

aside his unfortunate tone in communicating them. Yet I am

still puzzled why he seems to need to be so combative in

what is, quite frankly, a place where he should not expect

the type of serious review that he might gain by taking the

trouble to write up his ideas in an appropriate form for

scrutiny by a more rigorous mathematical community.

In any case, thanks Warren, for the maths.

David (not a mathematician) - --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
>

--I just saw it in wikipedia, not elsewhere. I did not "elevate" it,

>

>

> --- In primenumbers@yahoogroups.com,

> Chris Caldwell <caldwell@> wrote:

>

> > First, Caldwell (if that means me) made no such "conjecture."

> > Folks are too lose with that word.

>

> Indeed. It was an "obiter dictum", now changed in

> http://primes.utm.edu/glossary/xpage/WieferichPrime.html

> to the converse remark. Neither then nor now should Warren,

> or others, seek to elevate it to a "conjecture" by Chris.

I simply "reported what wikipedia said, and asked about it, in

a concise way."

> I have found Warren's contributions fruitful enough to set

--i am not being "combative." I was being "inquisitive."

> aside his unfortunate tone in communicating them. Yet I am

> still puzzled why he seems to need to be so combative in

YOU, however, are being combative. Right now.

> what is, quite frankly, a place where he should not expect

--look David, you seem to make a habit of complaining about my "tone".

> the type of serious review that he might gain by taking the

> trouble to write up his ideas in an appropriate form for

> scrutiny by a more rigorous mathematical community.

>

> In any case, thanks Warren, for the maths.

>

> David (not a mathematician)

But your usual complaint-method omits actually explaining what the problem is.

In the rare cases where you do explain, such as here... I find it unjustified.

Here, for reference, was my entire damn post, in full, verbatim:

"What is the reasoning behind this conjecture?

(Wikipedia says Caldwell conjectured this.)"

end. full stop. I am satisfied with the answer I got to this enquiry (though I was expecting something deeper :)

Quite frankly, I find it puzzling why David seems to need constantly to be so

worried about others' tone, and/or why -- given that he does feel that need --

he feels the urge to be so mysterious about it when he does so.

Indeed, the very word "tone" is a very mysterious one. Anyhow, let me conjecture

that, similarly to the way some appreciate Beethoven's symphonies, while others who

are "tone deaf" (also called "amusic") hear nothing but somewhat annoying noise --

I do not perceive a vast symphony of something, that apparently is so obvious to David Broadhurst, that he cannot stop complaining about it, but at the same time it is so obvious to him that he sees no reason to actually explain instances.

Perhaps Broadhurst should take this conjecture into account before/during

his issuings of future complaints. I would assume the amusic are annoyed at being subjected to Beethoven, but even more annoyed about being harangued about it by Beethoven-lovers. - --- In primenumbers@yahoogroups.com,

"WarrenS" <warren.wds@...> wrote:

> --look David, you seem to make a habit of complaining about

Twice (on this list) is hardly a habit.

> my "tone".

Phil has done so once:

http://tech.groups.yahoo.com/group/primenumbers/message/24018> You might also consider moderating your tone. I know from

Thanks again, Warren, for the maths, both on-list

> your private e-mails that you find that hard, but can you

> please try harder on-list?

and in your private emails to Phil and me.

David