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

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  • Bouk de
    ... 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
    Message 1 of 13 , Jun 1, 2001
      --- Andrey Kulsha <Andrey_601@...> wrote:
      > Hello!
      >
      > This is a complete list of prp's of the form
      > a^b+b^a, where
      > 1<a<b<1001:
      >
      >
      > Does anybody want to prove some of them prime via
      > Titanix?

      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.

      If I had the time I would help you out but to busy
      right now with Lucas and Fibonacci business.

      Bouk.


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    • Nathan Russell
      ... I d have to say (based on my limited knowledge) a LOT of time. A rough mental estimate using logs seems to indicate that some of his numbers are in the
      Message 2 of 13 , Jun 1, 2001
        On Fri, 1 Jun 2001 19:13:07 -0700 (PDT), Bouk wrote:

        >
        >--- Andrey Kulsha <Andrey_601@...> wrote:
        >> Hello!
        >>
        >> This is a complete list of prp's of the form
        >> a^b+b^a, where
        >> 1<a<b<1001:
        >>
        >>
        >> Does anybody want to prove some of them prime via
        >> Titanix?
        >
        >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.

        I'd have to say (based on my limited knowledge) a LOT of time.

        A rough mental estimate using logs seems to indicate that some of his
        numbers are in the range of nine thousand digits (though I could be
        off by a fair amount there). I didn't know such numbers were even
        close to being proveable at present.

        Of course, I might be in error on that.

        Nathan
      • Bouk de
        If I am correct none of the prp s has more than 3000 decimal digits which makes them all provable by Titanix in a sensible amount of time. 9000 digits would
        Message 3 of 13 , Jun 2, 2001
          If I am correct none of the prp's has more than 3000
          decimal digits which makes them all provable by
          Titanix in a sensible amount of time.

          9000 digits would indeed be way too large. Titanix can
          handle such numbers but to prove them would take ages.
          Real ages ;-)

          Bouk.

          --- Nathan Russell <nrussell@...> wrote:
          > On Fri, 1 Jun 2001 19:13:07 -0700 (PDT), Bouk wrote:
          >
          > >
          > >--- Andrey Kulsha <Andrey_601@...> wrote:
          > >> Hello!
          > >>
          > >> This is a complete list of prp's of the form
          > >> a^b+b^a, where
          > >> 1<a<b<1001:
          > >>
          > >>
          > >> Does anybody want to prove some of them prime via
          > >> Titanix?
          > >
          > >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.
          >
          > I'd have to say (based on my limited knowledge) a
          > LOT of time.
          >
          > A rough mental estimate using logs seems to indicate
          > that some of his
          > numbers are in the range of nine thousand digits
          > (though I could be
          > off by a fair amount there). I didn't know such
          > numbers were even
          > close to being proveable at present.
          >
          > Of course, I might be in error on that.
          >
          > Nathan
          >
          > Unsubscribe by an email to:
          > primenumbers-unsubscribe@egroups.com
          > The Prime Pages : http://www.primepages.org
          >
          >
          >
          > Your use of Yahoo! Groups is subject to
          > http://docs.yahoo.com/info/terms/
          >
          >


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        • 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 4 of 13 , Jun 2, 2001
            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
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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 5 of 13 , Jun 2, 2001
              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 6 of 13 , Jun 2, 2001
                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 7 of 13 , Jun 2, 2001
                  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 8 of 13 , Jun 2, 2001
                    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 9 of 13 , Jun 2, 2001
                      > 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 10 of 13 , Jun 2, 2001
                        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 11 of 13 , Jun 2, 2001
                          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 12 of 13 , Jun 4, 2001
                            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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