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


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-  Last update: May 20, 2024

- 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 

				
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 12, 2024   R471/c301: SNFS-difficulty = 314;
                  2115M unique raw relations and 2170M unique ideals are collected;
                  target: 3000M unique raw relations;  
                  currently progress 70 %;    

  
- 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
	

- Found by Kurt Beschorner 
   Jan 30, 2024  n = 7263: 45518092928487766421674692049;                           ecm: B1 = 1e6; sigma = 7088526130537034 
   Jan 30, 2024  n =10750: 463203376918616978211875828162251;                       ecm: B1 = 1e6; sigma = 4552105348097849 
   Jan 30, 2024  n =10982: 208734985170341186165263799659;                          ecm: B1 = 1e6; sigma = 3988817073548606 
   Jan 30, 2024  n =11732: 442226965725515979200555021;                             ecm: B1 = 1e6; sigma = 4621185563765660 
               
 
- Found by YOYO@home/p3d-cluster  
   Jan 24, 2024  n = 1190: 1965071455547075976451793652436868115828909241266827512665803201; ecm: B1 = 7.6e9; sigma = 0:15698366658329656990


- Found by Alfred Eichhorn
   Jan 18, 2024  n =69239: 910886990662166228413268011249;                          ecm: B1 = 5e4; sigma = 6280182721233907
   Jan 18, 2024  n =72103: 4460034397243806489721;                                  ecm: B1 = 5e4; sigma = 8461366130542283

- Found by Yousuke Koide 
   Jan 04, 2024  n =  838: 1574200835907997335817135918163629758761675764557540970547321; ecm: B1 =30e7; sigma = 2:6044893835634751021


- Found by Kurt Beschorner 
   Dec 29, 2023  n = 5218: 1549339884595838182802063495302219;                      ecm: B1 = 3e6; sigma = 397965861566570 
   Dec 29, 2023  n =13067: 381885318948041718125341213;                             P-1: B1 = 30e6
   

- Found by Kurt Beschorner 
   Dec 24, 2023  n =  995: 4496923550405592963004409447842948530549521;             ecm: B1 =11e7; sigma = 0:5671941614311594 
   Dec 24, 2023  n = 8007: 74443633132160172610790541671227;                        ecm: B1 = 1e6; sigma = 0:6028324384104991 
   Dec 24, 2023  n = 8037: 38508757046525878223205656060816329;                     ecm: B1 = 1e6; sigma = 0:3759056719098403 
   Dec 24, 2023  n = 8883: 12310848646124592471308612180728921;                     ecm: B1 = 1e6; sigma = 0:3494728591877324 
   Dec 24, 2023  n =11326: 40934864723372094733948186127;                           ecm: B1 = 1e6; sigma = 5146009827622450 
   Dec 24, 2023  n =11452: 7472836251387998526237506669 * 1826911946......P4825;    ecm: B1 = 1e6; sigma = 1977351273509168 
   Dec 24, 2023  n =13023: 230223522995046177583541761;                             P-1: B1 = 54e6 

   
- Found by Alfred Eichhorn
   Dec 24, 2023  n =77543: 77297845932591945905323363;                              ecm: B1 = 5e4; sigma = 3292210568046258


- Found by Alfred Reich
   Dec 21, 2023  n =18184: 2999683797882171117794957593
   Dec 21, 2023  n =18404: 28939901929607431090928021
   Dec 21, 2023  n =18572: 1395833760418327547808581
   Dec 21, 2023  n =19254: 8012907944831068727941411
   Dec 21, 2023  n =33320: 4427186909972179259838401


- Found by Alfred Reich
   Dec 20, 2023  n = 3011: 8942391479719801452292494613336089209   
   Dec 20, 2023  n =14455: 489319115826935587481         
   Dec 20, 2023  n =14661: 2165330367619921            
   Dec 20, 2023  n =14795: 4048097292935081
   Dec 20, 2023  n =14853: 511549491340399609
   Dec 20, 2023  n =15221: 113644547512332978607643
   Dec 20, 2023  n =15699: 10624829026502227
   Dec 20, 2023  n =16695: 755227848837566643841
   Dec 20, 2023  n =16701: 1227568110509881227264391
   Dec 20, 2023  n =16737: 168553822144677480521683
   Dec 20, 2023  n =16747: 74070322256744898297308507
   Dec 20, 2023  n =16841: 620455417003224993360171431
   Dec 20, 2023  n =16849: 24739034223678109074881
   Dec 20, 2023  n =17243: 814444883421117551614082147
   Dec 20, 2023  n =17245: 155693450841751574639034031
   Dec 20, 2023  n =17311: 14999480628769610993923
   Dec 20, 2023  n =17375: 739314538130107951001
   Dec 20, 2023  n =20071: 74547860758815373271
   Dec 20, 2023  n =20131: 47582407370784897455643173
   Dec 20, 2023  n =20797: 1786576375704401
   Dec 20, 2023  n =20797: 545083931830093828949827
   Dec 20, 2023  n =21245: 449449693573017271 
   Dec 20, 2023  n =21655: 78322892986293521
   Dec 20, 2023  n =21855: 1250215154727214321
   Dec 20, 2023  n =22197: 236105297414411041
   Dec 20, 2023  n =28343: 17154421679728688611733
   Dec 20, 2023  n =28683: 128269750956599848571083
   Dec 20, 2023  n =22813: 48889525947960512557
   Dec 20, 2023  n =28701: 26190257570986323889
   Dec 20, 2023  n =28707: 37968841700959424053
   Dec 20, 2023  n =28715: 7164324052002846998561
   Dec 20, 2023  n =28739: 3307617341965244677
   Dec 20, 2023  n =28741: 213281116559381933
   Dec 20, 2023  n =28771: 6839335443984322559791591
   Dec 20, 2023  n =28773: 1432473151044421351
   Dec 20, 2023  n =28787: 17452463683720934618443
   Dec 20, 2023  n =28793: 107729921768353339709278728271
   Dec 20, 2023  n =28827: 8965801237961719
   Dec 20, 2023  n =28851: 562907856025988923
   Dec 20, 2023  n =28857: 781696861139188693
   Dec 20, 2023  n =28863: 72626191769479286825479
   Dec 20, 2023  n =28889: 1836020337675150820850399
   Dec 20, 2023  n =28893: 1119609406628084929
   Dec 20, 2023  n =28917: 5016781796997460267
   Dec 20, 2023  n =28969: 29971869223020582290473283
   Dec 20, 2023  n =28973: 30035356299547571519
   Dec 20, 2023  n =28983: 2485184297947357
   Dec 20, 2023  n =33509: 183241489617927721
   Dec 20, 2023  n =33545: 341666355771684992831
   Dec 20, 2023  n =33731: 179483876541541877
   Dec 20, 2023  n =34021: 85102612807734679 
   Dec 20, 2023  n =34229: 15425102807783813
   Dec 20, 2023  n =34323: 4316303364408121
   Dec 20, 2023  n =34335: 476691729296970601
   Dec 20, 2023  n =34493: 181725387787542851677
   Dec 20, 2023  n =34601: 109590398634678361
   Dec 20, 2023  n =34701: 3699717585157714957
   Dec 20, 2023  n =35711: 3547134933742597523
   Dec 20, 2023  n =34727: 848750426478622794281
   Dec 20, 2023  n =35785: 308525947202492927694481 
   Dec 20, 2023  n =35967: 104786371002391933
   Dec 20, 2023  n =35981: 10913297684973476959
   Dec 20, 2023  n =36407: 187764261619621287222203
   Dec 20, 2023  n =36501: 63530141741093471083
   Dec 20, 2023  n =36599: 22908933029439221923559
   Dec 20, 2023  n =36651: 12313462832515609
   Dec 20, 2023  n =36993: 360367423259726573068159
   Dec 20, 2023  n =37259: 36120871319278778707
   Dec 20, 2023  n =37275: 4738831762857111151
   Dec 20, 2023  n =38051: 4998132147851203729889 
   Dec 20, 2023  n =38191: 1006862581086363643
   Dec 20, 2023  n =50023: 4764590035602476593642900627
   Dec 20, 2023  n =50033: 111396848810420973131254970077
   Dec 20, 2023  n =50053: 3332542117417047121
   Dec 20, 2023  n =50107: 739274547390854471267
   Dec 20, 2023  n =50161: 1185818574457825928808524849
   Dec 20, 2023  n =50165: 58757029733533021144561
   Dec 20, 2023  n =50167: 1921667933049467681969827
   Dec 20, 2023  n =50169: 122233627565365351561
   Dec 20, 2023  n =50169: 15545788938471163
   Dec 20, 2023  n =50179: 80836423819964062258281685561
   Dec 20, 2023  n =50217: 103752473896238200564849
   Dec 20, 2023  n =50237: 25065431837599561
   Dec 20, 2023  n =50257: 6847939337800443973
   Dec 20, 2023  n =50263: 27710492289574389441479
   Dec 20, 2023  n =50281: 5687482637315709077
   Dec 20, 2023  n =50293: 13374240956667438361
   Dec 20, 2023  n =50303: 8830608239134503692333
   Dec 20, 2023  n =50335: 41169581415000435413231
   Dec 20, 2023  n =50337: 1067956299378797599
   Dec 20, 2023  n =50343: 26573360388347783822173
   Dec 20, 2023  n =50347: 193887384394507
   Dec 20, 2023  n =50347: 2343977597107436159
   Dec 20, 2023  n =50371: 33601903199020899719
   Dec 20, 2023  n =50373: 14948265618296083
   Dec 20, 2023  n =50375: 325115776091070342079001
   Dec 20, 2023  n =50379: 25227746700749692564921
   Dec 20, 2023  n =50395: 42682697894075536841
   Dec 20, 2023  n =50403: 391075333227921472639
   Dec 20, 2023  n =50419: 26245281971114892371338151
   Dec 20, 2023  n =50435: 6298901266834986348001
   Dec 20, 2023  n =50475: 82090457132654401801
   Dec 20, 2023  n =50483: 331006874283646178073271
   Dec 20, 2023  n =50499: 1244334600058275757
   Dec 20, 2023  n =50499: 300677443743864513961
   Dec 20, 2023  n =50507: 5945467046556194551
   Dec 20, 2023  n =50515: 8292732448341241
   Dec 20, 2023  n =50555: 255982417916670432644911
   Dec 20, 2023  n =85011: 153007511300335462119871
   Dec 20, 2023  n =85011: 232709170133079769
   Dec 20, 2023  n =85019: 17443094606296892413
   Dec 20, 2023  n =85025: 592924356031373845340342801
   Dec 20, 2023  n =86013: 172382128070013257348413
   Dec 20, 2023  n =86021: 8465041416832770625883
   Dec 20, 2023  n =86039: 1397010786205026634801
   Dec 20, 2023  n =86045: 305298208311139013081
   Dec 20, 2023  n =86059: 4421540972306530329354356847209
   Dec 20, 2023  n =86089: 1350585733253581613
   Dec 20, 2023  n =86107: 146769172059705119
   Dec 20, 2023  n =86115: 189424363720506914761
   Dec 20, 2023  n =86117: 24450460650450892157
   Dec 20, 2023  n =86131: 97633641121672399
   Dec 20, 2023  n =86135: 182340085122473951
   Dec 20, 2023  n =86139: 2991253508299621633267
   Dec 20, 2023  n =86147: 384727887232145364679
   Dec 20, 2023  n =86153: 107367251262944032757
   Dec 20, 2023  n =86155: 2191331972732928983471
   Dec 20, 2023  n =86165: 234488903705217978332231
   Dec 20, 2023  n =86169: 3297589613093688138769
   Dec 20, 2023  n =86185: 3763308972446878471
   Dec 20, 2023  n =86195: 16219892223096883241
   Dec 20, 2023  n =86199: 590830280529735004723
   Dec 20, 2023  n =86227: 13258604500360151
   Dec 20, 2023  n =86231: 507285038495597027
   Dec 20, 2023  n =86247: 9054217173992034056797
   Dec 20, 2023  n =86253: 1187505818229219241
   Dec 20, 2023  n =86285: 4587258038248431751
   Dec 20, 2023  n =86289: 10416210115559681959
   Dec 20, 2023  n =86295: 47413425370219222711
   Dec 20, 2023  n =86303: 181535303215366285151
   Dec 20, 2023  n =86315: 1162916266135643614121
   Dec 20, 2023  n =86325: 172042522615287001
   Dec 20, 2023  n =86343: 124892184654067
   Dec 20, 2023  n =86375: 23375289651796005751
   Dec 20, 2023  n =86383: 4647596429612159
   Dec 20, 2023  n =86397: 5728786701675522613
   Dec 20, 2023  n =86431: 26538521786213413
   Dec 20, 2023  n =86433: 163740043475175485443
   Dec 20, 2023  n =86449: 231210066482152769881
   Dec 20, 2023  n =86457: 55622873351688133
   Dec 20, 2023  n =86465: 233640559961800241
   Dec 20, 2023  n =86469: 101317896121856707
   Dec 20, 2023  n =86475: 58267305374978790001
   Dec 20, 2023  n =86477: 18353810898330538895090137009
   Dec 20, 2023  n =86487: 420803923639304819764723
   Dec 20, 2023  n =86493: 12103887572821705849
   Dec 20, 2023  n =86505: 249422228370063391
   Dec 20, 2023  n =86513: 247295867808603618187
   Dec 20, 2023  n =86525: 4817268828673482853594201
   Dec 20, 2023  n =86527: 31215381315929231
   Dec 20, 2023  n =86541: 182200466272378202923
   Dec 20, 2023  n =86559: 2041431607993578439
   Dec 20, 2023  n =86567: 16435080963410897214672471773
   Dec 20, 2023  n =86575: 183562088733647891695034351
   Dec 20, 2023  n =86583: 232936458164286131557
   Dec 20, 2023  n =86595: 2203950449780923853178942391
   Dec 20, 2023  n =86597: 17361190988249081
   Dec 20, 2023  n =86603: 98169724723437049
   Dec 20, 2023  n =86605: 95168863923738791
   Dec 20, 2023  n =86611: 1781967587073920947
   Dec 20, 2023  n =86617: 106929326599631
   Dec 20, 2023  n =86619: 9012265857305568081362893
   Dec 20, 2023  n =86623: 125153542435533997081
   Dec 20, 2023  n =86637: 144736502030089
   Dec 20, 2023  n =86649: 1531470091074997
   Dec 20, 2023  n =86653: 72959338813451614333517
   Dec 20, 2023  n =86669: 13308375982048941751
   Dec 20, 2023  n =86683: 195974795808605317093
   Dec 20, 2023  n =86687: 125635351177897163249
   Dec 20, 2023  n =86689: 169953555311266216783520239
   Dec 20, 2023  n =86691: 10807655421701887849
   Dec 20, 2023  n =86697: 6236817986961731262709747
   Dec 20, 2023  n =86699: 1344173781299256740402292911
   Dec 20, 2023  n =86709: 516877046864047895551
   Dec 20, 2023  n =86711: 552883191657835460802457111
   Dec 20, 2023  n =86715: 238310515915927498157853191311
   Dec 20, 2023  n =86723: 11941360995299191
   Dec 20, 2023  n =86725: 25757429267543894403001
   Dec 20, 2023  n =86727: 1429615650652541083
   Dec 20, 2023  n =86729: 7192827878409029829881
   Dec 20, 2023  n =86737: 1166211644179052479
   Dec 20, 2023  n =86745: 445670432786861074231
   Dec 20, 2023  n =86763: 11485301536223961871
   Dec 20, 2023  n =86773: 176912840509964999837
   Dec 20, 2023  n =86793: 8276903445085129
   Dec 20, 2023  n =86795: 11391215673425588821882441
   Dec 20, 2023  n =86799: 216031593685511055601
   Dec 20, 2023  n =86819: 772716325079153060871883
   Dec 20, 2023  n =86845: 42140157888831985511
   Dec 20, 2023  n =86847: 2397685651276009
   Dec 20, 2023  n =86849: 3329918641774774298201
   Dec 20, 2023  n =86855: 1533409900143431911
   Dec 20, 2023  n =86859: 186941224833839187834547
   Dec 20, 2023  n =86867: 761837163085846717
   Dec 20, 2023  n =86871: 282482466391164199
   Dec 20, 2023  n =86873: 20069473248628003
   Dec 20, 2023  n =86883: 2254833001167136544883409
   Dec 20, 2023  n =86887: 5612431570273603
   Dec 20, 2023  n =86901: 307276354484316460203013
   Dec 20, 2023  n =86921: 41952504985766397447386879
   Dec 20, 2023  n =86927: 452888882130921479072231
   Dec 20, 2023  n =86937: 20892393354908311
   Dec 20, 2023  n =86945: 60259619432786801
   Dec 20, 2023  n =86959: 325147991607694020209
   Dec 20, 2023  n =86977: 1375303813878391
   Dec 20, 2023  n =86989: 1979272861060373929



ECM efforts
with Rn:           1 < n < 2000 (May 20, 2024) with Rn:     1999 < n < 3000 (Apr 30, 2024)
with Rn:     2999 < n < 4000 (Mar 24, 2024) with Rn:     3999 < n < 5000 (Apr 20, 2024)
with Rn:     4999 < n < 6000 (May 20, 2024) with Rn:     5999 < n < 7000 (May 12, 2024)
with Rn:     6999 < n < 8000 (Apr 04, 2024) with Rn:     7999 < n < 9000 (May 05, 2024)
with Rn:     8999 < n <10000 (Apr 15, 2024) with Rn:     9999 < n <11000 (May 20, 2024)
with Rn:   10999 < n <12000 (May 20, 2024) with Rn:   11999 < n <14980L/M (May 20, 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
1224
in progress
1248
in progress
....
in progress
....
in progress
....
in progress



Factorizations
Repunits: R1        - R2500 (Apr 30, 2024) Repunits:  R2501 - R5000 (Apr 30, 2024)
Repunits: R5001   - R7500 (Jan 30, 2024) Repunits: R7501 - R10000 (Mar 29, 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 ...
    - 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)




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