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2021-11-15, 05:52   #45
Batalov

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

25D116 Posts

Quote:
 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:
Code:
   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)

 2021-11-15, 06:34 #46 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·7·461 Posts CPAP-8 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
 2021-11-15, 07:03 #47 Cybertronic     Jan 2007 Germany 22·107 Posts >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 ! Last fiddled with by Cybertronic on 2021-11-15 at 07:04
2021-11-15, 07:33   #48
Batalov

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

3·7·461 Posts

Quote:
 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.)

 2021-11-15, 08:08 #49 Cybertronic     Jan 2007 Germany 22×107 Posts
 2021-11-20, 06:16 #50 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×7×461 Posts new CPAP-9 record A new CPAP-9 updated record 7661619169627*379#+x153+210*n, n=0..8 (167 digits) where Code: 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.
 2021-11-20, 08:10 #51 Cybertronic     Jan 2007 Germany 1AC16 Posts updated Congratulation Serge ! Site is updated: https://www.pzktupel.de/JensKruseAndersen/CPAP.htm
 2021-11-21, 20:55 #52 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100101110100012 Posts CPAP-7 CPAP-7 proper record: 145706980166212*1069#+x253+210*n, n=2..8 (466 digits)
 2021-11-22, 07:51 #53 Cybertronic     Jan 2007 Germany 1101011002 Posts CPAP7 is updated
 2021-11-26, 14:45 #54 Cybertronic     Jan 2007 Germany 22·107 Posts CPAP - new design 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
 2021-12-01, 09:03 #55 Cybertronic     Jan 2007 Germany 22×107 Posts CC BTW, the overworked page of CC is also online. https://www.pzktupel.de/JensKruseAndersen/cc.htm

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