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Re: a^b+b^a is PRP!

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  • d.broadhurst@open.ac.uk
    ... I forgot to add: if you do not have a code with Titanix in it, ask Chris Caldwell for a c? code, so Marcel get recognized. (c is the first first letter of
    Message 1 of 13 , Jun 2, 2001
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      I wrote:

      > Indeed, folk out there might already have 2k+ digits
      > Tx proofs that they have forgotten to post. If so,
      > just submit the prime with the comment ECPP.

      I forgot to add: if you do not have a code with Titanix
      in it, ask Chris Caldwell for a c? code, so Marcel
      get recognized. (c is the first first letter of Titanix :-)

      David
    • Phil Carmody
      ... Mod? _Mod_? Never has a rocker been so offended! (Yeah, yeah, I know what you meant.) Anyway, I was just curious - I noticed that 3 of the entries in the
      Message 2 of 13 , Jun 2, 2001
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        On Sat, 02 June 2001, d.broadhurst@... wrote:
        > Christ van Willegen wrote:
        > > Select a few large ones, so that I
        > > will be busy for a week or so.
        > Phil the mod might sleep easier on his bus

        Mod? _Mod_? Never has a rocker been so offended!
        (Yeah, yeah, I know what you meant.)

        Anyway, I was just curious - I noticed that 3 of the entries in the a^b+b^a list had a=b+1. Are there any witty decompositions of N-1 which could provide a BLS proof to this case?
        A was able to find the factor b by hand, but are there any others?

        Dues to mystical magical exploding computers I am without Mathematica presently, and unable to do symbolic mathematics!

        (Anyone know of a free symbolic maths tool?)

        I threw the 80/81 number at ECM, and split >33% of it, but that could be pure coincidence!

        Hmmm, back to work :-(

        Phil

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      • Paul Leyland
        ... List deleted. ... I posted to this very forum exactly the same list on Thursday 22nd February under the Subject: Primes and strong pseudoprimes of the
        Message 3 of 13 , Jun 2, 2001
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          > This is a complete list of prp's of the form a^b+b^a, where
          > 1<a<b<1001:

          List deleted.

          > Does anybody want to prove some of them prime via Titanix?

          I posted to this very forum exactly the same list on Thursday 22nd
          February under the Subject: "Primes and strong pseudoprimes of the form
          x^y+y^x". I can repost if wished, but assume that readers know how to
          examine the list archives. That post also included the pair (1015,384).
          Somewhere, still not found but probably on a backup tape, the list
          continues to about 1500 or so.

          Many of the primes were proved by me years ago, and I had two in the
          prime record tables until they were re-catalogued as uninteresting.

          I'd be interested in seeing some of them proved prime --- the ones I
          never got around to completing!


          Paul
        • d.broadhurst@open.ac.uk
          ... Hmm... a^(a-1)+(a-1)^a doesn t look circle cutting (cyclotomic) from here. I think cyclotomy is always a^n-b^n (and if you want the full Monty, set
          Message 4 of 13 , Jun 2, 2001
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            Phil Carmody wrote:

            > I noticed that 3 of the entries in the
            > a^b+b^a list had a=b+1.

            Hmm... a^(a-1)+(a-1)^a doesn't look circle cutting
            (cyclotomic) from here. I think cyclotomy is always
            a^n-b^n (and if you want the full Monty, set
            a=(1+sqrt(5))/2 and b=(1-sqrt(5))/2)
            and divide by a-b=sqrt(5) to get a well known integer)

            David
          • Andrey Kulsha
            Hello! ... for me ... Well, I may prove the numbers which have
            Message 5 of 13 , Jun 2, 2001
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              Hello!

              Christ wan Willegen wrote:

              >I have no prior Titanix experience, but I think it's time
              for me
              >to give it a try...
              >
              >Andrey, I am willing to use my Athlon-800 for a few days
              >to try to prove them. Select a few large ones, so that I
              >will be busy for a week or so. You yourself (or someone
              >else?) can perhaps take the smaller ones.

              Well, I may prove the numbers which have <=1000 digits.

              But:

              Paul Leyland wrote:

              >Many of the primes were proved by me years ago, and I had
              two in the
              >prime record tables until they were re-catalogued as
              uninteresting.

              Paul, please send us a list of primes you have proven, and
              we'll prove all remaining ones.

              I will prove less than 1000 digit numbers, Christ wan
              Willegen, for example, will prove numbers with 1001..2000
              digits, and someone third (maybe Paul Leyland) will prove
              numbers with >2000 digits.

              Note that 1000-digit prime 289^406+406^289 was proven by
              Paul, and then independently by me as the smallest titanic
              prime of such a kind. The primes 342^343+343^342,
              111^322+322^111, 122^333+333^122, 8^69+69^8 was also proven
              by me nearly 5 months ago; 365^444+444^365 was proven by me
              and Marcel Martin (he found a step with record polynomial
              degree of 100) nearly 3 months ago.

              Waiting for comments.

              Best wishes,

              Andrey
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            • Andrey Kulsha
              Hello! OK, I ll prove all remaining prps with less than 1200 digits, i.e.: 8^519+519^8, 20^471+471^20, 5^1036+1036^5, 56^477+477^56, 98^435+435^98,
              Message 6 of 13 , Jun 4, 2001
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                Hello!

                OK, I'll prove all remaining prps with less than 1200
                digits, i.e.:

                8^519+519^8,
                20^471+471^20,
                5^1036+1036^5,
                56^477+477^56,
                98^435+435^98,
                21^782+782^21,
                32^717+717^32,
                365^444+444^365,
                423^436+436^423,
                34^773+773^34.

                Best wishes,

                Andrey
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