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

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  • Chris Caldwell
    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
    Message 1 of 8 , Mar 26, 2013
      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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    • Phil Carmody
      ... 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
      Message 2 of 8 , Mar 27, 2013
        --- On Wed, 3/27/13, Chris Caldwell <caldwell@...> wrote:
        > 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."     

        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.

        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
        --
        () ASCII ribbon campaign () Hopeless ribbon campaign
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        [stolen with permission from Daniel B. Cristofani]
      • djbroadhurst
        ... 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
        Message 3 of 8 , Mar 27, 2013
          --- 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 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)
        • WarrenS
          ... --I just saw it in wikipedia, not elsewhere. I did not elevate it, I simply reported what wikipedia said, and asked about it, in a concise way. ...
          Message 4 of 8 , Mar 27, 2013
            --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
            >
            >
            >
            > --- 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 just saw it in wikipedia, not elsewhere. I did not "elevate" it,
            I simply "reported what wikipedia said, and asked about it, in
            a concise way."

            > 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

            --i am not being "combative." I was being "inquisitive."
            YOU, however, are being combative. Right now.

            > 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)

            --look David, you seem to make a habit of complaining about my "tone".
            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.
          • djbroadhurst
            ... Twice (on this list) is hardly a habit. Phil has done so once: http://tech.groups.yahoo.com/group/primenumbers/message/24018 ... Thanks again, Warren, for
            Message 5 of 8 , Mar 28, 2013
              --- In primenumbers@yahoogroups.com,
              "WarrenS" <warren.wds@...> wrote:

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

              Twice (on this list) is hardly a habit.

              Phil has done so once:
              http://tech.groups.yahoo.com/group/primenumbers/message/24018
              > You might also consider moderating your tone. I know from
              > your private e-mails that you find that hard, but can you
              > please try harder on-list?

              Thanks again, Warren, for the maths, both on-list
              and in your private emails to Phil and me.

              David
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