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 (Sep 24, 2016) with Rn:     1999 < n < 3000 (Sep 21, 2016)
with Rn:    2999 < n < 4000 (Apr 16, 2015) with Rn:     3999 < n < 6000 (Sep 04, 2016)



Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/6400 curves/
numbers < 1001 digits		 1141
working		 1143
working		 1157
working		 1161
working		 1165
working
B1 = 11e7/13500 curves/
numbers < 601 digits		 1131
working		 1132
working		 1167
working		 1168
working		 1174
working
B1 = 26e7/32000 curves/
numbers < 410 digits		 1128
working		 1130
working		 1136
working		 1142
working		 2380M
working
B1 = 85e7/52000 curves/
numbers < 225 digits		 415
working		 1062
working		 2420L
working		 2460L
working		  



News

  
 
- Last update: Sep 24, 2016      
    

- Maksym Voznyy/Wenjie Fang/Alfred Eichhorn/Kurt Beschorner
  
   Sep 23, 2016   R2700M/c197: GNFS -sieving; 160M unique relations 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      

   Jun 04, 2016   n =5740L: 160875812226384158341944785758910341
                            P36: P-1: 2^2 * 3 * 5 * 7 * 13^2 * 41 * 71719 * 770791071629871613985327
                                 P+1: 2 * 476713 * 168734450525142127802204665867
   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 
       

- Bo Chen/Wenjie Fang/Maksym Voznyy/Kurt Beschorner
  
   Feb 15, 2016   n =2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761; GNFS


- Found by Alfred Eichhorn

   Apr 06, 2016   n =44797: 627221432707536259129 * 1771481414......c44776; B1=11e3; sigma = 3400192084
   Apr 16, 2016   n = 8387: 70350195396742638557717;                        B1=5e4;  sigma = 699879868
   Apr 23, 2016   n =46679: 33213589575352142773 * 3345350879......c46659;  B1=11e3; sigma = 3791877031
   May 05, 2016   n =46877: 1810380864301035324119 * 6137443965......c46855; B1=11e3; sigma = 3418097178
   Jun 03, 2016   n = 9767: 54578074909849412344440427 * 2035819535......c9741; B1=5e4; sigma = 692329857
   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




- 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 YOYO@home

   errate     
   Jun 29, 2016   n = 1136: 155744533524951745226433500587796122871137105818580913; B1= 11e7; sigma = 2242550118 
                            P54: P-1: 2^4 * 71 * 12251 * 25577 * 838853 * 521587861130115715535575305632117107  
                                 P+1: 2 * 3 * 2083 * 1246155653104110619510589699054217657794643943439415793          
   congratulations!

   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  


- Found by Kurt Beschorner

   May 12, 2016   n = 5685: 384514396466713736537371759951;       B1=1e6; sigma = 1979618104  
                            P30: P-1: 2 * 3 * 5^2 * 89 * 379 * 401 * 983 * 24577939 * 7844202139 
                                 P+1: 2^4 * 23 * 2003 * 26903 * 19390237346934665671 
   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

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

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;