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


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News

- Last update: Aug 05, 2026

- Found by Kurt Beschorner 
   Aug 05, 2026  n = 3014: 3224257283821690911882860343913279673197968001;          ecm: B1 =20e6; sigma: 346575584497108
   Aug 05, 2026  n =11015: 38361476883252040573781321;                              ecm: B1 = 1e6; sigma: 5117826424394022 
   Aug 05, 2026  n =12295: 484743392732493780746667717991;                          ecm: B1 = 1e6; sigma: 1522186952526259
   Aug 05, 2026  n =12307: 333374801444055325819386005205439;                       ecm: B1 = 1e6; sigma: 5919142273543134
   Aug 05, 2026  n =12328: 1485186211524993980332189457327993;                      ecm: B1 =1.5e6; sigma: 8456453911070310 

 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 05, 2026   R477/c252: SNFS-difficulty = 318;
                  2869M unique raw relations and 2350M unique ideals are collected;
                  currently progress 100%;    
                  msieve-excerpts: linear algebra, msieve -nc2
                  - matrix is 87469788 x 87470195  with weight 6972368445 (79.71/col)
                  - sparse part has weight 6671602090 (76.27/col)
                  - using block size 8192 and superblock size 608256 for processor cache size 25344 kB
                  - commencing Lanczos iteration (36 threads)
                  - linear algebra completed 52.490M of 87470195 dimensions (60.0%, ETA 738h)   


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 05, 2026   R567/c287: SNFS-difficulty = 324;
                  300M unique raw relations are collected;
                  currently progress 10.5%;    
   

- Found by Alfred Eichhorn 
   Jul 26, 2026  n =33083: 6675715261589480685252905491003;                         ecm: B1 = 1e6; sigma: 0:8131647610823038
   Jul 26, 2026  n =70997: 12569762063305598037002812395517;                        ecm: B1 = 1e6; sigma: 0:7572621526288766   
   Jul 26, 2026  n =71011: 994162421596480115595396227;                             ecm: B1 = 1e6; sigma: 0:4672737597017891   
   

- Found by Alfred Eichhorn 
   Jul 09, 2026  n =59809: 2974461269600365487438093421721;                         ecm: B1 = 1e6; sigma: 0:6930322239139690
   Jul 09, 2026  n =62633: 4770048381930236202807868411187;                         ecm: B1 = 1e6; sigma: 0:4102478440982954
   Jul 09, 2026  n =62987: 285189180407754140621972589923;                          ecm: B1 = 1e6; sigma: =0:4048756822361665
   Jul 09, 2026  n =70039: 4515288873284468441685842687867;                         ecm: B1 = 1e6; sigma: 0:6070592813061543
   Jul 09, 2026  n =70241: 510387445962916661797514671;                             ecm: B1 = 1e6; sigma: 0:582790225641299

 
- Found by YOYO@home/Schildkroete
   Jun 26, 2026  n =3420M: 11910496620270230227967351103984592528826219533871461;   ecm: B1 = 850e6; sigma: 0:14888554157636030172
   

- Found by Alfred Eichhorn 
   Jun 22, 2026  n =59441: 658830707682755169056044723;                             ecm: B1 = 1e6; sigma: 0:6996752501839657
   Jun 22, 2026  n =59471: 190815741323077589216921714573;                          ecm: B1 = 1e6; sigma: 0:7404090761943369
   Jun 22, 2026  n =59539: 135548153477087092759519855361;                          ecm: B1 = 1e6; sigma: 0:5707363897398941
 
 
- Found by Kurt Beschorner 
   Jun 22, 2026  n = 3016: 79745540397089767290902971445484579513353729;            ecm: B1 =20e6; sigma: 2848204528186435 
   Jun 22, 2026  n =12278: 1045177907460420329867780401133867851;                   ecm: B1 =1.5e6; sigma: 4051930692612612 
   Jun 22, 2026  n =12279: 9637219349226698572164080730659317;                      ecm: B1 = 1e6; sigma: 7164493398039665 
   Jun 22, 2026  n =12324: 32860792314779471409511216930296349;                     ecm: B1 = 3e6; sigma: 309243589456182 


- Found by Kurt Beschorner 
   Jun 17, 2026  n = 3017: 49473518867236296999163440070344126523;                  ecm: B1 =11e6; sigma: 5943577211292700 
   Jun 17, 2026  n =12320: 12387457044434846313038653536577732392641;               ecm: B1 = 3e6; sigma: 383306035719674
   Jun 17, 2026  n =12321: 98481601921708468998211578895369;                        ecm: B1 = 1e6; sigma: 1985997901299033 


- Found by Alfred Eichhorn 
   May 29, 2026  n =32507: 2300930380372305197566072049639;                         ecm: B1 = 1e6; sigma: 0:7501853553690321
 
 
- Found by Kurt Beschorner 
   May 29, 2026  n = 1946: 27554793188997041736632096781280014586232237622274391333; ecm: B1 =30e6; sigma: 2268919098670077 
   May 29, 2026  n =33624: 421521330863204485354297;                                P-1: B1 =120e6 
   May 29, 2026  n =33624: 12796650901118026271423089;                              P-1: B1 =120e6
   May 29, 2026  n=100870: 595613554200944189681;                                   P-1: B1 =120e6


- Found by Kurt Beschorner 
   May 19, 2026  n = 1946: 1141091827346082725563186077734683523890652491324921;    ecm: B1 =30e6; sigma: 2391699717520293 
   May 19, 2026  n = 1948: 1245574263344236926178624905967619777496826201;          ecm: B1 =30e6; sigma: 298681832424430
   May 19, 2026  n =15109: 3126121653732181949392727677;                            P-1: B1 =330e6
   May 19, 2026  n=100851: 1331119777281831087651429151;                            P-1: B1 = 50e6
   May 19, 2026  n=100852: 35480851910324239338266251369;                           P-1: B1 =120e6
   May 19, 2026  n=100855: 3630007311475118671;                                     P-1: B1 = 55e6
   May 19, 2026  n=100863: 1015929284756244359406737203;                            P-1: B1 = 55e6
   May 19, 2026  n=100863: 2537548873731441460658709523;                            P-1: B1 = 55e6

		
- Found by Alfred Eichhorn 
   May 17, 2026  n =58043: 2462878157842741990086979241;                            ecm: B1 = 1e6; sigma: 5913375008734535
   May 17, 2026  n =58231: 8591284841513196276725154917039;                         ecm: B1 = 1e6; sigma: 0:4677710267393855

 
- Found by Kurt Beschorner 
   May 11, 2026  n = 1939: 2319804043020569784657764982312066706540009;             ecm: B1 =20e6; sigma: 1141204615990357
   May 11, 2026  n = 2370: 482449202423416486767475769973056969504388721;           ecm: B1 =43e6; sigma: 1028291333
   May 11, 2026  n =12271: 228199770997052675993096122519371289;                    ecm: B1 = 1e6; sigma: 4270726391921522
   May 11, 2026  n =12275: 4409632003308300498889025067767487751;                   ecm: B1 = 1e6; sigma: 7126292361183199
   May 11, 2026  n =12277: 118409763548324573394163349399;                          ecm: B1 = 1e6; sigma: 865464314463046
   May 11, 2026  n =20168: 36413245003538692345629330721;                           P-1: B1 =120e6
   May 11, 2026  n=100833: 218914320925344172603;                                   P-1: B1 = 50e6
   May 11, 2026  n=100840: 26923763855635207088748001;                              P-1: B1 =120e6
   May 11, 2026  n=100841: 263521074163247213;                                      P-1: B1 = 50e6
   May 11, 2026  n=100841: 1747747951842195723733;                                  P-1: B1 = 50e6
   May 11, 2026  n=100849: 837394980053163708359;                                   P-1: B1 = 50e6

 
- Found by Kurt Beschorner 
   Apr 28, 2026  n = 4079: 426915461085826624259143920722034774479;                 ecm: B1 = 1e6; sigma: 7104292139681039
   Apr 28, 2026  n =12223: 6369097247405237468604340064437;                         ecm: B1 = 1e6; sigma: 4266251454290015
   Apr 28, 2026  n =12233: 22472722653715903146492540430914710329;                  ecm: B1 = 1e6; sigma: 4346254638954307
   Apr 28, 2026  n =12247: 2776545656296308111024907187;                            ecm: B1 = 1e6; sigma: 5666394773832634
   Apr 28, 2026  n =12250: 621878902495839421287137521938451694251;                 ecm: B1 = 3e6; sigma: 5389300061366745
   Apr 28, 2026  n =12264: 3141173557231484342233218217422101569;                   ecm: B1 = 5e6; sigma: 3950502677650097
 

- Found by Alfred Eichhorn 
   Apr 27, 2026  n =57077: 3848471893272271808963508973;                            ecm: B1 = 1e6; sigma: 0:4742462032411031
   Apr 27, 2026  n =61469: 698138979099137779882713720563;                          ecm: B1 = 1e6; sigma: 7844869317150916
   Apr 27, 2026  n =61519: 3592374185368400157663594959;                            ecm: B1 = 1e6; sigma: 0:2912591680432495

   
- Found by Kurt Beschorner 
   Apr 27, 2026  n = 1909: 225703566525345000237290241654276163965649;              ecm: B1 =20e6; sigma: 5168216469123288
   Apr 27, 2026  n =12240: 263000468346705414367562319148772641;                    ecm: B1 = 3e6; sigma: 4513911137171856
   Apr 27, 2026  n =12256: 43376467754503927150112444601064993;                     ecm: B1 =1.5e6; sigma: 6872108156273792
   Apr 27, 2026  n =20163: 721292645808181608827351401;                             P-1: B1 = 50e6
   Apr 27, 2026  n =33606: 230893953674075061463927;                                P-1: B1 =120e6
   Apr 27, 2026  n =33607: 5964387365159475570403;                                  P-1: B1 = 50e6
   Apr 27, 2026  n =33609: 48248595085802769587549417191;                           P-1: B1 = 50e6
   Apr 27, 2026  n=100814: 776396116921274123891;                                   P-1: B1 =120e6
   Apr 27, 2026  n=100818: 54821518733674447939;                                    P-1: B1 =120e6
   Apr 27, 2026  n=100822: 8152588103725941068097397481;                            P-1: B1 =120e6
   Apr 27, 2026  n=100830: 394392699271528282561;                                   P-1: B1 =120e6


- Found by NFS@home        
   Apr 26, 2026  n =  784: 289541217302474902147738712574747645681665598761448687795987839125906245176246519610151449976343537460699905766689; SNFS 


- Found by Kurt Beschorner 
   Apr 09, 2026  n =12183: 109821907852656265834529348424560071;                    ecm: B1 = 1e6; sigma: 7051987285101674
   Apr 09, 2026  n =12185: 130322056866604174556330887201;                          ecm: B1 = 1e6; sigma: 2275484587771368
   Apr 09, 2026  n =12187: 4331894187607779562471947940622489759;                   ecm: B1 = 1e6; sigma: 899074588164263
   Apr 09, 2026  n =12197: 281192396724953094378341698240982668717;                 ecm: B1 = 1e6; sigma: 1544402678692367
   Apr 09, 2026  n =12198: 100121059314668298378348902933673188089;                 ecm: B1 = 3e6; sigma: 6858696947538165 
   Apr 09, 2026  n =12199: 1739280392832343482352334226643081;                      ecm: B1 = 1e6; sigma: 1208315919345894 
   Apr 09, 2026  n =12201: 109836927317630094632408443;                             ecm: B1 = 1e6; sigma: 3736292984657857
   Apr 09, 2026  n=12220L: 6973238477503511321447740394630472080633701;             ecm: B1 =11e6; sigma: 1197379811455370
   Apr 09, 2026  n= 33604: 291531278012433218181442837529809;                       P-1: B1 =120e6
   Apr 09, 2026  n=100807: 760773901018618018808663640224203;                       P-1: B1 = 50e6

 
- Found by Alfred Eichhorn 
   Mar 30, 2026  n =61099: 155172907171674539481224758667;                          ecm: B1 = 1e6; sigma: 7431135821234599


ECM efforts
with Rn:         1 < n < 2000 (Jul 26, 2026) with Rn:     1999 < n < 3000 (Jul 26, 2026)
with Rn:     2999 < n < 4000 (Aug 05, 2026) with Rn:     3999 < n < 5000 (Aug 05, 2026)
with Rn:     4999 < n < 6000 (Jul 26, 2026) with Rn:     5999 < n < 7000 (Feb 12, 2026)
with Rn:     6999 < n < 8000 (Jul 20, 2026) with Rn:     7999 < n < 9000 (Aug 05, 2026)
with Rn:     8999 < n <10000 (Jul 26, 2026) with Rn:     9999 < n <11000 (Aug 05, 2026)
with Rn:   10999 < n <12000 (Aug 05, 2026) with Rn:   11999 < n <14980L/M (Aug 05, 2026)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17000 curves/
numbers < 951 digits		 737
in progress		 ....
in progress		 ....
in progress		 ....
in progress		 ....
in progress
B1 = 26e7/42000 curves/
numbers < 650 digits		 607
in progress		 611
in progress		 713
in progress		 775
in progress		 1280
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits		 1332
in progress		 1656
in progress		 ....
in progress		 ....
in progress		 ....
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits		 1164
in progress		 1236
in progress		 1722
in progress		 ....
in progress		 ....
in progress



Factorizations
Repunits: R1      - R2500 (Jun 17, 2026) Repunits:  R2501 - R5000 (Aug 05, 2025)
Repunits: R5001   - R7500 (Feb 11, 2026) Repunits: R7501 - R10000 (Aug 05, 2026)
Repunits: R10001 - R12500 (Aug 05, 2026) Repunits: R12501 - R14980L/M (Apr 09, 2026)




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 ...
    - 10ˆ10     R2 = prime
    - 10ˆ20     R19 = prime
    - 10ˆ100     R23 = prime
    - 10ˆ1000     R317 = prime
    - 10ˆ10000     R1031 = prime                 WD (Dec 1985)
    - 10ˆ50000     R49081 = prime               Paul Underwood (Mar 2022)
    - 10ˆ100000     R86453 = prime               Andreas Enge (May 15, 2023)
    - 10ˆ250000     R109297 = prime             A. Enge/P. Underwood (May 2025)
    - 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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