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     1  11 [1st Prime]
   2     1  101 [2nd Prime]
   3     3  7.11.13
   4     2  73.137
   5     2  11.9091
   6     2  101.9901
   7     2  11.909091
   8     2  17.5882353
   9     5  7.11.13.19.52579
  10     3  101.3541.27961
  11     5  11.11.23.4093.8779
  12     3  73.137.99990001
  13     3  11.859.1058313049
  14     4  29.101.281.121499449
  15     7  7.11.13.211.241.2161.9091
  16     5  353.449.641.1409.69857
  17     4  11.103.4013.21993833369
  18     3  101.9901.999999000001
  19     2  11.909090909090909091
  20     4  73.137.1676321.5964848081
  21     8  7.7.11.13.127.2689.459691.909091
  22     4  89.101.1052788969.1056689261
  23     5  11.47.139.2531.549797184491917
  24     3  17.5882353.9999999900000001
  25     5  11.251.5051.9091.78875943472201
  26     3  101.521.1900381976777332243781
  27     7  7.11.13.19.52579.70541929.14175966169
  28     4  73.137.7841.127522001020150503761
  29     3  11.59.154083204930662557781201849
  30     7  61.101.3541.9901.27961.4188901.39526741
  31     2  11.909090909090909090909090909091
  32     4  19841.976193.6187457.834427406578561
  33     9  7.11.11.13.23.4093.8779.599144041.183411838171
  34     4  101.28559389.1491383821.2324557465671829
  35     5  11.9091.909091.4147571.265212793249617641
  36     6  73.137.3169.98641.99990001.3199044596370769
  37     4  11.7253.422650073734453.296557347313446299
  38     3  101.722817036322379041.1369778187490592461
  39    10  7.11.13.13.157.859.6397.216451.1058313049.388847808493
  40     4  17.5070721.5882353.19721061166646717498359681
  41     3  11.2670502781396266997.3404193829806058997303
  42     7  29.101.281.9901.226549.121499449.4458192223320340849
  43     4  11.57009401.2182600451.7306116556571817748755241
  44     4  73.137.617.16205834846012967584927082656402106953
  45    12  7.11.13.19.211.241.2161.9091.29611.52579.3762091.8985695684401
  46     4  101.1289.18371524594609.4181003300071669867932658901
  47     4  11.6299.4855067598095567.297262705009139006771611927
  48     9  97.353.449.641.1409.69857.206209.66554101249.75118313082913
  49     4  11.197.909091.5076141624365532994918781726395939035533
  50     7  101.3541.27961.60101.7019801.14103673319201.1680588011350901
  51     8  7.11.13.103.4013.21993833369.291078844423.377526955309799110357
  52     4  73.137.1580801.632527440202150745090622412245443923049201
  53     2  11.9090909090909090909090909090909090909090909090909091
  54     6  101.109.9901.153469.999999000001.59779577156334533866654838281
  55    10  11.11.23.331.4093.5171.8779.9091.20163494891.318727841165674579776721
  56     5  17.113.5882353.73765755896403138401.119968369144846370226083377
  57     6  7.11.13.1458973.909090909090909091.753201806271328462547977919407
  58     5  101.349.38861.618049.11811806375201836408679635736258669583187541
  59     4  11.1889.1090805842068098677837.4411922770996074109644535362851087
  60     6  73.137.1676321.99990001.5964848081.100009999999899989999000000010001
  61     3  11.81131.11205222530116836855321528257890437575145023592596037161
  62     3  101.2049349.483128549554512237305554588359039822397307149685578249
  63    12  7.7.11.13.19.127.2689.52579.459691.909091.5274739.189772422673235585874485732659
  64     3  1265011073.15343168188889137818369.515217525265213267447869906815873
  65     6  11.131.859.9091.1058313049.8396862596258693901610602298557167100076327481
  66     8  89.101.9901.1052788969.1056689261.5419170769.789390798020221.2361000305507449
  67     2  11.909090909090909090909090909090909090909090909090909090909090909091
  68     4  73.137.152533657.65552746171882583264230070868884366877803237222654400793
  69    10  7.11.13.47.139.2531.31051.143574021480139.549797184491917.24649445347649059192745899
  70    11  29.101.281.421.3541.27961.3471301.13489841.121499449.60368344121.848654483879497562821
  71     3  11.290249.31321069464181068355415209323405389541706979493156189716729115659
  72     5  17.8929.5882353.9999999900000001.111994624258035614290513943330720125433979169
  73     4  11.293.10826684964539959837294043117.286578888976194997999922592330908602103011
  74     7  101.149.3109.111149.708840373781.669031686661427842829.40548140514062774758071840361
  75    11  7.11.13.211.241.251.2161.5051.9091.78875943472201.10000099999999989999899999000000000100001
  76     6  73.137.457.1403417.5240808656722481737.297478330786365628414805305290302483555043017
  77    12  11.11.23.463.4093.8779.24179.590437.909091.7444361.4539402627853030477.4924630160315726207887
  78     7  101.521.3121.9901.53397071018461.1900381976777332243781.6060517860310398033985611921721
  79     4  11.1423.9615060929.66443174541490579097997510158021076958392938976011506949065646573
  80     9  353.449.641.1409.69857.1634881.18453761.947147262401.349954396040122577928041596214187605761
  81    11  7.11.13.19.1459.52579.70541929.2458921051.14175966169.456502382570032651.610600386089858349939139
  82     3  101.68389.1447745997018511893740076606031686237538345362413531560645573104006506749609
  83     7  11.167.997.3565183.2097307081.7742098247001476863.943176903141330068482602900960294299878841
  84     8  73.137.7841.99990001.11189053009.603812429055411913.127522001020150503761.148029423400750506553
  85     8  11.103.4013.9091.87211.787223761.21993833369.160220794821014452066741918303580917664386555934641
  86     3  101.338669.2923500556298303355222653948542706598448925085853709961673200056984872843366529
  87     8  7.11.13.59.638453709757.135080726389891.154083204930662557781201849.1274194732898148471766404179653
  88     4  17.5882353.10100113.9900879227786858424257223656804730798555422102713108259184822982673560177
  89     4  11.179.12147237304901893.4180967272673252032291190917188955510245874180001164839931077197586653
  90    11  61.101.181.3541.9901.27961.4188901.39526741.999999000001.4999437541453012143121.1105097795002994798105101
  91     6  11.859.909091.21705503.1058313049.50678387411703889101759125785290439894389920385627096501794498837
  92     4  73.137.2393.4178437150016715837818641871709193476807772628503969494400330129962348520684914375257
  93     8  7.11.13.373.44641.3590254957.909090909090909090909090909091.18381907262281244633158190677786966663091011
  94     4  101.45121.2144906157509411684424913774078958939881.1023037643093214557651333120422980213172396059301
  95     6  11.9091.1812604116731.121450506296081.909090909090909091.4996731930447843676185843959746621491531100801
  96     8  193.769.19841.976193.6187457.834427406578561.1253224535459902849.53763491189967221358575546107279034709697
  97     4  11.102527361354613106010527.323338434891034089173475790125293.27422699366054621683295623079471066588881
  98     5  29.101.281.121499449.999999999999990000000000000099999999999999000000000000009999999999999900000000000001
  99    13  7.11.11.13.19.23.4093.8779.52579.599144041.7093127053.183411838171.1411225248778861822822335393177961449383\
            05111168717
 100     8  73.137.401.1201.1601.1676321.5964848081.1296944190290577505513857711845642744990757009476567578215372915271\
            96801
 101     6  11.607.809.1213.1327067281.11500490394117824585468796003575163076836624586334794818271756072956027758946488\
            969
 102    11  101.409.3061.9901.5969449.28559389.134703241.1491383821.225974065503889.2324557465671829.443980004790079975\
            69751764249
 103     8  11.1237.44092859.102860539.984385009.612053256358933.182725114866521155647161.14718654539938553026608876141\
            37521979
 104     8  17.1249.49297.300977.648961.5882353.249227787818677482257.3336327664384090112747059870264076396700423055367\
            43429073
 105    17  7.7.11.13.127.211.241.2161.2689.9091.459691.909091.4147571.29970369241.1661378260814161.265212793249617641.
            18276168846821336356291
 106     5  101.1061.5051749.245391150214875249502685807421982149521.75277048352808729626679875852901448034540173569840\
            168229
 107     7  11.1499.28463.74687.392263.795653.9140689231828972552925524522037823147045937571379494322686226282352288670\
            801988451
 108     8  73.137.3169.98641.99990001.3199044596370769.1726290008991504500177463302688697.5792769434981542821236869998\
            81829009033
 109     4  11.3338786746233023.14060959683864286267405933000927102019.193643833211487192951805788533257418558589878486\
            20134943
 110    12  89.101.661.3541.18041.27961.148721.1052788969.1056689261.1121407321.1395900370916327245555441901.3638054502\
            9953205956377406702261
 111    10  7.11.13.223.4663.7253.422650073734453.296557347313446299.21606064498691505246200058094681.48911689110891303\
            706174193415115219
 112     9  353.449.641.673.1409.69857.43735845217.217860610452031121598489279950204653537.1559440092962140541006269160\
            03794407157304353
 113     4  11.4973.4426889.4129431088139783859996416179822426674855191197099407119426935537095172401142816292556850105\
            53886849303
 114    11  101.229.2281.4789.9901.304077901.52875286008709.722817036322379041.739653893349540289.1369778187490592461.3\
            3950736420661075851541
 115     8  11.47.139.691.2531.9091.549797184491917.1591879884384947756889998393793196655587713298134746583069625164819\
            2619376266439940521
 116     7  73.137.233.355193.21591416633.17468739848498438039329935679794457.32032699416316994338429506699243931665584\
            0979654890345228609
 117    15  7.11.13.13.19.157.859.6397.52579.216451.461917.60034573.1058313049.388847808493.360968001568288955682865782\
            24818258719817914995401933354161
 118     3  101.430148941.230175856669373992253976277974612031182496625023886807386072581333871027940087154579555293851\
            089822885094561
 119     8  11.103.4013.909091.1868879293.21993833369.5673320472670315859129.103746647830421551242486430622636901002236\
            971549990724717454338463
 120     8  17.5070721.5882353.1132716961.9999999900000001.19721061166646717498359681.281259985248437790051014401.31388\
            506438433752927908678241
 121    11  11.11.11.23.4093.4357.8779.25169.1485397.102502981431359171598893.54447100137257929633229165267564677464420\
            8265246405598834086237345292487
 122     5  101.1587221.81183810541.101444162656037151745878558385892753596849.7574338876826097411632784892018433752805\
            9461788181539337429709
 123     9  7.11.13.739.148339.16419517.2670502781396266997.3404193829806058997303.610517960355229692711712748765541785\
            04544683763248923853725596423
 124     7  73.137.1489.640543322297.27908132670449.384705444182230291105649.976459546680188464672871808663557583742631\
            20864803042536883990817097
 125     9  11.251.5051.9091.21001.162251.10893295001.78875943472201.26940979287173162766458619466228123385370101110890\
            6726055753272681082282441709251
 126    11  29.101.281.1009.9901.226549.121499449.43266855241.999999000001.4458192223320340849.229062468964372312278995\
            75633620139766044690040039603689929
 127     8  11.3557.857772733.1094479651.1125629957.616896149073719728613.10860110813777339731289.360995312736031382186\
            99301565567581705151216702113889
 128     4  257.15361.453377.558711876337536212257947750090161313464308422534640474631571587847325442162307811652237021\
            55223678309562822667655169
 129     8  7.11.13.57009401.2182600451.7306116556571817748755241.304768036847074491064894608014695867632997.3605696680\
            890791382725432167911038465896663
 130    10  101.521.3541.27961.2311921.1031498834064949381.12763852652999774041.1900381976777332243781.1211973050456797\
            7254081.2737820036624672031089487008281
 131     7  11.263.1397382241.306662501757259.525786373041914526306757.112506283680098168752627601991569.13636080831807\
            96048411168783196497071688492468691
 132    12  73.137.617.2377.16369.432961.99990001.6796152793.24387741577.126197002179733470481.283830826522232279893972\
            777.16205834846012967584927082656402106953
 133     6  11.909091.909090909090909091.247025236977306025681323889.61828645758322140842666144519962696417487.72021403\
            933746126426491665754465510017877
 134     7  101.269.4021.260587121.94927228208573594069.2302527353565357450759725122262880394277261.1607103056527759457\
            6986582552521799177065559188277159741
 135    18  7.11.13.19.211.241.2161.6481.9091.29611.52579.3762091.70541929.14175966169.577603663291.8985695684401.31023\
            833790241.8610583349234340055547908764091017276717091
 136     5  17.17.5882353.13355595217.440441087557478776852171834625638618412949059374084837579531425633661269203803741\
            415744566525108430933975383194546209
 137     7  11.364393423.117651465889.441651480271681.676321006412903.218801242136856556680173235529.324456958063495610\
            1009646791013296826459859399717968478099
 138    10  101.829.1289.9901.1569889.18371524594609.536430531035337769.757108543129939106221.4181003300071669867932658\
            901.19108466176791400681292709171992566565029
 139     4  11.557.2503.65206557093133416984651876211089535710403595333062378353092332941289776570384185949278036260192\
            6814638167836591846272150911969126521
 140     8  73.137.7841.851761.1676321.5964848081.127522001020150503761.11741556610363705311583871530863587320857611583\
            54280249987966107746175275693416345665039841
 141    10  7.11.13.6299.344887.9127213.4855067598095567.1160803383934463712259.297262705009139006771611927.30073566270\
            559048948142559741512708796590524703892560552659
 142     7  101.569.7669.380623849488714809.7716926518833508778689508504941.93611382287513950329431625811490669.8251988\
            2659061966708762483486719446639288430446081
 143    12  11.11.23.859.4093.8779.51767.1058313049.22144088539.264752347289.104730101107272149081.34607524609209512562\
            213651270561528862879196390936320471942325254862879783
 144    12  97.353.449.641.1409.13249.69857.206209.1067329.66554101249.75118313082913.707161470552577113741235757984286\
            08590219877617672752248112085912824160137075376116481
 145    10  11.59.1451.9091.30104611.58765601.2433146345771.17996132431060961.154083204930662557781201849.9786272766548\
            0231246011008935563207741144491224418517422691228321
 146     6  101.5911541.16692085818029.5774294197526381.182202742802607835615596881.95370375761037525458610714099673217\
            61728999089417907986752766348817191016093460769
 147    12  7.7.7.11.13.127.197.2689.459691.909091.5076141624365532994918781726395939035533.142857157142857142856999999\
            985714285714285857142857142855714285571428571428572857143
 148     5  73.137.61544617.16444765848115921.9879587347765036607308472984299267446449284274878503800385604286380709096\
            50210480224210297181360032908354907525523774393
 149     5  11.2087.9615683031450065714899.165459609176797865866134365329792270635207840943.273786943025270543291743981\
            4481839640694075521336313521691938014929169431049
 150    17  61.101.601.3541.9901.27961.60101.261301.3903901.4188901.7019801.39526741.168290119201.14103673319201.168058\
            8011350901.25074091038628125301.38654658795718156456729958859629701
 151     6  11.181288487.153653579173.12331942624071394811.2646756758131654397378192081701748003041997.9998823061783773\
            45161889846655198592766347086896770989636138585751423
 152     5  17.134369.5882353.31735795756961.23450468203945238547222860183739121710126330850830571913874990515654086653\
            4427238711769806579683320997636600725852987602204289
 153    16  7.11.13.19.103.4013.52579.2142001.5364487.832339891.21993833369.276402747619.291078844423.2405782797823.377\
            526955309799110357.157393477257579000092993572752789683416120273639369
 154     9  29.89.101.281.121499449.1052788969.1056689261.39511854229.2556194893173839918095986049303563300534667499721\
            9855227412314112685523898853595360610683149167147379131162769
 155     7  11.9091.11161.3925963357681.5167617497664851.909090909090909090909090909091.4857900688365130469291831549890\
            842547443917376935406225054646143856579892970236911030721
 156    10  73.137.313.1101673.1580801.99990001.1358074433371719716641.291593563046646669491593.63252744020215074509062\
            2412245443923049201.7323941687838105624847742701467683590147273
 157     4  11.4397.3641773.5677249457541767920914361261393637170284208419081725916171115977757756348333809389444733502\
            8905724214106839545113870547643014663862360146330362411
 158     5  101.5689.507998564486483655774880939989709.646301962916453492325383567253991760083617720844121.530084044837\
            791203267418958734478905892862260111193658629289735929681
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