Factorizations of Repunit Numbers

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

News

-  Last update: Jul 24, 2024  


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 24, 2024   R471/c301: SNFS-difficulty = 314;
                  2585M unique raw relations and 2275M unique ideals are collected;
                  target: 3000M unique raw relations;  
                  currently progress 86 %;    
                  msieve excerpts from Jul 18, 2024
                  - target-density = 98
                  - begin with 2574472832 relations and 2272862797 unique ideals
                  - reduce to 203733111 relation sets and 105036562 unique ideals
                  - found 102291144 cycles, need 89898762 (= matrix size)
                  - weight of 89898762 cycles is about 8810277412 (98.00/cycle)
                  - matrix is 89430574 x 89430821 (33297.9 MB) with weight 8427968875 (94.24/col)
                  The  matrix is still too big 
 

- Found by Alfred Eichhorn 
   Jul 21, 2024  n =13613: 15262282368599483015998894649;                           ecm: B1 = 1e6; sigma = 5210964136833681  


- Found by Kurt Beschorner  
   Jul 21, 2024  n =13733: 11066901234321643251415990246667;                        P-1: B1 = 150e6
   Jul 21, 2024  n =13739: 815051569821918488835533038711;                          P-1: B1 = 150e6 
   Jul 21, 2024  n =13751: 30084129960755867761834373333372723;                     P-1: B1 = 150e6
   Jul 21, 2024  n =13756: 3070906950345823080010940982444870941;                   P-1: B1 = 400e6 
   Jul 21, 2024  n =13769: 238899466227509549998368631;                             P-1: B1 = 175e6 
   Jul 21, 2024  n=100187: 4212448211184003403;                                     P-1: B1 = 23e6
   Jul 21, 2024  n=154459: 654674838797941477;                                      gr-mfaktc     
   Jul 21, 2024  n=154897: 288575490359805653;                                      gr-mfaktc 
   Jul 21, 2024  n=154981: 659143481425129271;                                      gr-mfaktc 
   Jul 21, 2024  n=154981: 725117156196649187;                                      gr-mfaktc 
   Jul 21, 2024  n=155017: 1537923485747759557;                                     gr-mfaktc 
   Jul 21, 2024  n=155137: 6213654742199632163;                                     gr-mfaktc 


- Found by Alfred Eichhorn 
   Jun 29, 2024  n =13523: 13387751970993012362901079637;                           ecm: B1 = 1e6; sigma = 5381565215536551  
   Jun 29, 2024  n =20411: 8856502355660511775523407391;                            ecm: B1 = 1e6; sigma = 7929625471060670  
   Jun 29, 2024  n =20431: 18699538092936415160078201691271;                        ecm: B1 = 1e6; sigma = 1168082089032586  
   Jun 29, 2024  n =20483: 41932266046649700904863383587;                           ecm: B1 = 1e6; sigma = 3257560573251327  
   Jun 29, 2024  n =20641: 84562062985268488366611846511;                           ecm: B1 = 1e6; sigma = 7612567426602960  
   Jun 29, 2024  n =20717: 466634734466535006245712555307;                          ecm: B1 = 1e6; sigma = 146688564762787  


- Found by Torbjörn Granlund
   Jul 16, 2024  n =  731: 1847429475936181681973479760912708743358821710551;       ecm: B1 =11e6; sigma = 1:3939899409  


- Found by Torbjörn Granlund
   Jul 14, 2024  n =3900M: 44612114135261049915172448202991314405938701;            ecm: B1 =11e6; sigma = 1:2348484157  
  

- Found by Torbjörn Granlund
   Jul 13, 2024  n = 1556: 1355157068675915381446032476103133130496209;             ecm: B1 =11e6; sigma = 1:3330891095	  


- Found by Torbjörn Granlund
   Jul 12, 2024  n = 1408: 106110538711611081989682173453117312268289;              ecm: B1 =11e6; sigma = 1:423379121   


- Found by Kurt Beschorner  
   Jul 11, 2024  n = 1525: 315847098431407555514016207329179201;                    P-1: B1 = 200e6
   Jul 11, 2024  n =13721: 1864073211647238592948736905104361;                      P-1: B1 = 150e6 
   Jul 11, 2024  n =33395: 1523915962744198013287961;                               P-1: B1 = 23e6
   Jul 11, 2024  n=100175: 290759670245407201;                                      P-1: B1 = 23e6
   Jul 11, 2024  n=153701: 1440092232895724267;                                     gr-mfaktc 
   Jul 11, 2024  n=154211: 17523178529846097809;                                    gr-mfaktc 


- Found by NFS@home   
   Jul 08, 2024  n =  365: 1304946319836672523549871511207656785231498701576036930724645238399101906921; SNFS 
   Jul 08, 2024  n =  365: 5528825275894858698684129584828307231241005568273768148118728392440732070424671; SNFS 

 
- Found by Anonymous  
   Jul 08, 2024  n = 8026: 11092134801718675055606994656545513411                    
   Jul 08, 2024  n = 9034: 2112314427024188715300943526715275533                    
 

- Found by Torbjörn Granlund
   Jul 07, 2024  n =3740M: 813728620031462038871992677376718544646779541;           ecm: B1 =11e6; sigma = 1:2213254673   
 
 
- Found by Torbjörn Granlund
   Jul 05, 2024  n = 1538: 9287243504302734314292246493018665305411;                ecm: B1 =11e6; sigma = 1:2599237159  
 

- Found by Kurt Beschorner  
   Jul 04, 2024  n =13687: 3352869000001257408071704371187;                         P-1: B1 = 150e6
   Jul 04, 2024  n =13692: 448790289019202435089828835874995221;                    P-1: B1 = 550e6


- Found by Anonymous  
   Jul 04, 2024  n = 3646: 7249609412129031102349676213675320028207                    
   Jul 04, 2024  n = 5426: 421794296629383911904809584049                    
   Jul 04, 2024  n = 5878: 1293862103310971228813269265251889                     
   Jul 04, 2024  n = 9806: 6856501055738088117609720236405115757649                     
   Jul 04, 2024  n = 9874: 116769305954826569316770086211501521                     
 

- Found by YOYO@home/philwire    
   Jul 04, 2024  n =  639: 108404283009093688449943940269189804724790189486660307;  ecm: B1 = 2.9e9; sigma = 10714174124914808047

 
- Found by Torbjörn Granlund
   Jul 04, 2024  n = 1484: 12934325238528583194928423610286679740731789;            ecm: B1 =11e6; sigma = 1:85680977    
   Jul 04, 2024  n = 1654: 2014736089669888940425352477546278092192268265858033129; ecm: B1 =11e6; sigma = 1:1681499511 


- Found by Kurt Beschorner  
   Jul 04, 2024  n = 7599: 4944885332403182509417069471681;                         ecm: B1 = 1e6; sigma = 3792909555228110
   Jul 04, 2024  n =13664: 17782554637005831866125656641;                           P-1: B1 = 450e6 
   Jul 04, 2024  n =13667: 5032044810625021177332187;                               P-1: B1 = 158e6
   Jul 04, 2024  n=100172: 340257492271303914975039056389;                          P-1: B1 = 55e6
   Jul 04, 2024  n=153077: 116991563943187237;                                      gr-mfaktc 
   Jul 04, 2024  n=153277: 283051850735220719;                                      gr-mfaktc 
 

- Found by Alfred Eichhorn 
   Jun 29, 2024  n =20143: 195336622099383139974192234034547;                       ecm: B1 = 1e6; sigma = 3729048310073734 
   

- Found by Kurt Beschorner  
   Jun 29, 2024  n = 6565: 967455252377753723469264601;                             ecm: B1 = 1e6; sigma = 5085665109651225
   Jun 29, 2024  n = 7209: 245876032391282720514670601435797;                       ecm: B1 = 1e6; sigma = 7176496071620092 
   Jun 29, 2024  n =13651: 63685984885065209582819476115071;                        P-1: 1e6 = 165e6
   Jun 29, 2024  n=152249: 667640256156011561;                                      gr-mfaktc 
   Jun 29, 2024  n=152407: 3863061623316166853;                                     gr-mfaktc 
   Jun 29, 2024  n=152417: 4384597323140904347;                                     gr-mfaktc 


- Found by Alfred Eichhorn 
   Jun 27, 2024  n =12611: 151596145122775505868566782271 * 7329415337......P12581  ecm: B1 = 1e6; sigma = 1891578441988465
 

- Found by Alfred Eichhorn 
   Jun 24, 2024  n =73847: 7891144115301619472022803497889;                         ecm: B1 = 5e4; sigma = 430692243951430
   Jun 24, 2024  n =74507: 1096611993139741046923;                                  ecm: B1 = 5e4; sigma = 6502661398168781
   Jun 24, 2024  n =74507: 144576321485621311976359;                                ecm: B1 = 5e4; sigma = 5710557500718102
   Jun 24, 2024  n =74527: 18472086123310264797552077;                              ecm: B1 = 5e4; sigma = 5012480456469592
   Jun 24, 2024  n =74587: 12585888766454654778477001;                              ecm: B1 = 5e4; sigma = 5787057121355163
   Jun 24, 2024  n =74707: 2246495418530976647385485111;                            ecm: B1 = 5e4; sigma = 4865186604072078
   Jun 24, 2024  n =74929: 23613576233446350795077641;                              ecm: B1 = 5e4; sigma = 3815193115992148
   
 
- Found by Torbjörn Granlund
   Jun 21, 2024  n = 1870: 30981838801127734361302339269066902886001;               ecm: B1 =11e6; sigma = 1:3306279234


- Found by Torbjörn Granlund
   Jun 18, 2024  n =3540M: 154364888033739260172380158583232052475743273261;        ecm: B1 =11e6; sigma = 1:1431821900 

  
- Found by Torbjörn Granlund
   Jun 17, 2024  n =  891: 5768352029220733367366868921292458501408214165423363;    ecm: B1 =11e7; sigma = 1:333812611


- Found by Torbjörn Granlund
   Jun 16, 2024  n = 1672: 545358172357012292201336067885308067971306777;           ecm 


- Found by Torbjörn Granlund
   Jun 15, 2024  n = 1392: 10825430995573655349911905703088339464977;               ecm 

 
- Found by Torbjörn Granlund
   Jun 14, 2024  n = 1792: 4560897401317754430626820629544566062629889;             ecm 
 
 
- Found by Kurt Beschorner
   Jun 14, 2024  n = 7821: 10391751287135966688011512453;                           ecm  B1 = 1e6; sigma = 409243078866167
   Jun 14, 2024  n =13548: 12997605280355035463166531521403529;                     P-1: B1 = 500e6
   Jun 14, 2024  n =13562: 15353741655549410028804307084051;                        P-1: B1 = 325e6
   Jun 14, 2024  n =13563: 77411955285810787348651626991;                           P-1: B1 = 165e6
   Jun 14, 2024  n =13593: 177925771645928134641547027;                             P-1: B1 = 150e6
   Jun 14, 2024  n =13612: 17167210449977525602398480599175117101;                  P-1: B1 = 375e6
   Jun 14, 2024  n =20032: 2505607329459631611641153;                               P-1: B1 = 55e6
   Jun 14, 2024  n =33385: 747826005686416007231;                                   P-1: B1 = 55e6
   Jun 14, 2024  n =33387: 106504353311117769139519;                                P-1: B1 = 20e6
   Jun 14, 2024  n=150883: 97118496609892523;                                       gr-mfaktc      
   Jun 14, 2024  n=150901: 563456271424457431;                                      gr-mfaktc      
   Jun 14, 2024  n=150919: 2079148442457322799;                                     gr-mfaktc      
   Jun 14, 2024  n=151171: 608634030260192639;                                      gr-mfaktc      
   Jun 14, 2024  n=151247: 113196576201967147;                                      gr-mfaktc      
   Jun 14, 2024  n=151429: 147222954843343733;                                      gr-mfaktc      
   Jun 14, 2024  n=151499: 146383186511736689;                                      gr-mfaktc      
                                               
 
- Found by Torbjörn Granlund
   Jun 12, 2024  n = 1496: 28330881496644957570065523400505204114494529;            ecm 
 

- Found by Torbjörn Granlund
   Jun 09, 2024  n = 1430: 82419252546478457878215964924871918728196281;            ecm 
 

- Found by Yousuke Koide 
   Jun 03, 2024  n =  938: 11562710405302740261753778982810543629872202227744910916651 * 6120646518......P312; ecm: B1 =3e8; sigma = 2:4970505043646219549 


- Found by Kurt Beschorner
   Jun 03, 2024  n =13475: 14034822309195006833617951;                              P-1: B1 = 150e6
   Jun 03, 2024  n =13501: 204470063667253089494397679362163;                       P-1: B1 = 150e6
   Jun 03, 2024  n =13505: 447230547521550428905961;                                P-1: B1 = 160e6
   Jun 03, 2024  n =33384: 7821295128811946507432484961;                            P-1: B1 = 55e6
   Jun 03, 2024  n=100145: 668544845427588593671;                                   P-1: B1 = 20e6
   Jun 03, 2024  n=100152: 2015344433453833;                                        P-1: B1 = 55e6
   Jun 03, 2024  n=149341: 337426151183136437;                                      gr-mfaktc      
   Jun 03, 2024  n=149729: 522185468610743293;                                      gr-mfaktc      
   Jun 03, 2024  n=149893: 234739865552796839;                                      gr-mfaktc 
   Jun 03, 2024  n=149911: 641276195249134517;                                      gr-mfaktc 
   Jun 03, 2024  n=149953: 3666251351417794037;                                     gr-mfaktc 
   Jun 03, 2024  n=150211: 4128566210846845711;                                     gr-mfaktc 
   Jun 03, 2024  n=150517: 1452830539950831049;                                     gr-mfaktc 
				

- Found by Alfred Eichhorn 
   May 29, 2024  n =73693: 200046209932683892220519 * 8236393422......c73650;       ecm  B1 = 5e4; sigma = 7063252640234059
   May 29, 2024  n =74279: 1643398485800760569800597963 * 6761057167......c74251;   ecm  B1 = 5e4; sigma = 0:3190123306072765


- Found by Sam Wagstaff    
   May 28, 2024  n =  433: 8824028723798902981997215284751342520751929886344438185486188157; ecm 


- Found by Kurt Beschorner
   May 20, 2024  n =13391: 1793492413423312326764415268439;                         P-1: B1 = 400e6
   May 20, 2024  n =13403: 1273543812643453522963599991;                            P-1: B1 = 150e6
   May 20, 2024  n =13405: 369025298556704617267721;                                P-1: B1 = 160e6
   May 20, 2024  n =13409: 194192011616958540654680651965361;                       P-1: B1 = 150e6
   May 20, 2024  n =13410: 152178270161972061588566451931;                          P-1: B1 = 650e6
   May 20, 2024  n=100135: 815970507695643165200161;                                P-1: B1 = 22e6
   May 20, 2024  n=100136: 1546658379143032144324057;                               P-1: B1 = 22e6
   May 20, 2024  n=100136: 29303671942968558470094241;                              P-1: B1 = 22e6
   May 20, 2024  n=149099: 191666476417472557;                                      gr-mfaktc 
   May 20, 2024  n=149197: 6018787351196629987;                                     gr-mfaktc 


- Found by Kurt Beschorner
   May 14, 2024  n =13310: 358431625219151747847359198249482811;                    P-1: B1 = 375e6
   May 14, 2024  n =13317: 310201028691515049948813827173;                          P-1: B1 = 150e6
   May 14, 2024  n =13335: 57025106614551649638121;                                 P-1: B1 = 160e6
   May 14, 2024  n =13383: 210951149080654081665994312063747;                       P-1: B1 = 160e6
   May 14, 2024  n =13387: 10821004067230761918288895517;                           P-1: B1 = 150e6
   May 14, 2024  n=100128: 12965255566706017;                                       P-1: B1 = 55e6
   May 14, 2024  n=100133: 1904718174391121;                                        P-1: B1 = 18e6
   May 14, 2024  n=148249: 5763577084308138631;                                     P-1: B1 = 17e6
   May 14, 2024  n=148853: 3201872038854169067;                                     gr-mfaktc 


- Found by Alfred Reich      
   Dec 30, 2023  n =11694: 25265936178377677271923695277;                           ecm  
 

- Found by Kurt Beschorner
   Apr 30, 2024  n = 1407: 1642802515245357383912944034418987319;                   ecm  B1 = 110e6; sigma = 2951090968820559
   Apr 30, 2024  n = 2564: 27189275929548127954581257800366864533484049;            ecm  B1 = 110e6; sigma = 2371963344321011
   Apr 30, 2024  n =13303: 70942071240313959608007929622671;                        P-1: B1 = 140e6
   Apr 30, 2024  n =13304: 57181546620162299318379978328716132443977;               P-1: B1 = 275e6


- Found by Alfred Eichhorn 
   Apr 29, 2024  n =73361: 1721423059346637677879;                                  ecm  B1 = 5e4; sigma = 1582421447520844
   Apr 29, 2024  n =73361: 408219527355823133818759;                                ecm  B1 = 5e4; sigma = 3826123512129081
   Apr 29, 2024  n =73433: 1480290724528512092611333441;                            ecm  B1 = 5e4; sigma = 7994314783584498
   Apr 29, 2024  n =79691: 10288546796776484035092067;                              ecm  B1 = 5e4; sigma = 5445195526405636


- Found by John Lee          
   Apr 29, 2024  n =12841: 4522160233632425161342305395203;                         ecm  B1 = 3e6; sigma = 851351432404823
   Apr 29, 2024  n =17573: 47231703533723987783810453;                              ecm  B1 = 1e6; sigma = 775071180902912
   Apr 29, 2024  n =35537: 330417476836465920785432053;                             ecm  B1 = 1e6; sigma = 7926625206541607


- Found by Kurt Beschorner
   Apr 20, 2024  n =13265: 1290668262735890884325761;                               P-1: B1 = 160e6
   Apr 20, 2024  n =13269: 2427709598953063772750559319;                            P-1: B1 = 140e6
   Apr 20, 2024  n =13282: 7480441362289212211418170076851;                         P-1: B1 = 275e6
   Apr 20, 2024  n=100118: 2213092040998752430410504041;                            P-1: B1 = 55e6
   Apr 20, 2024  n=100119: 135903373927930060098307;                                P-1: B1 = 16e6
 

- Found by YOYO@home/Gouik    
   Apr 14, 2024  n =  651: 18761726160436368465384904039916752385257524435903404839 * 1876172616......P298; ecm: B1 = 2.9e9; sigma = 0:15913088270609817167


- Found by Kurt Beschorner
   Apr 14, 2024  n =  659: 149909896971539560984652057797566890100299359259837 * 2846412051......P570; ecm  B1 =11e7; sigma = 0:4226535905387705
   Apr 14, 2024  n =13251: 12296428612923146794052172531037;                        P-1: B1 = 160e6
   Apr 14, 2024  n=100098: 17325552919871634468049;                                 P-1: B1 = 35e6
   Apr 14, 2024  n=100105: 144493170813628346471;                                   P-1: B1 = 17e6


- Found by Kurt Beschorner
   Apr 07, 2024  n =12771: 314224898531750364984013;                                P-1: B1 = 160e6
   Apr 07, 2024  n =12771: 238824929913673638997582363;                             P-1: B1 = 160e6 
   Apr 07, 2024  n =13158: 68581509075838066581670099156849;                        P-1: B1 = 140e6 
   Apr 07, 2024  n=100079: 6068994380637463834185467;                               P-1: B1 = 10e6 
   Apr 07, 2024  n=100363: 1016391456544433853547;                                  P-1: B1 = 15e6           
   Apr 07, 2024  n=100379: 66388841093949454147;                                    P-1: B1 = 15e6   
   Apr 07, 2024  n=100417: 286825064305738012150961;                                P-1: B1 = 15e6  
   Apr 07, 2024  n=100459: 22782665966376356329;                                    P-1: B1 = 15e6
   Apr 07, 2024  n=100517: 17361707890852059740855929;                              P-1: B1 = 16e6 
   Apr 07, 2024  n=100519: 101147426853941494945049;                                P-1: B1 = 16e6    
   Apr 07, 2024  n=100559: 95610786074378976307;                                    P-1: B1 = 16e6    
   Apr 07, 2024  n=100591: 1291405529277231477460435169;                            P-1: B1 = 16e6    
   Apr 07, 2024  n=100669: 2806386502390207284249241483;                            P-1: B1 = 16e6    
   Apr 07, 2024  n=100811: 281860909823518349338601;                                P-1: B1 = 16e6    
   Apr 07, 2024  n=100817: 507962247211408289;                                      P-1: B1 = 16e6    
   Apr 07, 2024  n=147941: 37558743005776041839 ***                                 P-1: B1 = 8.8e6  
   *** 37558743005776041839 = composite and all small factors are known 
   Apr 07, 2024  n=147977: 114084230812902508795841;                                P-1: B1 = 8.8e6    


- Found by Alfred Eichhorn 
   Apr 01, 2024  n =79337: 9145312312862925909640977721;                            ecm  B1 = 5e4; sigma = 7464158329682606
   Apr 01, 2024  n =79427: 1284283667245483471417172921;                            ecm  B1 = 5e4; sigma = 5590089294394130


- Found by Kurt Beschorner
   Apr 01, 2024  n =14549: 4005021584963302209471746401;                            P-1: B1 = 14e7
   Apr 01, 2024  n =14747: 252632181388341912925629401;                             P-1: B1 = 14e7           
   Apr 01, 2024  n=147799: 24724127378034035880566249;                              P-1: B1 = 8.8e6    


- Found by Kurt Beschorner
   Mar 29, 2024  n =  713: 31070861795268450321139284436817844468068239;            ecm: B1 = 11e7; sigma = 4800378595879534
   Mar 29, 2024  n =13175: 422686483673200816801;                                   P-1: B1 = 56e6           
   Mar 29, 2024  n =13187: 2072300747670825285092510827;                            P-1: B1 = 35e6     


- Found by Alfred Reich
   Mar 24, 2024  n = 8914: 1680862037183886151986766096284943;                      ecm

  
- Found by Anonymous   
   Mar 24, 2024  n =  695: 8397548714483238063663389786354175256018831              ecm: B1 = 3e6 
   Mar 24, 2024  n = 3019: 3139259690159845335135979206644089969  
   Mar 24, 2024  n = 3023: 107018760919046918330490860941009  
   Mar 24, 2024  n = 3097: 57179667256536688029715193166703488359641 
 


- Found by Kurt Beschorner
   Mar 22, 2024  n =  655: 2603347672124284040229582413722681735668626862241;       ecm: B1 =11e7; sigma = 0:3963412036452067 
   Mar 22, 2024  n =13108: 44331551068710498173013783881;                           P-1: B1 = 94e6           
   Mar 22, 2024  n =13131: 276600609054191780298991;                                P-1: B1 = 60e6     


- Found by Alfred Eichhorn 
   Mar 18, 2024  n =73019: 1323020047051919660237;                                  ecm  B1 = 5e4; sigma = 1341369107631264


- Found by NFS@home     
   Mar 17, 2024  n =1420L: 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901; SNFS 
        		

- Found by NFS@home     
   Mar 13, 2024  n =1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761; GNFS 


- Found by Alfred Eichhorn 
   Mar 07, 2024  n =72949: 11188142905007361998205693557 * 9931148721......c72920;  mprime: B1 = 5e4; sigma = 2465366403184896 
   Mar 07, 2024  n =78787: 30646987091435527679 * 3625514990......c78767;           ecm:    B1 = 5e4; sigma = 4416129323271267 
   Mar 07, 2024  n =79103: 3282162411477160845528807707 * 3385302041......c79075;   ecm:    B1 = 5e4; sigma = 3031437210351021 


- Found by Alfred Reich 
   Mar 05, 2024  n =16438: 8011505186691120932663584183
   Mar 05, 2024  n =31562: 35592147487676920463
   Mar 05, 2024  n =31604: 2431162452185039922126541
   Mar 05, 2024  n =31682: 13058845505765837
   Mar 05, 2024  n =31696: 849225733803273972858599153
   Mar 05, 2024  n =31732: 12771504608380995375745169
   Mar 05, 2024  n =31788: 105480823136736321938422081
   Mar 05, 2024  n =31792: 1124862107191521105889
   Mar 05, 2024  n =31794: 88267267172719831813
   Mar 05, 2024  n =31800: 2327427960927441388068001
   Mar 05, 2024  n =31808: 83385115506231195528257
   Mar 05, 2024  n =31816: 198354176884174670377
   Mar 05, 2024  n =31822: 21223407316494369009703
   Mar 05, 2024  n =31832: 3373542187061259737 2108806334021560983361
   Mar 05, 2024  n =31842: 121268577044650107133
   Mar 05, 2024  n =31854: 92478474903470166967
   Mar 05, 2024  n =31864: 517996647217868312873
   Mar 05, 2024  n =31866: 37189661286468510889 3098654567470609089997
   Mar 05, 2024  n =31890: 1551509199121673731
   Mar 05, 2024  n =31926: 332930426175643113828277
   Mar 05, 2024  n =31966: 123359708509810153686691 
   Mar 05, 2024  n =32130: 1101128720508897764041
   Mar 05, 2024  n =32250: 103526289664797293205001
   Mar 05, 2024  n =32264: 3506122191377189811281
   Mar 05, 2024  n =32354: 4806730864780971961801
   Mar 05, 2024  n =32530: 70162268702104794108054001
   Mar 05, 2024  n =32600: 135544576240587889388401
   Mar 05, 2024  n =32672: 13439466818282691185899297
   Mar 05, 2024  n =32702: 20917601776236212557397
   Mar 05, 2024  n =32730: 796330404308868018721
   Mar 05, 2024  n =32844: 690079785060125329306463041   
   Mar 05, 2024  n =32944: 412860491812863204455537
   Mar 05, 2024  n =33010: 416764638677805715091
   Mar 05, 2024  n =33024: 364050131659653121
   Mar 05, 2024  n =33054: 71589813152701862139157
   Mar 05, 2024  n =33054: 135387308179639106311687
   Mar 05, 2024  n =33066: 7387282999728627733
   Mar 05, 2024  n =33070: 16257062187566054875451
   Mar 05, 2024  n =33088: 34926628299166139009
   Mar 05, 2024  n =33104: 8551561512557816621435377
   Mar 05, 2024  n =33118: 231101417324066259413
   Mar 05, 2024  n =33154: 51802540286077905853 
   Mar 05, 2024  n =33192: 745340157524833631072553889
   Mar 05, 2024  n =33218: 9920977165696226539241
   Mar 05, 2024  n =33268: 484235742067818657125466001
   Mar 05, 2024  n =33274: 6113122020582917
   Mar 05, 2024  n =33280: 145579549664727792641
   Mar 05, 2024  n =33282: 88824651074901323677 24239066927517630699877
   Mar 05, 2024  n=196634: 17096212042074765825002047
   Mar 05, 2024  n=197074: 289351276331986049 


- Found by Kurt Beschorner
   Feb 29, 2024  n =10335: 1549956242052833162118620306401;                         ecm: B1 = 1e6; sigma = 0:6780271921532861 
   Feb 29, 2024  n =10408: 14370694506223165288707229970617;                        ecm: B1 = 1e6; sigma = 8806874869199137
   Feb 29, 2024  n =10424: 8606812592746882737809302233409;                         ecm: B1 = 1e6; sigma = 4247777747100720
   Feb 29, 2024  n =11414: 1167728903112961341541531507691;                         ecm: B1 = 1e6; sigma = 3216681011953137
   Feb 19, 2024  n=147449: 11828400848099433799;                                    gr-mfaktc


- Found by Sam Wagstaff    
   Feb 26, 2024  n =  818: 89909332182322637174267412766780073091874834080069255427757; ecm 


- Found by Kurt Beschorner 
   Feb 24, 2024  n =  649: 3185748559637643456066133367277689749860976255110653;    ecm: B1 =11e7; sigma = 0:3763781678208499 

                     
- Found by Alfred Eichhorn
   Feb 14, 2024  n =69859: 8434285361839984895778533;                               ecm: B1 = 5e4; sigma = 2445261498672925

					 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Oliver Kruse, Kurt Beschorner 
   Feb 10, 2024  n =  942: 9755872853901756680890615403191792297388117293582105055568357694889056982187114874692197915708047; SNFS  
   Details:
   - R942: SNFS-difficulty = 314 
     Sat Nov 11 11:17:54 2023  Msieve v. 1.54 (SVN r1044)
     Sat Nov 11 11:17:54 2023  random seeds: 60253a75 007cd855
     Sat Nov 11 11:17:54 2023  factoring 30862083832190969399642448329237079281358998786734541342232902569072683505580523380381489228423400116527554057338104357145657543175005161681489015756307835902130639405231933246244136812560041424780296737530889 (209 digits)
     Sat Nov 11 11:17:55 2023  no P-1/P+1/ECM available, skipping
     Sat Nov 11 11:17:55 2023  commencing number field sieve (209-digit input)
     Sat Nov 11 11:17:55 2023  R0: -10000000000000000000000000000000000000000000000000000
     Sat Nov 11 11:17:55 2023  R1: 1
     Sat Nov 11 11:17:55 2023  A0: 1
     Sat Nov 11 11:17:55 2023  A1: 0
     Sat Nov 11 11:17:55 2023  A2: 0
     Sat Nov 11 11:17:55 2023  A3: -10
     Sat Nov 11 11:17:55 2023  A4: 0
     Sat Nov 11 11:17:55 2023  A5: 0
     Sat Nov 11 11:17:55 2023  A6: 100
     Sat Nov 11 11:17:55 2023  skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     Sat Nov 11 11:17:55 2023  commencing relation filtering
     Sat Nov 11 11:17:55 2023  setting target matrix density to 130.0
     Sat Nov 11 11:17:55 2023  estimated available RAM is 130983.0 MB
     Sat Nov 11 11:17:55 2023  commencing duplicate removal, pass 1
     Sat Nov 11 11:52:23 2023  error -15 reading relation 196874611
     ...
     Sat Nov 11 15:51:51 2023  skipped 1120644 relations with b > 2^32
     Sat Nov 11 15:51:51 2023  skipped 2634 relations with composite factors
     Sat Nov 11 15:52:00 2023  found 325844461 hash collisions in 1439959899 relations
     Sat Nov 11 15:52:28 2023  commencing duplicate removal, pass 2
     Sat Nov 11 17:18:01 2023  found 8457401 duplicates and 1431502498 unique relations
     Sat Nov 11 17:18:01 2023  memory use: 16280.0 MB
     Sat Nov 11 17:18:03 2023  reading ideals above 812974080
     Sat Nov 11 17:18:03 2023  commencing singleton removal, initial pass
     Sat Nov 11 22:20:10 2023  memory use: 21024.0 MB
     Sat Nov 11 22:20:15 2023  reading all ideals from disk
     Sat Nov 11 22:22:13 2023  memory use: 26910.1 MB
     Sat Nov 11 22:25:23 2023  commencing in-memory singleton removal
     Sat Nov 11 22:28:29 2023  begin with 1431502498 relations and 1210425856 unique ideals
     Sat Nov 11 23:38:05 2023  reduce to 962297124 relations and 696430793 ideals in 15 passes
     Sat Nov 11 23:38:05 2023  max relations containing the same ideal: 53
     Sat Nov 11 23:42:10 2023  reading ideals above 720000
     Sat Nov 11 23:42:14 2023  commencing singleton removal, initial pass
     Sun Nov 12 03:28:50 2023  memory use: 21024.0 MB
     Sun Nov 12 03:28:54 2023  reading all ideals from disk
     Sun Nov 12 03:31:44 2023  memory use: 44648.7 MB
     ... 
     Tue Nov 14 08:39:49 2023  commencing in-memory singleton removal
     Tue Nov 14 08:40:17 2023  begin with 236428517 relations and 235660066 unique ideals
     Tue Nov 14 08:47:03 2023  reduce to 236285362 relations and 230413441 ideals in 6 passes
     Tue Nov 14 08:47:03 2023  max relations containing the same ideal: 85
     Tue Nov 14 08:51:28 2023  relations with 0 large ideals: 127875
     Tue Nov 14 08:51:28 2023  relations with 1 large ideals: 95486
     Tue Nov 14 08:51:28 2023  relations with 2 large ideals: 1301900
     Tue Nov 14 08:51:28 2023  relations with 3 large ideals: 7741623
     Tue Nov 14 08:51:28 2023  relations with 4 large ideals: 25166632
     Tue Nov 14 08:51:28 2023  relations with 5 large ideals: 49597077
     Tue Nov 14 08:51:28 2023  relations with 6 large ideals: 62285102
     Tue Nov 14 08:51:28 2023  relations with 7+ large ideals: 89969667
     Tue Nov 14 08:51:28 2023  commencing 2-way merge
     Tue Nov 14 08:56:46 2023  reduce to 150480987 relation sets and 144609066 unique ideals
     Tue Nov 14 08:56:47 2023  commencing full merge
     Tue Nov 14 10:39:21 2023  memory use: 18337.9 MB
     Tue Nov 14 10:39:51 2023  found 67501310 cycles, need 66981266
     Tue Nov 14 10:39:56 2023  weight of 66981266 cycles is about 8707922449 (130.01/cycle)
     Tue Nov 14 10:39:56 2023  distribution of cycle lengths:
     Tue Nov 14 10:39:56 2023  1 relations: 3801061
     Tue Nov 14 10:39:56 2023  2 relations: 4306316
     Tue Nov 14 10:39:56 2023  3 relations: 4711699
     Tue Nov 14 10:39:56 2023  4 relations: 4725778
     Tue Nov 14 10:39:56 2023  5 relations: 4836562
     Tue Nov 14 10:39:56 2023  6 relations: 4738034
     Tue Nov 14 10:39:56 2023  7 relations: 4697005
     Tue Nov 14 10:39:56 2023  8 relations: 4502168
     Tue Nov 14 10:39:56 2023  9 relations: 4303068
     Tue Nov 14 10:39:56 2023  10+ relations: 26359575
     Tue Nov 14 10:39:56 2023  heaviest cycle: 28 relations
     Tue Nov 14 10:40:32 2023  commencing cycle optimization
     Tue Nov 14 10:44:49 2023  start with 578109023 relations
     Tue Nov 14 11:23:20 2023  pruned 25164870 relations
     Tue Nov 14 11:23:21 2023  memory use: 15674.6 MB
     Tue Nov 14 11:23:21 2023  distribution of cycle lengths:
     Tue Nov 14 11:23:21 2023  1 relations: 3801061
     Tue Nov 14 11:23:21 2023  2 relations: 4418872
     Tue Nov 14 11:23:21 2023  3 relations: 4910588
     Tue Nov 14 11:23:21 2023  4 relations: 4919179
     Tue Nov 14 11:23:21 2023  5 relations: 5064834
     Tue Nov 14 11:23:21 2023  6 relations: 4959291
     Tue Nov 14 11:23:21 2023  7 relations: 4926516
     Tue Nov 14 11:23:21 2023  8 relations: 4712847
     Tue Nov 14 11:23:21 2023  9 relations: 4494751
     Tue Nov 14 11:23:21 2023  10+ relations: 24773327
     Tue Nov 14 11:23:21 2023  heaviest cycle: 28 relations
     Tue Nov 14 11:26:57 2023  RelProcTime: 259742
     Tue Nov 14 11:26:57 2023  elapsed time 72:09:03
 
   - Linear Algebra was performed by Oliver Kruse using CADO and MSIEVE-GPU
     - remove duplicates with CADO                                             
       - compile CADO with FLAGS_SIZE='-DSIZEOF_P_R_VALUES=8'.
       - run dup1.
       - run freerel to get the renumber table.
       - count the number of relations exactly (!).
       - run dup2.
       - run purge, making sure that -col-min-index is not too small and that -keep is set to 0.
       - convert all relations back to msieve format using convert_rels. 
       - the version used is not yet officially available; the currently used CADO version is not
         error-free	
       - build a matrix with the desired target density using msieve 
       - upload the matrix file to LambdaLabs, while building Greg Childers msieve-GPU on the target system
       - execute the LA (without root step) on a rented 80-GB-VRAM ( H100); time: about 73hours! 
       - get the dependency file (.dep) back to the local system
       - execute the root step (msieve -nc3) locally

ECM efforts
with Rn: 1 < n < 2000 (Jul 24, 2024)	with Rn: 1999 < n < 3000 (Jul 11, 2024)
with Rn: 2999 < n < 4000 (Jul 14, 2024)	with Rn: 3999 < n < 5000 (May 28, 2024)
with Rn: 4999 < n < 6000 (Jul 04, 2024)	with Rn: 5999 < n < 7000 (Jul 24, 2024)
with Rn: 6999 < n < 8000 (Jul 16, 2024)	with Rn: 7999 < n < 9000 (Jul 16, 2024)
with Rn: 8999 < n <10000 (Jul 16, 2024)	with Rn: 9999 < n <11000 (Jun 14, 2024)
with Rn: 10999 < n <12000 (Jun 12, 2024)	with Rn: 11999 < n <14980L/M (Jun 12, 2024)

currently ECM-efforts by yoyo@home: ecm-curves
B1 = 11e7/17500 curves/ numbers < 751 digits	617 in progress	619 in progress	629 in progress	641 in progress	643 in progress
B1 = 26e7/45000 curves/ numbers < 450 digits	527 in progress	557 in progress	625 in progress	1136 in progress	1160 in progress
B1 = 85e7/70000 curves/ numbers < 400 digits	535 in progress	651 in progress	1036 in progress	1386 in progress	1428 in progress
B1 = 29e8/nnnn curves/ numbers < 400 digits	639 in progress	1440 in progress	1530 in progress	.... in progress	.... in progress

Factorizations
Repunits: R1 - R2500 (Jul 16, 2024)	Repunits: R2501 - R5000 (Jul 14, 2024)
Repunits: R5001 - R7500 (Jul 04, 2024)	Repunits: R7501 - R10000 (Jul 09, 2024)
Repunits: R10001 - R12500 (May 03, 2024)	Repunits: R12501 - R14980L/M (Feb 27, 2024)

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 = 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)

Visitors since Oct 27, 2020: zur Webseite

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

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

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

Overview

Top of page

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

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

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

Overview

Top of page

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

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