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


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-  Last update: Apr 08, 2024

- 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    

				
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Apr 04, 2024   R471/c301: SNFS-difficulty = 314;
                  1688M unique raw relations and 1960M unique ideals are collected;
                  target: 3000M unique raw relations;  
                  currently progress 56 %;    


- 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


- Found by Alfred Reich
   Dec 15, 2023  n=100135: 3837462737953265401
   Dec 15, 2023  n=100173: 2969954606258713681
   Dec 15, 2023  n=100231: 2914352098217302241
   Dec 15, 2023  n=100375: 4607776309587001
   Dec 15, 2023  n=100381: 19584474697037077
   Dec 15, 2023  n=100461: 1543588566527893
   Dec 15, 2023  n=100533: 784155971193235573
   Dec 15, 2023  n=100625: 6187747093963751
   Dec 15, 2023  n=100723: 3056471727756902850809
   Dec 15, 2023  n=100789: 3418673430568813
   Dec 15, 2023  n=100841: 4362243266618329
   Dec 15, 2023  n=100867: 711526897239954563
   Dec 15, 2023  n=100897: 5888604761294197
   Dec 15, 2023  n=100951: 2554364607905813
   Dec 15, 2023  n=100955: 2734123743480191
   Dec 15, 2023  n=100997: 26555827334882705627
   Dec 15, 2023  n=101013: 129274221741124132399
   Dec 15, 2023  n=101029: 250532745483017969
   Dec 15, 2023  n=101093: 27700938064778930383483
   Dec 15, 2023  n=101125: 42666204444819001
   Dec 15, 2023  n=101227: 4090612959903653
   Dec 15, 2023  n=101245: 36188574289273287631
   Dec 15, 2023  n=101301: 321148260456397088922397
   Dec 15, 2023  n=101345: 4162330127811881
   Dec 15, 2023  n=101367: 41464815440580476533
   Dec 15, 2023  n=101491: 1594258423248401
   Dec 15, 2023  n=101565: 149868027410913543576511
   Dec 15, 2023  n=101589: 3143999213920929601
   Dec 15, 2023  n=101589: 7614368404345783519
   Dec 15, 2023  n=101601: 107321559496605501670875997
   Dec 15, 2023  n=101667: 3143777989348357
   Dec 15, 2023  n=101735: 20297398668389475551
   Dec 15, 2023  n=101825: 431825008439158751
   Dec 15, 2023  n=101867: 872157355506442751
   Dec 15, 2023  n=101885: 784674572749197742081
   Dec 15, 2023  n=102175: 293665357109039401
   Dec 15, 2023  n=102201: 814695681588870973
   Dec 15, 2023  n=102277: 3122977068292333547
   Dec 15, 2023  n=102289: 126748336203333307
   Dec 15, 2023  n=102465: 207107572459396099591
   Dec 15, 2023  n=102467: 7555451327561831
   Dec 15, 2023  n=102545: 370801842837453241
   Dec 15, 2023  n=102635: 61200245310873761
   Dec 15, 2023  n=102649: 81260329743351875293
   Dec 15, 2023  n=102651: 3492264482228879683
   Dec 15, 2023  n=102699: 182263241323164871
   Dec 15, 2023  n=102721: 179744652469762055464837
   Dec 15, 2023  n=102995: 183835357989580481
   Dec 15, 2023  n=103085: 932431536648643481
   Dec 15, 2023  n=103151: 4809941921451319
   Dec 15, 2023  n=103191: 16546105617914242129
   Dec 15, 2023  n=103345: 297885870585907561
   Dec 15, 2023  n=103351: 2146699373067199
   Dec 15, 2023  n=103355: 86198034626410591921
   Dec 15, 2023  n=103379: 498834504820599733
   Dec 15, 2023  n=103387: 1054001812218495236881
   Dec 15, 2023  n=103501: 29708713591543717
   Dec 15, 2023  n=103587: 115419307547119692733
   Dec 15, 2023  n=103731: 15441661173635077
   Dec 15, 2023  n=103805: 502694679147531001
   Dec 15, 2023  n=103897: 1421959882999511
   Dec 15, 2023  n=103911: 38661929840986726979587
   Dec 15, 2023  n=103941: 3971322750844219159
   Dec 15, 2023  n=104039: 1328134429968347
   Dec 15, 2023  n=104045: 457092448405210351
   Dec 15, 2023  n=104083: 8686106162973577157
   Dec 15, 2023  n=104179: 21279779120623334648147
   Dec 15, 2023  n=104403: 214812463280593047481
   Dec 15, 2023  n=104405: 180759156912895961
   Dec 15, 2023  n=104557: 5967681434215597951
   Dec 15, 2023  n=104585: 827602746591653761
   Dec 15, 2023  n=104825: 95568321451822801
   Dec 15, 2023  n=104863: 81923175399022583671
   Dec 15, 2023  n=104939: 33030670517942404991
   Dec 15, 2023  n=105025: 1832894758101088601
   Dec 15, 2023  n=105183: 248810634564639031
   Dec 15, 2023  n=105343: 10052122403340284569
   Dec 15, 2023  n=105493: 2133823579526959
   Dec 15, 2023  n=105535: 3212309889596111
   Dec 15, 2023  n=105551: 18630699774014234689
   Dec 15, 2023  n=105591: 4231208739438799
   Dec 15, 2023  n=105697: 1397106568159665373
   Dec 15, 2023  n=105709: 1279312203357107
   Dec 15, 2023  n=105857: 18376121591761450163
   Dec 15, 2023  n=105899: 47251222530599615917
   Dec 15, 2023  n=105913: 11607188817757815495119
   Dec 15, 2023  n=106025: 1699293051524681401
   Dec 15, 2023  n=106063: 32452825705922197
   Dec 15, 2023  n=106085: 62847272094664961
   Dec 15, 2023  n=106191: 157822803094190797
   Dec 15, 2023  n=106211: 3099924361660351
   Dec 15, 2023  n=106333: 1487230996431253
   Dec 15, 2023  n=106351: 488114500109675111
   Dec 15, 2023  n=106389: 1892357809243043203
   Dec 15, 2023  n=106481: 1683789986941862587
   Dec 15, 2023  n=106489: 3071056904705205037
   Dec 15, 2023  n=106587: 1523734470635599
   Dec 15, 2023  n=106675: 32019890393185001
   Dec 15, 2023  n=106741: 91231303979441359
   Dec 15, 2023  n=106777: 15443104098436169
   Dec 15, 2023  n=106885: 117266248077130038751
   Dec 15, 2023  n=106919: 47955034386944813
   Dec 15, 2023  n=106929: 830601200888179957
   Dec 15, 2023  n=107013: 2880076611770053
   Dec 15, 2023  n=107049: 1142136377959279
   Dec 15, 2023  n=107177: 33266524060889323
   Dec 15, 2023  n=107181: 1706060406505249
   Dec 15, 2023  n=107341: 160176806097297289
   Dec 15, 2023  n=107397: 5488065931492369
   Dec 15, 2023  n=107489: 48495106832112403
   Dec 15, 2023  n=107567: 36511360633631124083
   Dec 15, 2023  n=107751: 5009980645619083
   Dec 15, 2023  n=107777: 110439144397154542933
   Dec 15, 2023  n=107803: 1085853943084507
   Dec 15, 2023  n=107823: 5163493115786359
   Dec 15, 2023  n=107859: 21226233829029319
   Dec 15, 2023  n=107963: 472353529203679718401
   Dec 15, 2023  n=107975: 2568555393447751
   Dec 15, 2023  n=108017: 7306008478860001
   Dec 15, 2023  n=108039: 328549190415243037
   Dec 15, 2023  n=108047: 822493223707650311
   Dec 15, 2023  n=108133: 12387032989905877
   Dec 15, 2023  n=108177: 171099894013390366477
   Dec 15, 2023  n=108303: 140821880761709083
   Dec 15, 2023  n=108437: 5613735491012573
   Dec 15, 2023  n=108453: 16620626507489927551
   Dec 15, 2023  n=108467: 3806681380770523
   Dec 15, 2023  n=108523: 312745257752929889
   Dec 15, 2023  n=108527: 1814075573993069477
   Dec 15, 2023  n=108577: 1025437956573694427
   Dec 15, 2023  n=108579: 1892548991278357
   Dec 15, 2023  n=108801: 28294660608248803231
   Dec 15, 2023  n=108891: 61861143034857043
   Dec 15, 2023  n=108937: 314951847893125362543271
   Dec 15, 2023  n=108965: 1222688699234680511
   Dec 15, 2023  n=108981: 173078160296374287503893
   Dec 15, 2023  n=108983: 5769932437797431
   Dec 15, 2023  n=108983: 15298274105696359
   Dec 15, 2023  n=109219: 1500767402131867453
   Dec 15, 2023  n=109245: 404857376204925961
   Dec 15, 2023  n=109281: 1007210230511227
   Dec 15, 2023  n=109317: 815072972953274965755853
   Dec 15, 2023  n=109361: 21363620525646068867
   Dec 15, 2023  n=109419: 11808968710122043
   Dec 15, 2023  n=109505: 1698128483203793521
   Dec 15, 2023  n=109529: 10295720312597147
   Dec 15, 2023  n=109615: 150272834900921921
   Dec 15, 2023  n=109627: 2586140491753253
   Dec 15, 2023  n=109649: 471992327325974353387
   Dec 15, 2023  n=109669: 3128160982523249
   Dec 15, 2023  n=109825: 1066778190409801
   Dec 15, 2023  n=109887: 21934471123273243
   Dec 15, 2023  n=110259: 1811836946567467
   Dec 15, 2023  n=110289: 4041490592752573
   Dec 15, 2023  n=110405: 72872965020101921
   Dec 15, 2023  n=110525: 30599902441931401
   Dec 15, 2023  n=110549: 10359600801809323
   Dec 15, 2023  n=110549: 1464794141204058293
   Dec 15, 2023  n=110559: 15791777855837569
   Dec 15, 2023  n=110593: 1315182280298923
   Dec 15, 2023  n=110733: 20564201445896599
   Dec 15, 2023  n=110739: 53618918350318231
   Dec 15, 2023  n=110757: 61702090848726378079
   Dec 15, 2023  n=110763: 94121726153898529
   Dec 15, 2023  n=110797: 1180023707856124441
   Dec 15, 2023  n=110915: 1976092414032241
   Dec 15, 2023  n=110925: 2104133922586351
   Dec 15, 2023  n=110959: 4400759212849398494947
   Dec 15, 2023  n=110965: 2147054012123681
   Dec 15, 2023  n=110981: 863466738106791677
   Dec 15, 2023  n=110999: 172004495876274228077
   Dec 15, 2023  n=111019: 3165798633813492307
   Dec 15, 2023  n=111171: 730461908429774893
   Dec 15, 2023  n=111197: 56063990159297441
   Dec 15, 2023  n=111421: 19873787465690675761
   Dec 15, 2023  n=111525: 16382075180553151
   Dec 15, 2023  n=111545: 74962693130499511
   Dec 15, 2023  n=111683: 8770432091919499947089
   Dec 15, 2023  n=112079: 4094728195251761
   Dec 15, 2023  n=112143: 1243331950087483
   Dec 15, 2023  n=112235: 60453500620453631
   Dec 15, 2023  n=112373: 14767663648782907
   Dec 15, 2023  n=112377: 23189783849693722837
   Dec 15, 2023  n=112411: 40357361682456391
   Dec 15, 2023  n=112455: 14164153316926831
   Dec 15, 2023  n=112533: 48645513597081391
   Dec 15, 2023  n=112829: 25509858732142434707
   Dec 15, 2023  n=112857: 530854488744679279
   Dec 15, 2023  n=112863: 109287729669619213
   Dec 15, 2023  n=112897: 5208119049888191
   Dec 15, 2023  n=113055: 3897684646917151
   Dec 15, 2023  n=113057: 18272816353970327129
   Dec 15, 2023  n=113323: 290927000667873641
   Dec 15, 2023  n=113519: 4153695722375809
   Dec 15, 2023  n=113533: 1640256169423187
   Dec 15, 2023  n=113633: 39178941015154279
   Dec 15, 2023  n=113681: 73461005958611729
   Dec 15, 2023  n=113767: 79609807322522003
   Dec 15, 2023  n=113939: 1421871353169947
   Dec 15, 2023  n=113961: 5940695149229431
   Dec 15, 2023  n=113973: 153086658970467781723
   Dec 15, 2023  n=114085: 1123215780014351
   Dec 15, 2023  n=114099: 2568163970965471
   Dec 15, 2023  n=114249: 1079278665166921
   Dec 15, 2023  n=114275: 8886527645578801
   Dec 15, 2023  n=114293: 3745859640714801161
   Dec 15, 2023  n=114297: 20980452161136067
   Dec 15, 2023  n=114425: 16107717154754801
   Dec 15, 2023  n=114439: 95707240444230533
   Dec 15, 2023  n=114511: 364870659059502227
   Dec 15, 2023  n=114539: 5956528984881037
   Dec 15, 2023  n=114625: 3174716337430751
   Dec 15, 2023  n=114807: 368109918140380125403
   Dec 15, 2023  n=114813: 1166977694731969
   Dec 15, 2023  n=114867: 527812794542940300001
   Dec 15, 2023  n=115007: 653699808940014533 
   Dec 15, 2023  n =20100: 9662726996752755499068773593201
   Dec 15, 2023  n =23132: 590929466313489821402869
   Dec 15, 2023  n =60380: 5489303444931911663517401
   Dec 15, 2023  n =61260: 20803848204472329730901341
   Dec 15, 2023  n =61460: 113034432345960488485781
   Dec 15, 2023  n =62340: 752673643167614497799785541394241
   Dec 15, 2023  n =62660: 58828730801039608072318544761
   Dec 15, 2023  n =63020: 3051795672158010000082331741
   Dec 15, 2023  n =63540: 4100353212798453277070657101
   Dec 15, 2023  n =63620: 356898400373658530175204427175462741
   Dec 15, 2023  n =63700: 1499570870116484267020464001
   Dec 15, 2023  n =67660: 33555270039905405328461
   Dec 15, 2023  n =70300: 72263010384456334711970501
   Dec 15, 2023  n =70940: 10809515298855507478951981921671862661
   Dec 15, 2023  n =83420: 1461027981707744016319382101
   Dec 15, 2023  n =90700: 85415032842444600391991101
   Dec 15, 2023  n =92660: 1296044802473948687999681


- Found by Alfred Reich
   Dec 12, 2023  n =60337: 5568672008838260813;                                     ecm     
   Dec 12, 2023  n =60419: 2639148885143589521;                                     ecm     
   Dec 12, 2023  n =60437: 3286388182528049;                                        ecm     
   Dec 12, 2023  n =60511: 124616446994291701483;                                   ecm     
   Dec 12, 2023  n =60515: 139118657789148311;                                      ecm     
   Dec 12, 2023  n =60561: 1131847019916979352401;                                  ecm     
   Dec 12, 2023  n =60667: 7025355422879412427;                                     ecm     
   Dec 12, 2023  n =60699: 278133968442962197;                                      ecm     
   Dec 12, 2023  n =75625: 542516370778170978751;                                   ecm     
   Dec 12, 2023  n =75777: 61490101914688201;                                       ecm     
   Dec 12, 2023  n =75827: 22795183518565425900347;                                 ecm     
   Dec 12, 2023  n =75911: 93538524605199587;                                       ecm     
   Dec 12, 2023  n=100025: 152501370425473874211345401;                             ecm     


- Found by Kurt Beschorner 
   Dec 09, 2023  n = 5158: 12526504286553414480387071457504877;                     ecm: B1 = 3e6; sigma = 0:2553564566552160   
   Dec 09, 2023  n = 5941: 100907536708134675930973500425627843;                    ecm: B1 = 1e6; sigma = 0:5413159547376008   
   Dec 09, 2023  n = 6275: 8352737420744820793174812768694070571151 * 4324856989......P4936; ecm: B1 = 1e6; sigma = 0:598971611001117
   Dec 09, 2023  n = 9914: 21119725592364935371554207390169;                        ecm: B1 = 1e6; sigma = 0:8488974959025917   
   Dec 09, 2023  n =12981: 227455692714607938429312523;                             P-1: B1 = 50e6  
   Dec 09, 2023  n=147377: 6505129998515294448791;                                  ecm: B1 = 5e4; sigma = 0:670963036774753   


- Found by Alfred Reich
   Dec 07, 2023  n =11212: 83791510283897781068562569;                              ecm: B1 =25e4; sigma = 4305484695987158   
   Dec 07, 2023  n =11298: 405327039373714068134452699;                             ecm: B1 =25e4; sigma = 4462813532609925   
   Dec 07, 2023  n=11300L: 2182180350286462924030858025501;                         ecm: B1 = 1e6; sigma = 7144502905419721   
   Dec 07, 2023  n=11300L: 51476539527811997194031844173935851401;                  ecm: B1 = 1e6; sigma = 5918365906898771   
   Dec 07, 2023  n =11310: 17689651111602228006889768921;                           ecm: B1 =25e4; sigma = 8158972006967651   
   Dec 07, 2023  n =11358: 1117402462196473692911852287;                            ecm 
   Dec 07, 2023  n =11358: 428311146848369988856041100891;                          ecm: B1 =25e4; sigma = 5086655985489555   
   Dec 07, 2023  n =11366: 52303090474636039617938659612733;                        ecm: B1 =25e4; sigma = 5827917219724994   
   Dec 07, 2023  n =11658: 72329534173671071455834840507927;                        ecm: B1 =25e4; sigma = 5631683109611796   
   Dec 07, 2023  n=11660L: 40492576319292955850829024592793701609134641;            ecm: B1 = 1e6; sigma = 6343068577069312   
   Dec 07, 2023  n =11666: 186838644187268048751647381663;                          ecm: B1 =25e4; sigma = 571545193689189   
   Dec 07, 2023  n =11716: 192323520543231793960953379469;                          ecm: B1 =25e4; sigma = 2802833690821320   
   Dec 07, 2023  n =11762: 59087229310237473190324133;                              ecm: B1 =25e4; sigma = 4593314167755052   
   Dec 07, 2023  n=11820M: 306089199113717892024275119681;                          ecm: B1 = 1e6; sigma = 8309856703213704   
   Dec 07, 2023  n =11822: 55825391503338973544921658331;                           ecm: B1 =25e4; sigma = 8199557882983776   
   Dec 07, 2023  n =11996: 6354860762748834663192340609;                            ecm: B1 =25e4; sigma = 205576270073522   
   Dec 07, 2023  n =12026: 6893048385881275758815788126453931;                      ecm: B1 =25e4; sigma = 7294461903791317   
   Dec 07, 2023  n =12118: 171813130989462977163422287571;                          ecm: B1 =25e4; sigma = 1807550361382550   
   Dec 07, 2023  n =12472: 4460931746141906126885900765588297;                      ecm: B1 =25e4; sigma = 1694915245350751   


- Found by Alfred Reich
   Dec 06, 2023  n =10710: 35796682173053028162358962001;                           ecm: B1 = 1e6    
   Dec 06, 2023  n =10734: 2614042951033680019624870081;                            ecm: B1 =25e4; sigma = 7989499509182453   
   Dec 06, 2023  n =10736: 23833035179077111324245900289;                           ecm: B1 =25e4; sigma = 2401096546753386   
   Dec 06, 2023  n =10846: 79743601441260353939635797344699;                        ecm: B1 =25e4; sigma = 1280250833160802   
   Dec 06, 2023  n =10846: 10305097943509542737876418011074291;                     ecm: B1 =25e4; sigma = 1452405752900911   
   Dec 06, 2023  n =10864: 16717412159798663380636472177;                           ecm: B1 =25e4; sigma = 3501656591714898   
   Dec 06, 2023  n =10880: 6583700555707288764935464961;                            ecm  
   Dec 06, 2023  n =10892: 1431524229570210282674041885081;                         ecm: B1 =25e4; sigma = 274494665663402   
   Dec 06, 2023  n =10974: 13614572979286286502530862521731;                        ecm: B1 =25e4; sigma = 8574888540092621   
   Dec 06, 2023  n =10986: 4742648965537267382209475329;                            ecm   
   Dec 06, 2023  n =10990: 566556816853418729839417001;                             ecm: B1 =25e4; sigma = 8143587754056583   
   Dec 06, 2023  n =11032: 4733344496763640974691920410617;                         ecm 
   Dec 06, 2023  n =11036: 294573797733621430922028523081;                          ecm  
   Dec 06, 2023  n =11040: 273936751955640120264911619220481281;                    ecm   
   Dec 06, 2023  n =11142: 78670807981822580935210744213;                           ecm: B1 =25e4; sigma = 1749671451701082   
   Dec 06, 2023  n =11142: 22878072073574740342173268358677;                        ecm    
   Dec 06, 2023  n =11144: 70776007670260938515176443424241;                        ecm   
   Dec 06, 2023  n =11158: 109342335162557559820950948449;                          ecm   
   Dec 06, 2023  n=11180L: 43109862431095754405502938723895830021;                  ecm: B1 = 1e6; sigma = 5766415734821624   



ECM efforts
with Rn:           1 < n < 2000 (Apr 06, 2024) with Rn:     1999 < n < 3000 (Apr 01, 2024)
with Rn:     2999 < n < 4000 (Mar 24, 2024) with Rn:     3999 < n < 5000 (Dec 23, 2023)
with Rn:     4999 < n < 6000 (Mar 29, 2024) with Rn:     5999 < n < 7000 (Apr 04, 2024)
with Rn:     6999 < n < 8000 (Apr 04, 2024) with Rn:     7999 < n < 9000 (Apr 06, 2024)
with Rn:     8999 < n <10000 (Apr 04, 2024) with Rn:     9999 < n <11000 (Apr 06, 2024)
with Rn:   10999 < n <12000 (Apr 06, 2024) with Rn:   11999 < n <14980L/M (Apr 06, 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 (Mar 29, 2024) Repunits:  R2501 - R5000 (Mar 29, 2024)
Repunits: R5001   - R7500 (Jan 30, 2024) Repunits: R7501 - R10000 (Mar 29, 2024)
Repunits: R10001 - R12500 (Feb 29, 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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