Loading ...
Sorry, an error occurred while loading the content.

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

Expand Messages
  • Andrey Kulsha
    Hello! ... 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
    Message 1 of 13 , Jun 2 4:27 AM
    • 0 Attachment
      Hello!

      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.

      Thanks,

      Andrey
      ---------------------------------------------------
      лХТУЩ БОЗМЙКУЛПЗП СЪЩЛБ ОБ нБМШФЕ! дМС ДЕФЕК, РПДТПУФЛПЧ Й ЧЪТПУМЩИ.
      уТЕДЙЪЕНОПНПТШЕ. пУФТПЧ ЛТЕУФПОПУГЕЧ. лТХЗПН ВЙТАЪПЧБС, ЙУЛТСЭБСУС
      ОБ УПМОГЕ ЧПДБ...
      бЗЕОФУФЧП демйху-феттб, ФЕМ (017) 226-56-73, 220-86-71
    • 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 2 of 13 , Jun 2 9:35 AM
      • 0 Attachment
        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 3 of 13 , Jun 2 10:27 AM
        • 0 Attachment
          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 4 of 13 , Jun 2 10:35 AM
          • 0 Attachment
            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 5 of 13 , Jun 2 10:59 AM
            • 0 Attachment
              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

              Mathematics should not have to involve martyrdom;
              Support Eric Weisstein, see http://mathworld.wolfram.com
              Find the best deals on the web at AltaVista Shopping!
              http://www.shopping.altavista.com
            • 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 6 of 13 , Jun 2 11:43 AM
              • 0 Attachment
                > 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 7 of 13 , Jun 2 3:13 PM
                • 0 Attachment
                  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 8 of 13 , Jun 2 3:28 PM
                  • 0 Attachment
                    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
                    ---------------------------------------------------
                    лХТУЩ БОЗМЙКУЛПЗП СЪЩЛБ ОБ нБМШФЕ! дМС ДЕФЕК, РПДТПУФЛПЧ Й ЧЪТПУМЩИ.
                    уТЕДЙЪЕНОПНПТШЕ. пУФТПЧ ЛТЕУФПОПУГЕЧ. лТХЗПН ВЙТАЪПЧБС, ЙУЛТСЭБСУС
                    ОБ УПМОГЕ ЧПДБ...
                    бЗЕОФУФЧП демйху-феттб, ФЕМ (017) 226-56-73, 220-86-71
                  • 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 9 of 13 , Jun 4 4:26 AM
                    • 0 Attachment
                      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
                      --------------------------------------------------
                      13-14 ЙАОС Ч ЛМХВЕ тЕБЛФПТ РТПКДЈФ тЕУРХВМЙЛБОУЛЙК ЖЕУФЙЧБМШ
                      ИХДПЦЕУФЧЕООПК ФБФХЙТПЧЛЙ "SNAKE-TATTOO 2001" У ХЮБУФЙЕН
                      УБМПОПЧ нЙОУЛБ Й вЕМБТХУЙ. уРТБЧЛЙ РП ФЕМ. 232-82-51
                    Your message has been successfully submitted and would be delivered to recipients shortly.