Factorizations of Repunit Numbers

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

ECM EFFORTS
with Rn: 323 < n < 2000 (Aug 17, 2018)	with Rn: 1999 < n < 3000 (Aug 14, 2018)
with Rn: 2999 < n < 4000 (Aug 10, 2018)	with Rn: 3999 < n < 5000 (Oct 15, 2017)
with Rn: 4999 < n < 6000 (Aug 14, 2018)	with Rn: 5999 < n < 7000 (Feb 14, 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	943 working	947 working	949 working
B1 = 11e7/18400 curves/ numbers < 701 digits	865 working	869 working	873 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	407 working	515 working	1420L working	2420L working	2460L working

News

-  Last update: Aug 17, 2018

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 14, 2018   R447/c242/SNFS-difficult 300; 597M unique relations and 590M unique ideals are collected
                  currently progress ~ 82%:   
                  Msieve could build a matrix! The matrix is still too big!
                  
Mon Aug 13 12:17:15 2018  Msieve v. 1.53 (SVN unknown)
Mon Aug 13 12:17:15 2018  factoring 69321014077064724019571549358862835996841447139912495343062967983949554947479478571581383734991370175536866202887278999373991988107804240628646717482866215329222782659915672388735946673582832868303624397508087015243244997035632300227764933519 (242 digits)
Mon Aug 13 12:17:18 2018  commencing number field sieve (242-digit input)
...
Mon Aug 13 12:17:18 2018  commencing relation filtering
Mon Aug 13 12:17:18 2018  setting target matrix density to 70.0
Mon Aug 13 12:17:18 2018  estimated available RAM is 49069.6 MB
Mon Aug 13 12:17:18 2018  commencing duplicate removal, pass 1
Mon Aug 13 15:35:50 2018  skipped 13402 relations with b > 2^32
Mon Aug 13 15:35:50 2018  skipped 521 relations with composite factors
Mon Aug 13 15:35:50 2018  found 75423462 hash collisions in 604797948 relations
Mon Aug 13 15:36:15 2018  commencing duplicate removal, pass 2
Mon Aug 13 15:46:37 2018  found 7332257 duplicates and 597465691 unique relations
Mon Aug 13 15:46:37 2018  memory use: 2387.0 MB
Mon Aug 13 15:46:38 2018  reading ideals above 376766464
Mon Aug 13 15:46:38 2018  commencing singleton removal, initial pass
Mon Aug 13 18:21:27 2018  memory use: 11024.0 MB
Mon Aug 13 18:21:28 2018  reading all ideals from disk
Mon Aug 13 18:23:23 2018  memory use: 11489.6 MB
Mon Aug 13 18:24:49 2018  commencing in-memory singleton removal
Mon Aug 13 18:26:14 2018  begin with 597465691 relations and 590488402 unique ideals
Mon Aug 13 18:48:34 2018  reduce to 293976928 relations and 246397463 ideals in 26 passes
Mon Aug 13 18:48:34 2018  max relations containing the same ideal: 41
...
Mon Aug 13 23:25:17 2018  begin with 226894755 relations and 225337653 unique ideals
Mon Aug 13 23:31:17 2018  reduce to 226894507 relations and 225095840 ideals in 5 passes
Mon Aug 13 23:31:17 2018  max relations containing the same ideal: 178
Mon Aug 13 23:32:54 2018  relations with 0 large ideals: 39049
Mon Aug 13 23:32:54 2018  relations with 1 large ideals: 6830
Mon Aug 13 23:32:54 2018  relations with 2 large ideals: 116203
Mon Aug 13 23:32:54 2018  relations with 3 large ideals: 1119785
Mon Aug 13 23:32:54 2018  relations with 4 large ideals: 6100325
Mon Aug 13 23:32:54 2018  relations with 5 large ideals: 20457709
Mon Aug 13 23:32:54 2018  relations with 6 large ideals: 43727466
Mon Aug 13 23:32:54 2018  relations with 7+ large ideals: 155327140
Mon Aug 13 23:32:54 2018  commencing 2-way merge
Mon Aug 13 23:39:46 2018  reduce to 136111854 relation sets and 134313187 unique ideals
Mon Aug 13 23:39:46 2018  commencing full merge
Tue Aug 14 00:48:47 2018  memory use: 15055.8 MB
Tue Aug 14 00:49:47 2018  found 74383490 cycles, need 74139387
Tue Aug 14 00:49:53 2018  weight of 74139387 cycles is about 5189922173 (70.00/cycle)
Tue Aug 14 00:49:53 2018  distribution of cycle lengths:
Tue Aug 14 00:49:53 2018  1 relations: 12301708
Tue Aug 14 00:49:53 2018  2 relations: 11075559
Tue Aug 14 00:49:53 2018  3 relations: 10508792
Tue Aug 14 00:49:53 2018  4 relations: 8357724
Tue Aug 14 00:49:53 2018  5 relations: 7156088
Tue Aug 14 00:49:53 2018  6 relations: 5607256
Tue Aug 14 00:49:53 2018  7 relations: 4415458
Tue Aug 14 00:49:53 2018  8 relations: 3514807
Tue Aug 14 00:49:53 2018  9 relations: 2813567
Tue Aug 14 00:49:53 2018  10+ relations: 8388428
Tue Aug 14 00:49:53 2018  heaviest cycle: 22 relations
Tue Aug 14 00:56:59 2018  commencing cycle optimization
Tue Aug 14 01:00:31 2018  start with 355885976 relations
Tue Aug 14 01:27:27 2018  pruned 5458355 relations
Tue Aug 14 01:27:28 2018  memory use: 12868.8 MB
Tue Aug 14 01:27:28 2018  distribution of cycle lengths:
Tue Aug 14 01:27:28 2018  1 relations: 12301708
Tue Aug 14 01:27:28 2018  2 relations: 11283336
Tue Aug 14 01:27:28 2018  3 relations: 10783208
Tue Aug 14 01:27:28 2018  4 relations: 8456180
Tue Aug 14 01:27:28 2018  5 relations: 7191309
Tue Aug 14 01:27:28 2018  6 relations: 5568853
Tue Aug 14 01:27:28 2018  7 relations: 4367088
Tue Aug 14 01:27:28 2018  8 relations: 3457690
Tue Aug 14 01:27:28 2018  9 relations: 2754804
Tue Aug 14 01:27:28 2018  10+ relations: 7975211
Tue Aug 14 01:27:28 2018  heaviest cycle: 21 relations
Tue Aug 14 01:43:20 2018  RelProcTime: 48362
Tue Aug 14 01:43:20 2018  elapsed time 13:26:05
...
Tue Aug 14 03:33:51 2018  commencing linear algebra
Tue Aug 14 03:34:15 2018  read 74139387 cycles     <<<===== matrix size
Tue Aug 14 03:37:45 2018  cycles contain 224954330 unique relations
Tue Aug 14 04:29:19 2018  read 224954330 relations
Tue Aug 14 04:39:32 2018  using 20 quadratic characters above 4294917295
Tue Aug 14 05:01:06 2018  building initial matrix
...


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


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


-  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

   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
    

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


-  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
   
-  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

Factorizations
Repunits: R1 - R2500 (Aug 17, 2018)	Repunits: R2501 - R5000 (Jul 12, 2018)
Repunits: R5001 - R7500 (Aug 14, 2018)	Repunits: R7501 - R10000 (Feb 11, 2018)
Repunits: R10001 - R12500 (Sep 30, 2017)	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...)