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Factorizations of near-repdigit-related numbers

Table of contents

  1. Introduction
  2. How to contribute your factors ▶
  3. Wanted list ▶
  4. Reserved numbers and submitted numbers ▶
  5. Contributions ▶
  6. Records ▶
  7. Graphs ▶
  8. News
  9. Contributors
  10. Factor tables
  11. List of near-repdigit-related prime numbers
  12. Primality certifications ▶
  13. Expression generator of near-repdigit-related numbers ▶
  14. Related links ▶

1. Introduction

We are collecting prime factorizations of near-repdigit-related numbers and near-repdigit-related prime numbers.

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.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
19742542111121w(19·1074253-1)/9February 4, 2012Ray 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.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
303102972111121w(19·1010296-1)/9February 2, 2012Markus 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

12. Primality certifications ▶

13. Expression generator of near-repdigit-related numbers ▶

14. Related links ▶