Factorizations of repunit numbers of the form (10n-1)/9 (111111...)


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News

-  Last update: Mar 30, 2023 

- Found by Kurt Beschorner  
   Mar 30, 2023   n = 1409: 1658972136253211819285181026106657071203;               ecm: B1 =11e6; sigma = 0:7137899537840100
   Mar 30, 2023   n = 7713: 169080936973198939009695188449;                         ecm: B1 = 1e6; sigma = 8231107386027428 


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Mar 30, 2023   R942/c209: SNFS-difficulty = 314 
                  490M unique raw relations of 1250M are collected
                  currently progress 39.2 %;    
  				  
  
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Mar 30, 2023  - R1340L/c265: SNFS-difficult = 268; degree 8
                 - 691.4M unique r. relations and 610.3 unique ideals are collected
                 - msieve filtering: well done
                 - matrix is 65.7M x 65.7M with weight 7818384770 (118.98/col)  
                 - linear algebra completed 57380000 dimensions of 65.7M dim. (87.3%; estimated time of arrival 400 hours)   


- Found by Kurt Beschorner  
   Mar 26, 2023   n = 5925: 43863025793294149274559220201;                          ecm: B1 = 3e6; sigma = 4922290324811982
   Mar 26, 2023   n =12192: 469162401428727267767039337537134113;                   P-1: B1 =12e7 

- Found by Kurt Beschorner  
   Mar 19, 2023   n =12207: 10326528166018797350437  * 1715045130......c7454;       P-1: B1 =25e6 
   Mar 19, 2023   n =12213: 763235932545359903065517911  *  2819581486......c7565;  P-1: B1 =25e6 
   Mar 19, 2023   n =12235: 601591258998676485551127873393824231 * 2595076444......c9736; P-1: B1 =32e6 
   Mar 19, 2023   n =12261: 37955669373027254564443249 * 1482911212......c7840;     P-1: B1 =40e6 
   Mar 19, 2023   n =12265: 1813958675305432752569322631  * 4800373524......c8813;  P-1: B1 =36e6 
   Mar 19, 2023   n =12267: 18405350080498464623296129  * 4840124705......c7696;    P-1: B1 =47e6 
   Mar 19, 2023   n =12299: 22125123861628175114991691769399 * 4891881550......c10437; P-1: B1 =28e6 
   Mar 19, 2023   n=145381: 2814792192994658867 * 2189685857......c145354;          gr-mfaktc   
   

- Found by Kurt Beschorner  
   Mar 16, 2023   n =12163: 496260125167000972637979481 * 6088164284......c12112;   P-1: B1 =25e6 
   Mar 16, 2023   n =12197: 10004791369113378925808671 * 1125672810......c12139;    P-1: B1 =25e6 


- via factordb.com   
   Mar 16, 2023   n =12124: 2139064861096863878756665012801 * 4721689455......c5154 


- Found by Kurt Beschorner  
   Mar 11, 2023   n = 7671: 674395585663400091968059519;                            ecm: B1 = 1e6; sigma = 3409682457607698
   Mar 11, 2023   n =12032: 92983911220947001823535969927169 * 4585704060......c5799;    P-1: B1 =60e6 
   Mar 11, 2023   n =12049: 3372749981360027032747859544183787 * 2578564574......c12005; P-1: B1 =20e6 
   Mar 11, 2023   n =12067: 89906797410807096964226575517 * 7161228750......c10898;      P-1: B1 =25e6 
   Mar 11, 2023   n =12281:  248827112460081163452938551 * 4465394064......c12254;       P-1: B1 =25e6 

 
- Found by Kurt Beschorner   
   Mar 07, 2023   n = 5477: 4679405672910425988720134731403;                        ecm: B1 = 1e6; sigma = 0:3115122745024891
   Mar 07, 2023   n = 5479: 1175364770706692672051045921;                           ecm: B1 = 1e6; sigma = 0:1144629584039427 
   Mar 07, 2023   n =12520: 4068220734739164961413104154881 * 1710302891......c4952; P-1: B1 =60e6 
   Mar 07, 2023   n =12521: 769774332048986028482292393529 * 1169173824......c11815; P-1: B1 =22e6 
   Mar 07, 2023   n=144379: 1699316036580040519;                                    gr-mfaktc
   Mar 07, 2023   n=144427: 763086575042246237;                                     gr-mfaktc

 
- Found by anonymous   
   Mar 02, 2023   n =  535: 5524033451004407234027306056468463430580799351;         ecm: B1 =11e6; sigma = 18425523954857577889 


- Found by Kurt Beschorner   
   Feb 27, 2023   n = 1401: 58268747277891114808753379164057926641266957;           ecm: B1 =43e6; sigma = 0:6490871995892487 
   Feb 27, 2023   n = 5443: 443994631081204304270374441813;                         ecm: B1 = 1e6; sigma = 0:5948351044689566 
   Feb 27, 2023   n=144259: 76455980665279759;                                      gr-mfaktc
   Feb 27, 2023   n=144323: 172755778190621357;                                     gr-mfaktc

-  Found by Alfred Eichhorn 
   Feb 27, 2023   n =66067: 170472935791113746723 * 6517815311......c66046;         ecm: B1 = 5e4; sigma = 3477637411662594



- Found by Kurt Beschorner   
   Feb 21, 2023   n =4700L: 11808992310281998733369892724417205617004114801;        ecm: B1 =43e6; sigma = 0:7170719374266148 

 
- Found by YOYO@home/George Bradshaw   
   Feb 20, 2023   n =2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 * 1142522103......P220; ecm: B1 = 2.9e9    


   Feb 19, 2023   n = 5539: 1893231723717766314342428938609;                        ecm: B1 = 1e6; sigma = 0:7066187404725017
   Feb 19, 2023   n=143981: 2321713302266455397;                                    gr-mfaktc


-  Found by Alfred Eichhorn 
   Feb 13, 2023   n =85661: 6614343997747250116357 * 5117655327......c85621;        ecm: B1 = 5e4; sigma = 6480425124612577
   Feb 13, 2023   n =85717: 425606074726924486880292881 * 2610656137......c85690;   ecm: B1 = 5e4; sigma = 3051452821892657


- Found by Kurt Beschorner   
   Feb 13, 2023   n=143791: 1345704687193284449;                                    gr-mfaktc
   Feb 13, 2023   n=143873: 13969422389289652231;                                   gr-mfaktc
				  

- Found by Kurt Beschorner   
   Feb 06, 2023   n = 5393: 475100434323400295514257533;                            ecm: B1 = 1e6; sigma = 0:6611271429378146
   Feb 06, 2023   n=143413: 1308539818288185547;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Jan 27, 2023   n = 5387: 9695327619043500745964526925561 * 2796548747......P5266; ecm: B1 = 1e6; sigma = 0:7981023013264326

				  
- Found by Kurt Beschorner   
   Jan 22, 2023   n = 6515: 3767892910446507496334403721;                           ecm: B1 = 1e6; sigma = 3731867255296034
   Jan 22, 2023   n=143159: 2036663968824321689;                                    gr-mfaktc

				  
-  Found by Alfred Eichhorn 
   Jan 22, 2023   n =48767: 1167442730202131101408241;                              ecm: B1 = 5e4; sigma = 8294335290315311
   Jan 22, 2023   n =48809: 1374219663422487935701343573;                           ecm: B1 = 5e4; sigma = 3897725353774069
   Jan 22, 2023   n =65701: 119577379525448930631404597329;                         ecm: B1 = 5e4; sigma = 2055672717664719 
   

- via factordb.com   
   Jan 22, 2023   n =10216: 5409058353794643031157855569;                           ecm 


- Found by YOYO@home/user69   
   Jan 14, 2023   n = 1104: 22651858853653655359251914860948647902217772389947313979551649; ecm: B1 = 29e8; sigma = 0:17929758445905874757


- Found by Kurt Beschorner   
   Jan 08, 2023   n = 1427: 5103036982727761098957792950596409693 * 2786241011......P1380; ecm: B1 =11e6; sigma = 5634177607918577
   Jan 08, 2023   n=142871: 284235246048470947;                                     gr-mfaktc
   Jan 08, 2023   n=200100L: 180218186261101;                                       ecm: B1 = 5e4  
   Jan 08, 2023   n=200100L: 936682576624695001;                                    ecm: B1 = 5e4 
   Jan 08, 2023   n=200100L: 18748796798446051801;                                  ecm: B1 = 5e4; sigma = 0:15615885390781000624 
 

- Found by Kurt Beschorner   
   Jan 04, 2023   n = 1411: 3094716767820821084333461991848123;                     ecm: B1 =11e6; sigma = 0:1262114500939137
   Jan 04, 2023   n=142711: 4728660163685159483;                                    gr-mfaktc


- Found by YOYO@home/code740   
   Dec 29, 2022   n =  573: 8571171562010649843819977618730389789759904896874763 * P281; ecm: B1 = 85e7; sigma = 0:2075739498551464677
    

- Found by Makoto Kamada   
   Dec 26, 2022   n=262767: 10^262767-1)/((10^87589-1) * 111 * 259613797) = 3470158024......p175168 is probable prime    
                  see: http://www.primenumbers.net/prptop/prptop.php/prptop.php?page=8#haut: rank 1828 
				  

-  Found by Alfred Eichhorn 
   Dec 23, 2022   n =48539: 51815542479681876910933;                                ecm: B1 = 5e4; sigma = 452523639394007
   Dec 23, 2022   n =65419: 6950583483619562342590824241;                           ecm: B1 = 5e4; sigma = 7199896427566567
   Dec 23, 2022   n =84421: 38512525260957891101711;                                ecm: B1 = 5e4; sigma = 2290092539869875
   Dec 23, 2022   n =84467: 543506603324001612634763;                               ecm: B1 = 5e4; sigma = 1063663203889283


- Found by Kurt Beschorner   
   Dec 23, 2022   n = 5603: 292306358313079003551478311632597;                      ecm: B1 = 1e6; sigma = 0:926444492212831
   Dec 23, 2022   n=142169: 7126599804959124533;                                    gr-mfaktc

 -  Found by Yousuke Koide    
   Dec 20, 2022   n =1940M: 5571625642084498030602199756991965375293044719417529765342701; ecm: B1 = 3e8; sigma = 2:13803433046389983180


- Found by YOYO@home/grc.arikado.pool   
   Dec 17, 2022   n =  537: 2167451486375064397900184401899510260456269195385135677227157; ecm: B1 = 85e7; sigma = 0:5910846903816997764 
 

- Found by Kurt Beschorner   
   Dec 15, 2022   n = 1381: 71236855295678591990160932434313161;                    ecm: B1 =11e6; sigma = 6012605352570225 

- Found by Kurt Beschorner   
   Dec 13, 2022   n = 1315: 193413247904674241324507425343532732791 * 4212288434......P915; ecm: B1 =43e6; sigma = 0:7414637162882108
   
				 
- Found by Kurt Beschorner   

   Dec 10, 2022   n = 5209: 8418644810171006628494387152481;                        ecm: B1 = 1e6; sigma = 0:7909834062803979
   Dec 10, 2022   n = 5251: 109300163867965785141575385067;                         ecm: B1 = 1e6; sigma = 0:344522311621080
   Dec 10, 2022   n=141961: 444022226548698437;                                     gr-mfaktc

 
- Found by YOYO@home/Adrian Westlake   
   Dec 06, 2022   n = 1212: 10498042566741901780282937616325375954902715561 * 2002446477......P276; ecm: B1 = 85e7; sigma = 0:3738033742963211035  


 -  Found by Yousuke Koide    
   Dec 04, 2022   n =  880: 62716385987763617906038889384985304875217698799039986699716641; ecm: B1 = 3e8; sigma = 2:10560429264819151247

			  
-  Found by Alfred Eichhorn 
   Dec 02, 2022   n = 65257: 29021845406574177689182183471831;                      ecm: B1 = 5e4; sigma = 8827912087270031
   Dec 02, 2022   n = 65267: 196872763596771607155929;                              ecm: B1 = 5e4; sigma = 5907651863350580
   Dec 02, 2022   n = 65419: 77658403478600955160498507;                            ecm: B1 = 5e4; sigma = 5773479858856831
   Dec 02, 2022   n = 83903: 1072388632041797323856413;                             ecm: B1 = 5e4; sigma = 3013216190367338
   Dec 02, 2022   n = 83921: 935916352185237988152529;                              ecm: B1 = 5e4; sigma = 2096569748642875
   Dec 02, 2022   n = 83987: 971921165004064866353773;                              ecm: B1 = 5e4; sigma = 2917559887380640


ECM efforts
with Rn:           1 < n < 2000 (Mar 30, 2023) with Rn:     1999 < n < 3000 (Feb 27, 2023)
with Rn:     2999 < n < 4000 (Feb 04, 2023) with Rn:     3999 < n < 5000 (Feb 27, 2023)
with Rn:     4999 < n < 6000 (Mar 26, 2023) with Rn:     5999 < n < 7000 (Feb 27, 2023)
with Rn:     6999 < n < 8000 (Mar 30, 2023) with Rn:     7999 < n < 9000 (Jan 08, 2023)
with Rn:     8999 < n <10000 (Mar 16, 2023) with Rn:     9999 < n <11000 (Mar 16, 2023)
with Rn:   10999 < n <12000 (Mar 26, 2023) with Rn:   11999 < n <14980L/M (Mar 30, 2023)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 751 digits		 617
in progress		 619
in progress		 625
in progress		 629
in progress		 641
in progress
B1 = 26e7/45000 curves/
numbers < 450 digits		 645
in progress		 1136
in progress		 1160
in progress		 1254
in progress		 ....
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits		 645
in progress		 1056
in progress		 1086
in progress		 1254
in progress		 1386
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits		 537
in progress		 567
in progress		 609
in progress		 1104
in progress		 1218
in progress



Factorizations
Repunits: R1        - R2500 (Mar 30, 2023) Repunits:  R2501 - R5000 (Feb 27, 2023)
Repunits: R5001   - R7500 (Mar 26, 2023) Repunits: R7501 - R10000 (Mar 30, 2023)
Repunits: R10001 - R12500 (Mar 26, 2023) Repunits: R12501 - R14980L/M (Feb 27, 2023)




Rprime project; base 10

last update: Dec 19, 2022

old project page   -   out of date

Status:       3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M     5M - 6M     6M - 7M     7M - 8M     8M - 9M     9M - 10M    
Details:     3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M     5M - 6M     6M - 7M     7M - 8M     8M - 9M     9M - 10M    

active members:
    - Danilo Nitsche, Kurt Beschorner

all contributors:   Danilo Nitsche, Serge Batalov, Paul Bourdelais, Benjamin Chaffin, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria,
                              Fan Ming, Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Ryan Propper, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian,
                              MattStath, Maksym Voznyy, wims, Kurt Beschorner
Overview
 
    Exponent     Primes/PRP                     found by ...
    - 10ˆ20     R19 = prime
    - 10ˆ100     R23 = prime
    - 10ˆ1000     R317 = prime
    - 10ˆ10000     R1031 = prime                 WD (Dec 1985)
    - 10ˆ50000     R49081 = prime               Harvey Dubner (Sep 1999)
    - 10ˆ100000     R86453 = PRP                 Lew Baxter (Oct 2000)
    - 10ˆ250000     R109297 = PRP               Paul Bourdelais - Harvey Dubner (Apr 2007)
    - 10ˆ500000     R270343 = PRP               Maksym Voznyy - Anton Budnyy (Jul 2007)
    - 10ˆ7500000     R5794777 = PRP             S. Batalov - Ryan Propper (Apr 2021)
    - 10ˆ10000000     R8177207 = PRP             S. Batalov - Ryan Propper (May 2021)




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