Primes Arithmetic Progression (PAP) and CPAP

[Batalov]

Originally Posted by 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* ...

I have 5 more of these, which I will not report.
I only need ~20 to hit CPAP-8.

The pyramid constant for this form with a certain level of sieving is 20.
Pyramid goes like this: you test candidates, 1/20 of them yields hits of 1st order, 1/20² of them yields hits of 2nd order, etc... (each level is ~1/20)
Currently:

   53367736  ..6937
    2664600  ..7147
     132644  ..7357
       6621  ..7567
        309  ..7777
         24  ..7987 --> 1/20 of these can have a hit at ..6727 (i.e. CPAP-7)
          1  ..8197 --> CPAP-7, 1/20 of these can have a hit at ..6727 (i.e. CPAP-8)
          0  ..8417 --> CPAP-8, 1/20 of these can have a hit at ..6727 (i.e. CPAP-9)

[Batalov]

CPAP-8 is found [early, actually] (also improves CPAP-7):

8081110034864*619#+x253+210*n, n=1..8 (272 digits)

CPAP-7 new record is (interim): 8081110034864*619#+x253+210*n, n=2..8

[Cybertronic]

>Define B1 !
B1=1
I know, there a not all 100% composite but it is possible that k*1261#/2154317507668859+d,d=0,....1260 the only 7 primes.


I wish I had your CPU-park, Serge !

[Batalov]

Originally Posted by Cybertronic

>Define B1 !
B1=1
I know, there a not all 100% composite but it is possible that k*1261#/2154317507668859+d,d=0,....1260 the only 7 primes.

The probability is damn near zero, my man. You will spend too much bandwidth finding tons of quasi-CPAPs only to find that they have an intermingling prime between them which will negate the find.

That's why the construction of those x99, x253 and xOther addends is genial (they remove all that guess work), and "my"* x10 for CPAP-4-6 is also quite good (*I am pretty sure that I only "re"discovered it. I did put it to good practical use though.)

[Cybertronic]

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

[Batalov]

A new CPAP-9 updated record

7661619169627*379#+x153+210*n, n=0..8 (167 digits)

where

x153=965638364011503965472274037609810695853057694474510858763504060537115782698320398681243637298572057965220341992180981784112973206136355565433981118807417

Well, -- it would be no surprise that x153 = x253 % 379#.
This is not perfect for CPAP-9; you have to go small so the modulo leaves sacrifices in the sequence of [N .. N+1680]; note that the perfect presieved x253 has no sacrificed holes. x153 leaves 30 holes so you have to work for a while so that no intermingling primes creep in the 30 holes ... but the stats is on our side. You search for a while and you find one.

Next stop: updated CPAP-10.

[Cybertronic]

Congratulation Serge !
Site is updated: https://www.pzktupel.de/JensKruseAndersen/CPAP.htm

[Batalov]

CPAP-7 proper record:

145706980166212*1069#+x253+210*n, n=2..8 (466 digits)

[Cybertronic]

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

[Cybertronic]

Also I have now refreshed the CPAP-site.
It is more compact and CPAP-k history have more than 10 now.


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


regards
Norman

[Cybertronic]

BTW, the overworked page of CC is also online.
https://www.pzktupel.de/JensKruseAndersen/cc.htm