Talk:Repunit

message: Every repunit is a repdigit. --Abdull 20:08, 19 March 2006 (UTC)
thread_title:  Repunits & repdigits 

message: The sum of the reciprocals of the repunit primes converges. This result could suggest the finiteness of Repunit primes, just like Brun's theorem could suggest the finiteness of twins.
:The sum of the reciprocals of all repunit numbers also converges, but there are infinitely many repunit numbers. This says nothing about infinitude of repunit primes. Standard heuristics suggest there are probably infinitely many. PrimeHunter 12:48, 23 January 2007 (UTC)
replies: text: No. As I said above, the sum of the reciprocals of all repunit numbers converges. Only some of the repunit numbers are repunit primes, so the sum of reciprocals of repunit primes is smaller. It converges whether there are infinitely many or not. PrimeHunter 11:59, 15 February 2007 (UTC)

text: Yes. Anything is true when the premise is false.218.133.184.93 04:42, 16 February 2007 (UTC)
replies: text: The false premise is that 218.133.184.93's statement is relevant.  — Arthur Rubin |  (talk) 23:32, 13 August 2007 (UTC)

text: The false premise is that Arthur Rubin is busy.218.133.184.93 01:33, 16 August 2007 (UTC)

text: The article says "A repunit prime is a repunit that is also a prime number" and later "Only repunits (in any base) having a prime number of digits might be prime (necessary but not sufficient condition.)". Some repunits are prime but most are not. 111 is not. PrimeHunter (talk) 12:18, 6 February 2010 (UTC)
thread_title:  Finitely many repunit primes? 

message: "Except for this case of R_3, p can only divide R_n if p = 2kn + 1 for some k."
How does this fit to 11 dividing every R_2n? --91.13.253.19 (talk) 22:46, 7 December 2007 (UTC)
replies: text: Prime n had just been discussed and the quoted statement assumes n is prime. I have added it to the article for clarity. PrimeHunter (talk) 00:09, 8 December 2007 (UTC)
thread_title:  p = 2kn + 1 

message: "It is easy to show that if n is divisible by a, then R_n is divisible by R_a:"
Wouldn't this mean that R(ab) = R(a) * R(b) (which is obviously not true)? 213.216.248.212 (talk) 10:52, 29 October 2008 (UTC)
replies: text: No, it would mean that R(ab) is divisible by both R(a) and R(b). That doesn't mean it's equal to the product. For example, R(6) = R(2) * R(3) * 91. But R(ab) doesn't even have to be divisible by the product when a and b have a common factor. For example, R(4) = 1111 = 11 * 101 is divisible by R(2) but not by R(2)*R(2). PrimeHunter (talk) 11:36, 29 October 2008 (UTC)
thread_title:  Divisibility 

message: Hi All,
As the current world record holder for proving prime generalized repunits and maintainer of a page listing all known such primes, it would not be proper for me to edit the wiki page. In case anyone _else_ thinks my page would be a useful link, here it is:
http://www.primes.viner-steward.org/andy/titans.html
Also, there is a Repunit Primes collaborative project in progress at http://www.gruppoeratostene.com/ric-repunit/repunit.htm
Cheers,
Andy Steward
88.106.202.253 (talk) 14:12, 15 March 2010 (UTC)
thread_title:  Blowing My Own Trumpet 

message: Should we perhaps have a seperate article about repunit primes (like the way we have an article about Mersenne numbers and Mersenne primes)? Or should we really just keep all information about repunit primes in this article? Toshio Yamaguchi (talk) 16:26, 30 October 2010 (UTC)
replies: text: Repunits are generally only studied for the sake of finding their factors, so I don't think a split is needed. In any case Mersenne number redirects to Mersenne prime; it has never been a separate article. Xanthoxyl < 08:05, 31 October 2010 (UTC)
replies: text: Ok agreed. Regarding the Mersenne number article I must have missed something, sorry. Toshio Yamaguchi (talk) 11:27, 31 October 2010 (UTC)
thread_title:  Own article about repunit primes?

message: The article mentions many repunit numbers in different bases, but then lists the numbers in (presumably) decimal.  However, it does look extremely odd to read, for example: "The first few base-3 repunit primes are 13, 1093, 797161, ..." when the reader surely knows 0, 1 & 2 are the only valid digits in base-3.  I would have expected to read: "The first few base-3 repunit primes are 111, 1111111, 1111111111111, ..." Astronaut (talk) 13:21, 14 March 2011 (UTC)
replies: text: Rather than force the reader to sit counting a string of ones, I'd suggest inserting the words "in decimal". Xanthoxyl < 15:50, 14 March 2011 (UTC)
replies: text: Per WP:ORDINAL we could write 1113, 11111113, 11111111111113, ... but again the question is up to which lenght (number of ones) does this notation make sense? Toshio Yamaguchi (talk) 16:35, 14 March 2011 (UTC)
thread_title:  Invalid digits used in base-n 

message: What we need is WikiTable or HTML formatting elements to force (1) each entry to be at the top of the cell, rather than centered vertically, (2) (Left, rather than centered horizontally, which seems already to have been done), and (3) each Rn to be in line with the "=".  The anon's recent addition of improper HTML s doesn't really solve the problem, and doesn't maintain proper alignment.  — Arthur Rubin  (talk) 18:13, 21 August 2014 (UTC)
thread_title:  Formatting "factorization of decimal repunits" tables 

message: These are generalized repunit prime in base 2 to 257 and −2 to −257 and some other bases.
Positive bases (2 to 257):
   2   2 3 5 7 13 17 19 31 61 89 107 127 521 607 1279 2203 2281 3217 4253 4423 9689 9941 11213 19937 21701 23209 44497 86243
       110503 132049 216091 756839 859433 1257787 1398269 2976221 3021377 6972593 13466917 20996011 24036583 25964951 
       30402457 32582657 37156667 (?) 42643801 (?) 43112609 (?) 57885161 (?) 74207281 (?) 77232917
   3   3 7 13 71 103 541 1091 1367 1627 4177 9011 9551 36913 43063 49681 57917 483611 877843
   4   2 (no others)
   5   3 7 11 13 47 127 149 181 619 929 3407 10949 13241 13873 16519 201359 396413
   6   2 3 7 29 71 127 271 509 1049 6389 6883 10613 19889 79987 608099
   7   5 13 131 149 1699 14221 35201 126037 371669 1264699
   8   3 (no others)
   9   (none)
  10   2 19 23 317 1031 49081 86453 109297 270343
  11   17 19 73 139 907 1907 2029 4801 5153 10867 20161 293831
  12   2 3 5 19 97 109 317 353 701 9739 14951 37573 46889 769543
  13   5 7 137 283 883 991 1021 1193 3671 18743 31751 101089
  14   3 7 19 31 41 2687 19697 59693 67421 441697
  15   3 43 73 487 2579 8741 37441 89009 505117
  16   2 (no others)
  17   3 5 7 11 47 71 419 4799 35149 54919 74509
  18   2 25667 28807 142031 157051 180181 414269
  19   19 31 47 59 61 107 337 1061 9511 22051 209359
  20   3 11 17 1487 31013 48859 61403 472709
  21   3 11 17 43 271 156217 328129
  22   2 5 79 101 359 857 4463 9029 27823
  23   5 3181 61441 91943 121949
  24   3 5 19 53 71 653 661 10343 49307 115597
  25   (none)
  26   7 43 347 12421 12473 26717
  27   3 (no others)
  28   2 5 17 457 1423
  29   5 151 3719 49211 77237
  30   2 5 11 163 569 1789 8447 72871 78857 82883
  31   7 17 31 5581 9973 54493 101111
  32   (none)
  33   3 197 3581 6871
  34   13 1493 5851 6379
  35   313 1297
  36   2 (no others)
  37   13 71 181 251 463 521 7321 36473 48157 87421
  38   3 7 401 449 109037
  39   349 631 4493 16633 36341
  40   2 5 7 19 23 29 541 751 1277
  41   3 83 269 409 1759 11731
  42   2 1319
  43   5 13 6277 26777 27299 40031 44773
  44   5 31 167 100511
  45   19 53 167 3319 11257 34351
  46   2 7 19 67 211 433 2437 2719 19531
  47   127 18013 39623
  48   19 269 349 383 1303 15031
  49   (none)
  50   3 5 127 139 347 661 2203 6521
  51   4229 35227
  52   2 103 257 4229 6599
  53   11 31 41 1571 25771
  54   3 389 16481 18371 82471
  55   17 41 47 151 839 2267 3323 3631 5657 35543
  56   7 157 2083 2389 57787
  57   3 17 109 151 211 661 16963 22037
  58   2 41 2333 67853
  59   3 13 479 12251
  60   2 7 11 53 173
  61   7 37 107 769
  62   3 5 17 47 163 173 757 4567 9221 10889
  63   5 3067 38609
  64   (none)
  65   19 29 631
  66   2 3 7 19 19973
  67   19 367 1487 3347 4451 10391 13411
  68   5 7 107 149 2767
  69   3 61 2371 3557 8293 106397
  70   2 29 59 541 761 1013 11621 27631
  71   3 31 41 157 1583 31079 55079 72043
  72   2 7 13 109 227
  73   5 7 35401
  74   5 191 3257 31267
  75   3 19 47 73 739 13163 15607 93307
  76   41 157 439 593 3371 3413 4549
  77   3 5 37 15361
  78   2 3 101 257 1949 67141
  79   5 109 149 659 28621
  80   3 7
  81   (none)
  82   2 23 31 41 7607 12967
  83   5 2713
  84   17 3917
  85   5 19 2111
  86   11 43 113 509 1069 2909 4327 40583
  87   7 17
  88   2 61 577 3727 22811 40751
  89   3 7 43 47 71 109 571 11971 50069
  90   3 19 97 5209
  91   4421 20149
  92   439 13001 22669 44491
  93   7 4903
  94   5 13 37 1789 3581
  95   7 523 9283 10487 11483
  96   2 3343 46831
  97   17 37 1693
  98   13 47 2801
  99   3 5 37 47 383 5563
 100   2 (no others)
 101   3 337 677 1181 6599
 102   2 59 673 25087
 103   19 313 1549
 104   97 263 5437
 105   3 19 389 2687 4783
 106   2 149
 107   17 24251
 108   2 449 2477
 109   17 1193 13679 27061
 110   3 5 13 691 1721 3313 11827
 111   3 337
 112   2 79 107 701 1697 5657
 113   23 37 6563
 114   29 43 73 89 569 709
 115   7 241 1409 2341 2539 7673 12539 16879
 116   59 2503
 117   3 5 19 31
 118   5 163 193
 119   3 19 827 2243 3821
 120   5 373 1693
 121   (none)
 122   5 7 67 3803
 123   43 563 1693 4877 22741
 124   599 18367 28591
 125   (none)
 126   2 7 37 59 127 20947
 127   5 23 31 167 5281 8969 23297 165601
 128   7 (no others)
 129   5 17 109 8447
 130   2 37
 131   3 31 263
 132   47 71 3343
 133   13 599 991 1181 3083 14827
 134   5 37 353 2843 21379
 135   1171 15227
 136   2 227 293 4133
 137   11 19 1009 2939
 138   2 3 61 13679
 139   163 173 3821
 140   79 577 1721
 141   3 23 173 3217
 142   1231 6133
 143   3 5
 144   (none)
 145   5 31
 146   7 83 857 21961
 147   3 17 19 37 163 571 983 3697
 148   2 1201
 149   7 13 17 317 3251
 150   2 3 3389
 151   13 29 127 4831 5051 13249 18251
 152   270217
 153   3 5099
 154   5 8161
 155   3 61 449 2087
 156   2 7 199 5591
 157   17 107 2791 39047 53819 90239
 158   7 79 109 4003 6151 10453
 159   13 89 577 1433 9643
 160   7 17 151 1487 3989
 161   3 37 263
 162   2 3 5 311 1087
 163   7 43 241 1637 2543
 164   3 5 19 101 347 383
 165   5 53 109
 166   2 137 353 1289
 167   3 19 373 1213 2203
 168   3 823
 169   (none)
 170   17 23 79 1237 19843
 171   181 3373 12391
 172   2 5 11 37 47
 173   3 2687
 174   3251
 175   5 167 1699 5881
 176   3 151 2719 3923 11743 13397
 177   5 31
 178   2 347 911 4523
 179   19
 180   2 7 43 1913 2683 4637
 181   17 19 157
 182   167 509 1609
 183   223
 184   16703
 185   
 186   7 47 223 271 3947 4153 10177
 187   37 617
 188   3 59 3719
 189   3 17
 190   2 13 89 157 643 673 10427
 191   17 1399
 192   2 3 7 613
 193   5 317 11171
 194   3 8807
 195   11 73 379 2687
 196   2 (no others)
 197   31 47 283 11719
 198   2 5 9721 10771
 199   577 1831
 200   17807
 201   271 353
 202   37 829
 203   3 7 31 9587
 204   5 359
 205   19 61 6427 8147
 206   3 7
 207   13 17
 208   5 7 37 1229 1583 3517
 209   3 59 449 613
 210   2 19819
 211   41
 212   11
 213   137
 214   191
 215   3 73 461 751 3433
 216   (none)
 217   281 821
 218   3 331 701 971 1277
 219   13 107 223 1307
 220   7 19 47 307
 221   7 13 29 139 223 439 6907
 222   2 5 151 271 5077
 223   239 241 449
 224   11 401
 225   (none)
 226   2 127 619 7043
 227   5 1061 2687
 228   2 461 4801 11443
 229   11 29
 230   5333
 231   3 6907
 232   2 953 2801 4111
 233   113 9511
 234   61 89 97 1381 9011
 235   7 19 53 227 307
 236   3 197 467 587
 237   7 2621
 238   2 7 67 1093 1381
 239   5 109 2549
 240   2 109 227 271 941
 241   17 31
 242   19 541
 243   (none)
 244   3331 5099
 245   3 9277
 246   3 37 251
 247   17 331
 248   41 197 2203
 249   5 1249 2053 3319 8627
 250   2 127 1889
 251   7 13 17 89 227 461 3467
 252   541 947
 253   19 2659
 254   5 19 79 283 563 883
 255   5 151 701
 256   2 (no others)
 257   23 59 487 967 5657
Positive bases (some special bases > 257):    
 290 = 172+1      3 7
 325 = 182+1      31 1039
 344 = 73+1       3 23
 362 = 192+1      199 2663
 401 = 202+1      127 199 6551
 442 = 212+1      2 13 23 199 5309
 485 = 222+1      
 511 = 29−1       
 513 = 29+1       17 2663 6883
 530 = 232+1      3 5 599
 577 = 242+1      109 139 227
 626 = 54+1       3 11 61 1249
 730 = 36+1       13
 1001 = 103+1     3 1787
 1023 = 210−1     19
 1025 = 210+1     13 83
 1297 = 64+1      5 7 29 2423
 1332 = 113+1     17 3701
 1729 = 123+1     1097
 2047 = 211−1     877
 2049 = 211+1     3 17
 2188 = 37+1      7 3011 12437
 2402 = 74+1      3 19
 3126 = 55+1      11 2749 14431 14983
 4095 = 212−1     5479
 4097 = 212+1     7 37 3673 8311
 6562 = 38+1      2 701
 7777 = 65+1      5
 10001 = 104+1    11 569
 14642 = 114+1    3
 20737 = 124+1    227
 65535 = 216−1    
 65537 = 216+1    7 11
 100001 = 105+1   31 53
 1000001 = 106+1  11 277
Positive bases (perfect powers between 257 and 4096 and some other perfect powers):
 289 = 172      (none)
 324 = 182      (none)
 343 = 73       (none)
 361 = 192      (none)
 400 = 202      2 (no others)
 441 = 212      (none)
 484 = 222      (none)
 512 = 29       3 (no others)
 529 = 232      (none)
 576 = 242      2 (no others)
 625 = 54       (none)
 676 = 262      2 (no others)
 729 = 36       (none)
 784 = 282      (none)
 841 = 292      (none)
 900 = 302      (none)
 961 = 312      (none)
 1000 = 103     (none)
 1024 = 210     (none)
 1089 = 332     (none)
 1156 = 342     (none)
 1225 = 352     (none)
 1296 = 64      2 (no others)
 1331 = 113     3 (no others)
 1369 = 372     (none)
 1444 = 382     (none)
 1521 = 392     (none)
 1600 = 402     2 (no others)
 1681 = 412     (none)
 1728 = 123     (none)
 1764 = 422     (none)
 1849 = 432     (none)
 1936 = 442     (none)
 2025 = 452     (none)
 2048 = 211     (none)
 2116 = 462     (none)
 2187 = 37      (none)
 2197 = 133     (none)
 2209 = 472     (none)
 2304 = 482     (none)
 2401 = 74      (none)
 2500 = 502     (none)
 2601 = 512     (none)
 2704 = 522     (none)
 2744 = 143     (none)
 2809 = 532     (none)
 2916 = 542     2 (no others)
 3025 = 552     (none)
 3125 = 55      (none)
 3136 = 562     2 (no others)
 3249 = 572     (none)
 3364 = 582     (none)
 3375 = 153     (none)
 3481 = 592     (none)
 3600 = 602     (none)
 3721 = 612     (none)
 3844 = 622     (none)
 3969 = 632     (none)
 4096 = 212     (none)
 8192 = 213     (none)
 16384 = 214    (none)
 32768 = 215    (none)
 65536 = 216    2 (no others)
Positive bases (the special cases):
   N   2 3 19 31 7547 ==> (N^N-1)/(N-1)
Negative bases (2 to 257):
   2   3 4 5 7 11 13 17 19 23 31 43 61 79 101 127 167 191 199 313 347
       701 1709 2617 3539 5807 10501 10691 11279 12391 14479 42737 83339 95369 117239 127031 138937 141079
       267017 269987 374321 986191 4031399 (?) 13347311 13372531
   3   2 3 5 7 13 23 43 281 359 487 577 1579 1663 1741 3191 9209 11257 12743 13093 17027 26633
       104243 134227 152287 700897 1205459
   4   2 3 (no others)
   5   5 67 101 103 229 347 4013 23297 30133 177337 193939 266863 277183 335429
   6   2 3 11 31 43 47 59 107 811 2819 4817 9601 33581 38447 41341 131891 196337
   7   3 17 23 29 47 61 1619 18251 106187 201653
   8   2 (no others)
   9   3 59 223 547 773 1009 1823 3803 49223 193247 703393
  10   5 7 19 31 53 67 293 641 2137 3011 268207
  11   5 7 179 229 439 557 6113 223999 327001
  12   2 5 11 109 193 1483 11353 21419 21911 24071 106859 139739
  13   3 11 17 19 919 1151 2791 9323 56333 1199467
  14   2 7 53 503 1229 22637 1091401
  15   3 7 29 1091 2423 54449 67489 551927
  16   3 5 7 23 37 89 149 173 251 307 317 30197 1025393
  17   7 17 23 47 967 6653 8297 41221 113621 233689 348259
  18   2 3 7 23 73 733 941 1097 1933 4651 481147
  19   17 37 157 163 631 7351 26183 30713 41201 77951 476929
  20   2 5 79 89 709 797 1163 6971 140053 177967 393257
  21   3 5 7 13 37 347 17597 59183 80761 210599
  22   3 5 13 43 79 101 107 227 353 7393 50287
  23   11 13 67 109 331 587 24071 29881 44053
  24   2 7 11 19 2207 2477 4951
  25   3 7 23 29 59 1249 1709 1823 1931 3433 8863 43201 78707
  26   11 109 227 277 347 857 2297 9043
  27   (none)
  28   3 19 373 419 491 1031 83497
  29   7 112153 151153
  30   2 139 173 547 829 2087 2719 3109 10159 56543 80599
  31   109 461 1061 50777
  32   2 (no others)
  33   5 67 157 12211
  34   3
  35   11 13 79 127 503 617 709 857 1499 3823
  36   31 191 257 367 3061 110503
  37   5 7 2707
  38   2 5 167 1063 1597 2749 3373 13691 83891
  39   3 13 149 15377
  40   53 67 1217 5867 6143 11681 29959
  41   17 691
  42   2 3 709 1637 17911
  43   5 7 19 251 277 383 503 3019 4517 9967 29573
  44   2 7 41233
  45   103 157 37159
  46   7 23 59 71 107 223 331 2207 6841 94841
  47   5 19 23 79 1783 7681
  48   2 5 17 131 84589
  49   7 19 37 83 1481 12527 20149
  50   1153 26903 56597
  51   3 149 3253
  52   7 163 197 223 467 5281 52901 85259
  53   21943 24697
  54   2 7 19 67 197 991
  55   3 5 179 229 1129 1321 2251 15061
  56   37 107 1063 4019
  57   53 227 18211 20231 22973 87719 111119
  58   3 17 1447 11003
  59   17 43 991 33613
  60   2 3 937 1667 3917 18077 31393
  61   7 41 359 17657
  62   2 11 29 167 313 16567 38699
  63   3 37 41 2131 4027 22283 51439 102103
  64   (none)
  65   19 31
  66   7 17 211 643 28921 58741 63079 67349
  67   3 2347 2909 3203
  68   2 757 773 71713
  69   11 211 239 389 503 4649 24847
  70   3 61 97 13399 42737
  71   5 37 5351 7499 68539 77761
  72   2 3 7 79 277 3119
  73   7 39181
  74   2 13 31 37 109 17383
  75   5 83 6211
  76   3 5 191 269 23557
  77   37 317
  78   3 7 31 661 4217
  79   3 107 457 491 2011
  80   2 5 13 227 439
  81   3 5 701 829 1031 1033 7229 19463
  82   293 1279 97151
  83   19 31 37 43 421 547 3037 8839
  84   2 7 13 139 359 971 1087 3527
  85   167 3533 48677
  86   7 17 397 7159
  87   7 467 43189
  88   709 1373 61751
  89   13 59 137 1103 4423 82609 101363
  90   2 3 47
  91   3 11 43 397 21529 37507 61879
  92   37 59 113
  93   89 571 601 3877
  94   71 307 613 1787 3793 10391
  95   43 93377
  96   37 103 131 263 32369
  97   
  98   2 19 101
  99   7 37 41 71
 100   3 293 461 11867 90089
 101   7 229
 102   2 3
 103   
 104   2 673 839 1031
 105   11 149 1187 1627
 106   3 7 19 23 31 3989
 107   103 983 18049
 108   2 13 223 15731
 109   59 79 811
 110   2 23 101 17041
 111   3 5 23 53 383 2039 12109
 112   3
 113   
 114   2 7 13 1801 12487
 115   7 31 293
 116   113 1481 2089 16889
 117   271
 118   3 23 109 2357
 119   29 53 797 11491
 120   3 31 43 263 4919
 121   5 13 97 1499 11321
 122   293 3877 12889 22277
 123   29 739
 124   16427
 125   (none)
 126   5 13 47 163 239 4523
 127   317 1061 23887
 128   2 7 (no others)
 129   17 227 1753
 130   467
 131   5 101 3389 3581
 132   2 3 101 157 1303
 133   5 7 17 59 79 157
 134   13 1171 6733
 135   5 7 2671 11953
 136   5 7 23 59 199 2053 6067
 137   101 241 353 1999 21851
 138   2 103 577 10781
 139   3 17 47 2683 2719
 140   2 59
 141   5 1471
 142   3 7537
 143   7 17 19 47 103 4423 18287
 144   3 23 41 317 3371
 145   7 23 281
 146   17 1439 11027
 147   11 151 6599
 148   3 7 31 43 163 317 1933 5669 11789 19289 22171
 149   17 769
 150   2 6883 15139
 151   3 367 3203 7993 10273 14437
 152   2 13 19
 153   13 1063 5749
 154   3 29 263 601 619 809 1217 2267
 155   5
 156   3 1301
 157   5 157 809 1861 2203
 158   2 5 769 5023
 159   283 449 1949 7457
 160   11 37 1907 10487
 161   31 331 1483
 162   3 1823 7703
 163   3 11 31 661 1999 4079 6917
 164   2 7 103 541 1109
 165   3 5 383
 166   17 5437
 167   17 59 1301 3167
 168   2 3 31 1741 2099
 169   3 7 109 21943
 170   7
 171   13 149 257 4967
 172   37 283 647 4483 5417
 173   7 59 569 2647
 174   2 3 3191
 175   31627
 176   5 31 269 479 599 809 1307
 177   3 5 19 419
 178   61 167 227
 179   827 5011 8867
 180   2 5 13 7369 8101
 181   449 2687 4877
 182   2 1487 8081
 183   11 16363
 184   19 79 149 7283
 185   11
 186   
 187   
 188   22037
 189   3 31 71 8123
 190   3 19 1153
 191   479 1163
 192   2 109 197 587 727 1997 2441
 193   3 11 67 3253
 194   2 19 31
 195   3 13 19 43 89 1087 1949 2939
 196   43 1049 5441 18089
 197   31 37 101 163
 198   2 37 151 937
 199   313 2579 5387
 200   2 7 277
 201   43 587 593 2861 7841
 202   229
 203   5 439
 204   3 13 1693 11329
 205   5449
 206   101 1069
 207   3 199
 208   61
 209   311 433 883
 210   3 8311
 211   79 6659
 212   2 101
 213   59 239 6607 7177
 214   73 157 8867
 215   277
 216   3 (no others)
 217   499 5981
 218   241 2417
 219   3 7 251 709 1097
 220   
 221   149
 222   1657 2963 4231
 223   5 103 857 997 5923
 224   2 7 5189
 225   383 1277
 226   7 71 79 1459 1669 2887 5503
 227   89
 228   2 7 4241
 229   11 1117 4159
 230   2 13 23 37 41 313
 231   7 17 1217 4643
 232   3 11 283 7159
 233   11
 234   2 7 3253 6211
 235   223 1993 6043 9137
 236   11 71 149 827 1741
 237   3 8677
 238   23 353
 239   59 601 8867
 240   2 7
 241   19 37 853 3169 7507
 242   2 5 137 2011
 243   (none)
 244   71 613
 245   5 29 547 7207 8731
 246   3 227 5897
 247   3 43 1993 2801
 248   7 11 163 1951 2897 3391
 249   19 103 317
 250   857 1061 1373 3637
 251   5 61
 252   2 43 521
 253   5 383 1049
 254   569 2797
 255   7 59 179 263 4283 15527
 256   5 13 23029 50627 51479 72337
 257   5 47 2909 8747
Negative bases (some squares > 257 and some other bases):    
 289 = 172        3 179 181 683
 324 = 182        (none)
 361 = 192        5 23 223 4441
 400 = 202        263
 441 = 212        101 197
 484 = 222        257
 529 = 232        587 683
 576 = 242        379 461 1861
 625 = 54         3 7 11 31 67 9173 17737
 1296 = 64        3 2153 3517
 2401 = 74        37 3583 8059
 6561 = 38        19 29 11213
 10000 = 104      3 283 1087
 14641 = 114      13 211
 20736 = 124      7 593
 65536 = 216      239
 65537 = 216+1    5
 232              3 13619
Negative bases (some perfect powers between 257 and 100000):
 343 = 73       3 (no others)
 512 = 29       (none)
 729 = 93       3 (no others)
 1000 = 103     (none)
 1024 = 45      (none)
 1331 = 113     (none)
 1728 = 123     (none)
 2048 = 211     (none)
 2187 = 37      (none)
 2197 = 133     (none)
 2500 = 4×54    (none)
 2744 = 143     (none)
 3125 = 55      (none)
 3375 = 153     (none)
 4096 = 163     (none)
 4913 = 173     (none)
 5184 = 4×64    (none)
 5832 = 183     (none)
 6859 = 193     (none)
 7776 = 65      5 (no others)
 8000 = 203     (none)
 8192 = 213     2 (no others)
 9261 = 213     (none)
 9604 = 4×74    (none)
 10648 = 223    (none)
 12167 = 233    (none)
 13824 = 243    (none)
 15625 = 253    (none)
 16384 = 47     (none)
 16807 = 75     5 (no others)
 19683 = 39     (none)
 26244 = 4×94   (none)
 32768 = 215    (none)
 40000 = 4×104  (none)
 46656 = 363    (none)
 58564 = 4×114  (none)
 59049 = 95     (none)
 78125 = 57     (none)
 82944 = 4×124  (none)
 100000 = 105   (none)
Negative bases (the special cases):
    N   3 5 17 157 ==> (N^N+1)/(N+1)
  N^2   3 7 29 41 43 61 577 ==> (N^2N+1)/(N^2+1)
— Preceding unsigned comment added by 49.216.117.39 (talk) 13:50, 22 August 2015 (UTC)
replies: text: Is there a source for this? It looks like original research. Gap9551 (talk) 17:57, 17 December 2015 (UTC)
thread_title:  My generalized repunit data  

message: This is original research on my part, but perhaps it should be added if we can find a reliable source.
Theorem:  If the base b is uv, then any repunit in base b has at most v digits.
Proof: 
In general,
:R_m(n) = \frac {n^m-1}{n-1}.
If  b = u^v,
:R_w(b) = \frac { u^{vw} - 1} {u^v-1} = \frac {\left( {u^w-1} \right) R_v\left(u^w\right)} {u^v-1}
If w>v, both components of the numerator are larger than the denominator, so the expression is composite. 
A more careful proof can probably show that if w > 1, v and w cannot be relatively prime.
... or not.  A counter example is reported above. — Arthur Rubin  (talk) 22:47, 25 August 2018 (UTC)
thread_title:  Power bases 

message: I don't know how much detail we need to go into.  I cannot come up with a proof much simpler than:
:R_n(9) = \frac {\left(3^n+1\right) \left(3^n+1\right)} 8 .
If n is greater than 1, 3n + 1 and 3n − 1 are even and greater than 4; hence, writing
\frac {\left(3^n+1\right)\left(3^n-1\right)} 8 = \frac {3^n+1}{2^a} \frac{3^n-1}{2^b},, with (a, b) = (1, 2) or (2, 1), both factors are greater than 1.  — Arthur Rubin  (talk) 07:35, 14 November 2018 (UTC)
thread_title:  Base 9 repunit primes 

message: What repunit is 2417 and 557? I think that you need an infinity calculator...
--190.245.110.53 (talk) 22:08, 12 August 2019 (UTC)
thread_title:  Repunit of: 2417, 557 

message: Batalov and Propper found a new probable prime decimal repunit on 4/20/2021. Being one of the authors, I would like to add a sourced sentence about this new finding. This new probable prime also happens to be the largest currently known probable prime in the world.
Suggested edit:
now:
As of November 2012, all further candidates up to R2500000 have been tested, but no new probable primes have been found so far.
edit:
On April 20, 2021, Batalov and Propper found a new probable prime decimal repunit, R5794777. As of April 2021, all candidates up to R4300000 have been tested, and the search continues. Serge Batalov (talk) 05:38, 22 April 2021 (UTC)
replies: text: Not done: please provide reliable sources that support the change you want to be made. ScottishFinnishRadish (talk) 10:59, 22 April 2021 (UTC)
replies: text:  Done The authoritative source  was updated with both R5794777 and now R8177207. The article has been edited accordingly. -- P.T. Aufrette (talk) 01:33, 10 May 2021 (UTC)
thread_title:  Semi-protected edit request on 22 April 2021 

message: To complete the allocation of prime factors (lower than 100) for decimal repunit numbers:
R33 = 67, R35 = 71, R41 = 83, R44 = 89, R46 = 47, R58 = 59, R60 = 61, R96 = 97. AcerSpes (talk) 11:06, 29 December 2022 (UTC)
replies: text: Not done: Wikipedia is not a WP:INDISCRIMINATE collection of information. The summary is enough for reading on the information and people who'd like to check more can click on the external link. I see no reason to add this. Aaron Liu (talk) 15:21, 11 January 2023 (UTC)
thread_title:  Semi-protected edit request on 29 December 2022