Factorisations Of Cunningham Numbers C-(11,n) = 11n - 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  2.5
   2     5  2.2.2.3.5
   3     4  2.5.7.19
   4     7  2.2.2.2.3.5.61
   5     4  2.5.5.3221
   6     9  2.2.2.3.3.5.7.19.37
   7     4  2.5.43.45319
   8     9  2.2.2.2.2.3.5.61.7321
   9     5  2.5.7.19.1772893
  10     8  2.2.2.3.5.5.3221.13421
  11     4  2.5.15797.1806113
  12    13  2.2.2.2.3.3.5.7.13.19.37.61.1117
  13     4  2.5.1093.3158528101
  14     8  2.2.2.3.5.43.45319.1623931
  15     7  2.5.5.7.19.3221.195019441
  16    12  2.2.2.2.2.2.3.5.17.61.7321.6304673
  17     3  2.5.50544702849929377
  18    12  2.2.2.3.3.3.5.7.19.37.590077.1772893
  19     3  2.5.6115909044841454629
  20    11  2.2.2.2.3.5.5.61.3221.13421.212601841
  21    10  2.5.7.7.19.43.1723.8527.27763.45319
  22    11  2.2.2.3.5.23.89.199.15797.58367.1806113
  23     5  2.5.829.28878847.3740221981231
  24    17  2.2.2.2.2.3.3.5.7.13.19.37.61.1117.7321.10657.20113
  25     8  2.5.5.5.3001.3221.24151.1856458657451
  26    10  2.2.2.3.5.53.911.1093.59583967.3158528101
  27     6  2.5.7.19.1772893.5559917315850179173
  28    13  2.2.2.2.3.5.29.43.61.1933.45319.1623931.55527473
  29     4  2.5.523.303309617049998388989376043
  30    15  2.2.2.3.3.5.5.7.19.31.37.3221.13421.7537711.195019441
  31     5  2.5.50159.2428541.157571957584602258799
  32    15  2.2.2.2.2.2.2.3.5.17.61.7321.51329.6304673.447600088289
  33     9  2.5.7.19.661.1453.15797.1806113.637265428480297
  34     9  2.2.2.3.5.71707.264793.2218331.50544702849929377
  35     8  2.5.5.43.211.3221.45319.42437717969530394595211
  36    17  2.2.2.2.3.3.3.5.7.13.19.37.61.1117.590077.1772893.3138426605161
  37     6  2.5.2591.36855109.136151713.2615418118891695851
  38    10  2.2.2.3.5.191.229.83791.1390636259.6115909044841454629
  39    12  2.5.7.19.79.157.547.1093.84631.480091.32508061.3158528101
  40    15  2.2.2.2.2.3.5.5.41.61.3221.7321.13421.212601841.1120648576818041
  41     9  2.5.83.1231.27061.509221.14092193.29866451.840139875599
  42    17  2.2.2.3.3.5.7.7.19.37.43.1723.8527.27763.45319.1623931.3421169496361
  43     4  2.5.1416258521793067.42534656091583268045915654719
  44    15  2.2.2.2.3.5.23.61.89.199.15797.58367.251857.1806113.2649263870814793
  45     9  2.5.5.7.19.3221.1772893.195019441.9842332430037465033595921
  46    12  2.2.2.3.5.47.829.1013.241363.28878847.3740221981231.6493405343627
  47     5  2.5.2069.22666879066355177.18806327041824690595747113889
  48    24  2.2.2.2.2.2.3.3.5.7.13.17.19.37.61.97.241.1117.1777.7321.10657.20113.6304673.1106131489
  49     7  2.5.43.45319.510810301.1065264019.100641220283951395639601683
  50    14  2.2.2.3.5.5.5.3001.3221.13421.24151.46601.1856458657451.14436295738510501
  51     9  2.5.7.19.10711.457315063.15085812853.25994736109.50544702849929377
  52    13  2.2.2.2.3.5.53.61.911.1093.59583967.3158528101.9768997162071483134919121
  53     6  2.5.107.351497.6005113.6918082374901313855125397665325977135579
  54    16  2.2.2.3.3.3.3.5.7.19.37.379.590077.1772893.4889988840047743.5559917315850179173
  55    10  2.5.5.3221.15797.25301.39161.1806113.643170158708221.645654335737185721
  56    19  2.2.2.2.2.3.5.29.43.61.113.449.1933.2521.7321.45319.1623931.55527473.77001139434480073
  57     8  2.5.7.19.19.1047623475541.6115909044841454629.1412900479108654932024439
  58    10  2.2.2.3.5.59.523.10979607179423.204064664440913.303309617049998388989376043
  59     5  2.5.1181.70845409351.33083146850190391025301565142735000331370209599
  60    21  2.2.2.2.3.3.5.5.7.13.19.31.37.61.1117.3221.13421.7537711.195019441.212601841.46329453543600481
  61     5  2.5.440177.520518327319589.1461808298382111034194027645506019619578037
  62    12  2.2.2.3.5.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223
  63    16  2.5.7.7.19.43.127.1723.8317.8527.27763.45319.867259.1772893.106431697.316825425410373433
  64    19  2.2.2.2.2.2.2.2.3.5.17.61.193.257.7321.51329.6304673.447600088289.21283620033217629539178799361
  65     8  2.5.5.131.1093.3221.3158528101.673267426712748387612994804392183645147042355211
  66    22  2.2.2.3.3.5.7.19.23.37.67.89.199.661.1453.9439.15797.58367.991651.1806113.1169382127.637265428480297
  67     6  2.5.15277.2160349.76394148218203559.235335702141939072378977155172505285655211
  68    15  2.2.2.2.3.5.61.137.71707.264793.2218331.2481791513.9598959833.641625222857.50544702849929377
  69    10  2.5.7.19.139.829.28878847.8209475377.3740221981231.5283012903770196631383821046101707
  70    19  2.2.2.3.5.5.43.71.71.211.3221.7561.13421.17011.45319.1623931.1649341.10047871.42437717969530394595211
  71     7  2.5.1847.64327.159248456569.1273880539247.360426336941693434048414944508078750920763
  72    24  2.2.2.2.2.3.3.3.5.7.13.19.37.61.73.1117.7321.10657.20113.40177.590077.1772893.3138426605161.335833548731945\
            8201
  73     3  2.5.1051153199500053598403188407217590190707671147285551702341089650185945215953
  74    11  2.2.2.3.5.2591.36855109.136151713.2615418118891695851.2691614274040036601.10527743181888260981
  75    15  2.5.5.5.7.19.151.3001.3221.24151.59302051.195019441.1826934301.1856458657451.27665283091695977275201
  76    14  2.2.2.2.3.5.61.191.229.83791.1390636259.1990415149.6115909044841454629.15403468930064931175264655869
  77     8  2.5.43.15797.45319.1806113.593554036769.466345922275629775763320748688970211803553256223529
  78    23  2.2.2.3.3.5.7.19.37.53.79.157.313.547.911.1093.63649.84631.480091.32508061.59583967.3158528101.538953023961\
            943033
  79     5  2.5.317.185277551100523662054683911.31705898389348622756718888962810730367411163041955447
  80    20  2.2.2.2.2.2.3.5.5.17.41.61.3221.5281.7321.13421.6304673.212601841.1120648576818041.399806412551699044818733\
            915681
  81     9  2.5.7.19.1772893.139026457.5559917315850179173.14010692617072784593.88236431987113771637099217013
  82    15  2.2.2.3.5.83.1231.27061.509221.14092193.29866451.711628063.840139875599.1216150172449.479378523680060338823
  83     7  2.5.167.12119.178057577.52447614013.1442525225996981034595894901431683672700025887063977893738081
  84    26  2.2.2.2.3.3.5.7.7.13.19.29.37.43.61.1117.1723.1933.8527.19069.27763.45319.1623931.55527473.3421169496361.52\
            0799717831587692709
  85     8  2.5.5.3221.584916791.553393500180551.50544702849929377.12520270706155176007034654722092907499983681
  86     9  2.2.2.3.5.5333.1416258521793067.42534656091583268045915654719.9413099125139413690486707432096974989067
  87     9  2.5.7.19.523.398113.54415717.303309617049998388989376043.873360172275048609080552096817243827525632861
  88    21  2.2.2.2.2.3.5.23.61.89.199.353.7321.15797.58367.72689.251857.1806113.13585441.2649263870814793.129825679438\
            7169996154165633
  89     6  2.5.73111721.2103114787086589.4180235017418376525776333.75144689824702198592013444969850173811994737
  90    22  2.2.2.3.3.3.5.5.7.19.31.37.181.631.3221.13421.590077.1772893.7537711.195019441.86306335830799838011.9842332\
            430037465033595921
  91     7  2.5.43.1093.45319.3158528101.868721697058567435824108245607127696076153182930226460514053403127306646961
  92    18  2.2.2.2.3.5.47.61.829.1013.201757.241363.28878847.2004414397.3740221981231.6493405343627.24737721275161.656\
            943272596448809
  93    10  2.5.7.19.2791.3163.50159.2428541.157571957584602258799.3137876238000684620152119068677936364954475597711271\
            1197
  94    12  2.2.2.3.5.2069.844309.549524471.26097456317.22666879066355177.60699948346804199382437.188063270418246905957\
            47113889
  95     8  2.5.5.3221.67989221.6115909044841454629.180124441029509240214675551.709366429143448333528137335486039060202\
            91
  96    29  2.2.2.2.2.2.2.3.3.5.7.13.17.19.37.61.97.241.577.1117.1777.7321.10657.20113.51329.6304673.1106131489.4476000\
            88289.3659233404740477018363752843393
  97     5  2.5.389.4247091263.6266849507589571978149106488222106980975381364824424072801340422775737133656105189072051
  98    15  2.2.2.3.5.43.11467.45319.800171.1623931.176784259.510810301.1065264019.33761096386802842263303497.100641220\
            283951395639601683
  99    14  2.5.7.19.397.661.1453.2377.15797.1772893.1806113.1240500097.637265428480297.2599071362839584231023974669237\
            98834567695212357
 100    20  2.2.2.2.3.5.5.5.61.101.3001.3221.13421.24151.46601.212601841.1856458657451.2248313994601.14436295738510501.
            1993099906542710819727884501
 101     5  2.5.341459085477993311443.86408339296208914807632672776254957729.513767785847095403363378495505038747238330\
            8083
 102    20  2.2.2.3.3.5.7.19.37.103.10711.71707.264793.1348033.2218331.457315063.15085812853.25994736109.50544702849929\
            377.16576413357576409067287639
 103     6  2.5.24103.37723802531.995301206162659155091.202677471366153865787391434710952643545087969532720827000553398\
            46745091
 104    16  2.2.2.2.2.3.5.53.61.911.1093.7321.59583967.3158528101.9768997162071483134919121.970106078298260708735599372\
            68360584022789501553441
 105    21  2.5.5.7.7.19.43.211.421.1723.3221.8527.27763.45319.540751.599551.2598121.126713791.195019441.23731414400247\
            02184811.42437717969530394595211
 106    13  2.2.2.3.5.107.1697.351497.5353637.6005113.17148893.8357265774463208206521728596439861293.691808237490131385\
            5125397665325977135579
 107     5  2.5.1276033068038437.304971297664201988898688683700564748747693245597.6900751922429791724019506627192737704\
            11957106853
 108    25  2.2.2.2.3.3.3.3.5.7.13.19.37.61.109.379.541.1117.590077.1772893.388174681.3138426605161.4889988840047743.55\
            59917315850179173.1350472353550875103121929
 109     4  2.5.35970728459102446279558069.9033445926510666398384928207099769878625683305416602322341095021068020592318\
            51745003701
 110    23  2.2.2.3.5.5.23.89.199.3221.4951.13421.15797.25301.39161.58367.411841.1806113.21537414911.85480219991.131525\
            983711.643170158708221.645654335737185721
 111    10  2.5.7.19.2591.36855109.136151713.2615418118891695851.651950416864148392635280596760630561.13334983829534655\
            64843320786357871664401
 112    26  2.2.2.2.2.2.3.5.17.29.43.61.113.337.449.1933.2521.7321.45319.394129.1623931.6304673.55527473.77001139434480\
            073.236352238647181441.3090443962383595123379137
 113     7  2.5.227.45902861.20884152591287817709.22455907106840364577416382241618449.973554682812876324986927406779613\
            27574083833285959459
 114    20  2.2.2.3.3.5.7.19.19.37.191.229.6043.75013.83791.1390636259.1047623475541.6115909044841454629.14129004791086\
            54932024439.74337838382167137728921322559
 115    12  2.5.5.829.3221.95911.333041.9964291.28878847.3740221981231.17184010031686356151.729842693308300425195832421\
            6375350400730975973787843051
 116    16  2.2.2.2.3.5.59.61.349.523.16585333.32637413.10979607179423.204064664440913.303309617049998388989376043.1091\
            81877624126996017801852385627698243261
 117    16  2.5.7.19.79.157.547.1093.9127.84631.480091.1772893.1810693.32508061.3158528101.5777953519959062358597260246\
            2371982722687354954780675870640496251
 118    12  2.2.2.3.5.1181.22067.70845409351.32833036072593109.59845177539010249.53199025841281128499153.33083146850190\
            391025301565142735000331370209599
 119     9  2.5.43.239.45319.20580793913.50544702849929377.5787647502138040836760695667.3005681893232976654385404271528\
            23770594407695480022422691549
 120    29  2.2.2.2.2.3.3.5.5.7.13.19.31.37.41.61.1117.3221.7321.10657.13421.20113.7537711.195019441.212601841.52020741\
            601.1120648576818041.46329453543600481.40589999671017742452961
 121     8  2.5.15797.30977.1806113.1595696213.12407691244609.582793661124452623809041107212020076078733754671394043885\
            9172127240114655549487246036729
 122    11  2.2.2.3.5.440177.53320740257.520518327319589.137218978667473446671.38147158686655703132426388314683.1461808\
            298382111034194027645506019619578037
 123    15  2.5.7.19.83.1231.27061.174907.509221.14092193.28385941.29866451.840139875599.142971820992006871646588679396\
            397417.262535239929018061575878552691659119
 124    16  2.2.2.2.3.5.61.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223.431167290104638379\
            6549.70039146133823870629334170297294343364149
 125    12  2.5.5.5.5.3001.3221.24151.1632185486501.1856458657451.27678437808551251.61008089514108496781935498867728405\
            0229269951248774263726574682822715310251
 126    29  2.2.2.3.3.3.5.7.7.19.37.43.127.1723.8317.8527.27763.45319.590077.867259.1623931.1772893.3304981.106431697.4\
            68843103.71596275661.278853374647.3421169496361.316825425410373433
 127     6  2.5.2985212831443.6073732108394141.108345618426999904901.91966303295251191104971960132273397364144023351465\
            750399992554753980589155137853599
 128    22  2.2.2.2.2.2.2.2.2.3.5.17.61.193.257.7321.51329.6304673.447600088289.316955440822738177.21283620033217629539\
            178799361.7032401262704707649518767703756385761576062060673
 129    12  2.5.7.19.1549.1389891409.2338110553.44012945778511.1416258521793067.3440126314390780951.4253465609158326804\
            5915654719.3579868931117378066463082728904957
 130    18  2.2.2.3.5.5.53.131.911.1093.1301.3221.13421.25741.59583967.3158528101.3160327139569513638485230516120919120\
            957201.673267426712748387612994804392183645147042355211
 131     5  2.5.263.7791763956749016154215607697892626144401.1290774032138704646634687668236941308305597514202044201343\
            330196757304660698533426132941183587
 132    30  2.2.2.2.3.3.5.7.13.19.23.37.61.67.89.199.661.1117.1453.9439.15797.58367.251857.991651.1806113.1169382127.98\
            63099401.637265428480297.2649263870814793.46266666682081629547022793157801
 133     9  2.5.43.45319.292601.1889399.4085166784889.6115909044841454629.118907173249316196764766639893383431910454776\
            99764476320956042082843152214319805595150031
 134    15  2.2.2.3.5.269.15277.181303.2160349.2354458793.2778466094669.76388592846687031.76394148218203559.20288347913\
            774902979279.235335702141939072378977155172505285655211
 135    12  2.5.5.7.19.271.3221.1772893.195019441.5559917315850179173.9842332430037465033595921.35261764476828649109379\
            34141934983258605489440194538631398471107422118591
 136    22  2.2.2.2.2.3.5.61.137.409.7321.11969.71707.264793.2218331.2481791513.9598959833.641625222857.739755736441.14\
            387579997041.50544702849929377.85554906358182623545481335980971521
 137     8  2.5.8221.339761.3677081.136238281.394711476243912154244261783.848433067196473533441008868772447888723971966\
            6748414214743814637516122598288562123255444499
 138    24  2.2.2.3.3.5.7.19.37.47.139.691.829.1013.241363.28878847.394648951.8209475377.18013255921.932225927887.15773\
            86579003.3740221981231.6493405343627.5283012903770196631383821046101707
 139     3  2.5.5670002325217957396258282812671713444868053858812175750811496601630462174655445733557105920797699326519\
            89153833612198334843467861091902034340949
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