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?

Yes this is what I used (Thanks to Jens)

> aptreesieve.txt in aptreesieve03.zip says:

> "Version 0.3 can sieve to 10^14."

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