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
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 (Jul 20, 2017) with Rn:     1999 < n < 3000 (May 07, 2017)
with Rn:     2999 < n < 4000 (Jan 15, 2017) with Rn:     3999 < n < 5000 (Jul 14, 2017)
with Rn:     4999 < n < 6000 (Jul 21, 2017) with Rn:     5999 < n < 7000 (Jul 14, 2017)




Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/6400 curves/
numbers < 1001 digits
871
working
877
working
881
working
883
working
1137
working
B1 = 11e7/13500 curves/
numbers < 601 digits
833
working
835
working
1173
working
1174
working
1178
working
B1 = 26e7/32000 curves/
numbers < 410 digits
407
working
1136
working
1142
working
1160
working
2380M
working
B1 = 85e7/52000 curves/
numbers < 225 digits
477
working
515
working
1155
working
2420L
working
2460L
working



News

 
-  Last update:  Jul 27, 2017/2nd

- Bo Chen/Maksym Voznyy/Wenjie Fang/Alfred Eichhorn/Kurt Beschorner 
  
   May 07, 2017   R2700M/c197: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201(P83) * 
                               297134935059434848691686488189687003283048362636793125222145082651787396540653146423539079787300761023519093629701(P114) 
    
    Sun Mar 19 21:31:50 2017  Msieve v. 1.53 (SVN unknown) 
    Sun Mar 19 21:31:50 2017  random seeds: d5fd81e8 845709ec
    Sun Mar 19 21:31:50 2017  factoring 21280448635641401486510328517762590351439943598811358399598640553251953298510470654192816204660487515323060809477098730957626872339454764912971353172625018532645381873729423451499961548344338111901 (197 digits)
    Sun Mar 19 21:31:54 2017  searching for 15-digit factors
    Sun Mar 19 21:32:02 2017  commencing number field sieve (197-digit input)
    Sun Mar 19 21:32:02 2017  R0: -141926621190523315691802832773008516012
    Sun Mar 19 21:32:02 2017  R1: 439743569127268499611
    Sun Mar 19 21:32:02 2017  A0: -10032328728724823749690366080982188506588101242
    Sun Mar 19 21:32:02 2017  A1: -66162403300993622159317666900858130373
    Sun Mar 19 21:32:02 2017  A2: 22530084996917784842410009033582
    Sun Mar 19 21:32:02 2017  A3: 57740789299954457602329
    Sun Mar 19 21:32:02 2017  A4: -3448665872840304
    Sun Mar 19 21:32:02 2017  A5: -739080
    Sun Mar 19 21:32:02 2017  skew 90613729.88, size 1.998e-019, alpha -5.962, combined = 6.292e-015 rroots = 5
    Sun Mar 19 21:32:02 2017  
    Sun Mar 19 21:32:02 2017  commencing relation filtering
    Sun Mar 19 21:32:02 2017  setting target matrix density to 130.0
    Sun Mar 19 21:32:02 2017  estimated available RAM is 49069.6 MB
    ...
    Mon Mar 20 01:50:55 2017  found 6586207 duplicates and 735806931 unique relations
    ...
    Mon Mar 20 05:29:44 2017  begin with 735806931 relations and 623478442 unique ideals
    ...
    Mon Mar 20 22:06:39 2017  reduce to 133939759 relations and 130875065 ideals in 8 passes
    Mon Mar 20 22:06:39 2017  max relations containing the same ideal: 92
    Mon Mar 20 22:09:16 2017  relations with 0 large ideals: 9210
    Mon Mar 20 22:09:16 2017  relations with 1 large ideals: 38247
    Mon Mar 20 22:09:16 2017  relations with 2 large ideals: 560540
    Mon Mar 20 22:09:16 2017  relations with 3 large ideals: 3645305
    Mon Mar 20 22:09:16 2017  relations with 4 large ideals: 12832919
    Mon Mar 20 22:09:16 2017  relations with 5 large ideals: 27126649
    Mon Mar 20 22:09:16 2017  relations with 6 large ideals: 36104520
    Mon Mar 20 22:09:16 2017  relations with 7+ large ideals: 53622369
    Mon Mar 20 22:09:16 2017  commencing 2-way merge
    Mon Mar 20 22:12:27 2017  reduce to 84701604 relation sets and 81636910 unique ideals
    Mon Mar 20 22:12:27 2017  commencing full merge
    Mon Mar 20 23:08:57 2017  memory use: 9708.4 MB
    Mon Mar 20 23:09:28 2017  found 36965722 cycles, need 36741110
    Mon Mar 20 23:09:32 2017  weight of 36741110 cycles is about 4776633381 (130.01/cycle)
    Mon Mar 20 23:09:32 2017  distribution of cycle lengths:
    Mon Mar 20 23:09:32 2017  1 relations: 2506464
    Mon Mar 20 23:09:32 2017  2 relations: 2337599
    Mon Mar 20 23:09:32 2017  3 relations: 2486291
    Mon Mar 20 23:09:32 2017  4 relations: 2515204
    Mon Mar 20 23:09:32 2017  5 relations: 2615323
    Mon Mar 20 23:09:32 2017  6 relations: 2583004
    Mon Mar 20 23:09:32 2017  7 relations: 2563677
    Mon Mar 20 23:09:32 2017  8 relations: 2461209
    Mon Mar 20 23:09:32 2017  9 relations: 2346859
    Mon Mar 20 23:09:32 2017  10+ relations: 14325480
    Mon Mar 20 23:09:32 2017  heaviest cycle: 28 relations
    Mon Mar 20 23:13:13 2017  commencing cycle optimization
    Mon Mar 20 23:16:06 2017  start with 315653596 relations
    Mon Mar 20 23:42:50 2017  pruned 13760271 relations
    Mon Mar 20 23:42:51 2017  memory use: 8706.9 MB
    Mon Mar 20 23:42:51 2017  distribution of cycle lengths:
    Mon Mar 20 23:42:51 2017  1 relations: 2506464
    Mon Mar 20 23:42:51 2017  2 relations: 2402992
    Mon Mar 20 23:42:51 2017  3 relations: 2590910
    Mon Mar 20 23:42:51 2017  4 relations: 2619939
    Mon Mar 20 23:42:51 2017  5 relations: 2739807
    Mon Mar 20 23:42:51 2017  6 relations: 2704154
    Mon Mar 20 23:42:51 2017  7 relations: 2691211
    Mon Mar 20 23:42:51 2017  8 relations: 2576306
    Mon Mar 20 23:42:51 2017  9 relations: 2451235
    Mon Mar 20 23:42:51 2017  10+ relations: 13458092
    Mon Mar 20 23:42:51 2017  heaviest cycle: 28 relations
    Mon Mar 20 23:48:14 2017  RelProcTime: 94572

    Fri Mar 24 18:12:03 2017  Msieve v. 1.53 (SVN unknown)
    Fri Mar 24 18:12:03 2017  random seeds: cfed8480 a3aae439
    Fri Mar 24 18:12:03 2017  factoring 21280448635641401486510328517762590351439943598811358399598640553251953298510470654192816204660487515323060809477098730957626872339454764912971353172625018532645381873729423451499961548344338111901 (197 digits)
    Fri Mar 24 18:12:05 2017  searching for 15-digit factors
    Fri Mar 24 18:12:05 2017  commencing number field sieve (197-digit input)
    .... 
    Fri Mar 24 18:12:05 2017  commencing linear algebra
    Fri Mar 24 18:15:06 2017  matrix starts at (0, 0)
    Fri Mar 24 18:15:19 2017  matrix is 36739362 x 36739539 (18483.9 MB) with weight 5552479490 (151.13/col)
    Fri Mar 24 18:15:19 2017  sparse part has weight 4441312238 (120.89/col)
    Fri Mar 24 18:15:19 2017  saving the first 48 matrix rows for later
    Fri Mar 24 18:15:31 2017  matrix includes 64 packed rows
    Fri Mar 24 18:15:38 2017  matrix is 36739314 x 36739539 (18051.8 MB) with weight 4801336528 (130.69/col)
    Fri Mar 24 18:15:38 2017  sparse part has weight 4364771360 (118.80/col)
    Fri Mar 24 18:15:38 2017  using block size 8192 and superblock size 1179648 for processor cache size 12288 kB
    Fri Mar 24 18:21:06 2017  commencing Lanczos iteration (12 threads)
    Fri Mar 24 18:21:06 2017  memory use: 15680.2 MB
    Fri Mar 24 18:21:07 2017  restarting at iteration 39855 (dim = 2520017)
    Fri Mar 24 18:23:50 2017  linear algebra at 6.9%, ETA 1023h19m
    Fri Mar 24 18:24:43 2017  checkpointing every 40000 dimensions
    Fri May 05 22:58:12 2017  lanczos halted after 581001 iterations (dim = 36739312)
    Fri May 05 22:58:55 2017  recovered 30 nontrivial dependencies
    Fri May 05 23:00:01 2017  BLanczosTime: 23714
    Fri May 05 23:00:01 2017  elapsed time 06:35:16
  
    Fri May 05 23:08:54 2017  Msieve v. 1.53 (SVN unknown)
    Fri May 05 23:08:54 2017  random seeds: cfb65608 2fed8e0b
    Fri May 05 23:08:54 2017  factoring 21280448635641401486510328517762590351439943598811358399598640553251953298510470654192816204660487515323060809477098730957626872339454764912971353172625018532645381873729423451499961548344338111901 (197 digits)
    Fri May 05 23:08:55 2017  searching for 15-digit factors
    Fri May 05 23:08:56 2017  commencing number field sieve (197-digit input)
    ....
    Fri May 05 23:08:56 2017  commencing square root phase
    Fri May 05 23:08:56 2017  handling dependencies 1 to 64
    Fri May 05 23:08:56 2017  reading relations for dependency 1
    Fri May 05 23:09:05 2017  read 18366805 cycles
    Fri May 05 23:09:51 2017  cycles contain 66081656 unique relations
    Fri May 05 23:28:37 2017  read 66081656 relations
    Fri May 05 23:40:29 2017  multiplying 66081656 relations
    Sat May 06 03:07:49 2017  multiply complete, coefficients have about 4277.35 million bits
    Sat May 06 03:08:48 2017  initial square root is modulo 62653
    Sat May 06 06:59:22 2017  GCD is N, no factor found
    ....
    Sat May 06 22:02:49 2017  reading relations for dependency 4
    Sat May 06 22:03:14 2017  read 18370163 cycles
    Sat May 06 22:04:30 2017  cycles contain 66089724 unique relations
    Sat May 06 22:23:25 2017  read 66089724 relations
    Sat May 06 22:35:14 2017  multiplying 66089724 relations
    Sun May 07 02:03:17 2017  multiply complete, coefficients have about 4277.89 million bits
    Sun May 07 02:04:16 2017  initial square root is modulo 62761
    Sun May 07 05:54:36 2017  sqrtTime: 110740
    Sun May 07 05:54:36 2017  p83 factor: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201
    Sun May 07 05:54:36 2017  p114 factor: 297134935059434848691686488189687003283048362636793125222145082651787396540653146423539079787300761023519093629701
    Sun May 07 05:54:36 2017  elapsed time 30:45:42



- Alfred Eichhorn, Bo Chen, Wenjie Fang, Kurt Beschorner 
  
   Jul 27, 2017   R1030/c199/GNFS: norm 1.587617e-019 alpha -6.405212 e 4.818e-015 rroots 3
                  368M unique relations and 493M 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


- Found by Serge Batalov 

   May 20, 2017   n = 1664: 33705988330014732169259712855760222337             
                            P38: P-1: 2^7 * 7 * 13 * 109 * 158129 * 167887236965173647153941887  
                                 P+1: 2 * 3 * 41 * 163 * 301686997457 * 2786299274392871622433  
   May 20, 2017   n = 1800: 1216057084775405433757097429262954022602494154001;     B1=13544018; sigma = 1:453572236
                            P49: P-1: 2^4 * 3^2 * 5^3 * 9041 * 496029657073809329 * 15064590982733602929277  
                                 P+1: 2 * 59 * 103 * 179 * 137831 * 7079177207 * 828224509093 * 691677948817987 


- Found by Alfred Eichhorn 

   Apr 03, 2017   n =16937: 6251665249314887004750809 * 1777304233......c16912;    B1=5e4; sigma = 0:1018489458632521315
                            P25: P-1: 2^3 * 16937 * 46139112957687953923   
                                 P+1: 2 * 3 * 5 * 13 * 277 * 907 * 63803433764977561 
   Apr 03, 2017   n =16987: 955827790682023749639586693 * 3990405399......c16938;  B1=5e4; sigma = 0:15650036004653872100
                            P27: P-1: 2^2 * 3 * 16987 * 20021 * 234204888099874733 
                                 P+1: 2 * 29^2 * 131 * 4337928269154422441657 
   Apr 03, 2017   n =62983: 268394630580874707431 * 4139841056......c62962;        B1=11e3; sigma = 0:821110618675779848
                            P21: P-1: 2 * 5 * 29 * 62983 * 14694421131749 
                                 P+1: 2^3 * 3 * 37 * 1721 * 175622432079659 
   Apr 13, 2017   n =63347: 3298042073909444148653 * 3369002232......c63325;       B1=11e3; sigma = 8846093993496057511
                            P22: P-1: 2^2 * 63347 * 13015778465868329 
                                 P+1: 2 * 3 * 85853 * 87911 * 72829318423 
   Apr 13, 2017   n =63793: 1109202204184366101311 * 1001720972......c63772;       B1=11e3; sigma = 9439564110194837269
                            P22: P-1: 2 * 5 * 89 * 331 * 63793 * 59022784913 
                                 P+1: 2^6 * 3 * 19 * 540611 * 562433287079  
   Apr 16, 2017   n =63929: 18366857058874237034519 * 6049544064......c63906;      B1=11e3; sigma = 8055712542922237728
                            P23: P-1: 2 * 63929 * 180550393 * 795625147
                                 P+1: 2^3 * 3 * 5 * 7 * 16369 * 107839 * 12386755333

   May 08, 2017   n =64763: 48024420498631151 * 2313637727......c64746;            B1=11e3
   May 08, 2017   n =64871: 43551535586015803 * 2551255876......c64854;            B1=11e3
   May 08, 2017   n =64877: 143398381697712722991799 * 7748421550......c64853;     B1=11e3; sigma = 7252748956661455251
                            P24: P-1: 2 * 3^2 * 64877 * 1650097 * 74416889119  
                                 P+1: 2^3 * 5^2 * 13 * 19 * 3196031 * 908251906487  

   Jun 02, 2017   n =65837: 159965960321814151387 * 6945922175......c65816;        B1=11e3; sigma = 0:5486427398454941409
                            P21: P-1: 2 * 3 * 7^2 * 47 * 65837 * 175837846421   
                                 P+1: 2^2 * 13 * 101 * 878777 * 34659650447   

   Jun 02, 2017   n =65927: 1120051612956744157 * 9920177769......c65908;          B1=11e3  

   Jun 11, 2017   n =66071: 9993066842314402844671 * 1111881996......c66049;       B1=11e3; sigma = 0:11164370378004058442
                            P22: P-1: 2 * 3^2 * 5 * 66071 * 1680526645967453
                                 P+1: 2^12 * 631 * 3866424064262147 
                                 
   Jun 11, 2017   n =66169: 6272302301672502467249 * 1771456568......c66147;       B1=11e3; sigma = 0:16081097111148149247
                            P22: P-1: 2^4 * 727 * 66169 * 8149257048181   
                                 P+1: 2 * 3^2 * 5^3 * 61 * 45699834620564681 

   Jun 14, 2017   n =66491: 106053496274612641 * 1047689279......c66474;           B1=11e3

   Jun 21, 2017   n =66809: 22818647124008951 * 4869311949......c66792;            B1=11e3

   Jun 28, 2017   n =67021: 34255610010775387957363 * 3243588745......c66998;      B1=11e3; sigma = 1949138104147135111
                            P23: P-1: 2 * 3 * 9817 * 67021 * 8677422843511  
                                 P+1: 2^2 * 113 * 75786747811449973357  

   Jul 11, 2017   n =67369: 98597788467374587 * 1126912812......c67352;            B1=11e3

   Jul 19, 2017   n =18917: 23804677265339797421816437 * 4667616782......c18891;   B1=5e4;  sigma = 3449289100892796519 
                            P26: P-1: 2^2 * 3 * 18917 * 104864571837235455859 
                                 P+1: 2 * 7 * 23 * 1601 * 3592493 * 12853433756903  
   
   Jul 19, 2017   n =67579: 81376586347554751637 * 2533975418......c67543;         B1=11e3; sigma = 10368654149114041945
                            P20: P-1: 2^2 * 67579 * 226463 * 1329322817  
                                 P+1: 2 * 3 * 7 * 11 * 2539 * 1544317 * 44921923  

   Jul 19, 2017   n =67589: 1427490294222230833547 * 7783668411......c67567;       B1=11e3; sigma = 14405740484299038573
                            P22: P-1: 2 * 7 * 31 * 67589 * 48663956314921  
                                 P+1: 2^2 * 3 * 179 * 1481 * 5026289 * 89276339  

   Jul 19, 2017   n =67589: 193970010166543534511963 * 4012820541......c67544;     B1=11e3; sigma = 18257096447838522086
                            P24: P-1: 2 * 11 * 23 * 43 * 14831 * 67589 * 8893427321  
                                 P+1: 2^2 * 3 * 19886213 * 812832866362169  
   
   Jul 19, 2017   n =67631: 12288780393345628792003 * 9041671146......c67608;      B1=11e3; sigma = 16252894969633873995
                            P23: P-1: 2 * 3^3 * 31 * 43 * 67631 * 2524288943081      
                                 P+1: 2^2 * 7 * 11 * 107449 * 739699 * 501996463 

   Jul 27, 2017   n =67783: 4697195943330820726079 * 2365477456......c67761;       B1=11e3; sigma = 2796044459679236971
                            P22: P-1: 2 * 29 * 67783 * 1194785373234877
                                 P+1: 2^6 * 3 * 5 * 733 * 6675187504733431


- Found by  Yousuke Koide  

   Jun 16, 2017   n =  878: 2515873088287897454782011891518911571754342290096763019; B1= 12e7; sigma = 2:168411160075480502  
                            P55: P-1: 2 * 3^2 * 439 * 23269 * 13682768673045146064245165921233113568903662511  
                                 P+1: 2^2 * 5 * 11 * 13 * 19 * 37 * 848995024585270451041 * 1473880341547228807928977559 
   congratulations
   

- Found by  NFS@home   

   Apr 21, 2017   n =  608: 57060943016570586495482365104744705358198487226448999934446131233808207036744145484562761542433; SNFS  
   congratulations
 

- Found by  Maksym Voznyy 

   May 07, 2017   n = 7057: 260233763784616576397917;                 B1= 25e4; sigma = 8816571980844868 
                            P24: P-1: 2 * 17 * 23 * 332779749085187437849  
                                 P+1: 2^2 * 3^2 * 11 * 107 * 7057 * 34763 * 25034983733  
   May 07, 2017   n = 7213: 213427244417412864753373;                 B1= 25e4; sigma = 2021635174584492 
                            P24: P-1: 2^2 * 3 * 7213 * 30169 * 81731931798073 
                                 P+1: 2 * 157 * 2267 * 299825584497333473   
   May 08, 2017   n = 5791: 99995089425654267749831;                  B1= 25e4; sigma = 82917410873262 
                            P23: P-1: 2 * 5 * 17 * 5791 * 101572510513935689 
                                 P+1: 2^3 * 3 * 10159 * 410125215021386077 
   May 09, 2017   n = 8537: 661975068980586310077400009;              B1= 25e4; sigma = 2366332809178546 
                             P27: P-1: 2^3 * 3 * 11 * 1151 * 1367 * 8537 * 32579 * 5729950067 
                                  P+1: 2 * 5 * 19 * 1579397 * 2205955380708041407  
   May 10, 2017   n = 9901: 267769000737328369377044347;              B1= 25e4; sigma = 8516264195145008 
                             P27: P-1: 2 * 3 * 9901 * 4507440338304689246491  
                                  P+1: 2^2 * 17 * 109 * 2377 * 3943 * 5171597 * 7453225347

Correction


                            

- Found by YOYO@home 

  YOYO@home/Beyond      
   Apr 23, 2017   n =  839: 4228488005350493568025042754591087184669613; B1= 43e6; sigma = 1:3622605400
                            P43: P-1: 2^2 * 3 * 839 * 6452757853 * 65087340750822408792411219403 
                                 P+1: 2 * 23 * 8663 * 10611064560802045601295471381515307943 

  YOYO@home/Pulsar2017  
   May 13, 2017   n =1460L: 430290068517717503314541569581514324311872414409341453561896330801; B1= 85e7; sigma = 1:3948033333
                            P66: P-1: 2^4 * 3^2 * 5^2 * 7 * 11 * 13 * 73 * 85549 * 2174461 * 3037687 * 37630124352719818994423654388281859821801  
                                 P+1: 2 * 587 * 10997934499 * 67568056091 * 493219992175946257269732176919554441691547  

  YOYO@home/NeuralMiner 
   May 25, 2017   n = 1174: 552767636859084183383203313197359593414627006389177727; B1= 11e7; sigma = 1:2037690254
                            P54: P-1: 2 * 113 * 587 * 21487122109152328111369 * 193917862757305185429952517   
                                 P+1: 2^7 * 3^2 * 3571860442757 * 21452398435147 * 6262097029026831981667541 

  YOYO@home/F!refly      
   May 28, 2017   n = 1231: 1520806406498630620751479153475405302799387; B1= 11e6; sigma = 0:6903520683874638056
                            P43: P-1: 2 * 1231 * 34501 * 56009 * 183114629693 * 1745714984950609019  
                                 P+1: 2^2 * 3 * 17 * 10973 * 1283543 * 529307398133268217466244270823  

  YOYO@home/Crystal Pellet
   Jun 07, 2017   n =  853: 16142416787665692305826190665900875338773361; B1= 43e6; sigma = 1:1396378601
                            P44: P-1: 2^4 * 3 * 5 * 853 * 248051695189 * 3817143327167 * 83277488056351 
                                 P-1: 2 * 7 * 4523 * 100927 * 2525844257576067007669670398027523 


- Found by Kurt Beschorner  

   Mar 02, 2017   n = 5709: 5428244957579115469193605941733;      B1=1e6; sigma = 2137748794  
                            P31: P-1: 2^2 * 3 * 7 * 11 * 13 * 173 * 4621 * 10781 * 52432793481122207 
                                 P+1: 2 * 29 * 266501591 * 351181506841691604553  
 

Factorizations
Repunits: R1        - R2500 (Jul 27, 2017) Repunits:  R2501 - R5000   (Jul 27, 2017)
Repunits: R5001   - R7500 (Jul 27, 2017) Repunits: R7501 -  R10000 (Jul 27, 2017)
Repunits: R10001 - R12500 (Jul 27, 2017) Repunits: R12501 - R15000 (Jul 27, 2017)




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

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