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     3  2.2.3
   2     2  2.61
   3     5  2.2.3.3.37
   4     2  2.7321
   5     4  2.2.3.13421
   6     4  2.13.61.1117
   7     4  2.2.3.1623931
   8     3  2.17.6304673
   9     7  2.2.3.3.3.37.590077
  10     3  2.61.212601841
  11     7  2.2.3.23.89.199.58367
  12     4  2.7321.10657.20113
  13     6  2.2.3.53.911.59583967
  14     5  2.29.61.1933.55527473
  15     8  2.2.3.3.31.37.13421.7537711
  16     3  2.51329.447600088289
  17     6  2.2.3.71707.264793.2218331
  18     5  2.13.61.1117.3138426605161
  19     7  2.2.3.191.229.83791.1390636259
  20     4  2.41.7321.1120648576818041
  21     7  2.2.3.3.37.1623931.3421169496361
  22     4  2.61.251857.2649263870814793
  23     7  2.2.3.47.1013.241363.6493405343627
  24     7  2.17.97.241.1777.6304673.1106131489
  25     6  2.2.3.13421.46601.14436295738510501
  26     3  2.61.9768997162071483134919121
  27    10  2.2.3.3.3.3.37.379.590077.4889988840047743
  28     6  2.113.449.2521.7321.77001139434480073
  29     6  2.2.3.59.10979607179423.204064664440913
  30     6  2.13.61.1117.212601841.46329453543600481
  31     7  2.2.3.311.1303.10789.3658524738455131951223
  32     4  2.193.257.21283620033217629539178799361
  33    13  2.2.3.3.23.37.67.89.199.9439.58367.991651.1169382127
  34     6  2.61.137.2481791513.9598959833.641625222857
  35    11  2.2.3.71.71.7561.13421.17011.1623931.1649341.10047871
  36     7  2.73.7321.10657.20113.40177.3358335487319458201
  37     5  2.2.3.2691614274040036601.10527743181888260981
  38     4  2.61.1990415149.15403468930064931175264655869
  39    11  2.2.3.3.37.53.313.911.63649.59583967.538953023961943033
  40     5  2.17.5281.6304673.399806412551699044818733915681
  41     6  2.2.3.711628063.1216150172449.479378523680060338823
  42     9  2.13.29.61.1117.1933.19069.55527473.520799717831587692709
  43     5  2.2.3.5333.9413099125139413690486707432096974989067
  44     6  2.353.7321.72689.13585441.1298256794387169996154165633
  45    13  2.2.3.3.3.31.37.181.631.13421.590077.7537711.86306335830799838011
  46     6  2.61.201757.2004414397.24737721275161.656943272596448809
  47     7  2.2.3.844309.549524471.26097456317.60699948346804199382437
  48     5  2.577.51329.447600088289.3659233404740477018363752843393
  49     8  2.2.3.11467.800171.1623931.176784259.33761096386802842263303497
  50     6  2.61.101.212601841.2248313994601.1993099906542710819727884501
  51    11  2.2.3.3.37.103.71707.264793.1348033.2218331.16576413357576409067287639
  52     3  2.7321.97010607829826070873559937268360584022789501553441
  53     7  2.2.3.1697.5353637.17148893.8357265774463208206521728596439861293
  54     9  2.13.61.109.541.1117.388174681.3138426605161.1350472353550875103121929
  55    13  2.2.3.23.89.199.4951.13421.58367.411841.21537414911.85480219991.131525983711
  56     7  2.17.337.394129.6304673.236352238647181441.3090443962383595123379137
  57    12  2.2.3.3.37.191.229.6043.75013.83791.1390636259.74337838382167137728921322559
  58     6  2.61.349.16585333.32637413.109181877624126996017801852385627698243261
  59     7  2.2.3.22067.32833036072593109.59845177539010249.53199025841281128499153
  60     8  2.41.7321.10657.20113.52020741601.1120648576818041.40589999671017742452961
  61     6  2.2.3.53320740257.137218978667473446671.38147158686655703132426388314683
  62     4  2.61.4311672901046383796549.70039146133823870629334170297294343364149
  63    13  2.2.3.3.3.37.590077.1623931.3304981.468843103.71596275661.278853374647.3421169496361
  64     3  2.316955440822738177.7032401262704707649518767703756385761576062060673
  65    10  2.2.3.53.911.1301.13421.25741.59583967.3160327139569513638485230516120919120957201
  66     8  2.13.61.1117.251857.9863099401.2649263870814793.46266666682081629547022793157801
  67     9  2.2.3.269.181303.2354458793.2778466094669.76388592846687031.20288347913774902979279
  68     7  2.409.7321.11969.739755736441.14387579997041.85554906358182623545481335980971521
  69    14  2.2.3.3.37.47.691.1013.241363.394648951.18013255921.932225927887.1577386579003.6493405343627
  70     8  2.29.61.1933.2970941.55527473.212601841.32925268156330499785365829732750601117816501
  71     6  2.2.3.149852362577.5604196051154865381517.8620302099267300875307522246691084877239
  72    10  2.17.97.241.1777.110161.331921.6304673.1106131489.2653299576575651630603169124592864247361
  73     8  2.2.3.668243.147031637.51866303408957.9863258277206753.17427450503923264964680282877251
  74     8  2.61.149.243595717.254246981.3275634569.5555901630889277.5643352212924479303509278380689
  75    13  2.2.3.3.31.37.751.13421.46601.299401.7537711.14436295738510501.2012875525822725447651340174136551
  76     6  2.457.7321.35613601.52215193.1124384093561211759006825448167193716190524720926622040561
  77    12  2.2.3.23.89.199.58367.1623931.23577401.43037232701.160418704149053207551.2040583524866430994330651
  78    12  2.13.13.61.1117.7177.26833.225889.21493057.11771471409361.683665316878909.9768997162071483134919121
  79     7  2.2.3.7901.681676939.3238766178025207268898109882481893.88961197883605801425821968775222633
  80    10  2.641.2081.4001.51329.232961.447600088289.295090738600481.1037593750081121.11710273559942897538241
  81    14  2.2.3.3.3.3.3.37.163.379.590077.5705803.4889988840047743.61599809118365596724303287493080398613594222813
  82     5  2.61.2789.57073.1276324589909496813251127403760180491964358075504668934093870861051689695133
  83     6  2.2.3.325440677.47433880332031195178437273.1471807913921722283799977862411158403048843176734891
  84    11  2.113.449.2521.7321.10657.20113.201407641.70107576001.77001139434480073.6871280144418624289685328789001
  85     9  2.2.3.13421.34511.71707.264793.2218331.140915955794291381596090868811368536501646742211013295518273711
  86     5  2.61.173.11862832433.1449361076647763556046480383311898979520917866579543803095034909526729197869
  87    12  2.2.3.3.37.59.13399.7596493.1727522113.10979607179423.204064664440913.1289269224782205219032537855117489670\
            91
  88     8  2.17.3169.269281.6304673.2224106369.1409524185566665684709841121.76570022386531005372870206494246296641
  89    10  2.2.3.179.188606309.5089163291.75893828851.23510589261592841.371848407757843241773.353082502532286628861787
  90    11  2.13.61.1117.9001.16921.22501.212601841.3138426605161.46329453543600481.28309390942693823829766228460785185\
            421
  91     9  2.2.3.53.911.1623931.59583967.12343942084000822751.84451621887581647750880682185194110642059749383888588911
  92     5  2.7321.34961.324599369.3868967792250098248450110086386343042895409814136698442863741267447980557520249
  93    11  2.2.3.3.37.311.1303.10789.237843323473654847623.3658524738455131951223.139550866104193032581962716205911186\
            7514287
  94     7  2.61.1693.6678701.181894150853.1823151514157.170044315788568839331192444262564794666488196032760463244957137
  95    10  2.2.3.191.229.13421.83791.1390636259.125391374277955216479795494641.831364610304896938076192434596656578992\
            2617921
  96     9  2.193.257.2689.850177.7746049.13928006777524033.21283620033217629539178799361.18074341630577348555429415775\
            408321
  97     6  2.2.3.3881.200924352971689432250644561.11064530571690714453730400924822089371846415813484128967094900415848\
            041
  98     8  2.29.61.197.1933.55527473.33976720793233.448061744850569765386528729635682996109461034777276693515627127364\
            615221
  99    18  2.2.3.3.3.23.37.67.89.199.9439.58367.590077.991651.95885659.1169382127.166222146279939538766671.19118100293\
            995567795177984039909
 100     9  2.41.401.7321.2254601.5931105001.69084589801.1120648576818041.552947563691215268017880199633798414702158479\
            175508601
 101     7  2.2.3.20201.228104057.1732951869588220873.15819311422790435215889409528474122189791416412562996715979130823\
            153947141
 102    11  2.13.61.137.1117.2481791513.9598959833.641625222857.382645993638157.563620766036953.20841161015828740030207\
            016250006151501
 103     8  2.2.3.1237.51396929137.3842537250772226605747.128288938117946418355541.487698205182785810835005539128131683\
            672275286097
 104     5  2.17.6304673.86759222313428390812218077095850708048977.1084881048536374706129613998429729484098346115257905\
            77216753
 105    19  2.2.3.3.31.37.71.71.7561.13421.17011.1623931.1649341.7537711.10047871.275310421.137031343051.3421169496361.
            2359101627084759668315785103671
 106     7  2.61.410982353.23746234974173.22250800656016001.72744498860303958101.12667796019109754352066411884939323800\
            6955092974209
 107     5  2.2.3.841021.2660904118831225069351374903323531548627122700620087587591802861308909203624886230993288676031\
            12602644211
 108    10  2.73.433.7321.8209.10657.20113.40177.3358335487319458201.26884080018278857826967012292458876502681409920482\
            9048549907077238513
 109     6  2.2.3.11119.14389.16924860328413141214365629650474864848331631667162621285647949533748464809147546574145776\
            6540635771648351
 110    10  2.61.251857.1327481.212601841.36318547582241.110374378040081.2649263870814793.136371262802069831801.2846042\
            33173679136521738352001
 111    10  2.2.3.3.37.37.223.2691614274040036601.10527743181888260981.126249345637608650029153686851973084319021976823\
            501721176605898316609411
 112     8  2.10529.15233.51329.132833.447600088289.7782479531201887486913.56767692210863509237921611739434366077435616\
            458970709176918840577
 113     5  2.2.3.909877.4357220014122675184259919179380668633668941449742142981468187554807931862519633084677616319104\
            58201865781422893
 114     9  2.13.61.1117.1990415149.37820720459377.308673703543834165513.15403468930064931175264655869.8253119172808086\
            9985969416771354049347961
 115    11  2.2.3.47.1013.2531.13421.241363.6493405343627.558956737278445325461.338588199387527746331211270897090075844\
            65813794083046310289193779151
 116     7  2.233.7321.287681.60604269272032563100609.1502477990708696255525449.708553482774634872757217319786870088342\
            38471892366559611974577
 117    14  2.2.3.3.3.37.53.313.911.63649.590077.59583967.538953023961943033.956311769100660490503396992656891206874453\
            285835048997148999317765990784561
 118     6  2.61.1291321673.1013563312793953470363741024001073.64838817747578095323592827914385846481.74004240886932111\
            404174666525790714071569
 119    14  2.2.3.71707.264793.1623931.2218331.110917283.124214819.69796946717.256644509902201.63063653308203311.209145\
            6376138057349.315440418833726113081631
 120    14  2.17.97.241.1777.3121.5281.114001.6304673.1106131489.1698371041.12658046117876244394801.5828142647817387837\
            02162161.399806412551699044818733915681
 121    14  2.2.3.23.89.199.727.58367.122453.2095721.103569468207767.1663628038071022183838437.156316328176791781343592\
            9194983.71132117849274411458479346616793
 122     9  2.61.61.733.15373.19042493.615339081285269009.166945076296840267580084657135863728824204737.683822526820172\
            81321628552285946936349023283521
 123     9  2.2.3.3.37.711628063.1216150172449.479378523680060338823.22329407744580303934513868394925085808679300359256\
            5432816290249576309086373241746401
 124     8  2.1489.6449.7321.11161.5721113.92247817.1638950174786153691075952022215074731727187702580869943406736485973\
            251947792384699431022645116667161
 125    10  2.2.3.251.13421.46601.559001.14436295738510501.30877424283969568616368678353563069501.318083501938831797291\
            23443891378924908549472843225872344251
 126    14  2.13.29.61.1117.1933.2017.19069.21673.55527473.3138426605161.520799717831587692709.154021704779757520440774\
            8160801193.14192755503084386685349267103378497
 127     7  2.2.3.509.2140352083.4402640625848258016840688846660358437130425243742595514279.313887145284264795998540992\
            87726722553699547881667856766300787
 128     6  2.15361.111489577217.574341646346402207998363393.4018529583345312964042058778793458689.25138679918373623167\
            15332574077411130744618580176804609
 129     9  2.2.3.3.37.1291.5333.9413099125139413690486707432096974989067.253233817806661680794126682548488134256292565\
            2085779577235728569623852917746014092331
 130     6  2.61.521.212601841.9768997162071483134919121.18215223829103119871143009754672266047822632092109688566278477\
            058449896401786143420694541075159161
 131     6  2.2.3.9858799.119235724375228558113076040277225949839796708740043.18751244767116478769561770254758588183459\
            21167310635558927494336192342549513443
 132    11  2.353.7321.10657.20113.72689.13585441.57563039928769.504278350263601.1298256794387169996154165633.705716757\
            4674010261807047699037084178851570547276172529
 133    10  2.2.3.191.229.83791.1623931.1390636259.23204027016899114504903.13887854992134150485504500896345190378108653\
            21432371174936304520406104501526956813520954447
 134     6  2.61.47271776033.555596265747977.5653530366032833.194347524816188063157344917316163731510839472419689280815\
            3799712458776309964218037475956185945937
 135    19  2.2.3.3.3.3.31.37.181.379.631.13421.283771.590077.7537711.861465705211.4889988840047743.8630633583079983801\
            1.3909014919478257067611647254311892076465398578584589934681
 136     6  2.17.17.6304673.29584734433.3951364572165740533499223885379274688932880605900690343904021732819435255040666\
            3629632980855979005749712409762411371230481
 137     9  2.2.3.823.2467.12932527.666751384702583.33702237384570719055067.6618225834843701910882465020377513146074534\
            519708431589347550012959904179170066334607874103
 138    11  2.13.61.277.1117.201757.6128029.2004414397.24737721275161.656943272596448809.260813416520010869997945696781\
            73937248173282084703143498940836604277367886736092977
 139     7  2.2.3.48560832383207.23835478071413231.226911237770389320465096194749609274682969829.1799020021420670793955\
            452910062648782329345676350070250930470021301187
 140    11  2.41.113.281.449.2521.7321.1120648576818041.77001139434480073.7406965671094607547812305361.4522523011641833\
            124254190467380698665648996274963293418051231917039641
 141    11  2.2.3.3.37.2539.844309.549524471.26097456317.60699948346804199382437.27601121268595702663499475964138228754\
            9960710026365311501070014837044470192630725201808980699
 142     5  2.61.192553.6896695512898403271082223952161993974407591311981.465811407486640028940330582024245866580550375\
            64653708522157973308108576026344096114825014757
 143    20  2.2.3.23.53.89.199.859.911.2003.23167.36037.58367.59583967.2008696691.172626755159.303798181831.61915142248\
            6169.784071823409769959923.1376758841851098858192561441291859498245379
 144     8  2.577.3457.51329.114500564929.447600088289.3659233404740477018363752843393.23778845560226372843327820636243\
            112457967210053130898985010753129117249420547694635777
 145     9  2.2.3.59.13421.54521.10979607179423.204064664440913.8653719005168933795819192954442052944398178101271333803\
            063467458016405399722313222353196657036509056155169947241
 146     7  2.61.293.877.10851207624233.1642924373932604240398418631306800170146224088997.19770121700484944588827152871\
            7782524432344168525454840257403895055137223757102073861
 147    14  2.2.3.3.37.11467.800171.1623931.176784259.54447297367.3421169496361.593567588238393763.33761096386802842263\
            303497.92798096943647997760409196962615760375999913293276053417701
 148     5  2.1481.7321.10170146161160624507589185121238262249266667161256127057415217.60622626428062749376619618807622\
            668011972562662106003547080399907358442197151548735273
 149     7  2.2.3.1193.1530827.775322709138856254112793450158954494201167319485721463.865525327060749392778837283153902\
            5466268936040995557086831408002731188838672182099838786137
 150    11  2.13.61.101.1117.212601841.2248313994601.46329453543600481.7884604271247668072701.1993099906542710819727884\
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