Factorisations Of Cunningham Numbers C+(3,n) = 3n + 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  2.2
   2     2  2.5
   3     3  2.2.7
   4     2  2.41
   5     3  2.2.61
   6     3  2.5.73
   7     3  2.2.547
   8     3  2.17.193
   9     5  2.2.7.19.37
  10     4  2.5.5.1181
  11     4  2.2.67.661
  12     3  2.41.6481
  13     3  2.2.398581
  14     4  2.5.29.16493
  15     6  2.2.7.31.61.271
  16     2  2.21523361
  17     5  2.2.103.307.1021
  18     4  2.5.73.530713
  19     4  2.2.2851.101917
  20     3  2.41.42521761
  21     7  2.2.7.7.43.547.2269
  22     4  2.5.5501.570461
  23     3  2.2.23535794707
  24     6  2.17.97.193.577.769
  25     5  2.2.61.151.22996651
  26     4  2.5.53.4795973261
  27     7  2.2.7.19.37.19441.19927
  28     4  2.41.430697.647753
  29     5  2.2.523.6091.5385997
  30     6  2.5.5.73.1181.47763361
  31     4  2.2.6883.22434744889
  32     2  2.926510094425921
  33     7  2.2.7.67.661.25411.176419
  34     4  2.5.956353.1743831169
  35     5  2.2.61.547.374857981681
  36     4  2.41.6481.282429005041
  37     5  2.2.18427.107671.56737873
  38     4  2.5.5301533.25480398173
  39     8  2.2.7.79.157.2887.10141.398581
  40     5  2.17.193.14401.128653413121
  41     4  2.2.33703.270547105429567
  42     7  2.5.29.73.2857.16493.109688713
  43     3  2.2.82064241848634269407
  44     5  2.41.89.2382953.56625998353
  45    10  2.2.7.19.31.37.61.271.387631.755551
  46     4  2.5.12553493.70601370627701
  47     5  2.2.16921.256057.1534179947851
  48     4  2.76801.21523361.24127552321
  49     5  2.2.547.857643277.127522693159
  50     8  2.5.5.5.101.1181.394201.61070817601
  51     9  2.2.7.103.307.613.1021.30091.129159847
  52     4  2.41.2093124281.37644053098601
  53     4  2.2.78719947.61557605176233223
  54     5  2.5.73.530713.150094634909578633
  55     7  2.2.61.67.661.659671.24472341743191
  56     6  2.17.113.193.19489.36214795668330833
  57     8  2.2.7.2851.3079.53923.101917.1162320517
  58     4  2.5.12413.37945127666529000523013
  59     4  2.2.3187.1108439448677340328268341
  60     7  2.41.241.6481.298801.26050081.42521761
  61     4  2.2.367.86630432442539925437931403
  62     5  2.5.1403808961.2860659169.9500438809
  63    13  2.2.7.7.19.37.43.127.547.883.2269.2521.550554229
  64     2  2.1716841910146256242328924544641
  65     5  2.2.61.398581.105919308797935444986721
  66     6  2.5.73.5501.570461.13490012358249728401
  67     4  2.2.5390821.4299412981246169975118907
  68     5  2.41.137.6458150122561.3833564416504313
  69     9  2.2.7.139.5107.9109.132619.1476463.23535794707
  70     9  2.5.5.29.1181.16493.28596961.32839661.94373861
  71     7  2.2.853.2131.82219.3099719989.4052490063499
  72     8  2.17.97.193.577.769.1418632417.56227703611393
  73     4  2.2.439.38488154120055537150068589763279
  74     5  2.5.149.953861.142659759801404920771391593
  75    12  2.2.7.31.61.151.271.2551.26251.119101.1530601.22996651
  76     6  2.41.761.31769.3302353.278733912072436804273
  77     6  2.2.67.547.661.56495392933101222275861053369
  78     7  2.5.53.73.325729.4795973261.271722723752757889
  79     5  2.2.66361.327220181191.567239060331150635317
  80     5  2.8194721.21523361.700984481.597747428754241
  81    12  2.2.7.19.37.163.1297.19441.19927.208657.224209.5879415781
  82     5  2.5.2088869.110767897.574933708017116710865237
  83     6  2.2.499.997.2466097.813201725710097952736361977
  84    10  2.41.337.673.1009.6481.167329.430697.647753.2108826721
  85     9  2.2.61.103.307.1021.1531.224401.13271362257832586268931
  86     7  2.5.173.470593.2641485701.55473422113.903239908009
  87    11  2.2.7.349.523.6091.142159.261697.1383301.5385997.37464463
  88     6  2.17.193.6922081.15656839738849.1363620137403810529
  89     5  2.2.264331.1125706177.2444322641415331355533344283
  90     9  2.5.5.73.1181.176401.530713.47763361.452808441334403281
  91     8  2.2.547.8737.398581.595141.2354116499281.2452788561133
  92     4  2.41.1289.743170846305411756447828504941347481129
  93     9  2.2.7.373.6883.541447.3058399.22434744889.88239050462461
  94     4  2.5.563838649753.125384283132205265785477849439329
  95     8  2.2.61.2851.39901.101917.29574984661.25349956307509384561
  96     6  2.7297.68737.96948097.70613232600577.926510094425921
  97     5  2.2.459991849.503803759819.20591603926857377806745611
  98     9  2.5.29.197.16493.16661.251325313.426712077457.34013149495921
  99    14  2.2.7.19.37.67.199.397.661.4357.25411.176419.337448233.378450588583
 100     6  2.41.133201.42521761.18055139801.61459926512826500975801
 101     4  2.2.379963.1017291527198723292208309354658785077827527
 102     8  2.5.73.409.956353.49637281.1743831169.187668407555352123529
 103     5  2.2.619.3661040653.1535090713229126909942383374434289901
 104     7  2.17.193.1249.13729.475356961.780464337846444296785447886881
 105    16  2.2.7.7.31.43.61.211.271.547.1051.2269.24151.3369031.3454081.374857981681
 106     6  2.5.90313.609422621.1481588501.460740683381672021327601001
 107     5  2.2.643.100153.4375617272295428356111030724847180250451293
 108     9  2.41.2161.6481.15121.10512289.16569793.282429005041.3958044610033
 109     6  2.2.1992772009.5933538193981.7696680097963.27866471458012723
 110     8  2.5.5.1181.5501.177101.570461.927319729649066047885192700193701
 111    10  2.2.7.223.18427.107671.25709599.56737873.78539161.64326272436179833
 112     9  2.14561.45697.101921.643553.21523361.67765601.378369377.5685756833
 113     5  2.2.362053.156472231.3626038130651680583578933430931295416667
 114     9  2.5.73.457.2281.7753.5301533.25480398173.3093009324389492947932121
 115     7  2.2.61.6211.48991.23535794707.4232020527831352569905247101633701
 116     5  2.41.233.4177.277991360381003661564752468378981135693842991081
 117    16  2.2.7.19.37.79.157.937.1171.2887.10141.37441.398581.2161927.43264261.6079786129
 118     3  2.5.19966781110160346782368664772328944885905284750420567849
 119     8  2.2.103.307.547.1021.7719769.1098440018152695917905622020432593239209
 120    11  2.17.97.193.577.769.4801.13921.14401.128653413121.51383579021948491809121
 121     8  2.2.67.661.727.2179.74779.256900099994436377787031292704214632407889
 122     6  2.5.180317.262199473.39504363995133913.865923475887669700104067517
 123     9  2.2.7.33703.2337001.40049539.130099576237.15606752580607.270547105429567
 124     4  2.41.81516726600079249.21775844224805408923066692226998392022049
 125     8  2.2.61.151.2251.100501.22996651.2278135721427929786778229917312351656251
 126    11  2.5.29.73.2857.16493.530713.1180369.109688713.475110761833.40226570408250073
 127     6  2.2.22861.63247.52147471.13030796206528578864006320088875125740738871
 128     6  2.257.275201.138424618868737.3913786281514524929.153849834853910661121
 129     9  2.2.7.1549.27091.1651439941.28395735937.7822354593043.82064241848634269407
 130     8  2.5.5.53.1181.4795973261.82669546937641.85515537811724373585467087637721
 131     5  2.2.787.114742271896804438572098194909.881304930739946561320646289889
 132     9  2.41.89.6481.660001.2382953.11096576833.56625998353.20431242370346923068097
 133     9  2.2.547.2851.11173.101917.1084483.1256610601.295966423763788589324732476512991
 134     9  2.5.269.1609.1877.11257.50546266229.719571227339189.2583985068397606535128513
 135    18  2.2.7.19.31.37.61.271.3511.4591.19441.19927.387631.451441.487891.755551.73321201.86548771
 136     8  2.17.17.193.5641553.23229617.2670091735108484737.1981703105982814843334309489
 137     4  2.2.82093596209179.706712258201940254667826642673008768387229115048379
 138     6  2.5.73.12553493.70601370627701.1076050302914923449767311155851656076154481
 139     5  2.2.26436515641.1113626506203380968993.17735794220172313692220944999595159
 140     9  2.41.281.18481.430697.647753.42521761.369879560116990841.3353336738929580410561
 141     9  2.2.7.283.16921.256057.1534179947851.93953407627827115729.3798402051319990403467
 142     5  2.5.3672239816477.9159751032889.167649964410524100307472482005060261887957
 143     7  2.2.67.661.53197.398581.45040109496710622959391872603313706446921645052790773
 144     6  2.76801.21523361.24127552321.77826286120321.81754966841140318493187568203841
 145    10  2.2.61.523.6091.5385997.59086051.25481953741.3159421788711031.76455796243959454561
 146     6  2.5.293.18678646095653.86782247836514775846688349.961743544915378365754610333
 147    16  2.2.7.7.7.43.547.1471.2269.3529.15583.119471899.200568859.857643277.127522693159.882757098511
 148     6  2.41.410257.9537896093307601.31199592961514012689.4106523677041507922228794417
 149     4  2.2.4482722618976860674653013440107317.6878046306591338324108989767203186713
 150    13  2.5.5.5.73.101.1181.1201.55201.394201.47763361.61070817601.2229552891865882714320177992401
 151     6  2.2.472027.645979.135286639.6726812506767780473723505133857482672236342795606501
 152     4  2.17.193.507451442443788899165240329482668362950054541832902585238747279444641
 153    15  2.2.7.19.37.103.307.613.919.1021.30091.436357.129159847.133395235891527691.123343105382171675857
 154     8  2.5.29.5501.16493.570461.671352452318708161.2974112460006073547613794168096436806641
 155     9  2.2.61.1861.6883.22434744889.33131555630426311.318620421994509961.121462982451478217731
 156     7  2.41.6481.309746737.2093124281.37644053098601.20795134293690804171286866969789777553
 157     6  2.2.252457.159420524134654609.32129434337475049222622287.156438005527933564247063011
 158     5  2.5.317.10393819190815276250780568850989337.73675624514425268628805034064478665461
 159     8  2.2.7.48973.78719947.61557605176233223.395794533062864139307.2769035095381770614187391
 160     4  2.926510094425921.4151768361337614527605197761.2839798262237352133440978975949121
 161     8  2.2.547.967.1933.23535794707.5468575720021.124512589982501120520678542758850232589558399
 162     7  2.5.73.530713.150094634909578633.82434619394313344569.41019075946094411081052200020897
 163     5  2.2.8483499631.4956470591980320134353.3507171060957186767994912136200333814689659449
 164     6  2.41.41.2297.32326369.7088757890453145334311443322801793110058505541970400820190920577
 165    18  2.2.7.31.61.67.271.331.661.991.4951.25411.176419.659671.1286011.4968781621.11123788282861.24472341743191
 166     5  2.5.2591261.6956557366277.88353295700662823099667599460762780905604112393714626601849
 167     5  2.2.41332144291.196098784741.1473759805801789118598508577921021242424939524192662637837
 168    11  2.17.97.113.193.577.769.13441.19489.36214795668330833.473451024093683360527418040621798755737921
 169     7  2.2.4057.351859.398581.7336932438768271.25752967047580308239006833030039254422639813234017
 170     8  2.5.5.1181.956353.7674481.1743831169.1706953634650967930299490233845839250457448201276787601
 171    15  2.2.7.19.19.37.2851.3079.25309.53923.101917.1162320517.42509373931.102310358933917.1676620643529235921057
 172     5  2.41.226519873.21376165893692833.29241916907334820616557688889440878559426168577846725809
 173     7  2.2.993367.14427163.125330011023211.156026417563831897.31072285114904997233712868061148862483
 174     8  2.5.73.12413.19437193.1388985225193.37945127666529000523013.11256710946186882997409087921239729
 175    10  2.2.61.151.547.22996651.23185675801.374857981681.4260648635770037050051.18265797539870818825168051
 176     7  2.353.19009.21523361.62210098369.205188547169.255066113304108571577343700262256544056086044033
 177    10  2.2.7.3187.76819.15743388547.38926393657.1669126011067.363002702388730267.1108439448677340328268341
 178     4  2.5.1192464167514295068582330293.709803280757497203996320461865063802526226069876477910653
 179     6  2.2.3755779.47029186391731.9248363581047133.3886084268132710540164562649868800513379104792251
 180    11  2.41.241.6481.298801.26050081.42521761.116809201.282429005041.2081711451601.26166382506293070985608961
 181     5  2.2.51043.715722801240612811884999961.1563889515958819802226972824170738835419881870248693287
 182     7  2.5.29.53.16493.4795973261.563920755493974354012062097199694635409966586035902917973392670446241
 183    10  2.2.7.367.189223.279666823.6117064141.109870115206699.64961725048119249391.86630432442539925437931403
 184     9  2.17.193.112241.2057857.2190337.4475616001.79781171123090497.5205275952266186599636069674258967961777
 185    10  2.2.61.18427.107671.56737873.10322251861.4183611889192231.55223513719943993551.282595984982093378351221
 186     9  2.5.73.1403808961.2860659169.5853105289.9500438809.1137273143641.299544676041927564723805161992460049
 187     9  2.2.67.103.307.661.1021.18177792435744585993179560027.1602492098135068548896997626193620844099621992083
 188     5  2.41.4513.2563193.526908728620534667129849121206725791252980403065501629068461558054330796217049
 189    20  2.2.7.7.19.37.43.127.379.547.883.2269.2521.19441.19927.84673.30354157.550554229.60439117411.574377113178519\
            41680421581
 190     9  2.5.5.1181.5301533.25480398173.70578185345621.4975481820118441.1605850768243931752986453521337428048981
 191     5  2.2.176349919.854888497.22377672940509270880756801912134547524825420533660917137902318707609042309
 192     7  2.280321.15687169.339601921.3167109739009.2492798330262060062236523521.1716841910146256242328924544641
 193     7  2.2.167911.679747.7967041.32685391867.1021562573902349393666967130764482193088889012711317938252390919
 194     5  2.5.389.1209361321548310091770485682269470852086753.77449343291186907889503299808279247610860106861
 195    16  2.2.7.31.61.79.157.271.2887.10141.398581.419437201.54975287251.3785998525531.56919999055921.105919308797935\
            444986721
 196     6  2.41.430697.647753.342875768396449.418055555418935587626051091603744048562522536622075430660388662769
 197     6  2.2.8714655511.24742960162351.49676157359100536013871955394289.229602870983390658750727278114059547829
 198    10  2.5.73.5501.530713.570461.4401193897.3571691108833.13490012358249728401.114472588217384521018097943019137001
 199     5  2.2.2389.5484043.1689478606352600260310382688294322005349159187601803816212045717030717783562666965221
 200     7  2.17.193.401.14401.128653413121.54482419084387063896343257364278812798757304500791752529639086947312737201
 201    11  2.2.7.32563.275371.1351123.5390821.5931946571197.56755588835611.301027886874675599533.429941298124616997511\
            8907
 202     6  2.5.1189912513.69531972955397.96207837407260037.30031942012227933219100853982463211359125974731460998393
 203     8  2.2.523.547.6091.5385997.398858013926743539066881263.478952751436011946972423178548637101114935294309822847
 204     8  2.41.137.6481.6458150122561.3833564416504313.53958784909638588059956801.221200680720606092053543425481471681
 205     8  2.2.61.33703.1164811.270547105429567.6749930086876080531836671.36897861904835148688587290115319536428272306\
            21
 206     6  2.5.1522395676033.7625998476893.3276710054092300162911791926389341.508998148480825018649601011436723422737
 207    14  2.2.7.19.37.139.5107.9109.132619.1476463.5724793.23535794707.7671021268285255340377531.22550950495434610373\
            064930478243
 208     6  2.1614913.20634017.21523361.2763736726854088129.439593550072300534251634135007764475254567347223143808588769
 209    10  2.2.67.661.2851.8779.101917.146719.227123983153149333776852194879434768181.34719041814839626118877698892045\
            2842129
 210    17  2.5.5.29.73.1181.2857.4201.16493.28596961.32839661.47763361.94373861.109688713.7035101641.871383685710721.2\
            22665666643176401
 211     6  2.2.892531.189250543.2645385196586430249915420486682565415343.263254250526748520708907169471841314422031017\
            73
 212     6  2.41.1079398849.1135214993571937.1331247175934064574966369960667813849.105529378287347488808630393952458747\
            3513
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