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3-Carmichael

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  • Phil Carmody
    While people are chit-chatting about carmichaels, I shoudl interject that I ve been mucking around with a new algoritm, I came up with the following
    Message 1 of 6 , Nov 14, 2002
      While people are chit-chatting about carmichaels, I shoudl interject that
      I've been mucking around with a new algoritm, I came up with the following
      3-carmichael:

      p1 = 11528154013114759527...62125700268634920611 (10005 digits)
      p2 = 79544262690491840737...86673318535809522091 (10006 digits)
      p3 = 10309064764124217487...75722939056290633011 (10043 digits)
      C = 94533970401090605417...20121377039524326611 (30052 digits)

      It narrowly beats my previous record, because I'm a complete muppet.

      Phil





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    • David Broadhurst
      Congrats on the gigantic^3 Carmichael, Phil! I recall a message along the lines why did you push the Carmichael record up such a small bit when your smart new
      Message 2 of 6 , Nov 14, 2002
        Congrats on the gigantic^3 Carmichael, Phil!

        I recall a message along the lines

        "why did you push the Carmichael record up such
        a small bit when your smart new method could
        have stomped on it?" (as I recall)

        But I would never say a thing like that,
        would I? I wonder who would :-?

        David
      • Phil Carmody
        ... Murky buckets. ... Because I m a complete muppet, and I made a mistake. Fortunately there are enough primes out there for a newtonian random walk to
        Message 3 of 6 , Nov 15, 2002
          --- David Broadhurst <d.broadhurst@...> wrote:
          > Congrats on the gigantic^3 Carmichael, Phil!

          Murky buckets.

          > I recall a message along the lines
          >
          > "why did you push the Carmichael record up such
          > a small bit when your smart new method could
          > have stomped on it?" (as I recall)

          Because I'm a complete muppet, and I made a mistake.
          Fortunately there are enough primes out there for a newtonian
          random walk to eventually find one.

          What I lost in size, I made up for in quantity - I may have
          mis-calculated the heuristics, on top of the 6 I've already
          found, there's a good chance that I'll find another 3 or 4 more
          in my tidy-up over the next few days (bah, my PPro/200 is too
          slow for these things)

          So my advice to everyone is to thrash around randomly, and
          make sure that you get +2.5 sigma results all over the show.
          I can't recommend it highly enough.

          > But I would never say a thing like that,
          > would I? I wonder who would :-?

          Was it the same person who also repeatedly recommends "try a
          miniture one as a proof of concept"?

          Phil


          =====
          I Pledge Allegiance to the flag
          That appears on my Desktop Startup Screen.
          And to the Monopoly for which it Stands:
          One Operating System over all, inescapable,
          With Freedom and Privacy for none. -- Telecommando on /.

          __________________________________________________
          Do you Yahoo!?
          Yahoo! Web Hosting - Let the expert host your site
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        • David Broadhurst
          Phil: How will you secure yourself against someone doing 11k*11k*22k ? Just by winding up to (15k)^3 ? Or can your method produce a decent sized
          Message 4 of 6 , Nov 15, 2002
            Phil: How will you secure yourself against
            someone doing 11k*11k*22k ?
            Just by winding up to (15k)^3 ?
            Or can your method produce a decent sized
            3-Carmichael-factor as well?
            David
            PS: I failed, thus far, to devise
            a sensible 5k*10k*15k method.
            But I sometimes re-ponder it during the
            activity where Jonathan Swift said
            that the best thoughts originate.
          • Phil Carmody
            ... I m currently working on a single PC. To pretend there s anything even approximating security is foolish. Sure, I m now working on a mate s PIII rather
            Message 5 of 6 , Nov 15, 2002
              --- David Broadhurst <d.broadhurst@...> wrote:
              > Phil: How will you secure yourself against
              > someone doing 11k*11k*22k ?

              I'm currently working on a single PC. To pretend there's anything
              even approximating security is foolish.
              Sure, I'm now working on a mate's PIII rather than my PPRo/200,
              but still I don't have the guns to defend myself against the
              Toplics or Underbakkes.

              > Just by winding up to (15k)^3 ?

              I did think about a 15k problem size. I even pre-sieved it.
              I've decided against testing for it, though.

              How far away from mu do you let your results get before you
              decide that your predictions are incorrect? My predictions are
              way out, it's like I've forgotton e^-gamma or something, except
              of course, I haven't.

              That's why I'm doing another small test, smaller than 15k. I
              need more data. The first few bits of data have already started
              to appear, and it's worrying - the density's _wrong_ again.

              Either that of Monsier Poisson's laughing his head off currently.

              > Or can your method produce a decent sized
              > 3-Carmichael-factor as well?

              Have you worked out what the self-effacing muppet comments are about yet?
              I mucked one tiny detail in the maths up. Only slightly, but fatally.
              (hah, that's the first time I've seen a record described as a fatal error!)
              The muck up doesn't explain the deviation from expected density, however,
              which is why I'm still confused.

              > David
              > PS: I failed, thus far, to devise
              > a sensible 5k*10k*15k method.

              Maximal, or just big? Maximal's just a horrid sieve and brute force, as far
              as I can tell.

              I still have several ideas that I've not fully examined, and bumping up the
              size of factor 2 is has some merit, but is at 90 degrees to the philosophy
              of my current method. There are ways to make it work, but whether they
              "work" is different from whether they "work".

              I have more interest in something slightly bizarrer. However, that is so
              off-the-wall that I think it will be a miracle if it works. An exercise in
              cheating!

              > But I sometimes re-ponder it during the
              > activity where Jonathan Swift said
              > that the best thoughts originate.

              In McDonalds?
              http://story.news.yahoo.com/news?tmpl=story2&u=/nm/20021114/od_uk_nm/oukoe_life_sweden_seat&e=5

              Phil


              =====
              I Pledge Allegiance to the flag
              That appears on my Desktop Startup Screen.
              And to the Monopoly for which it Stands:
              One Operating System over all, inescapable,
              With Freedom and Privacy for none. -- Telecommando on /.

              __________________________________________________
              Do you Yahoo!?
              Yahoo! Web Hosting - Let the expert host your site
              http://webhosting.yahoo.com
            • David Broadhurst
              Further to Phil s http://groups.yahoo.com/group/primenumbers/message/9786 I offer http://listserv.nodak.edu/scripts/wa.exe?A2=ind0212&L=nmbrthry&P=R2 which
              Message 6 of 6 , Dec 2, 2002
                Further to Phil's

                http://groups.yahoo.com/group/primenumbers/message/9786

                I offer

                http://listserv.nodak.edu/scripts/wa.exe?A2=ind0212&L=nmbrthry&P=R2

                which record, it is reliably suggested, has a life expectancy of
                only a few weeks. [Readers may recall that Phil has promised
                "vigorous defence" of his Carmichael records.]

                Thanks Phil for the short window of opportunity
                and generous encouragement.

                David
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