Factorisations Of Cunningham Numbers C+(6,n) = 6n + 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  7 [1st Prime]
   2     1  37 [2nd Prime]
   3     2  7.31
   4     1  1297 [3rd Prime]
   5     3  7.11.101
   6     3  13.37.97
   7     4  7.7.29.197
   8     2  17.98801
   9     3  7.31.46441
  10     3  37.241.6781
  11     2  7.51828151
  12     2  1297.1678321
  13     4  7.53.937.37571
  14     3  37.421.5030761
  15     5  7.11.31.101.1950271
  16     3  353.1697.4709377
  17     3  7.190537.12690943
  18     6  13.37.73.97.541.55117
  19     3  7.1787.48713705333
  20     3  41.1297.68754507401
  21     6  7.7.29.31.197.2527867231
  22     4  37.58477.70489.863017
  23     3  7.113958101.990000731
  24     4  17.5953.98801.473896897
  25     4  7.11.101.3655688315536801
  26     4  37.313.2341.6291946695217
  27     5  7.31.46441.114967.883383463
  28     5  281.337.617.1297.81035189089
  29     4  7.59.32713.2727192763388813
  30     9  13.37.61.97.181.241.3541.6781.74161
  31     2  7.189491931189200021056951
  32     3  2753.145601.19854979505843329
  33     6  7.31.463.72073.51828151.127236649
  34     3  37.934117.8289713345361373993
  35    11  7.7.11.29.101.197.631.701.2311.9241.585131
  36     5  577.1297.3313.1678321.2478750186961
  37     4  7.3923.1096762734443.2054788991719
  38     3  37.1030762781149.9736145643041809
  39     9  7.31.53.79.937.9049.37571.868999.8857759
  40     5  17.17761.98801.3696985841.121206120881
  41     4  7.83.28537.4837453663777044375040181
  42     7  13.37.97.421.5030761.804146449.6055984789
  43     2  7.412482688627178079807598675848631
  44     3  89.1297.150080764792922988676714149209
  45     7  7.11.31.101.46441.1950271.4760317816590150361
  46     5  37.6073.2259889.9564781.128407494947883673
  47     2  7.534577564460822791430647883899825591
  48     7  193.353.1697.8641.4709377.688490113.6931400449
  49     7  7.7.7.29.197.762332681442053.90179616936384011
  50     6  37.241.6781.343801.22243201.1748016735462726601
  51     8  7.31.103.919.190537.12690943.980146969.99617785207
  52     4  1297.192193.14090441.8284434950526240125727017
  53     5  7.107.97351567.33685364386033.71080464397105403
  54    10  13.37.73.97.109.541.55117.591841.171467713.932461936453
  55     8  7.11.11.101.1031141.51828151.16336066781.84155540944421
  56     6  17.113.4817.98801.4048129.10189440239012883075423169
  57     7  7.31.457.1787.137713.48713705333.190324492938225748951
  58     3  37.349.105134528469779071670501631159328247729809
  59     2  7.1163658999540220416412446482708919139658591671
  60     6  41.1297.13441.1678321.68754507401.592575109627400042641
  61     3  7.9151.4577830180684945360162613198286645069141001
  62     2  37.47552767764994953232854569779888803761183529901
  63    10  7.7.29.31.127.197.46441.2527867231.154260982009.528921402377887
  64     3  4926056449.447183309836853377.28753787197056661026689
  65     8  7.11.53.101.131.937.37571.199930782298483523040584108028862541
  66    11  13.37.97.3037.58477.70489.96493.622513.863017.4629769.16266405013
  67     5  7.269.418349.90571543952974835963.191757760647639121941197
  68     5  137.1297.5849.1536052010629489.51420576374811381403609445473
  69     6  7.31.113958101.990000731.24648570768391.816214079084081564521
  70     7  37.241.421.6781.5030761.13509594555661.1708114263204222806519161
  71     4  7.37489.11735704315681.5757417485448059422914748320317168839
  72     5  17.5953.98801.473896897.22452257707354557235348829785471057921
  73     6  7.293.439.120855443.1389436303.4221883459378030470824476438562257
  74     5  37.37.4441.3300043400835529.190892407618022993841069346975403017
  75    10  7.11.31.101.151.168151.1950271.573178201.918628247364601.3655688315536801
  76     5  1297.4561.355518408146401.5028187486478069273.13038313680704041577
  77     6  7.7.29.197.51828151.57019087134151254061666621717728669167279862151
  78    11  13.13.37.97.157.313.2341.8893.6291946695217.197743936282933.6429178169720749
  79     6  7.317.5531.2832941.99687312908749681.8592319153827988586815914947213
  80     6  353.1697.9601.4709377.2810800069601.2347110840158563816028186318246561
  81     8  7.31.1783.46441.114967.149862151.883383463.3920344350409644507093715799617
  82     4  37.4046701.174521133001.246179376206361788466441901958293949537091001
  83     5  7.710813.6547890917.21608536062644851877771.54824363564629401758409941
  84     8  281.337.617.1297.1678321.81035189089.1176362433121.19100900655540830489319601
  85     8  7.11.101.190537.12690943.1383638161.72085651321561.740797672014674927371043791
  86     5  37.1033.6501601.2914764989376043020733.11510167124054813592781820845997449
  87    11  7.31.59.32713.68209.92569.1439329.380675809.519258631.24378360481.2727192763388813
  88     4  17.98801.9307950433.19197545705142827447183881455518760379441910619182497
  89     3  7.179.1437176850540020021056024701236917910178773041847685459251313907949
  90    16  13.37.61.73.97.181.241.541.3541.6781.9001.55117.74161.211501.2106930961.5597780112726834061
  91    12  7.7.29.53.197.937.2003.2549.36947.37571.52769627.12468702878009806771287543538567443817
  92     4  1297.14537.433176829049.47625006826357122080464279208098880721125912766130417
  93     5  7.31.31.189491931189200021056951.1830855782835393620827906093040965051783187521
  94     5  37.1693.1029538544148223697293.30585762365533687252981.7098996031830910703530849
  95    10  7.11.101.1787.6271.2666738161.37260330001.48713705333.61671024221.3229504809106404383981
  96     4  2753.145601.19854979505843329.63340286662973277706162278988150776663495577436161
  97     4  7.7449708398813963.6571212276076854019883.8826499007361715764052964663075774479
  98     5  37.421.5030761.288628033.802354924671793395266725600744864562917483072464133108417
  99    10  7.31.199.463.46441.72073.110881.51828151.127236649.2225208714917658550195227627861513418879
 100     8  41.1297.4801.5801.224401.68754507401.1006795824867486182291801.28398752673271140825020401
 101     5  7.607.82013.3866281.2909467055506170519577044616632832452708657352232253233553601781
 102     8  13.37.97.934117.1785001.8289713345361373993.12346985995648844989.2953728137900959095135649
 103     4  7.7211.135025379.20704743230318258100890022657208522727453596408722228548650415542999
 104     5  17.98801.36265841.141365953.98327998682892050307547688538841853424435944546993755800017
 105    16  7.7.11.29.31.101.197.631.701.2311.9241.71191.585131.1950271.2527867231.271613602977153099649378586566681
 106     4  37.26713.175436926004647658810244613736479118917.175787157418305877173455355755546870641
 107     2  7.26126771741159407024154726661022582007126551676422442131468770568230221685230103991
 108     9  433.577.1297.3313.1678321.115963921.2478750186961.8781208996949976153601.241282001155985351966017
 109     3  7.9661979.97346908193625617781778470000484678372469642125201050088483502236579895347349
 110     8  37.241.6781.58477.70489.863017.423852369601.433295951605870884187046138704268693683498331456101
 111     9  7.31.223.3923.7993.142969.1096762734443.2054788991719.484813024945269068265878512515024013260506641
 112     5  353.1697.4709377.490972383553.1026745888453552697436968844848917190436254094111712318750754497
 113     6  7.227.8363.586471.5043448999988542328333.217085653849206214541602569383859982900289160186960917
 114    11  13.37.97.229.25309.43321.2197693.1030762781149.300537265358917.9736145643041809.659334264781883756771821
 115     7  7.11.101.113958101.990000731.23126990778420152651.15138465280223101464931287568892526939099241284821
 116     7  233.1297.250793.4916777.6198809.9008169903032260803977.88574437255173019150535038179441097901397209
 117    12  7.31.53.79.937.1873.9049.37571.46441.868999.8857759.57063471642936858295625494275761490859413610922514697
 118     3  37.554971222573.3231285690411251549937535803579175660890272281294966380800039383396486737158017
 119     9  7.7.29.197.190537.12690943.22885730141.2681104713967.9584881019626035133999258735515025036249902934797053
 120    11  17.5953.17761.55201.98801.122401.21027841.473896897.3696985841.121206120881.4458139843615061052376640769667\
            21
 121     5  7.727.51828151.15186641018595718629290023681.3578008788069105048042400002837961114116977849537973223
 122     5  37.60757.348433.558416270857.196597122477434001699939656151715927005493674652801355438654544438291553
 123     8  7.31.83.1231.28537.4837453663777044375040181.268313928259442786323996685119.628260227263749127899296330959
 124     5  1297.106179166897.1062529732255153.505430595651453051641.41857485802028381142383903037144206683835077721
 125     9  7.11.101.251.751.5501.3655688315536801.2694730860384999001.233805293126289020639202084597666844981225400241\
            001
 126    15  13.37.73.97.421.541.1009.17389.55117.5030761.10339309.804146449.6055984789.48129311534221.12185192600132570\
            384611238029
 127     5  7.509.2287.6557252639250807127523.12514251972598061031154549270275982573061110378811783176435900357554799
 128     7  257.763649.50307329.3191106049.2339340566463317436161.2983028405608735541756929.182477700970213219240171852\
            81
 129     5  7.31.2322118361887.412482688627178079807598675848631.115814113322099366440280889676998813124941173548805953
 130    10  37.241.313.2341.6781.425101.571140885901.6291946695217.1095110988527465328644161.19486136423472309637684929\
            35356381
 131     7  7.118766959.5620905557.18059147791.1519139468453.137286124588876043259567675817.492370801281846683336965699\
            07047
 132     9  89.1297.602977.1678321.87917281.1581003091009.332526664667473.6416538652864923578689.1500807647929229886767\
            14149209
 133    10  7.7.29.197.1787.1050169.48713705333.27838508435875439051.6110613202111672866319.716622317368928663955050025\
            3057030611
 134     3  37.4021.1258148065662933435127171073866560143872261293533825733911764685311660688307770984681658280416519961
 135    12  7.11.31.101.271.46441.114967.1950271.883383463.2195738619437791.4760317816590150361.17878872997028128383097\
            2402140920212721
 136     5  17.17.98801.2376897969771200667937073.992888154555208408072359969200446002102251441040253906228951529060955\
            38881
 137     4  7.51480217.4582965162279152779295741463389.2448140495278291042529241912014354378530513227666594553134296023\
            8107
 138    12  13.37.97.277.6073.2259889.9564781.12344559539431993.14030036355387001.23027140435639321.128407494947883673.
            279219519230141641
 139     3  7.478404033683.43464123950634007416896270274528229077877085950620143478550278600897682734201302908605111172\
            4237
 140     9  41.281.337.617.1297.68754507401.81035189089.123099618068232205681.40982486632742791332750143162242392858449\
            31775661062561
 141     5  7.31.1129.534577564460822791430647883899825591.400093872648315443061680477735172345044266448557214947007104\
            507237639
 142     5  37.4485781.33571579633135513.969155837815909463425781176679854621.58220022739632174549950127401919425992936\
            844184277
 143     8  7.53.937.2861.37571.3712567.51828151.2623642616266140731907940608862422310623338001684178975972736179031671\
            72733704458773
 144    10  193.353.1697.8641.115777.4709377.31057921.688490113.6931400449.14019268835179638724593328298903017364203886\
            8198120943575131073
 145    10  7.11.59.101.32713.168491.35969851301.2727192763388813.71188611917485018014870131.38450776123542785985187808\
            85281690026242583211
 146     5  37.877.16658893.20007314401.3767439640217533991679971417792901973000703933565811241566664111171375550309696\
            7184005923301
 147    12  7.7.7.29.31.197.32670457.1152319183.2527867231.762332681442053.90179616936384011.61514653542036838838300629\
            06173218740292621286631
 148     4  1297.12950593.10742681826196124641.812910461537597351789277337708911744048426523234607657015392944064157118\
            19759159724497
 149     4  7.17808481.3908095969.1806534126100647194097596047551632860649143589145163864525913101120410386931607948881\
            33552030773239
 150    15  13.37.61.97.181.241.3541.6781.74161.343801.22243201.38149201.1748016735462726601.340800981614130538049401.1\
            3744019238016248925287701988601
 151     4  7.1877258342367076264555657.57719839964417489988525624247.4177260955133929558960631779921813101873322007065\
            786779841904569
 152     6  17.98801.417827633.505981859041.26836193435793601023998323852801.199492594262551677559234014856976616560844\
            8716213725436669937
 153    13  7.31.103.919.46441.147799.190537.12690943.980146969.99617785207.29274753335383.1888411753890127.61981850959\
            910422285012731307171469066599
 154     8  37.421.58477.70489.863017.5030761.40590776689.6048141008071456596259776949311257916837567558165203557375479\
            4818786652644638545909
 155     6  7.11.101.189491931189200021056951.73925704213704945236169449354196288841.3769168199699790684839649519999144\
            5129214809531978987311
 156     7  1297.192193.1678321.14090441.816213379522588431707233.8284434950526240125727017.618089408508629562797739046\
            557629942711588422796977
 157     6  7.1571.53381.259993.32577356503.297308882243938865484453677008309867648571856224118520242496051040995144993\
            90913563956124405913479
 158     3  37.10429.22985458387524760396049933956519941247062829865007890151235623482849657962098495040918310213730329\
            73033904327664158129
 159     9  7.31.107.97351567.33685364386033.71080464397105403.79850963147627239.886629624220623485114684453959.1388827\
            9563077823030315573706460911
 160     7  2753.82241.145601.19854979505843329.15954097282309262360999041.4903626466768570999224738379365121.623565458\
            885624857143366973953113921
 161     9  7.7.29.197.231841.113958101.990000731.3091531661.8463428877114283334832841135980685094133787815940779201328\
            511354558563105269202500000131
 162    13  13.37.73.97.109.541.55117.591841.171467713.932461936453.39661919912737.26411543817830547235357966561.104753\
            2535514129255363516988891792003940353
 163     7  7.11411.1712959177.52108050586547.417317792492527332337.390331841336302929436994813.59385353538185533999095\
            22760027592696327594011870339
 164     3  1297.90823862327833086800386352513067248343828857.351289460623725010305581894540945828444787270943557773540\
            836771459982767560667193
 165    15  7.11.11.31.101.463.72073.1031141.1950271.51828151.127236649.16336066781.84155540944421.661982172984001.2324\
            70996817349914740909949038496736983636813951
 166     9  37.997.778873.3020869.13852369.161184670755001.437801891817492814657.62492225855662442512009.28097049972396\
            2289858902531662958021839590057517
 167     4  7.2339.24362285875922356868655021961427.2240848611344433471047519923958679743088526810022077124471576209605\
            7091569159815413649881516047
 168    11  17.113.673.4817.5953.98801.4048129.473896897.10189440239012883075423169.3276974780364284482799810397121.228\
            576791406017659230547997507603024201377
 169     8  7.53.937.4057.37571.116720070342348721.3378307227685242623713508116989468524398534111.154008740494680898484\
            89148387594553074912242007981896423
 170    10  37.241.1021.6781.934117.8289713345361373993.372810476994982432801.2244807299700346905001.418196746744415875\
            29015061.115394656437025419824224817341
 171    10  7.31.457.1787.46441.137713.48713705333.62174327387790051073.190324492938225748951.1773086345556501045721501\
            5481519172763685683806181388676488969177
 172     7  1297.1721.1904729.5993513377.3449220534377.2400135849956129030979293221108376113.32947522230532454787172792\
            7490276948774179783794853789837408297
 173     3  7.347.17168754933680641828885328290196243178419334128667815027099365404387446550489987693378776240078242722\
            7477447336436457634084029167573
 174     9  13.37.97.349.104485957.3347320129.298589131777670304546904897.105134528469779071670501631159328247729809.13\
            995898620078159024779789479094697362727841
 175    17  7.7.11.29.101.197.631.701.2311.3851.9241.12601.585131.1305192701.66631795301.3655688315536801.5660713977589\
            80021514503314913468700952468138140520705435915823851
 176     5  353.1697.4709377.2653655703600055300471675940271611363631320368111914433.1203248936190203022591615664116879\
            4191545029882930365976044832157368897
 177     4  7.31.1163658999540220416412446482708919139658591671.2140355196559238331144625485410513513288018960171608816\
            987390371347305662078691899857664991
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