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Re: [PrimeNumbers] Re: a^b+b^a is PRP!

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  • Christ van Willegen
    Hi, ... 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
    Message 1 of 13 , Jun 2, 2001
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      Hi,

      > Bouk de wrote:
      >
      > >You might want to try that yourself. You'd
      > >be surprised at the speed at which Titanix
      > >can prove primes with less than 2000 digits.
      > >There are a few larger than that that will
      > >take a little more time.
      >
      > Yes, I know: 2057-digit prime took less than 4 days on
      > Duron-700 with Titanix 2.0.4b, so on Athlon-1200 all these
      > prp's can be proven in 2 weeks or so...
      >
      > But my computer has AMD K6-233 processor... :-(
      >
      > So I think it will be better if someone with faster machine
      > prove them prime. Of course, he will be a 100% prover.

      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.

      Just send me them off-list. I don't know if you have any time
      for coordinating this search, but the list doesn't look overly
      long, so perhaps you'd be able to distribute things
      yourself.

      Regards,

      Christ van Willegen
    • d.broadhurst@open.ac.uk
      ... Phil the mod might sleep easier on his bus if combined efforts resulted in 5 ECPP primes with more than 1905 digits. Then the illegal part of Chris
      Message 2 of 13 , Jun 2, 2001
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        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
        if combined efforts resulted in 5 ECPP primes
        with more than 1905 digits. Then the illegal
        part of Chris Caldwell's database will disappear.

        ECPP top-16:

        (348^1223-1)/347 3106
        (30^1789-1)/29 2642
        (2^7757-1)/233....361 2303
        (((((1361^3+....+894)^3+3636 2285
        (2^7331-1)/458072843161 2196
        Phi(4274,10) 2136
        (2^7039-1)/(125...721) 2074
        100^1013-99^1013 2026
        U(9677) 2023
        V(20460) 2007
        4915416*10^1999+19 2006
        4915416*10^1999+17 2006
        10^1999+7321 2000
        Phi(3927,10) 1920
        (10^1918-7)/3 1918
        'css_descramble.c.gz'*256^211+99 1905

        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.
      • 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 3 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 4 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 5 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 6 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 7 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 8 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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