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


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News

-  Last update: May 23, 2023 

- Found by Andreas Enge    
   May 15, 2023  n =86453 is proofen prime                                          ECPP
	 
	
- Found by Kurt Beschorner    
   May 22, 2023  n =11563: 288876102146873945958113077;                             P-1: B1 = 35e6
   May 22, 2023  n =11599: 14933221091440841710872172904603837;                     P-1: B1 = 42e6
 

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 22, 2023   R942/c209: SNFS-difficulty = 314 
                  720M unique raw relations of 1250M are collected
                  currently progress 57.6 %;    
				  		  

- Found by YOYO@home/ChelseaOilman   
   May 18, 2023   n =1190: 15670675217372765545752167365705617247353811;            ecm: B1 = 850e6; sigma = 0:10816724694808590541

	
- Found by Kurt Beschorner    
   May 18, 2023  n = 1479: 33549295409851770975125709849074683471;                  ecm: B1 = 43e6; sigma = 956110076594678
   May 18, 2023  n = 6167: 3675840732080772150325112719;                            ecm: B1 = 1e6; sigma = 5354000922392018
   May 18, 2023  n =11531: 2650979795946123118860305521;                            P-1: B1 = 37e6
   May 18, 2023  n =12530: 7688255015384454267929550281;                            P-1: B1 = 130e6


- Found by YOYO@home/[H]pututu   
   May 17, 2023   n =1182: 4551047530439682198526844933441545392551140771;          ecm: B1 = 850e6; sigma = 0:15946812152344745850


-  Found by Alfred Eichhorn 
   May 13, 2023   n =86837: 606921353312041199209590707159;                         ecm: B1 = 5e4; sigma = 3105880448041814
  

- Found by Kurt Beschorner  
   May 13, 2023  n = 6137: 43573850930276682505962068323;                           ecm: B1 = 1e6; sigma = 0:7345291352286289
   May 13, 2023  n=147163: 213471125449180111;                                      gr-mfaktc

- Found by YOYO@home/crashtech)   
   May 10, 2023   n =1086: 484165712170909795871964783465540188248186710475652666425207; ecm: B1 = 850e6; sigma = 0:10111744675193824145   
 
    
- Found by Kurt Beschorner  
   May 10, 2023  n=147047: 5140510902285228893;                                     gr-mfaktc


- Found by YOYO@home/biodoc)   
   May 06, 2023   n =1254: 6379603923183116557572498736754081808902892003349145377489; ecm: B1 = 850e6; sigma = 0:3927414157329920254 
 
  
- Found by Kurt Beschorner  
   May 05, 2023  n =11327: 40001730885786863979423041;                              P-1: B1 = 35e6 
   May 05, 2023  n =11349: 687835220902497655621008880119733;                       P-1: B1 = 65e6 
   May 05, 2023  n =11363: 872344334337956979629350525009;                          P-1: B1 = 40e6 
   May 05, 2023  n =11367: 237468520263209197782403;                                P-1: B1 = 60e6 
   May 05, 2023  n =11371: 4097375604489481212785218131199802399;                   P-1: B1 = 35e6 
   May 05, 2023  n=146893: 7885083320671676963;                                     gr-mfaktc


- Found by Kurt Beschorner  
   Apr 30, 2023  n = 5759: 147876912822130407898624760255369587274609;              ecm: B1 = 1e6; sigma = 0:6544452679604896
   Apr 30, 2023  n =11295: 604100121206666364956401591238472961;                    P-1: B1 = 70e6 


-  Found by Alfred Eichhorn 
   Apr 30, 2023   n =86561: 574110157886554629901013 * 1935362222......c86537;      ecm: B1 = 5e4; sigma = 3413144784808669
   Apr 30, 2023   n =86767: 46549778844938396044065311 * 2386931020......c86741;    ecm: B1 = 5e4; sigma = 8149454847368865 
   

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Apr 30, 2023   R942/c209: SNFS-difficulty = 314 
                  650M unique raw relations of 1250M are collected
                  currently progress 52.0 %;    
				  				    

- Found by Kurt Beschorner  
   Apr 28, 2023  n =11259: 31027084884604239383041102327843;                        P-1: B1 = 60e6
   Apr 28, 2023  n=146581: 196498205558343511;                                      gr-mfaktc
   Apr 28, 2023  n=146609: 75180824745686213;                                       gr-mfaktc
   Apr 28, 2023  n=146701: 1573991583080255237;                                     gr-mfaktc


- Found by Kurt Beschorner  
   Apr 24, 2023  n = 1461: 917744708434486635227273676744796912321;                 ecm: B1 = 43e6; sigma = 872312666755562
   Apr 24, 2023  n =11225: 112963042579976573200394401;                             P-1: B1 = 50e6
   Apr 24, 2023  n =11227: 223323479301368691853325640271;                          P-1: B1 = 35e6


- Found by YOYO@home/F!refly)   
   Apr 22, 2023   n = 505: 3045224293530819245851950041691189890170351;             ecm: B1 = 850e6; sigma = 0:8671687100396688982 


- Found by Kurt Beschorner  
   Apr 22, 2023  n =11203: 130498324924129479266749243;                             P-1: B1 = 40e6
   Apr 22, 2023  n =11215: 9427406075097023668093001;                               P-1: B1 = 50e6


- Found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner  
   Apr 18, 2023  n =1340L: 2724793634966652364625335678635927602947729873812054161996498021; SNFS           
   Apr 18, 2023  n =1340L: 599544315766066452392678279212562145297975293811672567632442645781; SNFS           
R1340L: msieve-log  
Sat Dec  3 19:04:36 2022  Msieve v. 1.54 (SVN r1044)
Sat Dec  3 19:04:36 2022  random seeds: 59fd110e 0892ecd5
Sat Dec  3 19:04:36 2022  factoring 2824060999717593900028240609997173114939282688506071731149392826886472747811352725218864727478113526687376447331262355266873764473312821236938717876306128212369387178706580062129341993787065800621293434058175656594182434340581756565939000282406099971759390002824061 (265 digits)
Sat Dec  3 19:04:37 2022  no P-1/P+1/ECM available, skipping
Sat Dec  3 19:04:37 2022  commencing number field sieve (265-digit input)
Sat Dec  3 19:04:37 2022  R0: -1000000000000000000000000000000000
Sat Dec  3 19:04:37 2022  R1: 1
Sat Dec  3 19:04:37 2022  A0: 1
Sat Dec  3 19:04:37 2022  A1: -10
Sat Dec  3 19:04:37 2022  A2: 50
Sat Dec  3 19:04:37 2022  A3: -200
Sat Dec  3 19:04:37 2022  A4: 700
Sat Dec  3 19:04:37 2022  A5: -2000
Sat Dec  3 19:04:37 2022  A6: 5000
Sat Dec  3 19:04:37 2022  A7: -10000
Sat Dec  3 19:04:37 2022  A8: 10000
Sat Dec  3 19:04:37 2022  skew 0.34, size 5.188e-08, alpha 1.092, combined = 3.006e-15 rroots = 0
Sat Dec  3 19:04:37 2022  commencing relation filtering
Sat Dec  3 19:04:37 2022  setting target matrix density to 124.0
Sat Dec  3 19:04:37 2022  estimated available RAM is 130983.0 MB
Sat Dec  3 19:04:37 2022  commencing duplicate removal, pass 1
Sat Dec  3 20:08:50 2022  error -1 reading relation 450182162
...
Sat Dec  3 20:43:37 2022  skipped 773801 relations with b > 2^32
Sat Dec  3 20:43:37 2022  skipped 380 relations with composite factors
Sat Dec  3 20:43:37 2022  found 90833359 hash collisions in 691395806 relations
Sat Dec  3 20:43:37 2022  added 28263 free relations
Sat Dec  3 20:43:37 2022  commencing duplicate removal, pass 2
Sat Dec  3 20:51:15 2022  found 7 duplicates and 691424062 unique relations
Sat Dec  3 20:51:15 2022  memory use: 4262.0 MB
Sat Dec  3 20:51:16 2022  reading ideals above 523042816
Sat Dec  3 20:51:16 2022  commencing singleton removal, initial pass
Sat Dec  3 22:21:02 2022  memory use: 11024.0 MB
Sat Dec  3 22:21:05 2022  reading all ideals from disk
Sat Dec  3 22:21:17 2022  memory use: 14213.3 MB
Sat Dec  3 22:22:31 2022  commencing in-memory singleton removal
Sat Dec  3 22:23:40 2022  begin with 691424062 relations and 610368432 unique ideals
Sat Dec  3 22:54:40 2022  reduce to 453608649 relations and 349375787 ideals in 15 passes
Sat Dec  3 22:54:40 2022  max relations containing the same ideal: 43
Sat Dec  3 22:56:20 2022  reading ideals above 720000
Sat Dec  3 22:56:22 2022  commencing singleton removal, initial pass
Sun Dec  4 00:26:08 2022  memory use: 11024.0 MB
Sun Dec  4 00:26:10 2022  reading all ideals from disk
Sun Dec  4 00:26:26 2022  memory use: 20762.8 MB
Sun Dec  4 00:28:18 2022  keeping 401976395 ideals with weight <= 200, target excess is 2401950
Sun Dec  4 00:30:49 2022  commencing in-memory singleton removal
Sun Dec  4 00:32:02 2022  begin with 453608649 relations and 401976395 unique ideals
Sun Dec  4 01:00:40 2022  reduce to 453583935 relations and 401951681 ideals in 11 passes
Sun Dec  4 01:00:40 2022  max relations containing the same ideal: 200
Sun Dec  4 01:08:40 2022  removing 16222977 relations and 14222977 ideals in 2000000 cliques
Sun Dec  4 01:09:12 2022  commencing in-memory singleton removal
Sun Dec  4 01:10:19 2022  begin with 437360958 relations and 401951681 unique ideals
Sun Dec  4 01:30:26 2022  reduce to 436904780 relations and 387269595 ideals in 8 passes
Sun Dec  4 01:30:26 2022  max relations containing the same ideal: 200
Sun Dec  4 01:38:10 2022  removing 12221780 relations and 10221780 ideals in 2000000 cliques
Sun Dec  4 01:38:39 2022  commencing in-memory singleton removal
Sun Dec  4 01:39:45 2022  begin with 424683000 relations and 387269595 unique ideals
Sun Dec  4 01:59:08 2022  reduce to 424401945 relations and 376765284 ideals in 8 passes
Sun Dec  4 01:59:08 2022  max relations containing the same ideal: 198
Sun Dec  4 02:06:39 2022  removing 10953784 relations and 8953784 ideals in 2000000 cliques
Sun Dec  4 02:07:07 2022  commencing in-memory singleton removal
Sun Dec  4 02:08:12 2022  begin with 413448161 relations and 376765284 unique ideals
Sun Dec  4 02:27:13 2022  reduce to 413210441 relations and 367572557 ideals in 8 passes
Sun Dec  4 02:27:13 2022  max relations containing the same ideal: 197
Sun Dec  4 02:34:45 2022  removing 10242355 relations and 8242355 ideals in 2000000 cliques
Sun Dec  4 02:35:13 2022  commencing in-memory singleton removal
Sun Dec  4 02:36:17 2022  begin with 402968086 relations and 367572557 unique ideals
Sun Dec  4 02:53:19 2022  reduce to 402753884 relations and 359114987 ideals in 7 passes
Sun Dec  4 02:53:19 2022  max relations containing the same ideal: 194
Sun Dec  4 03:00:46 2022  removing 9764427 relations and 7764427 ideals in 2000000 cliques
Sun Dec  4 03:01:14 2022  commencing in-memory singleton removal
Sun Dec  4 03:02:15 2022  begin with 392989457 relations and 359114987 unique ideals
Sun Dec  4 03:21:08 2022  reduce to 392788701 relations and 351148821 ideals in 8 passes
Sun Dec  4 03:21:08 2022  max relations containing the same ideal: 192
Sun Dec  4 03:28:20 2022  removing 9421551 relations and 7421551 ideals in 2000000 cliques
Sun Dec  4 03:28:45 2022  commencing in-memory singleton removal
Sun Dec  4 03:29:46 2022  begin with 383367150 relations and 351148821 unique ideals
Sun Dec  4 03:44:48 2022  reduce to 383175148 relations and 343534368 ideals in 7 passes
Sun Dec  4 03:44:48 2022  max relations containing the same ideal: 190
Sun Dec  4 03:51:29 2022  removing 9158675 relations and 7158675 ideals in 2000000 cliques
Sun Dec  4 03:51:54 2022  commencing in-memory singleton removal
Sun Dec  4 03:52:51 2022  begin with 374016473 relations and 343534368 unique ideals
Sun Dec  4 04:07:58 2022  reduce to 373829249 relations and 336187516 ideals in 7 passes
Sun Dec  4 04:07:58 2022  max relations containing the same ideal: 187
Sun Dec  4 04:14:47 2022  removing 8951493 relations and 6951493 ideals in 2000000 cliques
Sun Dec  4 04:15:11 2022  commencing in-memory singleton removal
Sun Dec  4 04:16:07 2022  begin with 364877756 relations and 336187516 unique ideals
Sun Dec  4 04:30:56 2022  reduce to 364694667 relations and 329052054 ideals in 7 passes
Sun Dec  4 04:30:56 2022  max relations containing the same ideal: 186
Sun Dec  4 04:37:35 2022  removing 8791311 relations and 6791311 ideals in 2000000 cliques
Sun Dec  4 04:38:00 2022  commencing in-memory singleton removal
Sun Dec  4 04:38:54 2022  begin with 355903356 relations and 329052054 unique ideals
Sun Dec  4 04:53:20 2022  reduce to 355722105 relations and 322078534 ideals in 7 passes
Sun Dec  4 04:53:20 2022  max relations containing the same ideal: 184
Sun Dec  4 04:59:34 2022  removing 8658898 relations and 6658898 ideals in 2000000 cliques
Sun Dec  4 04:59:57 2022  commencing in-memory singleton removal
Sun Dec  4 05:00:49 2022  begin with 347063207 relations and 322078534 unique ideals
Sun Dec  4 05:12:51 2022  reduce to 346882766 relations and 315238277 ideals in 6 passes
Sun Dec  4 05:12:51 2022  max relations containing the same ideal: 182
Sun Dec  4 05:19:07 2022  removing 8556397 relations and 6556397 ideals in 2000000 cliques
Sun Dec  4 05:19:31 2022  commencing in-memory singleton removal
Sun Dec  4 05:20:20 2022  begin with 338326369 relations and 315238277 unique ideals
Sun Dec  4 05:35:40 2022  reduce to 338145695 relations and 308500243 ideals in 8 passes
Sun Dec  4 05:35:40 2022  max relations containing the same ideal: 178
Sun Dec  4 05:41:31 2022  removing 8473066 relations and 6473066 ideals in 2000000 cliques
Sun Dec  4 05:41:52 2022  commencing in-memory singleton removal
Sun Dec  4 05:42:40 2022  begin with 329672629 relations and 308500243 unique ideals
Sun Dec  4 05:53:31 2022  reduce to 329491812 relations and 301845385 ideals in 6 passes
Sun Dec  4 05:53:31 2022  max relations containing the same ideal: 176
Sun Dec  4 05:59:11 2022  removing 8406694 relations and 6406694 ideals in 2000000 cliques
Sun Dec  4 05:59:31 2022  commencing in-memory singleton removal
Sun Dec  4 06:00:18 2022  begin with 321085118 relations and 301845385 unique ideals
Sun Dec  4 06:10:36 2022  reduce to 320901777 relations and 295254344 ideals in 6 passes
Sun Dec  4 06:10:36 2022  max relations containing the same ideal: 172
Sun Dec  4 06:16:09 2022  removing 8351915 relations and 6351915 ideals in 2000000 cliques
Sun Dec  4 06:16:30 2022  commencing in-memory singleton removal
Sun Dec  4 06:17:15 2022  begin with 312549862 relations and 295254344 unique ideals
Sun Dec  4 06:30:38 2022  reduce to 312363743 relations and 288715289 ideals in 8 passes
Sun Dec  4 06:30:38 2022  max relations containing the same ideal: 169
Sun Dec  4 06:36:01 2022  removing 8312441 relations and 6312441 ideals in 2000000 cliques
Sun Dec  4 06:36:22 2022  commencing in-memory singleton removal
Sun Dec  4 06:37:06 2022  begin with 304051302 relations and 288715289 unique ideals
Sun Dec  4 06:48:44 2022  reduce to 303860554 relations and 282210980 ideals in 7 passes
Sun Dec  4 06:48:44 2022  max relations containing the same ideal: 165
Sun Dec  4 06:54:05 2022  removing 8284959 relations and 6284959 ideals in 2000000 cliques
Sun Dec  4 06:54:24 2022  commencing in-memory singleton removal
Sun Dec  4 06:55:09 2022  begin with 295575595 relations and 282210980 unique ideals
Sun Dec  4 07:06:42 2022  reduce to 295381193 relations and 275730482 ideals in 7 passes
Sun Dec  4 07:06:42 2022  max relations containing the same ideal: 161
Sun Dec  4 07:12:00 2022  removing 8267593 relations and 6267593 ideals in 2000000 cliques
Sun Dec  4 07:12:20 2022  commencing in-memory singleton removal
Sun Dec  4 07:13:01 2022  begin with 287113600 relations and 275730482 unique ideals
Sun Dec  4 07:24:11 2022  reduce to 286915227 relations and 269263276 ideals in 7 passes
Sun Dec  4 07:24:11 2022  max relations containing the same ideal: 160
Sun Dec  4 07:29:20 2022  removing 8261889 relations and 6261889 ideals in 2000000 cliques
Sun Dec  4 07:29:39 2022  commencing in-memory singleton removal
Sun Dec  4 07:30:19 2022  begin with 278653338 relations and 269263276 unique ideals
Sun Dec  4 07:39:34 2022  reduce to 278449728 relations and 262796476 ideals in 6 passes
Sun Dec  4 07:39:34 2022  max relations containing the same ideal: 156
Sun Dec  4 07:44:30 2022  removing 8262784 relations and 6262784 ideals in 2000000 cliques
Sun Dec  4 07:44:48 2022  commencing in-memory singleton removal
Sun Dec  4 07:45:26 2022  begin with 270186944 relations and 262796476 unique ideals
Sun Dec  4 07:55:47 2022  reduce to 269975342 relations and 256320747 ideals in 7 passes
Sun Dec  4 07:55:47 2022  max relations containing the same ideal: 151
Sun Dec  4 08:00:38 2022  removing 8276204 relations and 6276204 ideals in 2000000 cliques
Sun Dec  4 08:00:55 2022  commencing in-memory singleton removal
Sun Dec  4 08:01:33 2022  begin with 261699138 relations and 256320747 unique ideals
Sun Dec  4 08:11:35 2022  reduce to 261480320 relations and 249824277 ideals in 7 passes
Sun Dec  4 08:11:35 2022  max relations containing the same ideal: 150
Sun Dec  4 08:16:14 2022  removing 8294455 relations and 6294455 ideals in 2000000 cliques
Sun Dec  4 08:16:31 2022  commencing in-memory singleton removal
Sun Dec  4 08:17:06 2022  begin with 253185865 relations and 249824277 unique ideals
Sun Dec  4 08:26:51 2022  reduce to 252958087 relations and 243300377 ideals in 7 passes
Sun Dec  4 08:26:51 2022  max relations containing the same ideal: 148
Sun Dec  4 08:31:06 2022  removing 8323100 relations and 6323100 ideals in 2000000 cliques
Sun Dec  4 08:31:23 2022  commencing in-memory singleton removal
Sun Dec  4 08:31:58 2022  begin with 244634987 relations and 243300377 unique ideals
Sun Dec  4 08:40:56 2022  reduce to 244395707 relations and 236736340 ideals in 7 passes
Sun Dec  4 08:40:56 2022  max relations containing the same ideal: 142
Sun Dec  4 08:45:08 2022  removing 8365688 relations and 6365688 ideals in 2000000 cliques
Sun Dec  4 08:45:24 2022  commencing in-memory singleton removal
Sun Dec  4 08:46:00 2022  begin with 236030019 relations and 236736340 unique ideals
Sun Dec  4 08:54:46 2022  reduce to 235780907 relations and 230119682 ideals in 7 passes
Sun Dec  4 08:54:46 2022  max relations containing the same ideal: 139
Sun Dec  4 08:58:56 2022  removing 8418328 relations and 6418328 ideals in 2000000 cliques
Sun Dec  4 08:59:11 2022  commencing in-memory singleton removal
Sun Dec  4 08:59:44 2022  begin with 227362579 relations and 230119682 unique ideals
Sun Dec  4 09:08:14 2022  reduce to 227098454 relations and 223435208 ideals in 7 passes
Sun Dec  4 09:08:14 2022  max relations containing the same ideal: 137
Sun Dec  4 09:12:13 2022  removing 4308275 relations and 3431292 ideals in 876983 cliques
Sun Dec  4 09:12:28 2022  commencing in-memory singleton removal
Sun Dec  4 09:12:58 2022  begin with 222790179 relations and 223435208 unique ideals
Sun Dec  4 09:20:04 2022  reduce to 222724758 relations and 219938274 ideals in 6 passes
Sun Dec  4 09:20:04 2022  max relations containing the same ideal: 137
Sun Dec  4 09:24:33 2022  relations with 0 large ideals: 116032
Sun Dec  4 09:24:33 2022  relations with 1 large ideals: 75213
Sun Dec  4 09:24:33 2022  relations with 2 large ideals: 429846
Sun Dec  4 09:24:33 2022  relations with 3 large ideals: 2969063
Sun Dec  4 09:24:33 2022  relations with 4 large ideals: 11847544
Sun Dec  4 09:24:33 2022  relations with 5 large ideals: 29838394
Sun Dec  4 09:24:33 2022  relations with 6 large ideals: 49754804
Sun Dec  4 09:24:33 2022  relations with 7+ large ideals: 127693862
Sun Dec  4 09:24:33 2022  commencing 2-way merge
Sun Dec  4 09:29:51 2022  reduce to 148546820 relation sets and 145760336 unique ideals
Sun Dec  4 09:29:52 2022  commencing full merge
Sun Dec  4 11:18:10 2022  memory use: 18214.5 MB
Sun Dec  4 11:18:39 2022  found 65812666 cycles, need 65714536
Sun Dec  4 11:18:44 2022  weight of 65714536 cycles is about 8148699392 (124.00/cycle)
Sun Dec  4 11:18:44 2022  distribution of cycle lengths:
Sun Dec  4 11:18:44 2022  1 relations: 4498289
Sun Dec  4 11:18:44 2022  2 relations: 4635359
Sun Dec  4 11:18:44 2022  3 relations: 5000319
Sun Dec  4 11:18:44 2022  4 relations: 4925280
Sun Dec  4 11:18:44 2022  5 relations: 4853403
Sun Dec  4 11:18:44 2022  6 relations: 4690886
Sun Dec  4 11:18:44 2022  7 relations: 4435118
Sun Dec  4 11:18:44 2022  8 relations: 4212995
Sun Dec  4 11:18:44 2022  9 relations: 3929581
Sun Dec  4 11:18:44 2022  10+ relations: 24533306
Sun Dec  4 11:18:44 2022  heaviest cycle: 28 relations
Sun Dec  4 11:19:22 2022  commencing cycle optimization
Sun Dec  4 11:23:23 2022  start with 554424154 relations
Sun Dec  4 12:03:20 2022  pruned 22965724 relations
Sun Dec  4 12:03:21 2022  memory use: 14924.6 MB
Sun Dec  4 12:03:22 2022  distribution of cycle lengths:
Sun Dec  4 12:03:22 2022  1 relations: 4498289
Sun Dec  4 12:03:22 2022  2 relations: 4755269
Sun Dec  4 12:03:22 2022  3 relations: 5219542
Sun Dec  4 12:03:22 2022  4 relations: 5124024
Sun Dec  4 12:03:22 2022  5 relations: 5077456
Sun Dec  4 12:03:22 2022  6 relations: 4878253
Sun Dec  4 12:03:22 2022  7 relations: 4624032
Sun Dec  4 12:03:22 2022  8 relations: 4363010
Sun Dec  4 12:03:22 2022  9 relations: 4058560
Sun Dec  4 12:03:22 2022  10+ relations: 23116101
Sun Dec  4 12:03:22 2022  heaviest cycle: 28 relations
Sun Dec  4 12:07:00 2022  RelProcTime: 61343
Sun Dec  4 12:07:00 2022  elapsed time 17:02:24

Sun Dec  4 13:24:59 2022  commencing linear algebra
Sun Dec  4 13:25:11 2022  read 65714536 cycles
Sun Dec  4 13:27:00 2022  cycles contain 221299907 unique relations
Sun Dec  4 13:41:01 2022  read 221299907 relations
Sun Dec  4 13:53:38 2022  using 20 quadratic characters above 4294917295
Sun Dec  4 14:03:46 2022  building initial matrix
Sun Dec  4 14:44:26 2022  memory use: 28701.6 MB
Sun Dec  4 14:45:06 2022  read 65714536 cycles
Sun Dec  4 14:45:12 2022  matrix is 65714359 x 65714536 (31915.3 MB) with weight 8957842656 (136.31/col)
Sun Dec  4 14:45:12 2022  sparse part has weight 7643554968 (116.31/col)
Sun Dec  4 15:00:04 2022  filtering completed in 2 passes
Sun Dec  4 15:00:16 2022  matrix is 65713334 x 65713511 (31915.3 MB) with weight 8957814090 (136.32/col)
Sun Dec  4 15:00:16 2022  sparse part has weight 7643547141 (116.32/col)
Sun Dec  4 15:02:50 2022  matrix starts at (0, 0)
Sun Dec  4 15:02:56 2022  matrix is 65713334 x 65713511 (31915.3 MB) with weight 8957814090 (136.32/col)
Sun Dec  4 15:02:56 2022  sparse part has weight 7643547141 (116.32/col)
Sun Dec  4 15:02:56 2022  saving the first 48 matrix rows for later
Sun Dec  4 15:03:06 2022  matrix includes 64 packed rows
Sun Dec  4 15:03:11 2022  matrix is 65713286 x 65713511 (30681.0 MB) with weight 7818384770 (118.98/col)
Sun Dec  4 15:03:11 2022  sparse part has weight 7385702074 (112.39/col)
Sun Dec  4 15:03:12 2022  using block size 8192 and superblock size 6291456 for processor cache size 65536 kB
Sun Dec  4 15:06:50 2022  commencing Lanczos iteration (24 threads)
Sun Dec  4 15:06:50 2022  memory use: 30612.5 MB
Sun Dec  4 15:11:35 2022  linear algebra at 0.0%, ETA 3280h33m
Sun Dec  4 15:13:07 2022  checkpointing every 20000 dimensions
Sun Apr 16 02:01:51 2023  lanczos halted after 1039177 iterations (dim = 65713285)
Sun Apr 16 02:02:52 2023  recovered 41 nontrivial dependencies
Sun Apr 16 02:03:25 2023  BLanczosTime: 310518
Sun Apr 16 02:03:25 2023  elapsed time 86:15:19
   
Sun Apr 16 02:10:41 2023  commencing square root phase
Sun Apr 16 02:10:42 2023  handling dependencies 1 to 64
Sun Apr 16 02:10:42 2023  reading relations for dependency 1
Sun Apr 16 02:10:57 2023  read 32853998 cycles
Sun Apr 16 02:11:52 2023  cycles contain 110657400 unique relations
Sun Apr 16 02:19:23 2023  read 110657400 relations
Sun Apr 16 02:26:26 2023  multiplying 110657400 relations
Sun Apr 16 07:01:31 2023  multiply complete, coefficients have about 4446.26 million bits
Sun Apr 16 07:02:43 2023  warning: no irreducible prime found, switching to small primes
Sun Apr 16 07:04:30 2023  initial square root is modulo 13
Sun Apr 16 14:43:15 2023  Newton iteration failed to converge
Sun Apr 16 14:43:15 2023  algebraic square root failed
Sun Apr 16 14:43:15 2023  reading relations for dependency 2
Sun Apr 16 14:43:37 2023  read 32856735 cycles
Sun Apr 16 14:45:26 2023  cycles contain 110660926 unique relations
Sun Apr 16 14:56:27 2023  read 110660926 relations
Sun Apr 16 15:12:41 2023  multiplying 110660926 relations
Sun Apr 16 19:45:33 2023  multiply complete, coefficients have about 4446.40 million bits
Sun Apr 16 19:46:28 2023  warning: no irreducible prime found, switching to small primes
Sun Apr 16 19:47:23 2023  initial square root is modulo 13
Mon Apr 17 03:16:32 2023  Newton iteration failed to converge
Mon Apr 17 03:16:32 2023  algebraic square root failed
Mon Apr 17 03:16:32 2023  reading relations for dependency 3
Mon Apr 17 03:16:53 2023  read 32853641 cycles
Mon Apr 17 03:18:40 2023  cycles contain 110646878 unique relations
Mon Apr 17 03:29:44 2023  read 110646878 relations
Mon Apr 17 03:46:17 2023  multiplying 110646878 relations
Mon Apr 17 08:22:31 2023  multiply complete, coefficients have about 4445.88 million bits
Mon Apr 17 08:23:29 2023  warning: no irreducible prime found, switching to small primes
Mon Apr 17 08:25:56 2023  initial square root is modulo 13
Mon Apr 17 15:54:03 2023  found factor: 599544315766066452392678279212562145297975293811672567632442645781
Mon Apr 17 15:54:03 2023  reading relations for dependency 4
Mon Apr 17 15:54:24 2023  read 32854254 cycles
Mon Apr 17 15:56:12 2023  cycles contain 110623390 unique relations
Mon Apr 17 16:07:15 2023  read 110623390 relations
Mon Apr 17 16:23:54 2023  multiplying 110623390 relations
Mon Apr 17 21:01:14 2023  multiply complete, coefficients have about 4444.91 million bits
Mon Apr 17 21:02:13 2023  warning: no irreducible prime found, switching to small primes
Mon Apr 17 21:05:23 2023  initial square root is modulo 13
Tue Apr 18 04:38:23 2023  sqrtTime: 181662
Tue Apr 18 04:38:23 2023  p64 factor: 2724793634966652364625335678635927602947729873812054161996498021
Tue Apr 18 04:38:23 2023  p66 factor: 599544315766066452392678279212562145297975293811672567632442645781
Tue Apr 18 04:38:23 2023  p136 factor: 1728698150280068137198270521277194937031098932707466058506795177976772363213163863959865690898047286154112976061009434446365564534720661
Tue Apr 18 04:38:23 2023  elapsed time 50:27:42

  	
- Found by YOYO@home/abc   
   Apr 18, 2023   n = 503: 30837329959354395729863043937455394320617332690757897759 * 6555624229......c269; ecm: B1 = 850e6; sigma = 0:13802949331132258992 


- Found by YOYO@home/vanos512   
   Apr 14, 2023   n = 503: 779021620901226065983070829336777930546503650107187843  * 2021579474......c325; ecm: B1 = 850e6; sigma = 0:977799155199813862

 
- Found by Kurt Beschorner  
   Apr 14, 2023  n =11057: 1986254099801763774631766559897990182201;                P-1: B1 = 35e6
   Apr 14, 2023  n =11091: 962500955804123759014304641;                             P-1: B1 = 70e6
   Apr 14, 2023  n=146221: 5998182708723144787;                                     gr-mfaktc


- Found by Kurt Beschorner  
   Apr 10, 2023   n =12453: 341796184231310250867486559;                            P-1: B1 =50e6 
   Apr 10, 2023   n=146093: 151661915761207597;                                     gr-mfaktc
   Apr 10, 2023   n=146141: 14371417644320176961;                                   gr-mfaktc


-  Found by Alfred Eichhorn 
   Apr 10, 2023   n =66491: 613389642977626279627;                                  ecm: B1 = 5e4; sigma = 4195255829314717
   Apr 10, 2023   n =86287: 4911898103137914869707;                                 ecm: B1 = 5e4; sigma = 4209134514182576
   Apr 10, 2023   n =86501: 15410977065428877220938889;                             ecm: B1 = 5e4; sigma = 8852113913822102

			  

- Found by Kurt Beschorner  
   Apr 04, 2023   n = 1499: 444025804128316092985120887216489504283;                ecm: B1 =11e6; sigma = 8568897179058893
   Apr 04, 2023   n =12446: 501279565140480220168322480009;                         P-1: B1 =72e6 
   Apr 04, 2023   n =12470: 54121400967366927427316132251;                          P-1: B1 =85e6 
   Apr 04, 2023   n=145931: 140529180232862467;                                     gr-mfaktc
   Apr 04, 2023   n=145931: 17203170484198361951;                                   gr-mfaktc
   Apr 04, 2023   n=146011: 9597686137133649559;                                    gr-mfaktc

- Found by Kurt Beschorner  
   Mar 30, 2023   n = 1409: 1658972136253211819285181026106657071203;               ecm: B1 =11e6; sigma = 0:7137899537840100
   Mar 30, 2023   n = 7713: 169080936973198939009695188449;                         ecm: B1 = 1e6; sigma = 8231107386027428 


- Found by Kurt Beschorner  
   Mar 26, 2023   n = 5925: 43863025793294149274559220201;                          ecm: B1 = 3e6; sigma = 4922290324811982
   Mar 26, 2023   n =12192: 469162401428727267767039337537134113;                   P-1: B1 =12e7 

- Found by Kurt Beschorner  
   Mar 19, 2023   n =12207: 10326528166018797350437  * 1715045130......c7454;       P-1: B1 =25e6 
   Mar 19, 2023   n =12213: 763235932545359903065517911  *  2819581486......c7565;  P-1: B1 =25e6 
   Mar 19, 2023   n =12235: 601591258998676485551127873393824231 * 2595076444......c9736; P-1: B1 =32e6 
   Mar 19, 2023   n =12261: 37955669373027254564443249 * 1482911212......c7840;     P-1: B1 =40e6 
   Mar 19, 2023   n =12265: 1813958675305432752569322631  * 4800373524......c8813;  P-1: B1 =36e6 
   Mar 19, 2023   n =12267: 18405350080498464623296129  * 4840124705......c7696;    P-1: B1 =47e6 
   Mar 19, 2023   n =12299: 22125123861628175114991691769399 * 4891881550......c10437; P-1: B1 =28e6 
   Mar 19, 2023   n=145381: 2814792192994658867 * 2189685857......c145354;          gr-mfaktc   
   

- Found by Kurt Beschorner  
   Mar 16, 2023   n =12163: 496260125167000972637979481 * 6088164284......c12112;   P-1: B1 =25e6 
   Mar 16, 2023   n =12197: 10004791369113378925808671 * 1125672810......c12139;    P-1: B1 =25e6 


- via factordb.com   
   Mar 16, 2023   n =12124: 2139064861096863878756665012801 * 4721689455......c5154 


- Found by Kurt Beschorner  
   Mar 11, 2023   n = 7671: 674395585663400091968059519;                            ecm: B1 = 1e6; sigma = 3409682457607698
   Mar 11, 2023   n =12032: 92983911220947001823535969927169 * 4585704060......c5799;    P-1: B1 =60e6 
   Mar 11, 2023   n =12049: 3372749981360027032747859544183787 * 2578564574......c12005; P-1: B1 =20e6 
   Mar 11, 2023   n =12067: 89906797410807096964226575517 * 7161228750......c10898;      P-1: B1 =25e6 
   Mar 11, 2023   n =12281:  248827112460081163452938551 * 4465394064......c12254;       P-1: B1 =25e6 

 
- Found by Kurt Beschorner   
   Mar 07, 2023   n = 5477: 4679405672910425988720134731403;                        ecm: B1 = 1e6; sigma = 0:3115122745024891
   Mar 07, 2023   n = 5479: 1175364770706692672051045921;                           ecm: B1 = 1e6; sigma = 0:1144629584039427 
   Mar 07, 2023   n =12520: 4068220734739164961413104154881 * 1710302891......c4952; P-1: B1 =60e6 
   Mar 07, 2023   n =12521: 769774332048986028482292393529 * 1169173824......c11815; P-1: B1 =22e6 
   Mar 07, 2023   n=144379: 1699316036580040519;                                    gr-mfaktc
   Mar 07, 2023   n=144427: 763086575042246237;                                     gr-mfaktc

 
- Found by anonymous   
   Mar 02, 2023   n =  535: 5524033451004407234027306056468463430580799351;         ecm: B1 =11e6; sigma = 18425523954857577889 


- Found by Kurt Beschorner   
   Feb 27, 2023   n = 1401: 58268747277891114808753379164057926641266957;           ecm: B1 =43e6; sigma = 0:6490871995892487 
   Feb 27, 2023   n = 5443: 443994631081204304270374441813;                         ecm: B1 = 1e6; sigma = 0:5948351044689566 
   Feb 27, 2023   n=144259: 76455980665279759;                                      gr-mfaktc
   Feb 27, 2023   n=144323: 172755778190621357;                                     gr-mfaktc

-  Found by Alfred Eichhorn 
   Feb 27, 2023   n =66067: 170472935791113746723 * 6517815311......c66046;         ecm: B1 = 5e4; sigma = 3477637411662594



- Found by Kurt Beschorner   
   Feb 21, 2023   n =4700L: 11808992310281998733369892724417205617004114801;        ecm: B1 =43e6; sigma = 0:7170719374266148 

 
- Found by YOYO@home/George Bradshaw   
   Feb 20, 2023   n =2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 * 1142522103......P220; ecm: B1 = 2.9e9    


   Feb 19, 2023   n = 5539: 1893231723717766314342428938609;                        ecm: B1 = 1e6; sigma = 0:7066187404725017
   Feb 19, 2023   n=143981: 2321713302266455397;                                    gr-mfaktc


-  Found by Alfred Eichhorn 
   Feb 13, 2023   n =85661: 6614343997747250116357 * 5117655327......c85621;        ecm: B1 = 5e4; sigma = 6480425124612577
   Feb 13, 2023   n =85717: 425606074726924486880292881 * 2610656137......c85690;   ecm: B1 = 5e4; sigma = 3051452821892657


- Found by Kurt Beschorner   
   Feb 13, 2023   n=143791: 1345704687193284449;                                    gr-mfaktc
   Feb 13, 2023   n=143873: 13969422389289652231;                                   gr-mfaktc
				  

- Found by Kurt Beschorner   
   Feb 06, 2023   n = 5393: 475100434323400295514257533;                            ecm: B1 = 1e6; sigma = 0:6611271429378146
   Feb 06, 2023   n=143413: 1308539818288185547;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Jan 27, 2023   n = 5387: 9695327619043500745964526925561 * 2796548747......P5266; ecm: B1 = 1e6; sigma = 0:7981023013264326

				  
- Found by Kurt Beschorner   
   Jan 22, 2023   n = 6515: 3767892910446507496334403721;                           ecm: B1 = 1e6; sigma = 3731867255296034
   Jan 22, 2023   n=143159: 2036663968824321689;                                    gr-mfaktc

				  
-  Found by Alfred Eichhorn 
   Jan 22, 2023   n =48767: 1167442730202131101408241;                              ecm: B1 = 5e4; sigma = 8294335290315311
   Jan 22, 2023   n =48809: 1374219663422487935701343573;                           ecm: B1 = 5e4; sigma = 3897725353774069
   Jan 22, 2023   n =65701: 119577379525448930631404597329;                         ecm: B1 = 5e4; sigma = 2055672717664719 
   

- via factordb.com   
   Jan 22, 2023   n =10216: 5409058353794643031157855569;                           ecm 


- Found by YOYO@home/user69   
   Jan 14, 2023   n = 1104: 22651858853653655359251914860948647902217772389947313979551649; ecm: B1 = 29e8; sigma = 0:17929758445905874757


- Found by Kurt Beschorner   
   Jan 08, 2023   n = 1427: 5103036982727761098957792950596409693 * 2786241011......P1380; ecm: B1 =11e6; sigma = 5634177607918577
   Jan 08, 2023   n=142871: 284235246048470947;                                     gr-mfaktc
   Jan 08, 2023   n=200100L: 180218186261101;                                       ecm: B1 = 5e4  
   Jan 08, 2023   n=200100L: 936682576624695001;                                    ecm: B1 = 5e4 
   Jan 08, 2023   n=200100L: 18748796798446051801;                                  ecm: B1 = 5e4; sigma = 0:15615885390781000624 
 

- Found by Kurt Beschorner   
   Jan 04, 2023   n = 1411: 3094716767820821084333461991848123;                     ecm: B1 =11e6; sigma = 0:1262114500939137
   Jan 04, 2023   n=142711: 4728660163685159483;                                    gr-mfaktc



ECM efforts
with Rn:           1 < n < 2000 (May 22, 2023) with Rn:     1999 < n < 3000 (May 18, 2023)
with Rn:     2999 < n < 4000 (May 18, 2023) with Rn:     3999 < n < 5000 (Feb 27, 2023)
with Rn:     4999 < n < 6000 (May 22, 2023) with Rn:     5999 < n < 7000 (May 18, 2023)
with Rn:     6999 < n < 8000 (May 18, 2023) with Rn:     7999 < n < 9000 (Jan 08, 2023)
with Rn:     8999 < n <10000 (May 18, 2023) with Rn:     9999 < n <11000 (May 22, 2023)
with Rn:   10999 < n <12000 (May 23, 2023) with Rn:   11999 < n <14980L/M (May 18, 2023)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 751 digits
617
in progress
619
in progress
625
in progress
629
in progress
641
in progress
B1 = 26e7/45000 curves/
numbers < 450 digits
479
in progress
481
in progress
557
in progress
1136
in progress
1160
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits
505
in progress
627
in progress
1086
in progress
1254
in progress
1386
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits
537
in progress
567
in progress
645
in progress
693
in progress
1218
in progress



Factorizations
Repunits: R1        - R2500 (May 22, 2023) Repunits:  R2501 - R5000 (Feb 27, 2023)
Repunits: R5001   - R7500 (May 18, 2023) Repunits: R7501 - R10000 (Mar 30, 2023)
Repunits: R10001 - R12500 (May 22, 2023) Repunits: R12501 - R14980L/M (Feb 27, 2023)




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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