mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > And now for something completely different

Reply
 
Thread Tools
Old 2022-02-01, 05:26   #67
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

569 Posts
Default

Quote:
Originally Posted by Batalov View Post
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
Cybertronic is offline   Reply With Quote
Old 2022-02-01, 16:17   #68
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

17D416 Posts
Default

Quote:
Originally Posted by Batalov View Post
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
Dr Sardonicus is offline   Reply With Quote
Old 2022-04-12, 00:23   #69
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7×1,427 Posts
Plus 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.
Batalov is offline   Reply With Quote
Old 2022-04-16, 07:00   #70
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

10718 Posts
Default 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
Cybertronic is offline   Reply With Quote
Old 2022-04-28, 15:55   #71
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

569 Posts
Default PAP-4 record

Congrats Serge !
https://www.pzktupel.de/JensKruseAnd...ds.htm#records
Cybertronic is offline   Reply With Quote
Old 2022-05-27, 19:05   #72
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·1,427 Posts
Default AP-5 at 13338 decimal digits

Bumped AP-5 high bar a little bit.

https://primes.utm.edu/primes/page.php?id=133987
Batalov is offline   Reply With Quote
Old 2022-05-27, 20:07   #73
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

569 Posts
Thumbs up Congrats Serge !

https://www.pzktupel.de/JensKruseAndersen/aprecords.htm
Cybertronic is offline   Reply With Quote
Old 2022-06-10, 01:44   #74
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100111000001012 Posts
Default

Refreshed AP-7, too:

https://primes.utm.edu/primes/page.php?id=134035
Batalov is offline   Reply With Quote
Old 2022-06-10, 10:39   #75
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

56910 Posts
Thumbs up

Thanks !
https://www.pzktupel.de/JensKruseAndersen/aprecords.htm
Cybertronic is offline   Reply With Quote
Old 2022-07-17, 09:52   #76
Cybertronic
 
Cybertronic's Avatar
 
Jan 2007
Germany

569 Posts
Default 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
Cybertronic is offline   Reply With Quote
Old 2022-09-25, 04:36   #77
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

7·1,427 Posts
Default

Facelifted AP-4 a little bit: 30083 digits
Batalov is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Exponent Progression storm5510 Information & Answers 15 2017-07-26 18:02
Bertrand's Theorem for Arithmetic Progression literka Math 0 2013-06-01 12:42
sieving primes in arithmetic progressions maxal Software 18 2010-10-04 17:11
nth prime number in an arithmetic progression Unregistered Information & Answers 1 2010-04-04 22:06
Arithmetic and Polynomial Progression of Primes? drake2 Math 13 2006-10-10 00:43

All times are UTC. The time now is 02:37.


Mon Dec 5 02:37:17 UTC 2022 up 109 days, 5 mins, 0 users, load averages: 2.52, 2.18, 1.59

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔