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Unsuccessful search for a 7725 digit triplet (corrections) Plus

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  • 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 1 of 2 , Jan 6, 2009
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      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
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