Factorisations Of Cunningham Numbers C-(10,n) = 10n - 1

Canonical Representation Of Factorisations

  1. Factorisations are given from smallest to largest factor, with a period '.' separating factors.
  2. Multiplicity of factors is indicated with the carat '^' in ascii tradition for the text version of the tables but not the HTML version.
  3. The backslash '\' is used to indicate continuation of a line, the decimal digit representation of the number does not stop but continues on the next line as if no break had occured. This can sometimes make for bad breaks, but such is life.

Notation Used In The Tables

  1. Composite exponents are in black. C±(b,n) is almost always composite for composite exponent. The rare exceptions are the Generalised Fermat primes C+(b,n) with b even and n a power of 2.
  2. Prime exponents are coloured orange. C±(b,n) is usually composite in this case too.
  3. C±(b,n) primes are coloured green. Ignoring n=1 cases, they can only occur for n prime in C(2,n) (Mersenne primes) and the Generalised Fermat primes.
  4. Unfactored composites are coloured red. No factors for these composites is known.
  5. Hyperlinked numbers occur in previous exponents in the same or related table.
  6. #Fac is the number of (non distinct) prime factors in the expression.
  7. A plussed #Fac means that more prime factors exist but they are unknown due to a unfactored composite in the expression.

Factored Expressions

   n  #Fac  Factorisation
   1     2  3.3
   2     3  3.3.11
   3     4  3.3.3.37
   4     4  3.3.11.101
   5     4  3.3.41.271
   6     7  3.3.3.7.11.13.37
   7     4  3.3.239.4649
   8     6  3.3.11.73.101.137
   9     6  3.3.3.3.37.333667
  10     6  3.3.11.41.271.9091
  11     4  3.3.21649.513239
  12     9  3.3.3.7.11.13.37.101.9901
  13     5  3.3.53.79.265371653
  14     6  3.3.11.239.4649.909091
  15     8  3.3.3.31.37.41.271.2906161
  16     8  3.3.11.17.73.101.137.5882353
  17     4  3.3.2071723.5363222357
  18    11  3.3.3.3.7.11.13.19.37.52579.333667
  19     3  3.3.1111111111111111111
  20     9  3.3.11.41.101.271.3541.9091.27961
  21     9  3.3.3.37.43.239.1933.4649.10838689
  22     9  3.3.11.11.23.4093.8779.21649.513239
  23     3  3.3.11111111111111111111111
  24    12  3.3.3.7.11.13.37.73.101.137.9901.99990001
  25     7  3.3.41.271.21401.25601.182521213001
  26     8  3.3.11.53.79.859.265371653.1058313049
  27     9  3.3.3.3.3.37.757.333667.440334654777631
  28    10  3.3.11.29.101.239.281.4649.909091.121499449
  29     7  3.3.3191.16763.43037.62003.77843839397
  30    15  3.3.3.7.11.13.31.37.41.211.241.271.2161.9091.2906161
  31     5  3.3.2791.6943319.57336415063790604359
  32    13  3.3.11.17.73.101.137.353.449.641.1409.69857.5882353
  33     8  3.3.3.37.67.21649.513239.1344628210313298373
  34     8  3.3.11.103.4013.2071723.5363222357.21993833369
  35     9  3.3.41.71.239.271.4649.123551.102598800232111471
  36    14  3.3.3.3.7.11.13.19.37.101.9901.52579.333667.999999000001
  37     5  3.3.2028119.247629013.2212394296770203368013
  38     5  3.3.11.909090909090909091.1111111111111111111
  39     8  3.3.3.37.53.79.265371653.900900900900990990990991
  40    13  3.3.11.41.73.101.137.271.3541.9091.27961.1676321.5964848081
  41     6  3.3.83.1231.538987.201763709900322803748657942361
  42    17  3.3.3.7.7.11.13.37.43.127.239.1933.2689.4649.459691.909091.10838689
  43     6  3.3.173.1527791.1963506722254397.2140992015395526641
  44    13  3.3.11.11.23.89.101.4093.8779.21649.513239.1052788969.1056689261
  45    12  3.3.3.3.31.37.41.271.238681.333667.2906161.4185502830133110721
  46     8  3.3.11.47.139.2531.549797184491917.11111111111111111111111
  47     4  3.3.35121409.316362908763458525001406154038726382279
  48    15  3.3.3.7.11.13.17.37.73.101.137.9901.5882353.99990001.9999999900000001
  49     6  3.3.239.4649.505885997.1976730144598190963568023014679333
  50    12  3.3.11.41.251.271.5051.9091.21401.25601.182521213001.78875943472201
  51    10  3.3.3.37.613.210631.2071723.52986961.5363222357.13168164561429877
  52    11  3.3.11.53.79.101.521.859.265371653.1058313049.1900381976777332243781
  53     6  3.3.107.1659431.1325815267337711173.47198858799491425660200071
  54    16  3.3.3.3.3.7.11.13.19.37.757.52579.333667.70541929.14175966169.440334654777631
  55    10  3.3.41.271.1321.21649.62921.513239.83251631.1300635692678058358830121
  56    14  3.3.11.29.73.101.137.239.281.4649.7841.909091.121499449.127522001020150503761
  57     8  3.3.3.37.21319.10749631.1111111111111111111.3931123022305129377976519
  58    10  3.3.11.59.3191.16763.43037.62003.77843839397.154083204930662557781201849
  59     4  3.3.2559647034361.4340876285657460212144534289928559826755746751
  60    22  3.3.3.7.11.13.31.37.41.61.101.211.241.271.2161.3541.9091.9901.27961.2906161.4188901.39526741
  61     9  3.3.733.4637.329401.974293.1360682471.106007173861643.7061709990156159479
  62     7  3.3.11.2791.6943319.57336415063790604359.909090909090909090909090909091
  63    16  3.3.3.3.37.43.239.1933.4649.10837.23311.45613.333667.10838689.45121231.1921436048294281
  64    17  3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.834427406578561
  65     9  3.3.41.53.79.271.265371653.162503518711.5538396997364024056286510640780600481
  66    17  3.3.3.7.11.11.13.23.37.67.4093.8779.21649.513239.599144041.183411838171.1344628210313298373
  67     5  3.3.493121.79863595778924342083.28213380943176667001263153660999177245677
  68    12  3.3.11.101.103.4013.2071723.28559389.1491383821.5363222357.21993833369.2324557465671829
  69     8  3.3.3.37.277.203864078068831.11111111111111111111111.1595352086329224644348978893
  70    14  3.3.11.41.71.239.271.4649.9091.123551.909091.4147571.102598800232111471.265212793249617641
  71     4  3.3.241573142393627673576957439049.45994811347886846310221728895223034301839
  72    20  3.3.3.3.7.11.13.19.37.73.101.137.3169.9901.52579.98641.333667.99990001.999999000001.3199044596370769
  73     5  3.3.12171337159.1855193842151350117.49207341634646326934001739482502131487446637
  74     9  3.3.11.7253.2028119.247629013.422650073734453.296557347313446299.2212394296770203368013
  75    14  3.3.3.31.37.41.151.271.4201.21401.25601.2906161.182521213001.15763985553739191709164170940063151
  76     8  3.3.11.101.722817036322379041.909090909090909091.1111111111111111111.1369778187490592461
  77    10  3.3.239.4649.5237.21649.42043.513239.29920507.136614668576002329371496447555915740910181043
  78    18  3.3.3.7.11.13.13.37.53.79.157.859.6397.216451.265371653.1058313049.388847808493.900900900900990990990991
  79     8  3.3.317.6163.10271.307627.49172195536083790769.3660574762725521461527140564875080461079917
  80    17  3.3.11.17.41.73.101.137.271.3541.9091.27961.1676321.5070721.5882353.5964848081.19721061166646717498359681
  81    15  3.3.3.3.3.3.37.163.757.9397.333667.2462401.440334654777631.676421558270641.130654897808007778425046117
  82     9  3.3.11.83.1231.538987.2670502781396266997.3404193829806058997303.201763709900322803748657942361
  83     5  3.3.3367147378267.9512538508624154373682136329.346895716385857804544741137394505425384477
  84    24  3.3.3.7.7.11.13.29.37.43.101.127.239.281.1933.2689.4649.9901.226549.459691.909091.10838689.121499449.445819\
            2223320340849
  85     9  3.3.41.271.2071723.262533041.5363222357.8119594779271.4222100119405530170179331190291488789678081
  86    10  3.3.11.173.1527791.57009401.2182600451.1963506722254397.2140992015395526641.7306116556571817748755241
  87    12  3.3.3.37.3191.4003.16763.43037.62003.72559.77843839397.310170251658029759045157793237339498342763245483
  88    17  3.3.11.11.23.73.89.101.137.617.4093.8779.21649.513239.1052788969.1056689261.1620583484601296758492708265640\
            2106953
  89     7  3.3.497867.103733951.104984505733.5078554966026315671444089.403513310222809053284932818475878953159
  90    24  3.3.3.3.7.11.13.19.31.37.41.211.241.271.2161.9091.29611.52579.238681.333667.2906161.3762091.8985695684401.4\
            185502830133110721
  91    14  3.3.53.79.239.547.4649.14197.17837.4262077.265371653.43442141653.316877365766624209.11074218647053005429131\
            8013
  92    12  3.3.11.47.101.139.1289.2531.18371524594609.549797184491917.11111111111111111111111.418100330007166986793265\
            8901
  93     8  3.3.3.37.2791.6943319.57336415063790604359.900900900900900900900900900900990990990990990990990990990991
  94     8  3.3.11.6299.35121409.4855067598095567.297262705009139006771611927.316362908763458525001406154038726382279
  95    10  3.3.41.191.271.59281.63841.1111111111111111111.1289981231950849543985493631.9651946171216407914560703479517\
            51
  96    24  3.3.3.7.11.13.17.37.73.97.101.137.353.449.641.1409.9901.69857.206209.5882353.99990001.66554101249.751183130\
            82913.9999999900000001
  97     5  3.3.12004721.846035731396919233767211537899097169.109399846855370537540339266842070119107662296580348039
  98    10  3.3.11.197.239.4649.909091.505885997.1976730144598190963568023014679333.50761416243655329949187817263959390\
            35533
  99    14  3.3.3.3.37.67.199.397.21649.34849.333667.513239.1344628210313298373.362853724342990469324766235474268869786\
            311886053883
 100    19  3.3.11.41.101.251.271.3541.5051.9091.21401.25601.27961.60101.7019801.182521213001.14103673319201.7887594347\
            2201.1680588011350901
 101     5  3.3.4531530181816613234555190841.129063282232848961951985354966759.18998088572819375252842078421374368604969
 102    18  3.3.3.7.11.13.37.103.613.4013.210631.2071723.52986961.5363222357.21993833369.291078844423.13168164561429877.
            377526955309799110357
 103     5  3.3.1031.7034077.153211620887015423991278431667808361439217294295901387715486473457925534859044796980526236\
            853
 104    15  3.3.11.53.73.79.101.137.521.859.1580801.265371653.1058313049.1900381976777332243781.63252744020215074509062\
            2412245443923049201
 105    19  3.3.3.31.37.41.43.71.239.271.1933.4649.123551.2906161.10838689.30703738801.625437743071.102598800232111471.
            57802050308786191965409441
 106     8  3.3.11.107.1659431.1325815267337711173.47198858799491425660200071.90909090909090909090909090909090909090909\
            09090909091
 107    10  3.3.643.999809.9885089.215257037.2386760191.511399538427507881.646826950155548399.1028807946722253879130231\
            1556310051849
 108    22  3.3.3.3.3.7.11.13.19.37.101.109.757.9901.52579.153469.333667.70541929.14175966169.999999000001.440334654777\
            631.59779577156334533866654838281
 109     6  3.3.1192679.712767480971213008079.5295275348767234696493.24682974398435543596240839091037821853728210515008\
            6881669547
 110    20  3.3.11.11.23.41.271.331.1321.4093.5171.8779.9091.21649.62921.513239.83251631.20163494891.318727841165674579\
            776721.1300635692678058358830121
 111    11  3.3.3.37.37.2028119.247629013.30557051518647307.2212394296770203368013.8845981170865629119271997.9007781439\
            6055017938257237117
 112    19  3.3.11.17.29.73.101.113.137.239.281.4649.7841.909091.5882353.121499449.73765755896403138401.127522001020150\
            503761.119968369144846370226083377
 113     5  3.3.227.908191467191.53895712312217719065267103426685397298498705173449226555003346881878523705781079015749\
            721646701723
 114    14  3.3.3.7.11.13.37.21319.1458973.10749631.909090909090909091.1111111111111111111.3931123022305129377976519.75\
            3201806271328462547977919407
 115    10  3.3.41.271.31511.19707665921.20414137203567631.11111111111111111111111.5799951513941382144830754391.1224035\
            69491783662720773144041
 116    15  3.3.11.59.101.349.3191.16763.38861.43037.62003.618049.77843839397.154083204930662557781201849.1181180637520\
            1836408679635736258669583187541
 117    14  3.3.3.3.37.53.79.333667.265371653.240396841140769.537947698126879.3352825314499987.900900900900990990990991.
            2304017384484085131816292573
 118     8  3.3.11.1889.2559647034361.1090805842068098677837.4411922770996074109644535362851087.43408762856574602121445\
            34289928559826755746751
 119    10  3.3.239.4649.923441.2071723.5363222357.3924966376871.768736559421401249042753476963.32301294214856275165081\
            4544437350454640448842187
 120    28  3.3.3.7.11.13.31.37.41.61.73.101.137.211.241.271.2161.3541.9091.9901.27961.1676321.2906161.4188901.39526741.
            99990001.5964848081.100009999999899989999000000010001
 121     8  3.3.15973.21649.38237.274187.513239.59714917620953041236079539149765734015994342199250253823083148168223296\
            9649167277637825641074323
 122    12  3.3.11.733.4637.81131.329401.974293.1360682471.106007173861643.7061709990156159479.112052225301168368553215\
            28257890437575145023592596037161
 123    12  3.3.3.37.83.1231.538987.1811791.626920594693.9425856976319889649.201763709900322803748657942361.84146400034\
            65161203119978906558054839526493
 124    10  3.3.11.101.2791.2049349.6943319.57336415063790604359.909090909090909090909090909091.48312854955451223730555\
            4588359039822397307149685578249
 125    11  3.3.41.271.751.21401.25601.1797655751.182521213001.176144543406001.4205177580495630455981085900830581997519\
            9677041099230574273451704628125001
 126    28  3.3.3.3.7.7.11.13.19.37.43.127.239.1933.2689.4649.10837.23311.45613.52579.333667.459691.909091.5274739.1083\
            8689.45121231.1921436048294281.189772422673235585874485732659
 127     5  3.3.18797.90679.6518718497852438209581196842331429821705369381473495010499558754235443718885196321031597538\
            36519854149224951224466197
 128    20  3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.1265011073.834427406578561.1534316\
            8188889137818369.515217525265213267447869906815873
 129    11  3.3.3.37.173.1527791.210769832431.1963506722254397.2140992015395526641.407429732767505248479163.10490974994\
            611747848197172839956039870723832569747
 130    15  3.3.11.41.53.79.131.271.859.9091.265371653.1058313049.162503518711.5538396997364024056286510640780600481.83\
            96862596258693901610602298557167100076327481
 131    11  3.3.80173.109517.141811693.446790173.7370364319027.15594845538029429933.7317723970031057677693.131758351065\
            116151205213.180222062287834025451247081
 132    25  3.3.3.7.11.11.13.23.37.67.89.101.4093.8779.9901.21649.513239.599144041.1052788969.1056689261.5419170769.183\
            411838171.789390798020221.2361000305507449.1344628210313298373
 133     8  3.3.239.1597.4649.2021015460335957.1111111111111111111.2788482998620431437549076793905857765163930062352097\
            86029420958416508667488018611321233079
 134     7  3.3.11.493121.79863595778924342083.28213380943176667001263153660999177245677.909090909090909090909090909090\
            909090909090909090909090909090909091
 135    20  3.3.3.3.3.31.37.41.271.757.238681.333667.1577071.2906161.16357951.310362841.258360989311.440334654777631.41\
            85502830133110721.483418418597220677238517353915231961831
 136    16  3.3.11.73.101.103.137.4013.2071723.28559389.152533657.1491383821.5363222357.21993833369.2324557465671829.65\
            552746171882583264230070868884366877803237222654400793
 137     7  3.3.2467.2535528323.1029879756928762117455431.140175894162990609843314797.123043880137417667485877804096702\
            26810319992722055173127328805633899245853
 138    18  3.3.3.7.11.13.37.47.139.277.2531.31051.143574021480139.203864078068831.549797184491917.11111111111111111111\
            111.24649445347649059192745899.1595352086329224644348978893
 139     4  3.3.119124859925363.932728157504043594282003041661807385390618120638384597314097345431032571052315101287361\
            4569275960380714495413018734336834397
 140    25  3.3.11.29.41.71.101.239.271.281.421.3541.4649.9091.27961.123551.909091.3471301.4147571.13489841.121499449.6\
            0368344121.102598800232111471.265212793249617641.848654483879497562821
 141     9  3.3.3.37.283.35121409.721030498171501831.316362908763458525001406154038726382279.44150634648836004848211413\
            5141919313523563714948107161215664533500695867
 142     7  3.3.11.290249.241573142393627673576957439049.45994811347886846310221728895223034301839.31321069464181068355\
            415209323405389541706979493156189716729115659
 143    11  3.3.53.79.21649.513239.2823679.180523201.265371653.47428676444591705727929369346443.37226581283489953701472\
            184267606576037130878873797366013283473311751294203
 144    25  3.3.3.3.7.11.13.17.19.37.73.101.137.3169.8929.9901.52579.98641.333667.5882353.99990001.999999000001.3199044\
            596370769.9999999900000001.111994624258035614290513943330720125433979169
 145    13  3.3.41.271.3191.16763.43037.62003.9605671.77843839397.15589280974996818911.80684370001269698853996151670133\
            742711.744909731145732233993613931089059528977143716201
 146     9  3.3.11.293.12171337159.1855193842151350117.10826684964539959837294043117.2865788889761949979999225923309086\
            02103011.49207341634646326934001739482502131487446637
 147    16  3.3.3.37.43.239.1933.4649.63799.4715467.10838689.505885997.267652966241599.2603941883787374089.197673014459\
            8190963568023014679333.4769337181464959147997704753876850429427
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