Factorizations of Repunit Numbers

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

ECM EFFORTS
with Rn: 323 < n < 2000 (Jan 23, 2019)	with Rn: 1999 < n < 3000 (Jan 14, 2019)
with Rn: 2999 < n < 4000 (Oct 12, 2018)	with Rn: 3999 < n < 5000 (Oct 15, 2017)
with Rn: 4999 < n < 6000 (Dec 08, 2018)	with Rn: 5999 < n < 7000 (Jan 27, 2019)
with Rn: 6999 < n < 8000 (Jan 23, 2019)	with Rn: 7999 < n < 9000 (Aug 14, 2018)
with Rn: 8999 < n <10000 (Aug 14, 2018)	with Rn: 9999 < n <11000 (Sep 17, 2017)
with Rn: 10999 < n <12000 (Oct 04, 2017)	with Rn: 11999 < n <12501 (Dec 28, 2018)

Efforts by yoyo@home: ecm-curves
B1 = 43e6/8600 curves/ numbers < 1001 digits	953 working	967 working	971 working	973 working	977 working
B1 = 11e7/18400 curves/ numbers < 701 digits	547 working	557 working	879 working	895 working	955 working
B1 = 26e7/46000 curves/ numbers < 450 digits	735 working	1136 working	1142 working	1160 working	2380M working
B1 = 85e7/75000 curves/ numbers < 250 digits	471 working	585 working	609 working	2420L working	2460L working

News

-  Last update: Jan 27, 2019/2nd      

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jan 27, 2019   R507, c200, GNFS: the R507-polynom was created by Makzym Voznyy in cooperation with mersenneforum - thanks!
                  458M unique relations and 531M unique ideals are collected
                  currently progress ~ 62.7%:    
                  

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Nov 18, 2018   n = 447:  171965701068496883745528184125987011516361211819168507125947606393599406276344599684907; SNFS                      

Sat Oct 06 04:58:46 2018  Msieve v. 1.54 (SVN 1018)
Sat Oct 06 04:58:46 2018  random seeds: e3918a68 32ce80a5
Sat Oct 06 04:58:46 2018  factoring 69321014077064724019571549358862835996841447139912495343062967983949554947479478571581383734991370175536866202887278999373991988107804240628646717482866215329222782659915672388735946673582832868303624397508087015243244997035632300227764933519 (242 digits)
Sat Oct 06 04:58:47 2018  searching for 15-digit factors
Sat Oct 06 04:58:48 2018  commencing number field sieve (242-digit input)
Sat Oct 06 04:58:48 2018  R0: -100000000000000000000000000000000000000000000000000
Sat Oct 06 04:58:48 2018  R1: 1
Sat Oct 06 04:58:48 2018  A0: 100
Sat Oct 06 04:58:48 2018  A1: 0
Sat Oct 06 04:58:48 2018  A2: 0
Sat Oct 06 04:58:48 2018  A3: 10
Sat Oct 06 04:58:48 2018  A4: 0
Sat Oct 06 04:58:48 2018  A5: 0
Sat Oct 06 04:58:48 2018  A6: 1
Sat Oct 06 04:58:48 2018  skew 2.95, size 1.246e-014, alpha -0.127, combined = 3.929e-015 rroots = 0
Sat Oct 06 04:58:48 2018  commencing relation filtering
Sat Oct 06 04:58:48 2018  setting target matrix density to 120.0
Sat Oct 06 04:58:48 2018  estimated available RAM is 65214.1 MB
Sat Oct 06 04:58:48 2018  commencing duplicate removal, pass 1
Sat Oct 06 04:59:37 2018  error -9 reading relation 4525107
...
Sat Oct 06 07:17:12 2018  skipped 20467 relations with b > 2^32
Sat Oct 06 07:17:12 2018  skipped 495 relations with composite factors
Sat Oct 06 07:17:12 2018  found 117072180 hash collisions in 755265371 relations
Sat Oct 06 07:17:23 2018  added 1 free relations
Sat Oct 06 07:17:23 2018  commencing duplicate removal, pass 2
Sat Oct 06 07:29:27 2018  found 25043240 duplicates and 730222132 unique relations
Sat Oct 06 07:29:27 2018  memory use: 4518.0 MB
Sat Oct 06 07:29:28 2018  reading ideals above 431030272
Sat Oct 06 07:29:28 2018  commencing singleton removal, initial pass
Sat Oct 06 09:29:40 2018  memory use: 11024.0 MB
Sat Oct 06 09:29:41 2018  reading all ideals from disk
Sat Oct 06 09:29:51 2018  memory use: 13762.1 MB
Sat Oct 06 09:31:03 2018  commencing in-memory singleton removal
Sat Oct 06 09:32:11 2018  begin with 730222132 relations and 624045914 unique ideals
Sat Oct 06 09:51:04 2018  reduce to 488536219 relations and 359290715 ideals in 16 passes
Sat Oct 06 09:51:04 2018  max relations containing the same ideal: 31
Sat Oct 06 09:52:11 2018  reading ideals above 720000
Sat Oct 06 09:52:13 2018  commencing singleton removal, initial pass
Sat Oct 06 11:48:09 2018  memory use: 11024.0 MB
Sat Oct 06 11:48:10 2018  reading all ideals from disk
Sat Oct 06 11:48:29 2018  memory use: 22023.2 MB
Sat Oct 06 11:50:26 2018  keeping 402483262 ideals with weight <= 200, target excess is 2607065
...
Sat Oct 06 21:45:43 2018  commencing in-memory singleton removal
Sat Oct 06 21:46:04 2018  begin with 141745329 relations and 142664143 unique ideals
Sat Oct 06 21:49:15 2018  reduce to 141616321 relations and 138591294 ideals in 7 passes
Sat Oct 06 21:49:15 2018  max relations containing the same ideal: 96
Sat Oct 06 21:51:39 2018  relations with 0 large ideals: 65943
Sat Oct 06 21:51:39 2018  relations with 1 large ideals: 30581
Sat Oct 06 21:51:39 2018  relations with 2 large ideals: 455061
Sat Oct 06 21:51:39 2018  relations with 3 large ideals: 3079754
Sat Oct 06 21:51:39 2018  relations with 4 large ideals: 11406833
Sat Oct 06 21:51:39 2018  relations with 5 large ideals: 25593658
Sat Oct 06 21:51:39 2018  relations with 6 large ideals: 36492971
Sat Oct 06 21:51:39 2018  relations with 7+ large ideals: 64491520
Sat Oct 06 21:51:39 2018  commencing 2-way merge
Sat Oct 06 21:54:38 2018  reduce to 90132240 relation sets and 87107213 unique ideals
Sat Oct 06 21:54:38 2018  commencing full merge
Sat Oct 06 22:56:57 2018  memory use: 11212.0 MB
Sat Oct 06 22:57:37 2018  found 41059399 cycles, need 40763413
Sat Oct 06 22:57:41 2018  weight of 40763413 cycles is about 4892357921 (120.02/cycle)
Sat Oct 06 22:57:41 2018  distribution of cycle lengths:
Sat Oct 06 22:57:41 2018  1 relations: 2860257
Sat Oct 06 22:57:41 2018  2 relations: 2953546
Sat Oct 06 22:57:41 2018  3 relations: 3046688
Sat Oct 06 22:57:41 2018  4 relations: 3036747
Sat Oct 06 22:57:41 2018  5 relations: 3030362
Sat Oct 06 22:57:41 2018  6 relations: 2980876
Sat Oct 06 22:57:41 2018  7 relations: 2881308
Sat Oct 06 22:57:41 2018  8 relations: 2760500
Sat Oct 06 22:57:41 2018  9 relations: 2588644
Sat Oct 06 22:57:41 2018  10+ relations: 14624485
Sat Oct 06 22:57:41 2018  heaviest cycle: 28 relations
Sat Oct 06 23:03:14 2018  commencing cycle optimization
Sat Oct 06 23:05:57 2018  start with 331593529 relations
Sat Oct 06 23:32:38 2018  pruned 13563958 relations
Sat Oct 06 23:32:38 2018  memory use: 9231.7 MB
Sat Oct 06 23:32:38 2018  distribution of cycle lengths:
Sat Oct 06 23:32:39 2018  1 relations: 2860257
Sat Oct 06 23:32:39 2018  2 relations: 3026923
Sat Oct 06 23:32:39 2018  3 relations: 3173026
Sat Oct 06 23:32:39 2018  4 relations: 3153050
Sat Oct 06 23:32:39 2018  5 relations: 3168168
Sat Oct 06 23:32:39 2018  6 relations: 3105685
Sat Oct 06 23:32:39 2018  7 relations: 3013415
Sat Oct 06 23:32:39 2018  8 relations: 2871297
Sat Oct 06 23:32:39 2018  9 relations: 2688554
Sat Oct 06 23:32:39 2018  10+ relations: 13703038
Sat Oct 06 23:32:39 2018  heaviest cycle: 28 relations
Sat Oct 06 23:39:30 2018  RelProcTime: 67242
Sat Oct 06 23:39:30 2018  
Sat Oct 06 23:39:30 2018  commencing linear algebra
Sat Oct 06 23:39:55 2018  read 40763413 cycles
Sat Oct 06 23:42:46 2018  cycles contain 140036147 unique relations
Sun Oct 07 00:04:43 2018  read 140036147 relations
Sun Oct 07 00:13:03 2018  using 20 quadratic characters above 4294917295
Sun Oct 07 00:24:18 2018  building initial matrix
Sun Oct 07 01:26:49 2018  memory use: 18710.3 MB
Sun Oct 07 01:29:40 2018  read 40763413 cycles
Sun Oct 07 01:29:52 2018  matrix is 40763236 x 40763413 (19269.0 MB) with weight 5597046678 (137.31/col)
Sun Oct 07 01:29:52 2018  sparse part has weight 4602849360 (112.92/col)
Sun Oct 07 01:44:03 2018  filtering completed in 2 passes
Sun Oct 07 01:44:14 2018  matrix is 40761323 x 40761500 (19268.8 MB) with weight 5596979276 (137.31/col)
Sun Oct 07 01:44:14 2018  sparse part has weight 4602828028 (112.92/col)
Sun Oct 07 01:51:44 2018  matrix starts at (0, 0)
Sun Oct 07 01:51:55 2018  matrix is 40761323 x 40761500 (19268.8 MB) with weight 5596979276 (137.31/col)
Sun Oct 07 01:51:55 2018  sparse part has weight 4602828028 (112.92/col)
Sun Oct 07 01:51:55 2018  saving the first 48 matrix rows for later
Sun Oct 07 01:52:16 2018  matrix includes 64 packed rows
Sun Oct 07 01:52:26 2018  matrix is 40761275 x 40761500 (18644.3 MB) with weight 4828877229 (118.47/col)
Sun Oct 07 01:52:26 2018  sparse part has weight 4479876000 (109.90/col)
Sun Oct 07 01:52:26 2018  using block size 8192 and superblock size 1081344 for processor cache size 11264 kB
Sun Oct 07 02:00:28 2018  commencing Lanczos iteration (16 threads)
Sun Oct 07 02:00:28 2018  memory use: 16396.0 MB
Sun Oct 07 02:03:00 2018  linear algebra at 0.0%, ETA 1071h55m
Sun Oct 07 02:03:48 2018  checkpointing every 40000 dimensions
Sun Nov 18 01:26:31 2018  lanczos halted after 644592 iterations (dim = 40761273)
Sun Nov 18 01:27:22 2018  recovered 39 nontrivial dependencies
Sun Nov 18 01:31:06 2018  BLanczosTime: 3639096
Sun Nov 18 01:31:06 2018  
Sun Nov 18 01:31:06 2018  commencing square root phase
Sun Nov 18 01:31:06 2018  handling dependencies 1 to 64
Sun Nov 18 01:31:06 2018  reading relations for dependency 1
Sun Nov 18 01:31:29 2018  read 20383058 cycles
Sun Nov 18 01:32:52 2018  cycles contain 70029230 unique relations
Sun Nov 18 01:49:39 2018  read 70029230 relations
Sun Nov 18 02:02:40 2018  multiplying 70029230 relations
Sun Nov 18 03:46:23 2018  multiply complete, coefficients have about 1982.47 million bits
Sun Nov 18 03:46:32 2018  initial square root is modulo 781234637
Sun Nov 18 05:25:03 2018  sqrtTime: 14037
Sun Nov 18 05:25:03 2018  p87 factor: 171965701068496883745528184125987011516361211819168507125947606393599406276344599684907
Sun Nov 18 05:25:03 2018  p156 factor: 403109536647967823252626198527435162419900299742827908005840017638975777612947999010862228355924998943486126966926981706492404007923365680835642750113174317
Sun Nov 18 05:25:03 2018  elapsed time 1033:26:17


-  Found by Kurt Beschorner 
   Nov 15, 2018   n = 5799: 407616517564686763737328159;                           B1= 1e6;  sigma = 196829594

   Jan 27, 2019   n =6380L: 2745820043425052285732308383257413452721;              B1= 11e6; sigma = 1168867487
   

-  Found by Alfred Eichhorn 
   Nov 11, 2018   n =25537: 1259296913639166167562326419639 * 8823265578......c25506; B1=5e4; sigma = 14892534724291470304
   
   Nov 11, 2018   n =83257: 59227921609062585437 * 1875992067......c83237;          B1=11e3; sigma = 17579053699389191557

   Nov 11, 2018   n =83299: 893226768070010831 * 1160078125......c83264;            B1=11e3; sigma = 11086780502315832603

   Nov 11, 2018   n =83311: 3481979901988725361079 * 3191032522......c83289;        B1=11e3; sigma = 6240338475624733737
   
   Dec 19, 2018   n =50417: 231761535272230289363 * 4794199821......c50396;         B1= 5e4; sigma = 3033579618245357906
   
   Dec 19, 2018   n =83987: 285272068532406380071 * 3894917286......c83966;         B1=11e3; sigma = 1182803978517703859 

   Dec 19, 2018   n =84011: 946115523837538007243 * 1174392643......c83990;         B1=11e3; sigma = 12024811436285266500 

-  Correction
   false:    Jan 02, 2019  n =88229: 168663925267282807631 * 6587722355......c85208;         B1=11e3; sigma = 7899039265179683671   

   false:    Jan 02, 2019  n =88297: 421924698407540082163 * 2633434627......c85276;         B1=11e3; sigma = 14753187368402742930  

   correct: Jan 02, 2019  n =85229: 168663925267282807631 * 6587722355......c85208;         B1=11e3; sigma = 7899039265179683671   

   correct: Jan 02, 2019  n =85297: 421924698407540082163 * 2633434627......c85276;         B1=11e3; sigma = 14753187368402742930  

   Find out by Alfred Eichhorn


-  Found by Alfred Reich 
   Dec 15, 2018   n = 2708: 1354592090378874321847140113114629;                    B1=11e7;  sigma= 12297352491712952550

   Dec 16, 2018   n =12064: 2546977868727768182069660426273;                       B1=1028e6; P-1 

   Dec 22, 2018   n =12121: 2407649538814710985900453;                             B1=5e4;   sigma= 13750623641237937222     

   Dec 28, 2018   n =12118: 37627065539202417697996134091;                         B1=1e6;   sigma= 13539547277930664860     

   Jan 16, 2019   n = 7022: 283348395018893878476537518650454921;                  B1=1e6;   sigma= 5134893878574285     

   Jan 25, 2019   n = 7028: 59084034101806249573177345121188082021;                B1=3e6;   sigma= 5134893878574285     


-  Found by YOYO@home 

-  YOYO@home/WhiteFire
   Nov 23, 2018   n = 953:  601571969724357908830782907588971858878664579169;      B1= 43e6; sigma = 0:2441301558609603979 
   
-  YOYO@home/Francis Butts
   Dec 06, 2018   n = 521:  491580859282283461621997489642141402831898607368043;   B1= 11e7; sigma = 0:7248104013312129170 
   
-  YOYO@home/bbmz  
   Dec 06, 2018   n = 955:  4611631116936866644619325113494274068514558656631;     B1= 43e6; sigma = 0:4773587962081043371  
   
-  YOYO@home/WhiteFire  
   Dec 14, 2018   n = 959:  39479260483646804613228566945758015357951;             B1= 43e6; sigma = 0:18072187453986147935  
   
-  YOYO@home/NYX.consulting 
   Dec 15, 2018   n = 541:  49209783772401428869185936838646522086059329;          B1= 11e7; sigma = 0:18331671264619453476  
   
-  YOYO@home/NeuralMiner 
   Dec 15, 2018   n = 705:  39684295305390393945033155364640501778802903740578801; B1= 26e7; sigma = 0:4005087120915227197  
   
-  YOYO@home/MartinOrpen
   Dec 25, 2018   n =1361:  3778133360275162515561392131873427;                    B1= 11e6; sigma = 0:11807715445759359346   
   
-  YOYO@home/lanbrown
   Dec 25, 2018   n = 675:  11302625411464361797455477156321087241022971504311406801; B1= 85e7; sigma = 0:5866504219856597377   
   
-  YOYO@home/user3928 
   Dec 26, 2018   n = 735:  1043724088777138410374757855271037976569452410073591;  B1= 26e7; sigma = 17739413172727101663    
   
-  YOYO@home/bbmz     
   Jan 05, 2019   n =1355:  64798931224892046095300386296961245938921;             B1= 11e6; sigma = 0:12395092201359388656    
   
-  YOYO@home/solo     
   Jan 14, 2019   n =2580L: 40577891868500992650677399803808454657267203875748156761; B1= 26e7; sigma = 0:2155320441625669934

Factorizations
Repunits: R1 - R2500 (Jan 05, 2019)	Repunits: R2501 - R5000 (Jan 14, 2019)
Repunits: R5001 - R7500 (Jan 27, 2019)	Repunits: R7501 - R10000 (Feb 11, 2018)
Repunits: R10001 - R12500 (Dec 26, 2018)	Repunits: R12540LM - R14980LM (Sep 30, 2017)

Visitors since March 09, 2015: besucherzaehler-homepage.de

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

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

Related links:

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