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


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News

- Last update: Jul 01, 2026
 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 01, 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 12.705M of 87470195 dimensions (14.5%, ETA 1635h)   
 
 
- 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 


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jun 21, 2026   R567/c287: SNFS-difficulty = 324;
                  120M unique raw relations are collected;
                  currently progress 4.2%;    

  
- 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


- Found by Kurt Beschorner 
   Mar 26, 2026  n = 1894: 1512040242246245347303337158506932100321187855884973;    ecm: B1 =43e6; sigma: 2352180745415083
   Mar 26, 2026  n=12220M: 17503457490665154492212181558514493368181;               ecm: B1 =11e6; sigma: 6555790569521410
   Mar 26, 2026  n=12220M: 113623897643786632271953538007199774915605819798424201;  ecm: B1 =11e6; sigma: 8822993252285549
   Mar 26, 2026  n =33596: 1781658338572350764089;                                  P-1: B1 =120e6
   Mar 26, 2026  n =33600: 10731965728151082958206342403201;                        P-1: B1 =120e6
   Mar 26, 2026  n=100783: 331889208058268916326599;                                P-1: B1 = 50e6
   Mar 26, 2026  n=100791: 24191352192673093987729;                                 P-1: B1 = 50e6
   Mar 26, 2026  n=100791: 3841788067001993876963773175947;                         P-1: B1 = 50e6
   Mar 26, 2026  n=100793: 44946200447096292037;                                    P-1: B1 = 50e6
   Mar 26, 2026  n=100797: 3798995746797623809;                                     P-1: B1 = 50e6
   Mar 26, 2026  n=100803: 774528427854324681075679;                                P-1: B1 = 50e6
 
 
- Found by Alfred Eichhorn 
   Mar 21, 2026  n =55501: 179415236655977957794788948197;                          ecm: B1 = 1e6; sigma: 5233838991530363
   Mar 21, 2026  n =55711: 7522611654359330152177025762203;                         ecm: B1 = 1e6; sigma: 8623120497894503
   Mar 21, 2026  n =55903: 822851426479938611856478390887246713041;                 ecm: B1 = 1e6; sigma: 0:7070923126811028
   Mar 21, 2026  n =60953: 3261986070109840155482956601;                            ecm: B1 = 1e6; sigma: 0:3584930978989392
 

- Found by Kurt Beschorner 
   Mar 19, 2026  n =10129: 137061543265544510246023119936431;                       ecm: B1 = 1e6; sigma: 4303296904464307
   Mar 19, 2026  n =12137: 2884688153237612712857957185605924010885591;             ecm: B1 = 1e6; sigma: 2853933179712878
   Mar 19, 2026  n =12151: 483321115435084391260670290302391;                       ecm: B1 = 1e6; sigma: 2568376364319099
   Mar 19, 2026  n =12164: 4840944858681522210038482753561;                         ecm: B1 = 1e6; sigma: 2346920958243026
   Mar 19, 2026  n=100759: 709330912817945237;                                      P-1: B1 = 50e6
   Mar 19, 2026  n=100764: 38365949444237829541;                                    P-1: B1 =100e6
   Mar 19, 2026  n=100776: 2941449484017304830961;                                  P-1: B1 =120e6
   Mar 19, 2026  n=100781: 177686681293963751808723812849;                          P-1: B1 = 50e6


- Found by Alfred Eichhorn 
   Mar 05, 2026  n =32003: 44752433366337719635418425431667;                        ecm: B1 = 1e6; sigma: 2934471607211332
   Mar 05, 2026  n =55337: 46992402339976441856346067;                              ecm: B1 = 1e6; sigma: 7210886858802239
 
 
- Found by Kurt Beschorner 
   Mar 05, 2026  n =12118: 283769541439347428049840514527438743;                    ecm: B1 = 1.5e6; sigma: 8457755426880321
   Mar 05, 2026  n =12119: 1586175574488674253019020557;                            ecm: B1 = 1e6; sigma: 5424355819946614
   Mar 05, 2026  n =12127: 484381015341399524755306879867;                          ecm: B1 = 1e6; sigma: 867414565140073
   Mar 05, 2026  n =12134: 2313826073736395901840463687042969;                      ecm: B1 = 1e6; sigma: 5985808295382385
   Mar 05, 2026  n =12138: 132544170344455895575066766596579;                       ecm: B1 = 3e6; sigma: 2104812381007890
   Mar 05, 2026  n= 33584: 1739068581406664436804284177;                            P-1: B1 =100e6
   Mar 05, 2026  n= 33585: 158835165671109101625271;                                P-1: B1 = 50e6

				  
- Found by Kurt Beschorner 
   Feb 24, 2026  n = 1863: 65621053967030030278032678666765356214396871;            ecm: B1 =30e6; sigma: 3990636431393341
   Feb 24, 2026  n = 1868: 1273247159083037727872305641759112951550672981;          ecm: B1 =43e6; sigma: 8168184316954561
   Feb 24, 2026  n = 1891: 14764045688817189934865309719992239643928483;            ecm: B1 =20e6; sigma: 8773572821694751
   Feb 24, 2026  n =12023: 503848949065062738693567523271;                          ecm: B1 = 1e6; sigma: 5478098394647358
   Feb 24, 2026  n =12025: 32417417230964498725173399401;                           ecm: B1 = 1e6; sigma: 7143038973026063
   Feb 24, 2026  n =12078: 5641363215630632413731581790771943;                      ecm: B1 = 3e6; sigma: 4559211936310747
   Feb 24, 2026  n =12083: 6537293072521298896944283;                               ecm: B1 = 1e6; sigma: 8501454539169600
   Feb 24, 2026  n =12083: 413670932564244988996645173338485144387;                 ecm: B1 = 1e6; sigma: 4908902462029792
   Feb 24, 2026  n =12087: 6672064100646552881097758902471;                         ecm: B1 = 1e6; sigma: 106839095463008
   Feb 24, 2026  n =12089: 15514948341089827268516023609;                           ecm: B1 = 1e6; sigma: 7339904742803186
   Feb 24, 2026  n =12091: 6199525333482716590744885025693;                         ecm: B1 = 1e6; sigma: 3943941778212094
   Feb 24, 2026  n =15093: 23788345844813150711586228481;                           P-1: B1 =550e6
   Feb 24, 2026  n =15098: 1733657569018522357037811573479453712503;                P-1: B1 =700e6
   Feb 24, 2026  n=100682: 16514482448539024406797;                                 P-1: B1 = 80e6
	  
				  
- Found by Kurt Beschorner 
   Feb 18, 2026  n=12020L: 5927129729595990779226807978094020721;                   ecm: B1 = 3e6; sigma: 1733734247424251
   Feb 18, 2026  n =12031: 59874773023798190758390512563;                           ecm: B1 = 1e6; sigma: 1135839981977504
   Feb 18, 2026  n =12054: 14321265067519654392935432158893160849374733099;         ecm: B1 = 3e6; sigma: 1484744847755487
   Feb 18, 2026  n =12059: 216715947375345172042633246277;                          ecm: B1 = 1e6; sigma: 2034964677036868
   Feb 18, 2026  n =12069: 1337569341662579206250374813;                            ecm: B1 = 1e6; sigma: 4544288176877572
   Feb 18, 2026  n =12069: 432340422496650699549485584879;                          ecm: B1 = 1e6; sigma: 6521220082461810
   Feb 18, 2026  n =12071: 80499647484101348167799941717;                           ecm: B1 = 1e6; sigma: 5190152304928739
   Feb 18, 2026  n =12072: 1011674937383879947534793401541386057;                   ecm: B1 = 3e6; sigma: 5358427617299025
   Feb 18, 2026  n =12073: 1681779199059947543250257286751;                         ecm: B1 = 1e6; sigma: 6507687772168919
   Feb 18, 2026  n =33572: 146339316647636822538520023949;                          P-1: B1 =80e6  
   Feb 18, 2026  n =33575: 8503366064194011120401;                                  P-1: B1 =35e6  
   Feb 18, 2026  n=100689: 24266685111684082489489;                                 P-1: B1 =35e6  
   Feb 18, 2026  n=100697: 40884705512444912399;                                    P-1: B1 =35e6  
   Feb 18, 2026  n=100700: 150468245489588431514801;                                P-1: B1 =80e6  
   Feb 18, 2026  n=100711: 452049063792720609151;                                   P-1: B1 =35e6  
   Feb 18, 2026  n=100714: 52812755786099226601;                                    P-1: B1 =80e6  
   Feb 18, 2026  n=100720: 948426247608507678804265293955712641;                    P-1: B1 =80e6  
   Feb 18, 2026  n=100722: 52189978457599534922173093;                              P-1: B1 =80e6  
   Feb 18, 2026  n=100725: 10151653870019894646411190962751;                        P-1: B1 =35e6  
   Feb 18, 2026  n=100726: 108932553815164248052950809;                             P-1: B1 =80e6  
   Feb 18, 2026  n=100726: 1602529010027853783042126711481;                         P-1: B1 =80e6  
   Feb 18, 2026  n=100727: 911876032809122852634791;                                P-1: B1 =35e6  


- Found by YOYO@home/[AF>HFR>Hop!] grao
   Feb 12, 2026  n = 1560: 2303737084496179509862982171386156189854552565653639960837121; ecm: B1 = 2.9e9; sigma: 0:13868635003750328954 


- Found by Makoto Kamada
   Feb 12, 2026  n=294917: 7528650353817041  
   Feb 12, 2026  n=294925: 2778464486527601  
   Feb 12, 2026  n=294933: 2472137325363787  
   Feb 12, 2026  n=294963: 1994027424002923   
   Feb 12, 2026  n=295009: 4386673965108293   
   Feb 12, 2026  n=295009: 6675968916864391   
   Feb 12, 2026  n=295105: 6509126135244431   
   Feb 12, 2026  n=295117: 6382613330250049   
   Feb 12, 2026  n=295127: 3006884839786759   
   Feb 12, 2026  n=295191: 6270904077893443   
   Feb 12, 2026  n=295209: 8558672272685569   
   Feb 12, 2026  n=295245: 1353072055439431


ECM efforts
with Rn:         1 < n < 2000 (Jul 01, 2026) with Rn:     1999 < n < 3000 (Jul 01, 2026)
with Rn:     2999 < n < 4000 (Jun 26, 2026) with Rn:     3999 < n < 5000 (Jun 26, 2026)
with Rn:     4999 < n < 6000 (Jul 01, 2026) with Rn:     5999 < n < 7000 (Feb 12, 2026)
with Rn:     6999 < n < 8000 (Jan 20, 2026) with Rn:     7999 < n < 9000 (Dec 01, 2025)
with Rn:     8999 < n <10000 (Dec 01, 2025) with Rn:     9999 < n <11000 (Jun 26, 2026)
with Rn:   10999 < n <12000 (May 17, 2026) with Rn:   11999 < n <14980L/M (Jul 01, 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 < 600 digits		 709
in progress		 775
in progress		 1280
in progress		 1332
in progress		 ....
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits		 1012
in progress		 1164
in progress		 1236
in progress		 1722
in progress		 ....
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits		 1800
in progress		 ....
in progress		 ....
in progress		 ....
in progress		 ....
in progress



Factorizations
Repunits: R1      - R2500 (Jun 17, 2026) Repunits:  R2501 - R5000 (Jun 26, 2025)
Repunits: R5001   - R7500 (Feb 11, 2026) Repunits: R7501 - R10000 (Dec 01, 2025)
Repunits: R10001 - R12500 (Jun 22, 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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