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2022-02-01, 05:26   #67
Cybertronic

Jan 2007
Germany

569 Posts

Quote:
 Originally Posted by Batalov New largest CPAP-5 - 2738129459017*4211#+3399421517+30*n, n=0..4 (1805 digits)

Thank you and congratulations, Serge !
Page is updated.
https://www.pzktupel.de/JensKruseAnd...AP.htm#largest

best
Norman

2022-02-01, 16:17   #68
Dr Sardonicus

Feb 2017
Nowhere

17D416 Posts

Quote:
 Originally Posted by Batalov New largest CPAP-5 - 2738129459017*4211#+3399421517+30*n, n=0..4 (1805 digits)
Fantastic!

It is easily verified using Pari-GP that
1. the number of decimal digits is correct;
2. the indicated numbers are BPSW PRP's;
3. the term in the AP for n = 5 is not a BPSW PRP (and is therefore composite);
4. the term in the AP with n = -1 has the factor 7; and
5. every odd number between the terms of the AP for n = 0 and 4 which is not in the AP has a small prime factor.

[In fact, most of them have a prime factor less than 100. The few remaining numbers with no prime factors less than 100 also have small prime factors, the largest minimal factor being 2557.]

The term in the AP for n = 5 has no prime factors less than 108. But it is composite by the BPSW test.

Last fiddled with by Dr Sardonicus on 2022-02-01 at 20:20 Reason: clarification

 2022-04-12, 00:23 #69 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7×1,427 Posts CPAP-3 updated to 15,004 decimal digits (pre-release) I now updated the "oldest" in this series: CPAP-3 -- to 15,004 decimal digits. Because I am waiting on the formal Primo proofs for the two out of the three, I will post it to UTM Primes around Friday.
 2022-04-16, 07:00 #70 Cybertronic     Jan 2007 Germany 10718 Posts sexy CPAP-3 Congratulation Serge ! Pages are updated. https://www.pzktupel.de/JensKruseAndersen/CPAP.htm Last fiddled with by Cybertronic on 2022-04-16 at 07:01
 2022-04-28, 15:55 #71 Cybertronic     Jan 2007 Germany 569 Posts PAP-4 record Congrats Serge ! https://www.pzktupel.de/JensKruseAnd...ds.htm#records
 2022-05-27, 19:05 #72 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7·1,427 Posts AP-5 at 13338 decimal digits Bumped AP-5 high bar a little bit. https://primes.utm.edu/primes/page.php?id=133987
 2022-05-27, 20:07 #73 Cybertronic     Jan 2007 Germany 569 Posts Congrats Serge !
 2022-06-10, 01:44 #74 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100111000001012 Posts Refreshed AP-7, too: https://primes.utm.edu/primes/page.php?id=134035
 2022-06-10, 10:39 #75 Cybertronic     Jan 2007 Germany 56910 Posts
 2022-07-17, 09:52 #76 Cybertronic     Jan 2007 Germany 569 Posts New AP26 record Today a new AP26 record was found ! https://www.pzktupel.de/JensKruseAnd...ds.htm#records Congratulation to Hans-Jürgen ! Last fiddled with by Cybertronic on 2022-07-17 at 09:53
 2022-09-25, 04:36 #77 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7·1,427 Posts Facelifted AP-4 a little bit: 30083 digits

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