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

Related links:



ECM EFFORTS
with Rn:      323 < n < 2000 (Feb 16, 2018) with Rn:     1999 < n < 3000 (Jan 16, 2018)
with Rn:     2999 < n < 4000 (Oct 18, 2017) with Rn:     3999 < n < 5000 (Oct 15, 2017)
with Rn:     4999 < n < 6000 (Jan 29, 2018) with Rn:     5999 < n < 7000 (Feb 14, 2018)
with Rn:     6999 < n < 8000 (Oct 16, 2017) with Rn:     7999 < n < 9000 (Feb 11, 2018)
with Rn:     8999 < n <10000 (Feb 07, 2018) with Rn:     9999 < n <11000 (Sep 17, 2017)
with Rn:   10999 < n <12000 (Oct 04, 2017) with Rn:   11999 < n <12501 (Oct 05, 2017)




Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/8600 curves/
numbers < 1001 digits
911
working
913
working
917
working
991
working
1211
working
B1 = 11e7/18400 curves/
numbers < 601 digits
837
working
1197
working
1202
working
1208
working
2500M
working
B1 = 26e7/46000 curves/
numbers < 450 digits
413
working
1136
working
1142
working
1160
working
2380M
working
B1 = 85e7/75000 curves/
numbers < 250 digits
407
working
515
working
1420L
working
2420L
working
2460L
working



News
-  Last update: Feb 20, 2018

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Feb 20, 2018   R447/c242/SNFS-difficult 300; 115M unique relations and 254M unique ideals are collected
                  currently progress ~ 16%:   
                  

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Kurt Beschorner 
   thanks to Max Voznyy for poly-file
   Feb 16, 2018   n = 1030: 2102173879615901190724805905901825960646731569309620829374935176385195435873285181866611; GNFS   
         
   Mon Dec 18 19:26:49 2017  Msieve v. 1.53 (SVN unknown)
   Mon Dec 18 19:26:49 2017  random seeds: 8fd6e0d8 ceb8f5bb
   Mon Dec 18 19:26:49 2017  factoring 1552763077808108686959865607960420017609486444677474079573318397532331366773641133556205133826829279435347604731178897784112330091512036060951765570415593479848057498566056614137801535257211165871091 (199 digits)
   Mon Dec 18 19:26:51 2017  searching for 15-digit factors
   Mon Dec 18 19:26:52 2017  commencing number field sieve (199-digit input)
   Mon Dec 18 19:26:52 2017  R0: -262207264182244965566501989754094701687
   Mon Dec 18 19:26:52 2017  R1: 35260964440695209765221
   Mon Dec 18 19:26:52 2017  A0: 61273646333056248631393145049744489856776032064
   Mon Dec 18 19:26:52 2017  A1: 10420727777495411411387820457257803823560
   Mon Dec 18 19:26:52 2017  A2: 145201440064897386425846123841612
   Mon Dec 18 19:26:52 2017  A3: 259088764547269247676230
   Mon Dec 18 19:26:52 2017  A4: -3111278570304511
   Mon Dec 18 19:26:52 2017  A5: 1252800
   Mon Dec 18 19:26:52 2017  skew 244424374.97, size 1.313e-019, alpha -6.405, combined = 4.818e-015 rroots = 3
   Mon Dec 18 19:26:52 2017  
   Mon Dec 18 19:26:52 2017  commencing relation filtering
   Mon Dec 18 19:26:52 2017  setting target matrix density to 130.0
   Mon Dec 18 19:26:52 2017  estimated available RAM is 49069.6 MB
   Mon Dec 18 19:26:52 2017  commencing duplicate removal, pass 1
   Mon Dec 18 19:28:12 2017  error -9 reading relation 3744616
   ...
   Mon Dec 18 23:46:54 2017  skipped 100 relations with composite factors
   Mon Dec 18 23:46:54 2017  found 100364806 hash collisions in 722814449 relations
   Mon Dec 18 23:48:01 2017  commencing duplicate removal, pass 2
   Tue Dec 19 00:00:06 2017  found 3857480 duplicates and 718956969 unique relations
   Tue Dec 19 00:00:06 2017  memory use: 4262.0 MB
   Tue Dec 19 00:00:07 2017  reading ideals above 376373248
   Tue Dec 19 00:00:07 2017  commencing singleton removal, initial pass
   Tue Dec 19 03:26:32 2017  memory use: 11024.0 MB
   Tue Dec 19 03:26:34 2017  reading all ideals from disk
   Tue Dec 19 03:26:47 2017  memory use: 14047.3 MB
   Tue Dec 19 03:28:41 2017  commencing in-memory singleton removal
   Tue Dec 19 03:30:34 2017  begin with 718956969 relations and 622835940 unique ideals
   Tue Dec 19 03:52:55 2017  reduce to 477243804 relations and 357663131 ideals in 15 passes
   Tue Dec 19 03:52:55 2017  max relations containing the same ideal: 38
   Tue Dec 19 03:54:41 2017  reading ideals above 720000
   ...
   Tue Dec 19 18:57:12 2017  begin with 145660370 relations and 146431260 unique ideals
   Tue Dec 19 19:01:05 2017  reduce to 145549676 relations and 142640790 ideals in 6 passes
   Tue Dec 19 19:01:05 2017  max relations containing the same ideal: 99
   Tue Dec 19 19:04:08 2017  relations with 0 large ideals: 8608
   Tue Dec 19 19:04:08 2017  relations with 1 large ideals: 32141
   Tue Dec 19 19:04:08 2017  relations with 2 large ideals: 483831
   Tue Dec 19 19:04:08 2017  relations with 3 large ideals: 3290692
   Tue Dec 19 19:04:08 2017  relations with 4 large ideals: 12201363
   Tue Dec 19 19:04:08 2017  relations with 5 large ideals: 27283605
   Tue Dec 19 19:04:08 2017  relations with 6 large ideals: 38538418
   Tue Dec 19 19:04:08 2017  relations with 7+ large ideals: 63711018
   Tue Dec 19 19:04:08 2017  commencing 2-way merge
   Tue Dec 19 19:07:52 2017  reduce to 92351677 relation sets and 89442791 unique ideals
   Tue Dec 19 19:07:52 2017  commencing full merge
   Tue Dec 19 20:11:45 2017  memory use: 10667.8 MB
   Tue Dec 19 20:12:20 2017  found 40448970 cycles, need 40222991
   Tue Dec 19 20:12:24 2017  weight of 40222991 cycles is about 5229498284 (130.01/cycle)
   Tue Dec 19 20:12:24 2017  distribution of cycle lengths:
   Tue Dec 19 20:12:24 2017  1 relations: 2839370
   Tue Dec 19 20:12:24 2017  2 relations: 2638524
   Tue Dec 19 20:12:24 2017  3 relations: 2782441
   Tue Dec 19 20:12:24 2017  4 relations: 2806335
   Tue Dec 19 20:12:24 2017  5 relations: 2876110
   Tue Dec 19 20:12:24 2017  6 relations: 2829788
   Tue Dec 19 20:12:24 2017  7 relations: 2773698
   Tue Dec 19 20:12:24 2017  8 relations: 2667964
   Tue Dec 19 20:12:24 2017  9 relations: 2532163
   Tue Dec 19 20:12:24 2017  10+ relations: 15476598
   Tue Dec 19 20:12:24 2017  heaviest cycle: 28 relations
   Tue Dec 19 20:16:47 2017  commencing cycle optimization
   Tue Dec 19 20:20:00 2017  start with 342169522 relations
   Tue Dec 19 20:50:01 2017  pruned 14583710 relations
   Tue Dec 19 20:50:02 2017  memory use: 9468.9 MB
   Tue Dec 19 20:50:02 2017  distribution of cycle lengths:
   Tue Dec 19 20:50:02 2017  1 relations: 2839370
   Tue Dec 19 20:50:02 2017  2 relations: 2712498
   Tue Dec 19 20:50:02 2017  3 relations: 2900844
   Tue Dec 19 20:50:02 2017  4 relations: 2920192
   Tue Dec 19 20:50:02 2017  5 relations: 3009995
   Tue Dec 19 20:50:02 2017  6 relations: 2956051
   Tue Dec 19 20:50:02 2017  7 relations: 2906501
   Tue Dec 19 20:50:02 2017  8 relations: 2783475
   Tue Dec 19 20:50:02 2017  9 relations: 2636477
   Tue Dec 19 20:50:02 2017  10+ relations: 14557588
   Tue Dec 19 20:50:02 2017  heaviest cycle: 28 relations
   Tue Dec 19 20:56:32 2017  RelProcTime: 91780
   Tue Dec 19 20:56:32 2017  
   Tue Dec 19 20:56:32 2017  commencing linear algebra
   Tue Dec 19 20:57:06 2017  read 40222991 cycles
   Tue Dec 19 21:00:00 2017  cycles contain 143999269 unique relations
   Tue Dec 19 21:40:45 2017  read 143999269 relations
   Tue Dec 19 21:49:49 2017  using 20 quadratic characters above 4294917295
   Tue Dec 19 22:03:40 2017  building initial matrix
   Tue Dec 19 23:17:03 2017  memory use: 20131.3 MB
   Tue Dec 19 23:21:47 2017  read 40222991 cycles
   Tue Dec 19 23:22:08 2017  matrix is 40222814 x 40222991 (20412.9 MB) with weight 6124559285 (152.27/col)
   Tue Dec 19 23:22:08 2017  sparse part has weight 4868444598 (121.04/col)
   Tue Dec 19 23:42:50 2017  filtering completed in 2 passes
   Tue Dec 19 23:43:11 2017  matrix is 40221281 x 40221458 (20412.8 MB) with weight 6124493389 (152.27/col)
   Tue Dec 19 23:43:11 2017  sparse part has weight 4868427644 (121.04/col)
   Tue Dec 19 23:54:42 2017  matrix starts at (0, 0)
   Tue Dec 19 23:55:03 2017  matrix is 40221281 x 40221458 (20412.8 MB) with weight 6124493389 (152.27/col)
   Tue Dec 19 23:55:03 2017  sparse part has weight 4868427644 (121.04/col)
   Tue Dec 19 23:55:03 2017  saving the first 48 matrix rows for later
   Tue Dec 19 23:55:27 2017  matrix includes 64 packed rows
   Tue Dec 19 23:55:38 2017  matrix is 40221233 x 40221458 (19852.4 MB) with weight 5280135315 (131.28/col)
   Tue Dec 19 23:55:38 2017  sparse part has weight 4801981234 (119.39/col)
   Tue Dec 19 23:55:38 2017  using block size 8192 and superblock size 1179648 for processor cache size 12288 kB
   Wed Dec 20 00:06:59 2017  commencing Lanczos iteration (12 threads)
   Wed Dec 20 00:06:59 2017  memory use: 17197.3 MB
   Wed Dec 20 00:12:50 2017  checkpointing every 30000 dimensions
   Thu Feb 15 20:25:19 2018  lanczos halted after 636065 iterations (dim = 40221231)
   Thu Feb 15 20:26:11 2018  recovered 31 nontrivial dependencies
   Thu Feb 15 20:28:19 2018  BLanczosTime: 5009507
   Thu Feb 15 20:28:19 2018  
   Thu Feb 15 20:28:19 2018  commencing square root phase
   Thu Feb 15 20:28:19 2018  handling dependencies 1 to 64
   Thu Feb 15 20:28:19 2018  reading relations for dependency 1
   Thu Feb 15 20:28:31 2018  read 20108165 cycles
   Thu Feb 15 20:29:12 2018  cycles contain 71992354 unique relations
   Thu Feb 15 20:45:07 2018  read 71992354 relations
   Thu Feb 15 20:52:54 2018  multiplying 71992354 relations
   Thu Feb 15 22:59:01 2018  multiply complete, coefficients have about 4621.15 million bits
   Thu Feb 15 22:59:39 2018  initial square root is modulo 152189
   Fri Feb 16 01:19:03 2018  sqrtTime: 17444
   Fri Feb 16 01:19:03 2018  p88 factor: 2102173879615901190724805905901825960646731569309620829374935176385195435873285181866611 (Bo Chen/W. Fang/A. Eichhorn/Beschorner) * 7386463569......P111 
   Fri Feb 16 01:19:03 2018  p111 factor: 738646356928296470476307267086332729186390523609043172055510815591989993873426438257667855075703812004308119681
   Fri Feb 16 01:19:03 2018  elapsed time 1421:52:14


-  Found by Alfred Eichhorn 
   Nov 20, 2017   n =72383: 135363222773136132720403 * 8208367740......c72359;     B1=11e3; sigma = 13065345815521750303

   Dec 04, 2017   n =21467: 981327476030973157844191921 * 1132253134......c21440;  B1=5e4;  sigma = 5287251095017369153

   Dec 13, 2017   n =21563: 1078461254893613345267 * 1030274482......c21542;       B1=5e4;  sigma = 8829156589234567335
                            3802666255534666859036119361 * 2709347634......c21514; B1=5e4;  sigma = 13679764725772405092   

   Jan 14, 2018   n =74489: 548483507421525665359 * 2025787641......c74468;        B1=11e3; sigma = 8824790011742622963

   Jan 22, 2018   n =22093: 2218950397796766056972719 * 5007372459......c22068;    B1=5e4;  sigma = 1200187250184623421

   Feb 04, 2018   n =74861: 10118695845434464399231 * 1098077388......c74839;      B1=11e3; sigma = 14956490505633226152

   Feb 18, 2018   n =22367: 491910083939628543752308667 * 2258768720......c22340;  B1=5e4;  sigma = 4226822665876942407

   Feb 18, 2018   n =75329: 132185469097395644849 * 8405697832......c75308;        B1=11e3; sigma = 12551643461909185634

        
-  Found by  Yousuke Koide  
   Aug 01, 2017   n =  976: 1333621378380781329750868926173511152429445865079521;  B1=12e7; sigma = 2:17156338585742940671  
                            P52: P-1: 2^5 * 3^2 * 5 * 61 * 149873 * 101301720397463942798137769864149153298111 
                                 P+1: 2 * 77977 * 2211557 * 3866676983397728874053445954723111344549 

   Feb 15, 2018   n =  982: 44467075182005846868530065551693426652606026434296940573; B1=12e7; sigma = 2:5690539589092232789


-  Found by Alfred Reich 
   Sep 29, 2017   n = 7352: 2623552005321388434037145143121                        B1=43e3; sigma = 1:2655621899          
                            P31: P-1: 2^4 * 5 * 7 * 17 * 61^2 * 503 * 919 * 160217356770367823
                                 P+1: 2 * 3^2 * 139 * 1597 * 4555319 * 144138056118609977                                   

   Oct 14, 2017   n =7700M: 38041784784146774130170998462735601;                   B1=12e5; sigma = 1:337140686  
                            P35: P-1: 2^4 * 5^2 * 7 * 11^2 * 13 * 8637222955259916022652574349   
                                 P+1: 2 * 3 * 61 * 536479 * 97084640021 * 1995614026067533  

   Oct 14, 2017   n =8940M: 5275415368338873197815559526085771801;                 B1=135e4; sigma = 1:1113189447

   Oct 14, 2017   n =9220M: 116887569046811596896977743981921;                     B1=125e4; sigma = 1:2773280274

   Oct 15, 2017   n =4340L: 952846312570007577050723081040768241;                  B1=2e6;   sigma = 1:1381967755
   
   Oct 15, 2017   n =4700L: 780599108882572060886313194155724085701;               B1=2e6;   sigma = 1:3828270230 
   
   Oct 16, 2017   n =6420M: 635390420419704778459322819229975601;                  B1=2e6;   sigma = 1:4033305829

   Oct 17, 2017   n = 3390: 302841383970711301680945052526521;                     B1=1e6;   sigma = 1:1509310649

   Nov 03, 2017   n =6020M: 377659045698120991814418877959941381;                  B1=28e6;  sigma = 1:612335155

   Dec 26, 2017   n = 9610: 3122476819207517804807857327849801;                    B1=125e3; sigma= 1:962736268         

   Jan 14, 2018   n = 8130: 399043838982071991709808323681;                        B1=25e4; sigma = 1:2297325767    

   Jan 15, 2018   n = 8542: 48202989597749068566661266155887;                      B1= 3e5; sigma = 1:1521831316

   Jan 15, 2018   n = 9114: 8547974217374353152743331757;                          B1= 1e6; sigma = 0:16990652822588331830

   Jan 20, 2018   n = 9046: 29106719227380924261687718736389163183;                B1= 3e6; sigma = 1:4247153634

   Jan 22, 2018   n = 8476: 1963726703284756552906455136069;                       B1= 9e5; sigma = 1:3513372185
 
   Jan 22, 2018   n = 9252: 4192371437070223690660387107541;                       B1= 29e5; sigma= 1:1315231828
 
   Jan 24, 2018   n = 8150: 549692094842681735580674239279801;                     B1= 28e5; sigma= 0:18237555407987570567

   Jan 27, 2018   n = 8308: 162671769021508746091227108361;                        B1= 13e5; sigma= 1:261055998  
  
   Jan 27, 2018   n = 8402: 47962315664132037883886339559337823;                   B1= 2025e3; sigma= 1:4103960558  
  
   Feb 01, 2018   n = 9908: 3859183268538790375453543769;                          B1= 3e6;  sigma= 1:410615560  

   Feb 03, 2018   n = 9824: 18198559922005306277650072144139297;                   B1= 6e5;  sigma= 1:3894282002   

   Feb 03, 2018   n = 9586: 343575467224788555287460428801;                        B1= 8e5;  sigma= 1:4256511204

   Feb 06, 2018   n = 9716: 13762552890503863967484529230589;                      B1= 9e5;  sigma= 1:4087205298

   Feb 10, 2018   n =8300L: 267352619706048404954978381518286405201;               B1= 1e6;  sigma= 1:525732917


-  Found by YOYO@home 
   YOYO@home/Deltik
   Sep 26, 2017   n =2180L: 7152063279176360267550161080960805856216521; B1= 26e7; sigma = 0:9003880645049902030
                            P43: P-1: 2^3 * 5 * 17 * 79 * 109 * 193 * 331 * 19119808738790939987048934343253
                                 P+1: 2 * 3^3 * 311 * 6545966477 * 68433584544361 * 950679510039829
                                                                                                                
-  YOYO@home/bbmz   
   Oct 09, 2017   n =  407: 5944944413111812771074601841233247644294218555674708828050801; B1= 26e7; sigma = 17148592561077535369       
                                                                                                             
-  YOYO@home/astroboylok
   Nov 07, 2017   n = 1186: 2909076542620598524499532435958736860811671130747534094532375046661903161; B1= 11e7; sigma = 0:16299314430696221325      
                            group order: instruction according to Serge Batalov (thanks)
                            2^4 * 3^2 * 73 * 9013 * 38639 * 380983 * 857743 * 934441 * 2221907 * 2747597 * 6117583 * 13622467 * 16300793 * 313788197 
   congratulations!
                                                                                                                
-  YOYO@home/mussman   
   Dec 24, 2017   n = 1197: 127299829734328501871992084225690229563 * 1083353809......c587; B1= 11e7; sigma = 0:13789025679953582860       
   YOYO@home/Legoman
   Dec 24, 2017   n = 1197: 22005900343041974560744274934676975393449397;          B1= 11e7; sigma = 0:14260221117156359926
                                                                                                             
-  YOYO@home/NeuralMiner
   Dec 25, 2017   n =5780M: 566172533277589638952637358217083696315144309601;      B1= 11e6; sigma = 0:8915823689914353778     

-  YOYO@home/WhiteFire  
   Jan 07, 2018   n = 1291: 1824300601696080281746056851529399947969;              B1= 11e6; sigma = 0:15632398092653511799

-  YOYO@home/WhiteFire     
   Jan 25, 2018   n =  907: 5808730604484537495106777140578352936337679;           B1= 43e6; sigma = 0:6571224515312869036  

-  YOYO@home/corris     
   Jan 25, 2018   n =6460M: 269834533853067177744952487725981;                     B1= 11e6; sigma = 0:6089771197226634237    


-  YOYO@home/NeuralMiner
   Feb 12, 2018   n = 1373: 229016141864852008546928682385264917916393201;         B1= 11e6; sigma = 0:3460683030665955377 
     
   
  

Factorizations
Repunits: R1        - R2500 (Feb 16, 2018) Repunits:  R2501 - R5000 (Oct 18, 2017)
Repunits: R5001   - R7500 (Jan 28, 2018) Repunits: R7501 - R10000 (Feb 11, 2018)
Repunits: R10001 - R12500 (Sep 30, 2017) Repunits: R12540LM - R14980LM (Sep 30, 2017)


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