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6913-digit AP5

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  • David Broadhurst
    2799788209*16001#/5+1 2813053969*16001#/5+1 2826319729*16001#/5+1 2839585489*16001#/5+1 2852851249*16001#/5+1
    Message 1 of 9 , Jun 23, 2008
      2799788209*16001#/5+1
      2813053969*16001#/5+1
      2826319729*16001#/5+1
      2839585489*16001#/5+1
      2852851249*16001#/5+1
    • Phil Carmody
      Posted by: David Broadhurst ... I know in some of your previous sets, the /5 (or /30, or whatever) has been there to shrink a larger pattern to be the right
      Message 2 of 9 , Jun 24, 2008
        Posted by: "David Broadhurst"
        >
        > 2799788209*16001#/5+1
        > 2813053969*16001#/5+1
        > 2826319729*16001#/5+1
        > 2839585489*16001#/5+1
        > 2852851249*16001#/5+1

        I know in some of your previous sets, the /5 (or /30, or whatever) has been there to shrink a larger pattern to be the right size for a tuplet/CPAP, but I don't see why you've included such a construction here. What would have been wrong with a simple k*p#+1 search?

        Well found, anyway.

        Phil
      • David Broadhurst
        ... Indeed. This was a consolation prize for a failed triplet search. I had 175591 singlets, 540 twins and hence the probability of failure was
        Message 3 of 9 , Jun 24, 2008
          --- In primeform@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:

          > I know in some of your previous sets,
          > the /5 (or /30, or whatever)
          > has been there to shrink a larger pattern to be the
          > right size for a tuplet/CPAP

          Indeed. This was a consolation prize for a failed triplet
          search. I had 175591 singlets, 540 twins and hence the
          probability of failure was

          exp(-540^2/175591) = 19%

          but I drew that short straw. Then I realized that (since I
          had triple sieved) there might be ways of turning this
          failure into an AP5 success. So I took all threesomes of
          the form (a+k*d)*16001#/5+1 for which three of the integers
          k=0,1,2,3,4 had given primes and tested for the two holes,
          which had not been tested in the triplet search, since
          NewPGen had found that the corresponding numbers
          (a+k*d)*16001#/5-1 and/or (a+k*d)*16001#/5+5 were composite.
          In the AP5 the two holes were at k=1 and k=3 and
          have cognate factors that

          pfgw -f -e1000000000

          can quickly recover

          > 2813053969*16001#/5+5 has factors: 25841
          > 2839585489*16001#/5-1 has factors: 572332339

          Thanks for your interest,

          David

          PS: There would have been a tedious ECPP job if the triplet
          search had succeeded.
        • nluhn
          Congratulations to you, David ! Have you try to make a PRP-Test of your 540 twins - k*16001#/5 -5 ? Best wishes Norman
          Message 4 of 9 , Jun 24, 2008
            Congratulations to you, David !

            Have you try to make a PRP-Test of your 540 twins - > k*16001#/5 -5 ?

            Best wishes


            Norman
          • David Broadhurst
            ... Yes Norman, I tried those too, but with no luck: grep fact pfgw.out | wc 190 760 8616 grep comp pfgw.out | wc 350 1750 26767 grep prime
            Message 5 of 9 , Jun 24, 2008
              --- In primeform@yahoogroups.com, "nluhn" <nluhn@...> wrote:

              > k*16001#/5-5

              Yes Norman, I tried those too, but with no luck:

              grep fact pfgw.out | wc
              190 760 8616
              grep comp pfgw.out | wc
              350 1750 26767
              grep prime pfgw.out | wc
              0 0 0

              Here, of course, the prospect of failure is larger

              exp(-exp(Euler)*540*log(16001)/log(10^6913)) = 56%

              as opposed to

              exp(-540^2/175591) = 19%

              for the channel sieved by NewPGen.
              The probability of a double failure was thus

              0.19*0.56 = 11%.

              which quantifies my lack of luck for the triplet search.
              It's a pity that NewPGen doesn't have an option to sieve
              all 4 of the cases k*n#/5 +/- 1 and k*n#/5 +/- 5.
              Then the prospect of success would have been

              1-exp(-2*540^2/175591) = 96.4%

              for this amount of effort.

              How's your 10k-digit search going?
              Do your really expect to use Primo
              at 10k digits, if your find a PRP?

              David
            • nluhn
              ... Good. Up to date, I have found 67 gigantic (k*2^33333 +/- 1 , +5) twins between k=1 and 5000*10^9. I will stop newpgen at p=4*10^14. ... Hm, yes I try it.
              Message 6 of 9 , Jun 24, 2008
                > How's your 10k-digit search going?

                Good.

                Up to date, I have found 67 gigantic (k*2^33333 +/- 1 , +5) twins
                between k=1 and 5000*10^9.

                I will stop newpgen at p=4*10^14.

                > Do your really expect to use Primo
                > at 10k digits, if your find a PRP?

                Hm, yes I try it. I hope my new Phenom system can verify this 10k digit
                number in 6-8 months, but it is a lot of manuell work.

                Norman
              • David Broadhurst
                ... Here s a slightly smaller AP5 668285521*16001#/5+1 1101157031*16001#/5+1 1534028541*16001#/5+1 1966900051*16001#/5+1 2399771561*16001#/5+1 Puzzle for Phil
                Message 7 of 9 , Jun 24, 2008
                  --- In primeform@yahoogroups.com, "David Broadhurst"
                  <d.broadhurst@...> wrote:
                  >
                  > 2799788209*16001#/5+1
                  > 2813053969*16001#/5+1
                  > 2826319729*16001#/5+1
                  > 2839585489*16001#/5+1
                  > 2852851249*16001#/5+1

                  Here's a slightly smaller AP5

                  668285521*16001#/5+1
                  1101157031*16001#/5+1
                  1534028541*16001#/5+1
                  1966900051*16001#/5+1
                  2399771561*16001#/5+1

                  Puzzle for Phil et al:
                  ======================
                  Which were the two NewPGen holes in this case?

                  [Note that I'm not telling you whether pfgw -f
                  is the best way of solving this. How about
                  GMP-ECM, for example? Or some other factoring
                  algorithm? All you know is that at least
                  2 and at most 4 of 10 cognate numbers have a
                  factor found by NewPgen.]

                  David
                • Jens Kruse Andersen
                  ... Congratulations! http://hjem.get2net.dk/jka/math/aprecords.htm is updated. ... I never got around to making a public version of APTreeSieve but if you want
                  Message 8 of 9 , Jun 24, 2008
                    David Broadhurst wrote:
                    > 2799788209*16001#/5+1
                    > 2813053969*16001#/5+1
                    > 2826319729*16001#/5+1
                    > 2839585489*16001#/5+1
                    > 2852851249*16001#/5+1

                    Congratulations!
                    http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

                    > It's a pity that NewPGen doesn't have an option to sieve
                    > all 4 of the cases k*n#/5 +/- 1 and k*n#/5 +/- 5.

                    I never got around to making a public version of APTreeSieve but if you want
                    a Windows DOS-box alpha version with poor user interface and documentation
                    then I could mail it. It can sieve k*a+b+c_i for k < 2^32, any a, b, and as
                    many simultaneous c_i < +/-2^31 as anybody could want. It uses 1 bit per k.
                    There is no option to sieve the first part in different runs and then reduce
                    memory use.

                    --
                    Jens Kruse Andersen
                  • David Broadhurst
                    ... Thanks for the offer, but I ll stick to nix boxes, and leave that Windoze advantage to Ken. David (ever a light siever)
                    Message 9 of 9 , Jun 24, 2008
                      --- In primeform@yahoogroups.com, "Jens Kruse Andersen"
                      <jens.k.a@...> wrote:

                      > I never got around to making a public version of APTreeSieve
                      > but if you want a Windows DOS-box alpha version...

                      Thanks for the offer, but I'll stick to 'nix boxes,
                      and leave that Windoze advantage to Ken.

                      David (ever a light siever)
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