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


related links     news     ecm efforts     currently efforts by YOYO     factor tables     Rprime project    


Related links:

News

-  Last update: Oct 31, 2020                                                     
 

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Oct 31, 2020   R337, c202, GNFS: the R337-polynom was created by Gimarel and Maksym Voznyy - thanks!
                  494M unique relations and 545M unique ideals are collected           
                  currently progress ~ 67 %:    


-  Found by Kurt Beschorner 
   Oct 26, 2020   n = 9139: 102323103870499479272499972352456883;                   ecm: B1= 1e6;  sigma = 0:32605637501090 


-  Found by Sam Wagstaff 
   Oct 21, 2020   n =  742:  2548171182130492354464113595833821781588064140986874348075459263402328971040215243200625902015381883224397137647; SNFS 
    

-  Found by Alfred Eichhorn 
   Oct 13, 2020   n =35251:  119046480308568500886427 * 9333422611......c35227;     ecm: B1= 5e4;  sigma = 0:620255578917684
   Oct 13, 2020   n =35363:  2931190842118437948895849 * 3790647456......c35338;    ecm: B1= 5e4;  sigma = 0:3356793723748038
   Oct 13, 2020   n =56671:  17327625606417916093196681 * 3881606412......c56626;   ecm: B1= 5e4;  sigma = 0:8039459931350690

      
-  Found by Kurt Beschorner 
   Oct 11, 2020   n=299912: 26483555133285114793;                                   ecm: B1=11e3;  sigma = 0:2255661832190991 
   Oct 11, 2020   n=299912: 107911061915460883817;                                  ecm: B1=11e3;  sigma = 0:1224499426851938


-  Found by Kurt Beschorner 
   Oct 05, 2020   n = 9097: 55502243290677967041853006539414761;                    ecm: B1= 1e6;  sigma = 0:3429806618658913 


-  Found by YOYO@home 
   James C. Owens       
   Oct 04, 2020   n =  469: 6958997628875965569003769582314963273475677604340583053; ecm: B1=26e7      


-  Found by Alfred Eichhorn 
   Oct 03, 2020   n =35227:  61546699056988639875393323 * 1805313896......c35201;   ecm: B1= 5e4;  sigma = 0:4422238530267184 
   Oct 03, 2020   n =56501:  833735079549139025506013 * 9484523591......c56454;     ecm: B1= 5e4;  sigma = 0:8776110477941862 

 
-  Found by Alfred Eichhorn 
   Sep 30, 2020   n =56267:  1835991125691172513172823643 * 6051832688......c56239; ecm: B1= 5e4;  sigma = 0:6886219702756561
   Sep 30, 2020   n =92353:  9936534644772715742414803 * 1118207856......c92328;    ecm: B1= 5e4;  sigma = 0:7757038471345416


-  Found by YOYO@home 
   Possix      
   Sep 27, 2020   n =6580M: 5226300854932192952818901175186968159161;               ecm: B1=11e6;  sigma = 0:6986030302957500225         

   
-  Found by YOYO@home 
   Domstang68    
   Sep 26, 2020   n =7980L: 7852530157762803085617492355913151301;                  ecm: B1=43e6;  sigma = 0:6858431455024526459         

   
-  Found by Kurt Beschorner 
   Sep 21, 2020   n = 9155: 7616089497844942161161351656201;                        ecm: B1= 1e6;  sigma = 0:6590737663680927 


-  Found by Kurt Beschorner 
   Sep 19, 2020   n =12501: 6535104588045721;                                       ecm: B1= 1e6;  sigma = 1760487021690192 

 
-  Found by Alfred Eichhorn 
   Sep 17, 2020   n =56041:  102321462089518541403732043 * 1085902300......c56015;  ecm: B1= 5e4;  sigma = 3303935810774227


-  Found by Alfred Eichhorn 
   Sep 11, 2020   n =34613:  1120910859943369124449753067 * 9912573343......c34585; ecm: B1= 5e4; sigma = 0:3124205414575670 
   Sep 11, 2020   n =34631:  1865442867892204591011209 * 5956285932......c34606;    ecm: B1= 5e4; sigma = 1303306403291282 
   Sep 11, 2020   n =55949:  763128123673032584695757159 * 1455995496......c55922;  ecm: B1= 5e4; sigma = 0:756659182058430 
   Sep 11, 2020   n =92237:  13137107473702256458541917 * 8457806357......c92211;   ecm: B1= 5e4; sigma = 1934092352120563 


-  Found by Alfred Eichhorn 
   Sep 03, 2020   n =55717:  32755939171857795635814010711 * 3392090531......c55688; ecm:B1= 5e4; sigma = 0:4984892550861418 


-  Found by YOYO@home 
   Barrie   
   Aug 30, 2020   n = 1465: 4124958033208387919306004986222829222160703448431;      ecm: B1= 11e6;        
 
      
-  Found by Alfred Eichhorn 
   Aug 22, 2020   n =34213:  1447483603198972631826271 * 7676156805......c34188;    ecm: B1= 5e4; sigma = 2299520442601417
   Aug 22, 2020   n =91823:  150710591896116987435871 * 7372481901......c91799;     ecm: B1= 5e4; sigma = 5727404210433105
   Aug 22, 2020   n =91943:  4423729066459701825541397 * 2511706965......c91918;    ecm: B1= 5e4; sigma = 4538722838662089


-  Found by Kurt Beschorner 
   Aug 10, 2020   n = 9125: 731542295610070635675114751;                            ecm: B1= 1e6;  sigma = 8234450462098695 


-  Found by Kurt Beschorner 
   Aug 03, 2020   n = 9051: 25812255150720206620915150429891843;                    ecm: B1= 3e6;  sigma = 0:4029561786297060

    
-  Found by Kurt Beschorner 
   Aug 02, 2020   n = 9113: 17245749127283658743551012523;                          ecm: B1= 1e6;  sigma = 1521521902935765


-  Found by Alfred Eichhorn 
   Jul 30, 2020   n =33851:  1089612291588859083100799 * 1019730705......c33827;    ecm: B1= 5e4; sigma = 6941267710365863


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 24, 2020   n =  459: 287743709071765679519005572592282086727787894852332081977696568112925297043603; SNFS
   details:
Fri Apr 03 17:25:47 2020  Msieve v. 1.53 (SVN unknown)
Fri Apr 03 17:25:47 2020  random seeds: a997da14 c0f798bb
Fri Apr 03 17:25:47 2020  factoring 28097663627596496902274031141491145315198561003423811939570768213737090759678697671003530296081683917890273394247547501189864859965856340788100033713344868576734124225081468514935749802816307889082656350436177478956926883 (221 digits)
Fri Apr 03 17:25:49 2020  searching for 15-digit factors
Fri Apr 03 17:25:49 2020  commencing number field sieve (221-digit input)
Fri Apr 03 17:25:49 2020  R0: -1000000000000000000000000000000000000000000000000000
Fri Apr 03 17:25:49 2020  R1: 1
Fri Apr 03 17:25:49 2020  A0: 1
Fri Apr 03 17:25:49 2020  A1: 0
Fri Apr 03 17:25:49 2020  A2: 0
Fri Apr 03 17:25:49 2020  A3: 1
Fri Apr 03 17:25:49 2020  A4: 0
Fri Apr 03 17:25:49 2020  A5: 0
Fri Apr 03 17:25:49 2020  A6: 1
Fri Apr 03 17:25:49 2020  skew 1.00, size 6.089e-015, alpha 1.996, combined = 2.206e-015 rroots = 0
Fri Apr 03 17:25:50 2020  
Fri Apr 03 17:25:50 2020  commencing relation filtering
Fri Apr 03 17:25:50 2020  setting target matrix density to 130.0
Fri Apr 03 17:25:50 2020  estimated available RAM is 65214.1 MB
Fri Apr 03 17:25:50 2020  commencing duplicate removal, pass 1
Fri Apr 03 18:04:02 2020  error -15 reading relation 145002227
...
Fri Apr 03 20:40:56 2020  skipped 157173 relations with b > 2^32
Fri Apr 03 20:40:56 2020  skipped 3 relations with composite factors
Fri Apr 03 20:40:56 2020  found 102149573 hash collisions in 737848016 relations
Fri Apr 03 20:40:56 2020  added 3 free relations
Fri Apr 03 20:40:56 2020  commencing duplicate removal, pass 2
Fri Apr 03 20:50:17 2020  found 4110 duplicates and 737843909 unique relations
Fri Apr 03 20:50:17 2020  memory use: 4262.0 MB
Fri Apr 03 20:50:18 2020  reading ideals above 599064576
Fri Apr 03 20:50:18 2020  commencing singleton removal, initial pass
Fri Apr 03 23:25:21 2020  memory use: 11024.0 MB
Fri Apr 03 23:25:22 2020  reading all ideals from disk
Fri Apr 03 23:25:59 2020  memory use: 13386.8 MB
Fri Apr 03 23:27:08 2020  commencing in-memory singleton removal
Fri Apr 03 23:28:15 2020  begin with 737843909 relations and 616314055 unique ideals
Fri Apr 03 23:44:02 2020  reduce to 504736196 relations and 361956209 ideals in 14 passes
Fri Apr 03 23:44:02 2020  max relations containing the same ideal: 41
Fri Apr 03 23:45:10 2020  reading ideals above 720000
Fri Apr 03 23:45:11 2020  commencing singleton removal, initial pass
Sat Apr 04 02:14:50 2020  memory use: 11024.0 MB
Sat Apr 04 02:14:51 2020  reading all ideals from disk
Sat Apr 04 02:15:56 2020  memory use: 23131.9 MB
Sat Apr 04 02:18:10 2020  keeping 421785409 ideals with weight <= 200, target excess is 2724899
Sat Apr 04 02:20:25 2020  commencing in-memory singleton removal
Sat Apr 04 02:22:02 2020  begin with 504736196 relations and 421785409 unique ideals
Sat Apr 04 02:40:49 2020  reduce to 504722501 relations and 421771714 ideals in 9 passes
Sat Apr 04 02:40:49 2020  max relations containing the same ideal: 200
Sat Apr 04 02:48:26 2020  removing 14346634 relations and 12562686 ideals in 2000000 cliques
Sat Apr 04 02:48:36 2020  commencing in-memory singleton removal
Sat Apr 04 02:50:03 2020  begin with 490375867 relations and 421771714 unique ideals
...
Sat Apr 04 12:17:10 2020  begin with 170227179 relations and 172785920 unique ideals
Sat Apr 04 12:21:45 2020  reduce to 169963756 relations and 166800361 ideals in 8 passes
Sat Apr 04 12:21:45 2020  max relations containing the same ideal: 104
Sat Apr 04 12:24:49 2020  relations with 0 large ideals: 206417
Sat Apr 04 12:24:49 2020  relations with 1 large ideals: 35137
Sat Apr 04 12:24:49 2020  relations with 2 large ideals: 439347
Sat Apr 04 12:24:49 2020  relations with 3 large ideals: 3019770
Sat Apr 04 12:24:49 2020  relations with 4 large ideals: 11565343
Sat Apr 04 12:24:49 2020  relations with 5 large ideals: 27231596
Sat Apr 04 12:24:49 2020  relations with 6 large ideals: 41413029
Sat Apr 04 12:24:49 2020  relations with 7+ large ideals: 86053117
Sat Apr 04 12:24:49 2020  commencing 2-way merge
Sat Apr 04 12:28:28 2020  reduce to 110760814 relation sets and 107597419 unique ideals
Sat Apr 04 12:28:28 2020  commencing full merge
Sat Apr 04 13:56:48 2020  memory use: 14622.2 MB
Sat Apr 04 13:57:40 2020  found 49189882 cycles, need 49115619
Sat Apr 04 13:57:44 2020  weight of 49115619 cycles is about 6385166686 (130.00/cycle)
Sat Apr 04 13:57:44 2020  distribution of cycle lengths:
Sat Apr 04 13:57:44 2020  1 relations: 3045635
Sat Apr 04 13:57:44 2020  2 relations: 3191268
Sat Apr 04 13:57:44 2020  3 relations: 3385894
Sat Apr 04 13:57:44 2020  4 relations: 3381649
Sat Apr 04 13:57:44 2020  5 relations: 3400284
Sat Apr 04 13:57:44 2020  6 relations: 3327590
Sat Apr 04 13:57:44 2020  7 relations: 3252571
Sat Apr 04 13:57:44 2020  8 relations: 3123119
Sat Apr 04 13:57:44 2020  9 relations: 2976096
Sat Apr 04 13:57:44 2020  10+ relations: 20031513
Sat Apr 04 13:57:44 2020  heaviest cycle: 28 relations
Sat Apr 04 14:06:34 2020  commencing cycle optimization
Sat Apr 04 14:10:29 2020  start with 438058474 relations
Sat Apr 04 14:52:10 2020  pruned 19603883 relations
Sat Apr 04 14:52:11 2020  memory use: 11519.8 MB
Sat Apr 04 14:52:11 2020  distribution of cycle lengths:
Sat Apr 04 14:52:11 2020  1 relations: 3045635
Sat Apr 04 14:52:11 2020  2 relations: 3267379
Sat Apr 04 14:52:11 2020  3 relations: 3528083
Sat Apr 04 14:52:11 2020  4 relations: 3522005
Sat Apr 04 14:52:11 2020  5 relations: 3563405
Sat Apr 04 14:52:11 2020  6 relations: 3479104
Sat Apr 04 14:52:11 2020  7 relations: 3414085
Sat Apr 04 14:52:11 2020  8 relations: 3265392
Sat Apr 04 14:52:11 2020  9 relations: 3107054
Sat Apr 04 14:52:11 2020  10+ relations: 18923477
Sat Apr 04 14:52:11 2020  heaviest cycle: 28 relations
Sat Apr 04 15:02:14 2020  RelProcTime: 77784
Sat Apr 04 15:02:14 2020  elapsed time 21:36:27

Fri May 15 20:03:29 2020  commencing linear algebra
Fri May 15 20:04:31 2020  matrix starts at (0, 0)
Fri May 15 20:04:44 2020  matrix is 49114833 x 49115010 (24803.7 MB) with weight 7031998278 (143.17/col)
Fri May 15 20:04:44 2020  sparse part has weight 5961868268 (121.39/col)
Fri May 15 20:04:44 2020  saving the first 48 matrix rows for later
Fri May 15 20:04:57 2020  matrix includes 64 packed rows
Fri May 15 20:05:06 2020  matrix is 49114785 x 49115010 (23840.4 MB) with weight 6111460112 (124.43/col)
Fri May 15 20:05:06 2020  sparse part has weight 5758479444 (117.24/col)
Fri May 15 20:05:06 2020  using block size 8192 and superblock size 1081344 for processor cache size 11264 kB
Fri May 15 20:10:25 2020  commencing Lanczos iteration (16 threads)
Fri May 15 20:10:25 2020  memory use: 21169.4 MB
Fri May 15 20:10:29 2020  restarting at iteration 37005 (dim = 2340052)
Fri May 15 20:13:52 2020  linear algebra at 4.8%, ETA 1728h22m
Fri May 15 20:14:51 2020  checkpointing every 30000 dimensions
Thu Jul 23 18:43:22 2020  lanczos halted after 776689 iterations (dim = 49114781)
Thu Jul 23 18:44:11 2020  recovered 37 nontrivial dependencies
Thu Jul 23 18:46:29 2020  BLanczosTime: 5956980
Thu Jul 23 18:46:29 2020  elapsed time 1654:43:01
 
Thu Jul 23 19:25:05 2020  commencing square root phase
Thu Jul 23 19:25:05 2020  handling dependencies 1 to 64
Thu Jul 23 19:25:05 2020  reading relations for dependency 1
Thu Jul 23 19:25:13 2020  read 24559187 cycles
Thu Jul 23 19:26:08 2020  cycles contain 84141086 unique relations
Thu Jul 23 19:37:11 2020  read 84141086 relations
Thu Jul 23 19:44:35 2020  multiplying 84141086 relations
Thu Jul 23 20:38:56 2020  multiply complete, coefficients have about 2351.40 million bits
Thu Jul 23 20:39:10 2020  initial square root is modulo 187877
Thu Jul 23 21:36:30 2020  sqrtTime: 7885
Thu Jul 23 21:36:30 2020  p78 factor: 287743709071765679519005572592282086727787894852332081977696568112925297043603
Thu Jul 23 21:36:30 2020  p143 factor: 97648229107204235650441206754425845388055840946224275373388075321223543065113417752695410418408653172411245982360494127850309706544173670915761
Thu Jul 23 21:36:30 2020  elapsed time 02:11:27
    

-  Found by Kurt Beschorner 
   Jul 22, 2020   n = 9107: 2102333137776831192401353613;                           ecm: B1= 1e6;  sigma = 3467006848464782 


-  Found by Kurt Beschorner 
   Jul 20, 2020   n = 9159: 7458071133126696400638318787;                           ecm: B1= 3e6;  sigma = 5685064070024516 


-  Found by Alfred Eichhorn 
   Jul 15, 2020   n =33563:  6048976971971164235785867 * 1836857895......c33538;    ecm: B1= 5e4; sigma = 8315090112117856


-  Found by Alfred Eichhorn 
   Jul 01, 2020   n =33113:  24353329584974226507401 * 4562460780......c33090;      ecm: B1= 5e4; sigma = 7127985045140319
   Jul 01, 2020   n =54361:  665592461889878795163841 * 1669356512......c54337;     ecm: B1= 5e4; sigma = 5447122642957776 
           


ECM efforts
with Rn:      323 < n < 2000 (Oct 25, 2020) with Rn:     1999 < n < 3000 (Feb 14, 2020)
with Rn:     2999 < n < 4000 (Jun 12, 2019) with Rn:     3999 < n < 5000 (Jun 12, 2019)
with Rn:     4999 < n < 6000 (Mar 15, 2020) with Rn:     5999 < n < 7000 (Sep 28, 2020)
with Rn:     6999 < n < 8000 (Sep 27, 2020) with Rn:     7999 < n < 9000 (Aug 22, 2020)
with Rn:     8999 < n <10000 (Oct 28, 2020) with Rn:     9999 < n <11000 (Jun 12, 2019)
with Rn:   10999 < n <12000 (Jun 12, 2019) with Rn:   11999 < n <12500L/M (Oct 31, 2020)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 43e6/8600 curves/
numbers < 1001 digits
1117
working
1255
working
1257
working
1465
working
1475
working
B1 = 11e7/18400 curves/
numbers < 701 digits
593
working
599
working
607
working
611
working
617
working
B1 = 26e7/46000 curves/
numbers < 450 digits
467
working
469
working
521
working
1136
working
1160
working
B1 = 85e7/75000 curves/
numbers < 250 digits
609
working
675
working
1008
working
1188
working
1200
working



Factorizations
Repunits: R1        - R2500 (Oct 04, 2020) Repunits:  R2501 - R5000 (Feb 14, 2020)
Repunits: R5001   - R7500 (Sep 28, 2020) Repunits: R7501 - R10000 (Oct 05, 2020)
Repunits: R10001 - R12500 (Jun 12, 2019) Repunits: R12501 - R14980L/M (Sep 19, 2020)




Rprime project; base 10

last update: Oct 17, 2020

project page  

Status:       3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M    
Details:     3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M    

active members: Danilo Nitsche, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

all contributors:   Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming,
                                Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian, MattStath,
                                Maksym Voznyy, wims, Kurt Beschorner
Overview
 
    Exponent     Primes/PRP                     found by ...
    - 10ˆ20     R19 = prime
    - 10ˆ100     R23 = prime
    - 10ˆ1000     R317 = prime
    - 10ˆ10000     R1031 = prime                 WD (Dec 1985)
    - 10ˆ50000     R49081 = PRP                 Harvey Dubner (Sep 1999)
    - 10ˆ100000     R86453 = PRP                 Lew Baxter (Oct 2000)
    - 10ˆ250000     R109297 = PRP               Paul Bourdelais - Harvey Dubner (Apr 2007)
    - 10ˆ500000     R270343 = PRP               Maksym Voznyy - Anton Budnyy (Jul 2007)
    - 10ˆ 4273033     no further probable primes




Visitors since Oct 27, 2020: zur Webseite

Top of page