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


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News

-  Last update: Jan 27, 2023 

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


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jan 27, 2023   R942/c209: SNFS-difficulty = 314 
                  194M unique raw relations from 1250M are collected
                  currently progress 15.5 %;    


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jan 27, 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 26950000 dimensions of 65.7M dim. (41.0%; estimated time of arrival 1862 hours)   
				  
				  
- 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


- Found by Kurt Beschorner   
   Dec 02, 2022   n = 5167: 58534812511619307791582990857213930867;                 ecm: B1 = 1e6; sigma = 0:8576584531991617 
   Dec 02, 2022   n=141551: 683294806297822001;                                     gr-mfaktc


- Found by Kurt Beschorner   
   Nov 20, 2022   n = 5087: 855696576819526114321368468241;                         ecm: B1 = 1e6; sigma = 0:2338557618126682 
   Nov 20, 2022   n=140779: 1886531517329207467;                                    gr-mfaktc
   Nov 20, 2022   n=141067: 3019266738055160111;                                    gr-mfaktc


- Found by YOYO@home/Lars_Seidel   
   Nov 24, 2022   n =  497: 4247178976042868082665679915673747026882614569 * 1712111424......P321; ecm: B1 = 85e7; sigma = 0:17252997664838270985 


- Found by Kurt Beschorner   
   Nov 20, 2022   n = 9525: 246411272719873911988478401;                            ecm: B1 = 1e6; sigma = 0:1153280773493264
   Nov 20, 2022   n=140443: 3420910228546247551;                                    gr-mfaktc
   Nov 20, 2022   n=140587: 11931743520497439239;                                   gr-mfaktc

			  
-  Found by Alfred Eichhorn 
   Nov 18, 2022   n = 47857: 267862652398859882975627;                              ecm: B1 = 5e4; sigma = 8846267970344855
   Nov 18, 2022   n = 47857: 5814050299123021647722194082747;                       ecm: B1 = 5e4; sigma = 8795177300895013


- Found by Kurt Beschorner   
    Nov 18, 2022   n=139921: 121435939069357037;                                    gr-mfaktc
    Nov 18, 2022   n=139987: 5328475787572005311;                                   gr-mfaktc
    Nov 18, 2022   n=140227: 439337271274130849;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Nov 05, 2022   n = 5999: 30098469727206035303519014883;                          ecm: B1 = 1e6; sigma = 5200900600359875 
   Nov 05, 2022   n=139703: 268697501287103723;                                     gr-mfaktc


- Found by Kurt Beschorner   
   Nov 01, 2022   n = 1389: 39307144309365706756279849773434495203 * 9193907609......P840;  ecm: B1 =43e6; sigma = 1509003123809924 
   Nov 01, 2022   n=139343: 1506620826908739203;                                    gr-mfaktc
   Nov 01, 2022   n=139387: 76653039033857987;                                      gr-mfaktc
   Nov 01, 2022   n=139387: 4376783573901975947;                                    gr-mfaktc
   Nov 01, 2022   n=139457: 88280371885189489;                                      gr-mfaktc


- Found by Kurt Beschorner   
   Oct 27, 2022   n =7380L: 18083439727099436159112817133086310461;                 ecm: B1 =43e6; sigma = 2954795763367013 
   Oct 27, 2022   n=138587: 13456808017227013951;                                   gr-mfaktc
   Oct 27, 2022   n=138599: 4336913339749953827;                                    gr-mfaktc
   Oct 27, 2022   n=138661: 4253629350519214951;                                    gr-mfaktc
   Oct 27, 2022   n=138661: 11518943054098475483;                                   gr-mfaktc

				  
-  Found by Alfred Eichhorn 
   Oct 21, 2022   n =64877: 58307945412705205493;                                   ecm: B1 = 5e4; sigma = 4058862805750220


- Found by Kurt Beschorner   
   Oct 20, 2022   n = 7595: 53301899984916861489592976390111;                       ecm: B1 = 1e6; sigma = 2862452422412262 
   Oct 20, 2022   n=138511: 16639782600533415413;                                   gr-mfaktc


- Found by YOYO@home/Scottie McKinley   
   Oct 19, 2022   n = 1290: 46918389192417684252494192977798983971157315180037905073531; ecm: B1 =2.9e9; sigma = 0:15756483711164029501 
   
 
- Found by Kurt Beschorner   
   Oct 18, 2022   n=138181: 260118541625705071;                                     gr-mfaktc
   Oct 18, 2022   n=138251: 128617317085653479;                                     gr-mfaktc
   Oct 18, 2022   n=138389: 377328885591268151;                                     gr-mfaktc


- Found by Kurt Beschorner   
   Oct 11, 2022   n=12180L: 2750865191314983385202411742967911795988441;            ecm: B1 =11e6; sigma = 0:3511433398072626 


- Found by Kurt Beschorner   
   Oct 09, 2022   n = 8613: 36357990161285007949864483;                             ecm: B1 = 1e6; sigma = 3516630546511552 
   Oct 09, 2022   n =10414: 161529899335536848415319865023163477;                   ecm: B1 = 1e6; sigma = 6236160411899970 
   Oct 09, 2022   n=137597: 139698058612259729;                                     gr-mfaktc
   Oct 09, 2022   n=137597: 3554455399781350373;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Oct 03, 2022   n = 7593: 112887580911050204414751529;                            ecm: B1 = 1e6; sigma = 0:7734327110386253 
   Oct 03, 2022   n=136373: 5918722751609848889;                                    gr-mfaktc
   Oct 03, 2022   n=136537: 987858503096180231;                                     gr-mfaktc
   Oct 03, 2022   n=136651: 1146491861927584649;                                    gr-mfaktc
   Oct 03, 2022   n=136733: 107300944919547803;                                     gr-mfaktc

 
- YOYO@home/Boone    
   Oct 01, 2022   n =2580M: 5450116210658743893234594584043237507827598349697948371796539141; ecm: B1 = 29e8; sigma = 0:10511886308721671557 


-  Found by Sam Wagstaff 
   Sep 19, 2022   n =  878: 3127889058329352843751138723028784195008863188510913210373 * 3758889450......P303 


 -  Found by Yousuke Koide    
   Sep 10, 2022   n =  892: 6159486985016013075067913427429040588111855293215481915322769; ecm: B1 = 3e8; sigma = 2:10607718275885008793



ECM efforts
with Rn:           1 < n < 2000 (Jan 15, 2023) with Rn:     1999 < n < 3000 (Dec 15, 2022)
with Rn:     2999 < n < 4000 (Dec 19, 2022) with Rn:     3999 < n < 5000 (Dec 15, 2022)
with Rn:     4999 < n < 6000 (Jan 27, 2023) with Rn:     5999 < n < 7000 (Jan 22, 2023)
with Rn:     6999 < n < 8000 (Dec 22, 2022) with Rn:     7999 < n < 9000 (Jan 08, 2023)
with Rn:     8999 < n <10000 (Jan 22, 2023) with Rn:     9999 < n <11000 (Jan 22, 2023)
with Rn:   10999 < n <12000 (Jan 27, 2023) with Rn:   11999 < n <14980L/M (Dec 15, 2022)



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
2940M
in progress



Factorizations
Repunits: R1        - R2500 (Jan 15, 2023) Repunits:  R2501 - R5000 (Oct 01, 2022)
Repunits: R5001   - R7500 (Jan 27, 2023) Repunits: R7501 - R10000 (Jan 22, 2023)
Repunits: R10001 - R12500 (Jan 22, 2023) Repunits: R12501 - R14980L/M (Sep 19, 2020)




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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