Primes Arithmetic Progression (PAP) and CPAP

[Cybertronic]

http://www.pzktupel.de/JensKruseAndersen/CPAP.htm#news

[Batalov]

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)

[paulunderwood]

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?

[Batalov]

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.

[paulunderwood]

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.

[Batalov]

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.

[Cybertronic]

Congratulation , Serge !
http://www.pzktupel.de/JensKruseAndersen/CPAP.htm#news
______

Norman

[sweety439]

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.

[Batalov]

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* ...

[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]



???

[Batalov]

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 !