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 2021-11-07, 06:16 #34 Cybertronic     Jan 2007 Germany 1DE16 Posts updated
2021-11-13, 23:16   #35
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·23·61 Posts

Quote:
 Originally Posted by Batalov And, to warm up, -- a small update to CPAP-6 (this is too small for PrimePages; working on larger size now...) 357807940468*1361#+3399421517+30*n, n=0..5 (581 digits)
And now, --a proper CPAP-6 record for 2021.

533098369554*2357#+3399421517+30*n, n=0..5 (1012 digits)

2021-11-13, 23:23   #36
paulunderwood

Sep 2002
Database er0rr

10000000101012 Posts

Quote:
 Originally Posted by Batalov And now, --a proper CPAP-6 record for 2021. 533098369554*2357#+3399421517+30*n, n=0..5 (1012 digits)
Very nice! Did you use a lot of cycles sieving and PRP'ing?

2021-11-13, 23:58   #37
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·23·61 Posts

Quote:
 Originally Posted by paulunderwood Very nice! Did you use a lot of cycles sieving and PRP'ing?
~3000 core-days for testing and ~100 core days for sieving with custom sieve.

I am thinking about merging sieve with PFGW some time later (for larger CPAPs), or else the sieved files are wasting rather large disk space (even though I use the ABCD format).
TL;DR: Larger CPAPs actually require quite a different approach as well.

For CPAP-4 through CPAP-6, this form with carefully chosen A=3399421517, k*p# ± (A+30*n) is a nearly guaranteed hit sequence (in appropriate limits, i.e. p<9929), except for one composite to test (with 3399421549). But with higher forms, k*p# ± (C+210*n), it is easy to obtain 7 or 8 primes but a fat subset of intermediates will also have a chance of being prime. Interesting "minimax-type" challenge.

2021-11-14, 00:06   #38
paulunderwood

Sep 2002
Database er0rr

23·179 Posts

Quote:
 Originally Posted by Batalov ~3000 core-days for testing and ~100 core days for sieving with custom sieve. I am thinking about merging sieve with PFGW some time later (for larger CPAPs), or else the sieved files are wasting rather large disk space (even though I use the ABCD format). TL;DR: Larger CPAPs actually require quite a different approach as well. For CPAP-4 through CPAP-6, this form with carefully chosen A=3399421517 k*p# ± (A+30*n) is a nearly guaranteed hit sequence (in appropriate limits, i.e. p<9929), except for one composite to test (with 3399421549). But with higher forms, k*p# ± (C+210*n) is easy to obtain 7 or 8 primes but a fat subset of intermediates will also have a chance of being prime. Interesting "minimax-type" challenge.
The same reasoning why a CPAP-11 has yet to be found: https://en.wikipedia.org/wiki/Primes...ic_progression

I found precomputing the primorial shaved off ~8% of PRP'ing when I ran AP8. You need GWNUM skilz for it.

Last fiddled with by paulunderwood on 2021-11-14 at 00:08

2021-11-14, 00:37   #39
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·23·61 Posts

Quote:
 Originally Posted by paulunderwood The same reasoning why a CPAP-11 has yet to be found: https://en.wikipedia.org/wiki/Primes...ic_progression
Of course.

 2021-11-14, 04:23 #40 Cybertronic     Jan 2007 Germany 2·239 Posts is updated Congratulation , Serge ! http://www.pzktupel.de/JensKruseAndersen/CPAP.htm#news ______ Norman Last fiddled with by Cybertronic on 2021-11-14 at 04:30
2021-11-14, 06:11   #41
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

64568 Posts

Quote:
 Originally Posted by paulunderwood The same reasoning why a CPAP-11 has yet to be found: https://en.wikipedia.org/wiki/Primes...ic_progression I found precomputing the primorial shaved off ~8% of PRP'ing when I ran AP8. You need GWNUM skilz for it.
If Dickson conjecture is true, then there are infinitely many CPAP-11, and Dickson conjecture is believed to be true.

 2021-11-15, 02:20 #42 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100110010111012 Posts CPAP-7 And, to warm up, -- a small update to CPAP-7 (leading to possible CPAP-8 and/or CPAP-9): 2022541154997*619#+x253+210*n, n=0..6 (271 digits) Don't ask about intermediates. They are all sieved out. But you can check: replace 210* by 2* ...
 2021-11-15, 04:19 #43 Cybertronic     Jan 2007 Germany 2·239 Posts is updated Is there a chance to find a CPAP-7 without a big constant ,like this: k*1261#/2154317507668859 + B1+d,d=0,210,...1260 [>500 digits] ??? Last fiddled with by Cybertronic on 2021-11-15 at 04:31
2021-11-15, 05:44   #44
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·23·61 Posts

Quote:
 Originally Posted by Cybertronic Is there a chance to find a CPAP-7 without a big constant ,like this: k*1261#/2154317507668859 + B1+d,d=0,210,...1260 [>500 digits]
Define B1 !

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