Factorizations of Repunit Numbers of the form (10n-1)/9 (111111...)



Related links:

Factor tables of Richard Brent
Jonathan Crombies extensive factor tables
Factordb: Factor tables - Downloads
Repunit factors of Torbjörn Granlund
Factorizations of Repunit numbers of Makoto Kamada
Factor tables of Yousuke Koide
Factor tables of Sam Wagstaff
The Ecmnet of Paul Zimmermann
__________________________________________________________________________

Contributions of new factors are welcome - email:




ECM EFFORTS
with Rn:      323 < n < 2000 (Nov 28, 2016) with Rn:     1999 < n < 3000 (Sep 21, 2016)
with Rn:    2999 < n < 4000 (Nov 28, 2016) with Rn:     3999 < n < 6000 (Sep 04, 2016)



Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/6400 curves/
numbers < 1001 digits
809
working
1175
working
1177
working
1179
working
1183
working
B1 = 11e7/13500 curves/
numbers < 601 digits
801
working
1167
working
1168
working
1173
working
1174
working
B1 = 26e7/32000 curves/
numbers < 410 digits
1130
working
1136
working
1142
working
1160
working
2380M
working
B1 = 85e7/52000 curves/
numbers < 225 digits
477
working
1155
working
2420L
working
2460L
working
 



News

  
 
- Last update: Dec 01, 2016      
    

- Maksym Voznyy/Wenjie Fang/Alfred Eichhorn/Kurt Beschorner
  
   Dec 01, 2016   R2700M/c197: GNFS -sieving; 425M unique relations and 527M unique ideals are collected


- Bo Chen/Wenjie Fang/Alfred Reich/Alfred Eichhorn/Maksym Voznyy/Kurt Beschorner
  

   Sep 02, 2016   n =  343: 108164182562832081427746076140676111780117904145681235787387789905399551977213797293596351; SNFS
                  see: http://blog.sina.com.cn/s/blog_571ae3fa0102vxmi.html
   
   Thu Jul 14 04:57:56 2016  Msieve v. 1.53 (SVN unknown)
   Thu Jul 14 04:57:56 2016  random seeds: 5d5bd310 333accbc
   Thu Jul 14 04:57:56 2016  factoring 1041538392663678721744627767447975174554864664802981589056272533978765479104328842774810531075395035448479880771306518231151836676526152889638368446163913231685310581362164519745104832194171738525173207940628720136356785368184044457805801 (238 digits)
   Thu Jul 14 04:57:58 2016  no P-1/P+1/ECM available, skipping
   Thu Jul 14 04:57:58 2016  commencing number field sieve (238-digit input)
   Thu Jul 14 04:57:58 2016  R0: 10000000000000000000000000000000000000000000000000
   Thu Jul 14 04:57:58 2016  R1: -1
   Thu Jul 14 04:57:58 2016  A0: 1
   Thu Jul 14 04:57:58 2016  A1: 1
   Thu Jul 14 04:57:58 2016  A2: 1
   Thu Jul 14 04:57:58 2016  A3: 1
   Thu Jul 14 04:57:58 2016  A4: 1
   Thu Jul 14 04:57:58 2016  A5: 1
   Thu Jul 14 04:57:58 2016  A6: 1
   Thu Jul 14 04:57:58 2016  skew 1.00, size 1.945e-014, alpha 2.428, combined = 5.590e-015 rroots = 0
   Thu Jul 14 04:57:58 2016  commencing linear algebra
   Thu Jul 14 05:01:06 2016  matrix starts at (0, 0)
   Thu Jul 14 05:01:17 2016  matrix is 37792085 x 37792262 (18502.6 MB) with weight 5216314755 (138.03/col)
   Thu Jul 14 05:01:17 2016  sparse part has weight 4434640950 (117.34/col)
   Thu Jul 14 05:01:17 2016  saving the first 48 matrix rows for later
   Thu Jul 14 05:01:29 2016  matrix includes 64 packed rows
   Thu Jul 14 05:01:36 2016  matrix is 37792037 x 37792262 (17789.5 MB) with weight 4548076717 (120.34/col)
   Thu Jul 14 05:01:36 2016  sparse part has weight 4285489422 (113.40/col)
   Thu Jul 14 05:01:36 2016  using block size 8192 and superblock size 1179648 for processor cache size 12288 kB
   Thu Jul 14 05:06:58 2016  commencing Lanczos iteration (12 threads)
   Thu Jul 14 05:06:58 2016  memory use: 15680.2 MB
   Thu Jul 14 05:07:11 2016  restarting at iteration 4270 (dim = 270054)
   Thu Jul 14 05:10:08 2016  linear algebra at 0.7%, ETA 1212h 4m
   Thu Jul 14 05:11:02 2016  checkpointing every 40000 dimensions
   Fri Sep 02 07:59:48 2016  lanczos halted after 597629 iterations (dim = 37792035)
   Fri Sep 02 08:00:24 2016  recovered 39 nontrivial dependencies
   Fri Sep 02 08:01:35 2016  BLanczosTime: 4331017
   Fri Sep 02 08:01:35 2016  elapsed time 1203:03:39
   
   Fri Sep 02 08:02:23 2016  commencing square root phase
   Fri Sep 02 08:02:23 2016  handling dependencies 1 to 64
   Fri Sep 02 08:02:23 2016  reading relations for dependency 1
   Fri Sep 02 08:02:47 2016  read 18891611 cycles
   Fri Sep 02 08:03:32 2016  cycles contain 66733608 unique relations
   Fri Sep 02 08:24:56 2016  read 66733608 relations
   Fri Sep 02 08:34:43 2016  multiplying 66733608 relations
   Fri Sep 02 10:23:03 2016  multiply complete, coefficients have about 1843.03 million bits
   Fri Sep 02 10:23:26 2016  initial square root is modulo 185062181
   Fri Sep 02 12:21:17 2016  sqrtTime: 15534
   Fri Sep 02 12:21:17 2016  prp90 factor: 108164182562832081427746076140676111780117904145681235787387789905399551977213797293596351
   Fri Sep 02 12:21:17 2016  prp148 factor: 9629235556406611857650195218600476538144804813919226550962087129420209841171513191629905668596180108950582877533858087255532817046381504168675076951
   Fri Sep 02 12:21:17 2016  elapsed time 04:18:55
   

- Found: anonymous      

   Jul 11, 2016   n = 1435: 76477989624050565171649436387228238961441
                            P41: P-1: 2^5 * 3^3 * 5 * 7 * 41 * 1039 * 1279 * 2750535751 * 16875919043365694311
                                 P+1: 2 * 38238994812025282585824718193614119480721  
   Jul 13, 2016   n = 2277: 37341797099678068414681695694866038173
                            P38: P-1: 2^2 * 3^2 * 11^2 * 23 * 397 * 938834414466497403387467724277
                                 P+1: 2 * 19 * 3715559 * 3890639 * 67977708469668187097773 


- Found by Alfred Eichhorn

   Jul 11, 2016   n =50153: 3911026339398525737707317283 * 2840970667......c50125; B1=11e3; sigma = 1038073320
   Jul 25, 2016   n =51061: 229487628774536927117 * 4841703742......c51040;       B1=11e3 
   Jul 25, 2016   n =51071: 10731584737317918345437 * 1035365361......c51049;     B1=11e3 
   Jul 25, 2016   n =51341: 275686936071137547291518399 * 4030336464......c51314; B1=11e3
   Jul 26, 2016   n =51517: 43016504259697737763 * 2582987925......c51497;        B1=11e3
   Aug 11, 2016   n =52223: 7245089570324712801427 * 1533605761......c52201;      B1=11e3
   Sep 30, 2016   n =53381: 18071060784680147973881 * 6148566065......c53358;     B1=11e3
   Oct 14, 2016   n =56509: 29937758871345161950627 * 3711403769......c56486;     B1=2e3
   Oct 14, 2016   n =58049: 9967885391327771879 * 1114690897......c58030;         B1=2e3
   Oct 25, 2016   n =27073: 3023978371436805872948083 * 3674335509......c27048;   B1=5e4; sigma = 1:87405253
                            P25: P-1: 2 * 3^2 * 7 * 43 * 5639 * 27073 * 3655958035267 
                                 P+1: 2^2 * 29 * 103 * 80911 * 378269 * 8269421837 
   Oct 25, 2016   n =27427: 894635590550599633125493 * 1241970611......c27403;    B1=5e4; sigma = 1:1107166074 
                            P24: P-1: 2^2 * 3^2 * 27427 * 906077537696632711  
                                 P+1: 2 * 13 * 19 * 331 * 2239 * 7731299 * 316071011 
   Oct 25, 2016   n =65651: 18399221396142871 * 6038902881......c65634;           B1=2e3
   Oct 25, 2016   n =67261: 207127323896648367271 * 5364386939......c67240;       B1=2e3
                            P21: P-1: 2 * 3 * 5 * 67261 * 102648550123969 
                                 P+1: 2^3 * 161323 * 160491160510783     
   Nov 02, 2016   n =55399: 2288856241024717845347 * 2096079066......c55358;      B1=11e3; sigma = 2794405507697790298
                            P22: P-1: 2 * 55399 * 20657920188313127 
                                 P+1: 2^2 * 3^3 * 7 * 59 * 1597 * 37061 * 867007111 
   Nov 06, 2016   n =55889: 22725551385595799107 * 4889259196......c55869;        B1=11e3; sigma = 12720872794617635669
                            P20: P-1: 2 * 3 * 47 * 1033 * 55889 * 1395849709  
                                 P+1: 2^2 * 79 * 557 * 129113647851259 
   Nov 06, 2016   n =77867: 12146261490914239566523 * 9147762148......c77844;     B1=2e3;  sigma = 9656516878805326347
                            P23: P-1: 2 * 3^2 * 23 * 907 * 77867 * 415414408267
                                 P+1: 2^2 * 19 * 29 * 5081 * 1084630571932001
   Nov 12, 2016   n =80657: 290433298476811653481 * 2158763957......c80615;       B1=2e3;  sigma = 0:10596707231362242639
                            P21: P-1: 2^3 * 3 * 5 * 37 * 2671 * 80657 * 303631961
                                 P+1: 2 * 11 * 70858519 * 186308065049                             
   Nov 16, 2016   n =31567: 271696556465943213043 * 4089529604......c31546;       B1=5e4;  sigma = +1:187854045
                            P21: P-1: 2 * 3^3 * 31567 * 159388529550869 
                                 P+1: 2^2 * 11 * 53 * 499067 * 233451535201   
   Nov 22, 2016   n =86381: 221330036551319831 * 5020155096......c86363;          B1=2e3


- Found by  Maksym Voznyy

   Sep 13, 2016   n = 6949: 7963383644007615893833498728502409;  B1= 5e4 
                            P34: P-1: 2^2 * 6949 * 20887927 * 38970596011 * 175975801217 
                                 P+1: 2 * 3 * 5 * 11 * 19 * 1180031 * 14232641 * 75622527133983173 
   Sep 13, 2016   n = 7759: 106221660948091790295289965372773;   B1= 5e4 
                            P33: P-1: 2^2 * 1931 * 7759 * 72379 * 24487953534842704223 *
                                 P+1: 2 * 3 * 15662419 * 1130324131796965614478091  
   Sep 13, 2016   n = 8317: 140206236806008891970798191603;      B1= 5e4 
                            P30: P-1: 2 * 3 * 853 * 8317 * 22705193993 * 145069172219 
                                 P+1: 2^2 * 11 * 59 * 313 * 857 * 1823 * 110446209763116443                         
   

- Found by Ryan Propper

   Jul 17, 2016   n =  429: 12998514909869151807098212773862100794044705428424741778699159434241; GNFS 


- Found by Alfred Reich 

   Oct 08, 2016   n = 7494: 4695948608569732308219433681 
                            P28: P-1: 2^4 * 3 * 5 * 7 * 19 * 167 * 179 * 1249 * 3940292955710747
                            P+1: 2 * 2347974304284866154109716841  


- Found by YOYO@home

   Sir Thomas W. Kilburn     
   Jul 12, 2016   n = 1216: 3928012193813155346711857127951417921651415863617; B1= 11e7; sigma = 1216426183 
                            P49: P-1: 2^6 * 3 * 7 * 19 * 883031911209533 * 174198158299578441666647841607       
                                 P+1: 2 * 11 * 2911435957003009734721 * 61325755210319505283641539

   Eric_ch      
   Aug 23, 2016   n =2820M: 832530561417330269513686172453574642103980456844602894975421; B1= 26e7; sigma = 793769511 
                            P60: P-1:  2^2 * 3 * 5 * 47 * 26417 * 284897 * 39226513065341426579571975683345588244157363519
                                 P+1:  2 * 109 * 301501 * 12666450623504714127923171378614786983742115128691479
   congratulations

   Bodao      
   Sep 03, 2016   n = 1145: 4436672723558212976001763691029474593961; B1= 43e6; sigma = 4038135113 
                            P40: P-1: 2^3 * 3^2 * 5 * 7 * 53 * 229 * 145059274459125152393826685389079
                                 P+1: 2 * 29 * 3583 * 396377 * 1765508473 * 30507339800789496823  
   
   Retnek     
   Oct 10, 2016   n = 1167: 5399028320003378981935733251080096325009; B1= 11e7; sigma = 1997936022 
                            P40: P-1: 2^4 * 3 * 103 * 163 * 389 * 17222648485066204617030447833851  
                                 P+1: 2 * 5 * 13 * 56131 * 557779 * 652772117 * 2032103009653573069 

   YOYO@home/WhiteFire      
   Nov 05, 2016   n = 1173: 51127988434642542343102991812662340182552388237; B1= 43e6; sigma = 1917067894 
                            P47: P-1: 2^2 * 3 * 17 * 23 * 143501 * 1063908899311 * 71374213183233448799205053 
                                 P+1: 2 * 11^2 * 18917 * 9291151 * 1202047302465772945690121428987517
   YOYO@home/Mumps        
   Nov 07, 2016   n = 1167: 613485710812313000516466620592830345835145382211665323; B1= 11e7; sigma = 2673943130 
                            P54: P-1: 2 * 3 * 13 * 17 * 271 * 389 * 20107 * 567151789059199 * 384853509350856790220468341
                                 P+1: 2^2 * 2495963 * 18696651208559641517 * 3286567005949648678073114261 
   YOYO@home/[P3D] Crashtest      
   Nov 07, 2016   n = 1213: 14539506681835624339134436400997541040884253; B1= 11e6; sigma = 166611344 
                            P44: P-1: 2^2 * 1213 * 1055591 * 2838789566800334106319351234281461  
                                 P+1: 2 * 3 * 131 * 52697 * 18034573690451 * 19464145963634411472437    
                                                                                        

- Found by Kurt Beschorner

   Jun 15, 2016   n = 5559: 3454768257833537574682119090531523;   B1=1e6; sigma = 1133486984  
                            P34: P-1: 2 * 3 * 11 * 13 * 17 * 109 * 17653233613283 * 123092599988291
                                 P+1: 2^2 * 19 * 2135060324674969 * 21290956771292771

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Factorizations

n =   250; n =   500; n =   750; n = 1000; n = 1250; n = 1500; n = 1750; n = 2000; n = 2250; n = 2500; n = 2750; n = 3000; n = 3250;
n = 3500; n = 3750; n = 4000; n = 4250; n = 4500; n = 4750; n = 5000; n = 5250; n = 5500; n = 5750; n = 6000; n = 6250; n = 6500;
n = 6750; n = 7000; n = 7250; n = 7500; n = 7750; n = 8000; n = 8250; n = 8500; n = 8750; n = 9000; n = 9250; n = 9500; n = 9750;
n = 10000; n = 10250; n = 10500; n = 10750; n = 11000; n = 11250; n = 11500; n = 11750; n = 12000; n = 12250; n = 12500;
n = 12750; n = 13000; n = 13500; n = 14000; n = 14500;