Factorizations of near-repdigit-related numbers
Table of contents
- Introduction
- How to contribute your factors ▶
- Wanted list ▶
- Reserved numbers and submitted numbers ▶
- Contributions ▶
- Records ▶
- Graphs ▶
- News
- Contributors
- Factor tables
- List of near-repdigit-related prime numbers
- Primality certifications ▶
- Expression generator of near-repdigit-related numbers ▶
- Related links ▶
1. Introduction
We are collecting prime factorizations of near-repdigit-related numbers and near-repdigit-related prime numbers.
- Near-repdigit-related numbers
- Repunit numbers (all digits are the same; 11...11)
- Near-repdigit numbers (all but one digit are the same; AA...AAB, ABB...BB, etc)
- Near-repdigit-palindrome numbers (near-repdigit and palindrome; AA...AABAA...AA)
- Quasi-repdigit numbers (all but two digits are the same; ABB...BBC, etc)
- Plateau-and-depression numbers (ABB...BBA)
- others (all but three or more digits are the same)
2. How to contribute your factors ▶
3. Wanted list ▶
4. Reserved numbers and submitted numbers ▶
5. Contributions ▶
6. Records ▶
7. Graphs ▶
8. News
February 7, 2012
Factorizations of 799...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.
February 5, 2012
Factorizations of 755...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.
February 4, 2012
Ray Chandler found an 74254-digit unprovable near-repdigit PRP of the form 21w.
| digits | flabel | wlabel | expression | when | who | |
|---|---|---|---|---|---|---|
| 19 | 74254 | 21111 | 21w | (19·1074253-1)/9 | February 4, 2012 | Ray Chandler |
February 2, 2012
Factorizations of 33...33733...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.
Markus Tervooren proved the primality of a 10297-digit near-repdigit number (19·1010296-1)/9 by Primo.
| digits | flabel | wlabel | expression | when | who | |
|---|---|---|---|---|---|---|
| 303 | 10297 | 21111 | 21w | (19·1010296-1)/9 | February 2, 2012 | Markus Tervooren |
Factorizations of 55...553 have been extended up to n=250 by Serge Batalov. Added composite numbers had passed ECM iterations 530 times at the level 30. Most unknown factors are supposed to be greater than 1030.
News of 2012 ▶
News of 2011 ▶
News of 2010 ▶
9. Contributors
I am thankful to contributors 10metreh, [AF>France] intello222222, [AF>Le_Pommier>MacBidouille.com]m.o.u.s.t.i.c, [boinc.at] Fireman69, [GPU Force] Robert 7NBI, [SG]marodeur6, [TiDC] Chulma, [XTBA>TSA] IvanleFou, [XTBA>TSA]+IvanleFou, Agnew yoyo, Alessandro Freda, Alexander Mkrtychyan, Alfred Reich, Andreas Tete, Anton Korobeynikov, Bart Jans, bbd in ep, bbmz, Beyond, Bob Price, Bouk de Water, Bryan Koen, bundaboy, Carlos Pinho, Cedric Vonck, centylion torun, Chris Monico, Christopher Birkbeck, Crunchers For More Power, David Broadhurst, Dennis Bertels, Dmitry Domanov, ERBrouwer, Erik Branger, Familie, Frank Villasenor, G.L.I.S., GRB IV, Greg Childers, Grubix, Ha Seok woo, honeycrack7, Hugo Platzer, Ignacio Santos, Jamoko, Jan Ptacek, jdommer, Jeff Gilchrist, Jeff17, Jens, JMB, Jo Yeong Uk, Joshua2, JPascoa, Julien Peter Benney, juno1369, Justin Card, K, Maemondo, Kenichiro Yamaguchi, Kenji Ibusuki, Lazarusuk, Lionel Debroux, Luigi Morelli, Makoto Kamada, Makso, Maksym Voznyy, MarcinGorecki, Markus Tervooren, matsui, Max Dettweiler, mia7077, Michael Peterson, Michael Rao, mikkovi, Mitchell, Mr. Hankey, Naoki Yamamoto, Nechaev Sergey, nenym, Nicolai Caraibendko, Norbert Schneider, Patrick Keller, Phil Carmody, Philippe Strohl, Pipao, Polybius, processing-home, Raffi Chaglassian, Ray Chandler, RAZIELakaALIN, Rich Dickerson, rkillian, Robert Backstrom, RSALS, ruffenach timothee, Samuel Chong, Sander Hoogendoorn, Sean A. Irvine, Serge Batalov, Shaopu Lin, shauge, shima@engei, Shusuke Kubota, shyguy7129, Sinkiti Sibata, skneo, steinrar, stelf, suberi, Takahiro Nohara, Tetsuya Kobayashi, Thomas Womack, Tomoya Adachi, toms83, ToolboxNL, Tyler Cadigan, UA_ReMMeR, VictordeHollander, Warut Roonguthai, Wataru Sakai, Wojciech Florek, Yang Hae Hun, Yoichi Hanatani, yoshida, yoyo and Zeta-Flux.
10. Factor tables
Repunit numbers ▶
Near-repdigit numbers of the form AA...AAB ▶
Near-repdigit numbers of the form ABB...BB ▶
Near-repdigit palindrome numbers of the form AA...AABAA...AA ▶
Plateau and depression numbers of the form ABB...BBA ▶
Quasi-repdigit numbers of the form ABB...BBC ▶
11. List of near-repdigit-related prime numbers
- primesize.txt (primesize.zip) sorted by size, 100 digits or more
Example 1: "88881 8w1 (8*10^27811-71)/9 -33.00%_7334" means that the ratio of the factored part of (8·1027811-71)/9-1 is 33.00% and the largest known (probable) prime factor of (8·1027811-71)/9-1 is a 7334-digit number. In other words, to prove the primality of (8·1027811-71)/9, you have to prove primality of the 7334-digit number by ECPP and use N-1/N+1 test with Konyagin-Pomerance extension.
Command line to find PRPs for N-1/N+1/KP/CHG:
grep "\(2[5-9]\|[3-9][0-9]\|100\)\.[0-9][0-9]%" primesize.txt
Example 2: "71111 71w (64*10^83461-1)/9 -1:1:2:2" means that (64·1083461-1)/9-1 is factored algebraically into four parts. In fact, (64·1083461-1)/9-1 = 10·(2·1013910+1)/3·(2·1013910-1)·(4·1027820-2·1013910+1)/3·(4·1027820+2·1013910+1). Such numbers may be easily factored than other numbers.
Example 3: "37773 37w3 (34*10^15768-43)/9 +proven@7884" means that the primality of (34·1015768-43)/9 was proved by N-1/N+1 test with ECPP certification of a prime cofactor of Phi7884(10). See Primality certifications page. - primecount.txt, primecount2.txt and primecount3.txt sorted by count
- primedifficulty.txt sorted by difficulty