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

Related links:



ECM EFFORTS
with Rn:      323 < n < 2000 (Sep 22, 2018) with Rn:     1999 < n < 3000 (Aug 31, 2018)
with Rn:     2999 < n < 4000 (Sep 18, 2018) with Rn:     3999 < n < 5000 (Oct 15, 2017)
with Rn:     4999 < n < 6000 (Sep 20, 2018) with Rn:     5999 < n < 7000 (Sep 03, 2018)
with Rn:     6999 < n < 8000 (Oct 16, 2017) 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 (Oct 05, 2017)




Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/8600 curves/
numbers < 1001 digits		 937
working		 941
working		 947
working		 949
working		 953
working
B1 = 11e7/18400 curves/
numbers < 701 digits		 873
working		 875
working		 879
working		 1202
working		 1208
working
B1 = 26e7/46000 curves/
numbers < 450 digits		 437
working		 1136
working		 1142
working		 1160
working		 2380M
working
B1 = 85e7/75000 curves/
numbers < 250 digits		 515
working		 585
working		 609
working		 2420L
working		 2460L
working



News
-  Last update: Sep 23, 2018

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Sep 23, 2018   R447/c242/SNFS-difficult 300; 701M unique relations and 616M unique ideals are collected
                  currently progress ~ 97%:   
                  Msieve could build a matrix! The matrix (45.6M with target density=100) is still a little too big!
                  

Sat Sep 22 19:27:38 2018  Msieve v. 1.54 (SVN 1018)
Sat Sep 22 19:27:38 2018  factoring 69321014077064724019571549358862835996841447139912495343062967983949554947479478571581383734991370175536866202887278999373991988107804240628646717482866215329222782659915672388735946673582832868303624397508087015243244997035632300227764933519 (242 digits)
...
Sat Sep 22 19:27:40 2018  commencing relation filtering
Sat Sep 22 19:27:40 2018  setting target matrix density to 100.0
Sat Sep 22 19:27:40 2018  estimated available RAM is 65214.1 MB
Sat Sep 22 19:27:40 2018  commencing duplicate removal, pass 1
Sat Sep 22 21:39:58 2018  skipped 19363 relations with b > 2^32
Sat Sep 22 21:39:58 2018  skipped 515 relations with composite factors
Sat Sep 22 21:39:58 2018  found 103712484 hash collisions in 715955896 relations
Sat Sep 22 21:40:09 2018  added 1 free relations
Sat Sep 22 21:40:10 2018  commencing duplicate removal, pass 2
Sat Sep 22 21:51:14 2018  found 14441433 duplicates and 701514464 unique relations
...
Sun Sep 23 09:37:57 2018  begin with 155443516 relations and 158590981 unique ideals
Sun Sep 23 09:41:45 2018  reduce to 155066933 relations and 151608351 ideals in 7 passes
Sun Sep 23 09:41:45 2018  max relations containing the same ideal: 108
Sun Sep 23 09:44:09 2018  removing 3663918 relations and 2971463 ideals in 692455 cliques
Sun Sep 23 09:44:13 2018  commencing in-memory singleton removal
Sun Sep 23 09:44:37 2018  begin with 151403015 relations and 151608351 unique ideals
Sun Sep 23 09:48:17 2018  reduce to 151337578 relations and 148571173 ideals in 7 passes
Sun Sep 23 09:48:17 2018  max relations containing the same ideal: 105
Sun Sep 23 09:50:56 2018  relations with 0 large ideals: 60289
Sun Sep 23 09:50:56 2018  relations with 1 large ideals: 23151
Sun Sep 23 09:50:56 2018  relations with 2 large ideals: 356768
Sun Sep 23 09:50:56 2018  relations with 3 large ideals: 2579793
Sun Sep 23 09:50:56 2018  relations with 4 large ideals: 10245583
Sun Sep 23 09:50:56 2018  relations with 5 large ideals: 24717137
Sun Sep 23 09:50:56 2018  relations with 6 large ideals: 37911863
Sun Sep 23 09:50:56 2018  relations with 7+ large ideals: 75442994
Sun Sep 23 09:50:56 2018  commencing 2-way merge
Sun Sep 23 09:54:16 2018  reduce to 95513838 relation sets and 92747433 unique ideals
Sun Sep 23 09:54:16 2018  commencing full merge
Sun Sep 23 10:50:44 2018  memory use: 11565.6 MB
Sun Sep 23 10:51:29 2018  found 46037180 cycles, need 45675633
Sun Sep 23 10:51:33 2018  weight of 45675633 cycles is about 4568055335 (100.01/cycle)
Sun Sep 23 10:51:33 2018  distribution of cycle lengths:
Sun Sep 23 10:51:33 2018  1 relations: 4474653
Sun Sep 23 10:51:33 2018  2 relations: 4136781
Sun Sep 23 10:51:33 2018  3 relations: 4153598
Sun Sep 23 10:51:33 2018  4 relations: 3965941
Sun Sep 23 10:51:33 2018  5 relations: 3889384
Sun Sep 23 10:51:33 2018  6 relations: 3705589
Sun Sep 23 10:51:33 2018  7 relations: 3466152
Sun Sep 23 10:51:33 2018  8 relations: 3159028
Sun Sep 23 10:51:33 2018  9 relations: 2853177
Sun Sep 23 10:51:33 2018  10+ relations: 11871330
Sun Sep 23 10:51:33 2018  heaviest cycle: 25 relations
Sun Sep 23 10:57:19 2018  commencing cycle optimization
Sun Sep 23 11:00:01 2018  start with 310970779 relations
Sun Sep 23 11:23:30 2018  pruned 10055404 relations
Sun Sep 23 11:23:31 2018  memory use: 9408.9 MB
Sun Sep 23 11:23:31 2018  distribution of cycle lengths:
Sun Sep 23 11:23:31 2018  1 relations: 4474653
Sun Sep 23 11:23:31 2018  2 relations: 4236714
Sun Sep 23 11:23:31 2018  3 relations: 4312567
Sun Sep 23 11:23:31 2018  4 relations: 4097312
Sun Sep 23 11:23:31 2018  5 relations: 4033312
Sun Sep 23 11:23:31 2018  6 relations: 3819129
Sun Sep 23 11:23:31 2018  7 relations: 3571154
Sun Sep 23 11:23:31 2018  8 relations: 3238138
Sun Sep 23 11:23:31 2018  9 relations: 2904791
Sun Sep 23 11:23:31 2018  10+ relations: 10987863
Sun Sep 23 11:23:31 2018  heaviest cycle: 25 relations
Sun Sep 23 11:32:02 2018  RelProcTime: 57862
Sun Sep 23 11:32:02 2018  elapsed time 16:04:24

Sun Sep 23 13:20:16 2018  commencing linear algebra
Sun Sep 23 13:20:27 2018  read 45675633 cycles
Sun Sep 23 13:23:09 2018  cycles contain 149840465 unique relations
Sun Sep 23 13:44:23 2018  read 149840465 relations
Sun Sep 23 13:52:33 2018  using 20 quadratic characters above 4294917295
Sun Sep 23 14:04:37 2018  building initial matrix
Sun Sep 23 15:05:28 2018  memory use: 20479.8 MB
Sun Sep 23 15:06:59 2018  read 45675633 cycles
Sun Sep 23 15:07:12 2018  matrix is 45675456 x 45675633 (18556.4 MB) with weight 5421036167 (118.69/col)
Sun Sep 23 15:07:12 2018  sparse part has weight 4362028166 (95.50/col)
Sun Sep 23 15:20:57 2018  filtering completed in 2 passes
Sun Sep 23 15:21:09 2018  matrix is 45670283 x 45670460 (18556.1 MB) with weight 5420877245 (118.70/col)
Sun Sep 23 15:21:09 2018  sparse part has weight 4361985112 (95.51/col)
Sun Sep 23 15:27:26 2018  matrix starts at (0, 0)
Sun Sep 23 15:27:37 2018  matrix is 45670283 x 45670460 (18556.1 MB) with weight 5420877245 (118.70/col)
Sun Sep 23 15:27:37 2018  sparse part has weight 4361985112 (95.51/col)
Sun Sep 23 15:27:37 2018  saving the first 48 matrix rows for later
Sun Sep 23 15:28:01 2018  matrix includes 64 packed rows
Sun Sep 23 15:28:10 2018  matrix is 45670235 x 45670460 (17930.2 MB) with weight 4583932618 (100.37/col)
Sun Sep 23 15:28:10 2018  sparse part has weight 4243588069 (92.92/col)
Sun Sep 23 15:28:11 2018  using block size 8192 and superblock size 1081344 for processor cache size 11264 kB
Sun Sep 23 15:37:01 2018  commencing Lanczos iteration (16 threads)
Sun Sep 23 15:37:01 2018  memory use: 15765.9 MB
Sun Sep 23 15:40:24 2018  linear algebra at 0.0%, ETA 1616h 4m
...


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Kurt Beschorner 
   Feb 16, 2018   n = 1030: 2102173879615901190724805905901825960646731569309620829374935176385195435873285181866611; GNFS


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Sep 09, 2018   Next Number: R507, c200, GNFS
                  The R507-polynom was created by Makzym Voznyy in cooperation with mersenneforum - Thanks!


-  Found by Kurt Beschorner 
   Aug 14, 2018   n = 5763: 284156578135574224432914847837;                        B1= 1e6;  sigma= 3029120048

   Sep 18, 2018   n = 5769: 498268955994589849741317466453;                        B1= 1e6;  sigma= 3296470939


-  Found by Alfred Eichhorn 
   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

   Jul 01, 2018   n =24103: 5627527839932453599792169 * 1974421349......c24078;     B1=5e4;  sigma = 204637590329197301

   Aug 03, 2018   n =24499: 18174893231459131283319569 * 6113439550......c24473;    B1=5e4;  sigma = 8634299472218058874

   Aug 16, 2018   n =24767: 335279891709129662539397 * 7376413727......c24719;      B1=5e4;  sigma = 18035853098425951272

   Aug 16, 2018   n =50129: 6289652660414968016773 * 1766569906......c50107;        B1=5e4;  sigma = 9173810817472448840

   Aug 24, 2018   n =24859: 732758049762982336409489 * 1516341050......c24835;      B1=5e4;  sigma = 13838281173430418896 

   Sep 14, 2018   n =25033: 26379408690395699720505923 * 4212039489......c25007;    B1=5e4;  sigma = 17699047658806986723

   Sep 14, 2018   n =50147: 84543021478589310587493493 * 1314255265......c50121;    B1=5e4;  sigma = 5370675363275971662

   Sep 22, 2018   n =25037: 811768176143826688793987 * 1368754213......c25013;      B1=5e4;  sigma = 11091549647073987954

   
-  Found by  Yousuke Koide  
   Feb 15, 2018   n =  982: 44467075182005846868530065551693426652606026434296940573; B1=12e7; sigma = 2:5690539589092232789


-  Found by Alfred Reich 
   Aug 25, 2018   n = 2000: 2918934658137053157142763595766996896001;              B1= 8e7;  sigma= 1:422066992


-  Found by  Sam Wagstaff
   Jun 30, 2018   n =  776: 89889606269073901082901578436277965983883967076039535258233; ecm


-  Found by YOYO@home 
-  YOYO@home/WhiteFire
   Jun 05, 2018   n =  439: 4420197369389321682193651680706705688987;              B1= 26e7; sigma = 0:18058967600223373828  

-  YOYO@home/WhiteFire  
   Jun 05, 2018   n =  439: 221873542765174880268698440076944289246071;            B1= 26e7; sigma = 0:16712880220435730410   

-  YOYO@home/Deltik
   Jun 26, 2018   n =  929: 443771757418389946333550544711719925863831;            B1= 43e6; sigma = 0:9461729732758165730

-  YOYO@home/ebahapo
   Jun 29, 2018   n = 1321: 31337427608867251262904500110595867;                   B1= 11e6; sigma = 0:3388369777661332901

-  YOYO@home/NeuralMiner
   Jul 04, 2018   n = 1319: 14390577104652629414853222197261272650807833666740820489; B1= 11e6; sigma = 0:9515467317591503677

-  YOYO@home/Deltik
   Jul 26, 2018   n =5660M: 1369840259774549318827876634983169895121;              B1= 11e6; sigma = 0:8001543717994501796

-  YOYO@home/Danny
   Aug 15, 2018   n = 937:  829044297281482845905510544752736064447147;            B1= 43e6; sigma = 0:17347482564892651207

-  YOYO@home/Danny
   Aug 16, 2018   n = 941:  2416277668973171349313713089855425966192452863373961;  B1= 43e6; sigma = 0:8598628182170899200

-  YOYO@home/biodoc
   Aug 24, 2018   n =5860L: 2837267642075799218843167929960912181;                 B1= 11e6; sigma = 0:4074972538232797766

-  YOYO@home/Deltik
   Sep 05, 2018   n = 947:  48654367388531252592760353317455806428703907;          B1= 43e6; sigma = 0:3047487473098335725

-  YOYO@home/CCPLogibro
   Sep 15, 2018   n =1225:  148034167812084215700206443550170966001;               B1= 43e6; sigma = 0:671077335727112008

-  YOYO@home/pi
   Sep 17, 2018   n =5900M: 593243597135622945022444401922545308692618865123732027101; B1= 11e6; sigma = 0:12823567598948732363

-  YOYO@home/Loaded
   Sep 18, 2018   n =1202:  12319072731805329005802468132076248505842564849805129; B1= 11e7; sigma = 0:14036092255227619769

-  YOYO@home/Lennox84
   Sep 19, 2018   n = 463:  212135711098934921098108241314382773839707263659206851643; B1= 26e7; sigma = 0:18442255449381683540

Factorizations
Repunits: R1        - R2500 (Sep 19, 2018) Repunits:  R2501 - R5000 (Sep 13, 2018)
Repunits: R5001   - R7500 (Sep 18, 2018) Repunits: R7501 - R10000 (Feb 11, 2018)
Repunits: R10001 - R12500 (Sep 30, 2017) Repunits: R12540LM - R14980LM (Sep 30, 2017)


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