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

Related links:



ECM EFFORTS
with Rn:      323 < n < 2000 (May 18, 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 (May 17, 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 (Apr 24, 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		 923
working		 929
working		 931
working		 937
working		 941
working
B1 = 11e7/18400 curves/
numbers < 701 digits		 851
working		 865
working		 869
working		 1202
working		 1208
working
B1 = 26e7/46000 curves/
numbers < 450 digits		 431
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: May 22, 2018

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 22, 2018   R447/c242/SNFS-difficult 300; 396M unique relations and 507M unique ideals are collected
                  currently progress ~ 55%:   
                  

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

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

   Feb 24, 2018   n =22441: 7298364414889854463192187 * 1522411115......c22416;    B1=5e4;  sigma = 4083876554834783578

   Feb 24, 2018   n =22501: 224637008050525613746832050125853 * 2484995657......c22450; B1=5e4; sigma = 16084220879206326459

   Mar 12, 2018   n =22511: 133597932869817732503685853 * 1099292464......c22463;  B1=5e4;  sigma = 13021235081596185428

   May 07, 2018   n =23357: 271754693239811669470333 * 4088654727......c23333;     B1=5e4;  sigma = 13657867932100063494

   May 07, 2018   n =23447: 17021960507400565282497842551 * 6527515503......c23418; B1=5e4; sigma = 7981419157208808342

   May 18, 2018   n =78511: 320033709185399054711 * 3471856492......c78490;         B1=11e3; sigma = 16782052464410323985

   May 18, 2018   n =78853: 711436450651091027 * 1561785469......c78835;            B1=11e3; sigma = 7333631212948291910
 
          
-  Found by  Yousuke Koide  
   Feb 15, 2018   n =  982: 44467075182005846868530065551693426652606026434296940573; B1=12e7; sigma = 2:5690539589092232789


-  Found by Alfred Reich 
   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/NeuralMiner
   Feb 12, 2018   n = 1373: 229016141864852008546928682385264917916393201;         B1= 11e6; sigma = 0:3460683030665955377 

-  YOYO@home/NeuralMiner
   Mar 04, 2018   n =  845: 212791029980380683788275402661746746635743222681;      B1= 11e6; sigma = 0:12524453152895746251

Factorizations
Repunits: R1        - R2500 (Mar 04, 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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