## Unsuccessful search for a 7725 digit triplet

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• 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
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

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
• 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
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

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?"

> 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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