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



Related links:

Factor tables of Richard Brent
Repunit factors of Torbjörn Granlund
Factorizations of Repunit numbers of Makoto Kamada
Factor tables of Yousuke Koide
Factorizations of numbers of the form 10n+1 of Alfred Reich
Factor tables of Sam Wagstaff
The Ecmnet of Paul Zimmermann
__________________________________________________________________________

Contributions of new factors are welcome. Please send them by email to Kurt Beschorner

most wanted:
n =  924 / c159 n =  572 / c161 n =  495 / c164
n =  870 / c164 n = 1050 / c165 n =  876 / c166
n=1860L/c166 n =  960 / c172 n =  509 / c509




Efforts:  ecm-curves
ecm details n = ... n = ... n = ... n = ... n = ... n = ... n = ... n = ... n = ...
B1/B2: 12e3/1e7
50 curves
all
numbers
               
B1/B2: 5e4/269e6
130 curves
< 6599                
B1 = 1e6 all L/M-
numbers
< 12460
               
B1/B2 = 25e4/973e6
320 curves
1745 1825 3425 3505 4089 4755 5402 5894 6076
6825 7035 8295 12012 12030 12090 12102 12340L 12380L/M
B1/B2: 1e6/2167e6
820 curves
12460L/M
working
12540L/M 12660L/M 12740L/M 12780L/M        
                 
B1/B2: 11e6/111e9
4000 curves
1005 1012 1104 1155 1368 1518 2010    
B1/B2: 43e6/565e9
7000 curves
1008                


Efforts by    yoyo@home:    ecm-curves
ecm details n = ... n = ... n = ... n = ... n = ... n = ... n = ... n = ... n = ...
B1 = 11e6/
4600 curves
1036 1064 1070 1160 1284 1296 1360 1464 1476
1590 1596 5140L
working
           
B1 = 43e6/
8000 curves
1006
working
1018
working
1022 1058/
working
1078 1106 1130 1150 1196
1210 1240 12881314 1330 1488
working
1512 1542 1644
1884 1890 1914 2500M 5020L 5020M
working
5060L
working
5060M 5180L
5180M
working
               
B1 = 11e7/
17500 curves
1016
working
1086 1548 1710 2130
working
5100L
working
     


News

 
- Last update July 22, 2010
-  next update: August 01, 2010 

  
- Found by Juno Fukos

   July      22, 2010,  n =10647: 1228881852249604948284662683; B1 = 5e4; sigma = 3023631877


- Found by NFS@HOME 

   June      15, 2010,  n =  544: 32834183607181658456698862190332942753904274373750127864196636481293558631166688587638325415670849; SNFS
   June      18, 2010,  n =  768: 142018149548859447798990430842371897431582393270575475042667940048026473157944321; SNFS  
   June      21, 2010,  n =  774: 35037423610997086622096063353212253926195272207441939622830330161546317292588303;  SNFS 
   June      29, 2010,  n =  387: 1716647120944708147671447461422244736431889206579721400376110588630763194268685679597826668704163; SNFS
   congratulations!


- Found by yoyo@home
     
   Frank Boerner
   June      28, 2010,  n =5100L: 185898550709887865845976723509058449254706894935901; B1 = 11e7; B2=829850101096; sigma = 1251403100
   is the largest known factor that appears after n = 1780L; congratulations! 
  
  
- Found by Kurt Beschorner

   June      13, 2010,  n = 6713: 16781907202667851427;        B1 = 5e4; sigma = 3130070241
   June      13, 2010,  n = 6791: 380300590340725143163;       B1 = 5e4; sigma = 3726135095
   June      13, 2010,  n = 6857: 1240709935976283389252249;   B1 = 5e4; sigma = 1913792862
   June      13, 2010,  n = 6883: 121446708448114548909187;    B1 = 5e4; sigma = 3503913791
   June      13, 2010,  n = 7019: 640480216938380778277;       B1 = 5e4; sigma = 3150742521
   June      13, 2010,  n = 7019: 551140442181784047265591;    B1 = 5e4; sigma = 279551126
   June      13, 2010,  n = 8979: 324822097522604006911;       B1 = 5e4; sigma = 360964958 
   June      15, 2010,  n = 6313: 211982608339239529925191;    B1 = 5e4; sigma = 405400652
   June      15, 2010,  n = 6331: 90207610699757336406947;     B1 = 5e4; sigma = 873764990
   June      15, 2010,  n = 8703: 1441540662113424056793787;   B1 = 5e4; sigma = 4166106148   
   June      15, 2010,  n = 9603: 22110513303273460071639733;  B1 = 5e4; sigma = 714602308
   June      16, 2010,  n = 6173: 944221386563408154401;       B1 = 5e4; sigma = 968453854
   June      16, 2010,  n = 6191: 8994305703343909121  
   June      16, 2010,  n = 7349: 317834298314063333729;       B1 = 5e4; sigma = 3241569633 
   June      16, 2010,  n = 8011: 31481903205483062148026466236506733; B1 = 5e4; sigma = 1991154823
   June      16, 2010,  n=12100L: 56746303877997841892355060601; B1=1e6; sigma = 3764647909    
   June      20, 2010,  n = 7481: 854828075036287892342223773969;B1=5e4; sigma = 2033549454
   June      20, 2010,  n = 7499: 9764597849230401081382187;   B1 = 5e4; sigma = 32573195
   June      20, 2010,  n = 7537: 28636905206494439849;        B1 = 5e4; sigma = 30837838
   June      20, 2010,  n = 7757: 458134471238184611578639;    B1 = 5e4; sigma = 822218798
   June      21, 2010,  n = 7705: 2331063021496611560111;      B1 = 5e4; sigma = 3357812295
   June      21, 2010,  n = 8059: 761757276741949114966643;    B1 = 5e4; sigma = 3669371254 
   June      25, 2010,  n =10269: 1390870033721660001862662031;B1 = 5e4; sigma = 393839019
   June      25, 2010,  n =10755: 10932810041473992334448551;  B1 = 5e4; sigma = 3825902609
   June      27, 2010,  n = 7189: 70262109760685770776921437;  B1 = 5e4; sigma = 77755782
   June      27, 2010,  n = 7885: 414154302471878204471;       B1 = 5e4; sigma = 947646561
   June      27, 2010,  n = 8575: 19269287074383453086351;     B1 = 5e4; sigma = 2634348579   
   June      27, 2010,  n = 8817: 307316002416543304867;       B1 = 5e4; sigma = 3951536702
   June      27, 2010,  n = 8859: 179769003021910030456830545077; B1 = 5e4; sigma = 1665920026
   June      27, 2010,  n =11205: 25634730454615768735441;     B1 = 5e4; sigma = 3766277471
   June      27, 2010,  n =11205: 178086505935480789794041;    B1 = 5e4; sigma = 2360869455
   June      29, 2010,  n = 7553: 4165861779695874769163563;   B1 = 5e4; sigma = 3042501040 
   June      29, 2010,  n =10521: 475938539252308553211631;    B1 = 5e4; sigma = 968786222
   June      29, 2010,  n =12110: 73203742475613302503384211;  B1 = 5e4; sigma = 1875253556
   July      02, 2010,  n = 6427: 10252910946319410979660877;  B1 = 5e4; sigma = 2594359204 
   July      02, 2010,  n = 6449: 1641354500544414785449;      B1 = 5e4; sigma = 235125227
   July      02, 2010,  n = 6449: 16739417885171475752499431;  B1 = 5e4; sigma = 3419891330   
   July      02, 2010,  n = 7163: 61358725457968491906128414927003; B1 = 5e4; sigma = 4217173973 
   July      02, 2010,  n = 7495: 2674763213597667128727281;   B1 = 5e4; sigma = 2153065452
   July      02, 2010,  n = 9213: 40370837122694693285553962231209; B1 = 5e4; sigma = 1628794106  
   July      02, 2010,  n =12115: 27034927642921838306154001;  B1 = 5e4; sigma = 527338562
   July      05, 2010,  n = 6467: 40913935672229021968256323;  B1 = 5e4; sigma = 1625470417
   July      05, 2010,  n = 6473: 12001332370057422792347;     B1 = 5e4; sigma = 4124374450
   July      05, 2010,  n = 8305: 317651320298238491057791;    B1 = 5e4; sigma = 3518299552  
   July      05, 2010,  n = 9003: 5792204976596170286448187;   B1 = 5e4; sigma = 401653398
   July      05, 2010,  n = 9123: 1668837133556452535587;      B1 = 5e4; sigma = 3449363708
   July      05, 2010,  n = 9417: 60872730592259578504147;     B1 = 5e4; sigma = 4096325091    
   July      05, 2010,  n =12115: 3453217502373635446231751;   B1 = 5e4; sigma = 2582836572
   July      05, 2010,  n =12340L:17840606029938490276754751093341; B1 = 1e6; sigma = 3075048016
   July      07, 2010,  n = 6809: 881498826999535152871;       B1 = 5e4; sigma = 300719426
   July      07, 2010,  n = 7091: 142217186259619914689;       B1 = 5e4; sigma = 3423140636 
   July      07, 2010,  n = 9171: 20275047808279783053319;     B1 = 5e4; sigma = 462550580
   July      07, 2010,  n =10689: 28378933424769565681;        B1 = 5e4; sigma = 631914617
   July      07, 2010,  n =10689: 5107066778195380729123;      B1 = 5e4; sigma = 3845540702   
   July      07, 2010,  n =12117: 99790884232574019787;        B1 = 5e4; sigma = 3842005490 
   July      13, 2010,  n = 6533: 84394462738704528845563;     B1 = 5e4; sigma = 1732854607
   July      13, 2010,  n = 7147: 460722331941333286020325403; B1 = 5e4; sigma = 717862559     
   July      13, 2010,  n = 7273: 9415368381475938239  
   July      13, 2010,  n =10089: 10897449031180249265057293;  B1 = 5e4; sigma = 382822785
   July      13, 2010,  n =10689: 1419385583876756360747401;   B1 = 5e4; sigma = 2105811958 
   July      16, 2010,  n = 6551: 28567447395474592730557;     B1 = 5e4; sigma = 914105464
   July      16, 2010,  n = 8635: 7065967983966382587905161;   B1 = 5e4; sigma = 391395772
   July      16, 2010,  n =12126: 1649009847556920673302907837;B1 =25e4; sigma = 3417266792
   July      16, 2010,  n =12460M:11325306711919864144476865825321801; B1 = 1e6; sigma = 3669318446 
   July      16, 2010,  n =12500L:7355683307782160268476171662501; B1 = 1e6; sigma = 1761027376
   July      19, 2010,  n = 6569: 178184708606143049573489359; B1 = 5e4; sigma = 3092301110
   July      19, 2010,  n = 6859: 6236185604775603125041;      B1 = 5e4; sigma = 3112634807
   July      19, 2010,  n = 7835: 6704063410365652102507121;   B1 = 5e4; sigma = 518545083   
   July      19, 2010,  n = 8515: 162158620480063489648991;    B1 = 5e4; sigma = 3017047868
   July      19, 2010,  n =12129: 1292289739102618571563;      B1 = 5e4; sigma = 3576266109  
   July      20, 2010,  n =12580L:28023250907119295576858038564333784221; B1 = 1e6; sigma = 3211123764   
   July      22, 2010,  n = 7051: 10233250707709193086806049;  B1 = 5e4; sigma = 3232615814
   July      22, 2010,  n = 7357: 13799611926418431967883;     B1 = 5e4; sigma = 874124410
   July      22, 2010,  n = 7855: 55671079438234808680639711;  B1 = 5e4; sigma = 1828972537
   July      22, 2010,  n = 8965: 143971108461336502171600391; B1 = 5e4; sigma = 2717167387
   July      22, 2010,  n = 9205: 3116748019245495652711;      B1 = 5e4; sigma = 3534349394 
   July      22, 2010,  n = 9411: 644418622759574580283;       B1 = 5e4; sigma = 4202638287 
             
- visitors since March 26, 2010: 
counter
 

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;