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

Unsuccessful search for a 7725 digit triplet

Expand Messages
  • Ken Davis
    Hi All, Last year I completed an unsuccessful search for a 7725 digit triplet (CPAP3). I did 2 searches using numbers of the form
    Message 1 of 2 , Jan 6, 2009
    • 0 Attachment
      Hi All,

      Last year I completed an unsuccessful search for a 7725 digit triplet
      (CPAP3).
      I did 2 searches using numbers of the form
      ((n*35+11)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+x
      and
      ((n*35+31)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+x

      0 <= n <= 2^32, x = 1,5,7,11,13

      For the 11 form I sieved to 4e12 for x = 1,5,7,11,13
      I then tested the form

      ((n*35+11)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+7

      for the remaining 10765642 n which yielded 31281 prps

      I then tested these with x=1,5,11,13 and got 349 pairs but no triples.


      For the 31 form I sieved to 4e12 for x = 1,5,7,11,13
      I then tested the form

      ((n*35+11)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+7

      for the remaining 10765642 n whic yielded 31281 prps
      I then tested these with x=1,5,11,13 and got 349 pairs but no triples.

      For the secon search I changed my sieving strategy and sieved
      to 1e12 for x=1,5,11,13 and 5.11e14 for x=7
      This time I did 12595886 prp yielding 36660 prs and 416 pairs

      But again, sadly, no triples.

      Before I have a another go, at something similr, I have a question.
      Was I just unlucky is there some underlying mathematical reason for
      my lack of success?

      Cheers
      Ken
    • Ken Davis
      Hi all, Jens Anderson, in a personal email, kindly pointed out a number of errors in my original post so here it is again corrected. Last year I completed an
      Message 2 of 2 , Jan 6, 2009
      • 0 Attachment
        Hi all,

        Jens Anderson, in a personal email, kindly pointed out a number of
        errors in my original post so here it is again corrected.

        "Last year I completed an unsuccessful search for a 7725 digit
        triplet (CPAP3).
        I did 2 searches using numbers of the form ((n*35+11)*328963*6011#*
        (328963*6011#+1)+210)*(328963*6011#-1)/35+x
        and
        ((n*35+31)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+x

        0 <= n <= 2^32, x = 1,5,7,11,13

        For the 11 form I sieved to 4e12 for x = 1,5,7,11,13 I then tested
        the form

        ((n*35+11)*328963*6011#*(328963*6011#+1)+210)*(328963*6011#-1)/35+7

        for the remaining 10765642 n which yielded 31281 prps

        I then tested these with x=1,5,11,13 and got 349 pairs but no triples.

        For the second search I changed my sieving strategy and sieved to
        1e12 for x=1,5,11,13 and 5.84e12 for x=7 This time I did 12595886 prp
        yielding 36660 prs and 416 pairs

        But again, sadly, no triples.

        Before I have another go, at something similar, I have a question.
        Was I just unlucky is there some underlying mathematical reason for
        my lack of success?"

        In addition Jens asked a couple of questions

        > Do I include the useless (1,7,11) and (5,7,13) are also counted as
        triples.

        Yes. Neither search got any combination of 3 prps.

        > Did you use APTreeSieve?
        > aptreesieve.txt in aptreesieve03.zip says:
        > "Version 0.3 can sieve to 10^14."

        Yes this is what I used (Thanks to Jens)
        Call log for the 31 search being
        Wed Apr 09 15:15:39 2008
        aptreesievep4 -e1000000000000 -j0 -k4294967295 -c1,5,7,11,13
        Sun Apr 13 23:21:26 2008
        aptreesievep4 -s1000000000000 -e10000000000000 -j0 -k4294967295 -c7
        Tue Apr 15 21:37:47 2008
        aptreesievep4 -s1570000000000 -e10000000000000 -j0 -k4294967295 -c7
        Sun Apr 27 11:26:16 2008
        aptreesievep4 -s5110000000000 -e10000000000000 -j0 -k4294967295 -c7

        The restarts being due to unexpected pc outages.
        > I guess your pairs were roughly evenly distributed between 1, 5,
        11, 13. If
        > so, then each of them occurred approximately the expected number of
        times
        > and everything points to just being unlucky by not getting two of
        them at
        > the same time. If they are very unevenly distributed between 1, 5,
        11, 13
        > then it could be a sign of an error in the sieve. I'm not aware of
        such an
        > error in APTreeSieve.

        +11 distribution = 92 76 89 92
        +31 distribution = 101 109 102 103

        Based on the above I will go with Jens' conclusion that

        > If there were two searches with respectively 20.5% and 18.6% risk
        of 0
        > triples then the risk of 0 triples after both searches is 3.8%.

        It appears I was unlucky!

        Any suggestion for optimal sieving for my next attempt would be
        appreciated.

        Cheers
        Ken
      Your message has been successfully submitted and would be delivered to recipients shortly.