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     1  2 [1st Prime]
   2     3  2.2.2
   3     2  2.13
   4     5  2.2.2.2.5
   5     3  2.11.11
   6     5  2.2.2.7.13
   7     2  2.1093
   8     7  2.2.2.2.2.5.41
   9     3  2.13.757
  10     6  2.2.2.11.11.61
  11     3  2.23.3851
  12     8  2.2.2.2.5.7.13.73
  13     2  2.797161
  14     5  2.2.2.547.1093
  15     5  2.11.11.13.4561
  16    10  2.2.2.2.2.2.5.17.41.193
  17     3  2.1871.34511
  18     8  2.2.2.7.13.19.37.757
  19     3  2.1597.363889
  20    10  2.2.2.2.5.5.11.11.61.1181
  21     4  2.13.1093.368089
  22     7  2.2.2.23.67.661.3851
  23     3  2.47.1001523179
  24    11  2.2.2.2.2.5.7.13.41.73.6481
  25     5  2.11.11.8951.391151
  26     5  2.2.2.398581.797161
  27     6  2.13.109.433.757.8209
  28     9  2.2.2.2.5.29.547.1093.16493
  29     4  2.59.28537.20381027
  30    11  2.2.2.7.11.11.13.31.61.271.4561
  31     4  2.683.102673.4404047
  32    12  2.2.2.2.2.2.2.5.17.41.193.21523361
  33     5  2.13.23.3851.2413941289
  34     8  2.2.2.103.307.1021.1871.34511
  35     6  2.11.11.71.1093.2664097031
  36    12  2.2.2.2.5.7.13.19.37.73.757.530713
  37     3  2.13097927.17189128703
  38     7  2.2.2.1597.2851.101917.363889
  39     7  2.13.13.313.6553.7333.797161
  40    13  2.2.2.2.2.5.5.11.11.41.61.1181.42521761
  41     4  2.83.2526913.86950696619
  42    11  2.2.2.7.7.13.43.547.1093.2269.368089
  43     3  2.431.380808546861411923
  44    11  2.2.2.2.5.23.67.661.3851.5501.570461
  45     9  2.11.11.13.181.757.1621.4561.927001
  46     6  2.2.2.47.1001523179.23535794707
  47     5  2.1223.21997.5112661.96656723
  48    17  2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481
  49     7  2.491.1093.4019.8233.51157.131713
  50    10  2.2.2.11.11.61.151.8951.391151.22996651
  51     6  2.13.1871.12853.34511.99810171997
  52     9  2.2.2.2.5.53.398581.797161.4795973261
  53     4  2.107.24169.3747607031112307667
  54    13  2.2.2.7.13.19.37.109.433.757.8209.19441.19927
  55     8  2.11.11.11.23.1321.3851.560088668384411
  56    13  2.2.2.2.2.5.29.41.547.1093.16493.430697.647753
  57     7  2.13.229.1597.248749.363889.1824179209
  58     9  2.2.2.59.523.6091.28537.5385997.20381027
  59     3  2.14425532687.489769993189671059
  60    17  2.2.2.2.5.5.7.11.11.13.31.61.73.271.1181.4561.47763361
  61     3  2.603901.105293313660391861035901
  62     8  2.2.2.683.6883.102673.4404047.22434744889
  63     6  2.13.757.1093.368089.144542918285300809
  64    14  2.2.2.2.2.2.2.2.5.17.41.193.21523361.926510094425921
  65     7  2.11.11.131.797161.3701101.110133112994711
  66    12  2.2.2.7.13.23.67.661.3851.25411.176419.2413941289
  67     4  2.221101.441019876741.475384700124973
  68    12  2.2.2.2.5.103.307.1021.1871.34511.956353.1743831169
  69     6  2.13.47.277.1001523179.2461243576713869557
  70    11  2.2.2.11.11.61.71.547.1093.2664097031.374857981681
  71     2  2.3754733257489862401973357979128773
  72    16  2.2.2.2.2.5.7.13.19.37.41.73.757.6481.530713.282429005041
  73     5  2.11243.20149.15768033143.9460375336977361
  74     8  2.2.2.18427.107671.13097927.56737873.17189128703
  75    10  2.11.11.13.601.4561.8951.9601.391151.2098303812601
  76    11  2.2.2.2.5.1597.2851.101917.363889.5301533.25480398173
  77     7  2.23.1093.3851.51457561.7151459701.76831835389
  78    15  2.2.2.7.13.13.79.157.313.2887.6553.7333.10141.398581.797161
  79     4  2.432853009.392038110671.145171177264407947
  80    18  2.2.2.2.2.2.5.5.11.11.17.41.61.193.1181.14401.42521761.128653413121
  81     9  2.13.109.433.757.3889.8209.1190701.12557612956332313
  82     8  2.2.2.83.33703.2526913.86950696619.270547105429567
  83     5  2.167.12119.1036745531.950996059627210897943351
  84    18  2.2.2.2.5.7.7.13.29.43.73.547.1093.2269.2857.16493.368089.109688713
  85     7  2.11.11.1871.34511.2663568851051.862970652262943171
  86     6  2.2.2.431.380808546861411923.82064241848634269407
  87     8  2.13.59.28537.74821.20381027.32234893.150224123975857
  88    16  2.2.2.2.2.5.23.41.67.89.661.3851.5501.570461.2382953.56625998353
  89     4  2.179.1611479891519807.5042939439565996049162197
  90    19  2.2.2.7.11.11.13.19.31.37.61.181.271.757.1621.4561.387631.755551.927001
  91     5  2.1093.797161.4011586307.3745603812007166116831643
  92    10  2.2.2.2.5.47.12553493.1001523179.23535794707.70601370627701
  93     7  2.13.683.1117.102673.4404047.26273701844015319144827917
  94    10  2.2.2.1223.16921.21997.256057.5112661.96656723.1534179947851
  95     7  2.11.11.191.1597.363889.78958087694609321439660131899631
  96    21  2.2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481.76801.21523361.24127552321
  97     4  2.76631.2549755542947.48845962828028421155731228333
  98    12  2.2.2.491.547.1093.4019.8233.51157.131713.857643277.127522693159
  99     8  2.13.23.757.3851.3186217.2413941289.12812432238302009985937
 100    18  2.2.2.2.5.5.5.11.11.61.101.151.1181.8951.391151.394201.22996651.61070817601
 101     4  2.33034273.465092326319.50316775668019759306202964023
 102    15  2.2.2.7.13.103.307.613.1021.1871.12853.30091.34511.129159847.99810171997
 103     2  2.6957596529882152968992225251835887181478451547013
 104    13  2.2.2.2.2.5.41.53.398581.797161.2093124281.4795973261.37644053098601
 105    13  2.11.11.13.71.421.1093.4561.6301.368089.1616161.2664097031.26751945361
 106     8  2.2.2.107.24169.78719947.61557605176233223.3747607031112307667
 107     4  2.50077.229837.48965028505045123993421250406516036571557
 108    18  2.2.2.2.5.7.13.19.37.73.109.433.757.8209.19441.19927.530713.150094634909578633
 109     6  2.1091.521402591.3499901929.239789806103.10624346875389299603
 110    15  2.2.2.11.11.11.23.61.67.661.1321.3851.659671.24472341743191.560088668384411
 111     7  2.13.13097927.18702169.119779213.17189128703.6962353413269964253
 112    19  2.2.2.2.2.2.5.17.29.41.113.193.547.1093.16493.19489.430697.647753.36214795668330833
 113     5  2.227.1583.2172539.526256453012063980796131127321354599535039
 114    15  2.2.2.7.13.229.1597.2851.3079.53923.101917.248749.363889.1162320517.1824179209
 115     8  2.11.11.47.1975931.1001523179.6273542442241.52370346649565455417091
 116    13  2.2.2.2.5.59.523.6091.12413.28537.5385997.20381027.37945127666529000523013
 117    11  2.13.13.313.757.6553.7333.797161.4162861.1846794457.2821964307371847613
 118     7  2.2.2.3187.14425532687.489769993189671059.1108439448677340328268341
 119     7  2.239.1093.1871.34511.44626806191326911791.397881837642577477902049
 120    24  2.2.2.2.2.5.5.7.11.11.13.31.41.61.73.241.271.1181.4561.6481.298801.26050081.42521761.47763361
 121     6  2.23.3851.11617.3981923614021.657890411545272648205502849240259841
 122     7  2.2.2.367.603901.105293313660391861035901.86630432442539925437931403
 123     7  2.13.83.51169.2526913.86950696619.1999827817517387044561568810795329
 124    13  2.2.2.2.5.683.6883.102673.4404047.1403808961.2860659169.9500438809.22434744889
 125    10  2.11.11.251.8951.391151.358291751.14781691751.391632555001.989947158849251
 126    19  2.2.2.7.7.13.19.37.43.127.547.757.883.1093.2269.2521.368089.550554229.144542918285300809
 127     6  2.5843.681229.21520151.76082653.301515315752300874236564235591357673
 128    16  2.2.2.2.2.2.2.2.2.5.17.41.193.21523361.926510094425921.1716841910146256242328924544641
 129     7  2.13.431.4129.2199072289.380808546861411923.912851565662857110894244969
 130    12  2.2.2.11.11.61.131.398581.797161.3701101.110133112994711.105919308797935444986721
 131     3  2.263.605199588591144003100881306574406851660288427740394885828171
 132    18  2.2.2.2.5.7.13.23.67.73.661.3851.5501.25411.176419.570461.2413941289.13490012358249728401
 133     6  2.1093.1597.363889.8757948941961838067.257513776243156826379279929309507
 134     8  2.2.2.221101.5390821.441019876741.475384700124973.4299412981246169975118907
 135    15  2.11.11.13.109.181.433.541.757.1621.4561.8209.927001.53825041.773618132427345151923061
 136    17  2.2.2.2.2.5.41.103.137.307.1021.1871.34511.956353.1743831169.6458150122561.3833564416504313
 137     4  2.4933.217629707.108081809773839995188256800499141543684393035450350551
 138    15  2.2.2.7.13.47.139.277.5107.9109.132619.1476463.1001523179.23535794707.2461243576713869557
 139     4  2.1669.5430731.115215201111546538317696820901417129607616709798043944747
 140    20  2.2.2.2.5.5.11.11.29.61.71.547.1093.1181.16493.28596961.32839661.94373861.2664097031.374857981681
 141     9  2.13.1223.21997.5112661.96656723.161969595577.2031161085853.165301473942399079669
 142     9  2.2.2.853.2131.82219.3099719989.4052490063499.3754733257489862401973357979128773
 143     5  2.23.3851.797161.1198014380856762535048758241151960180137876946928788681521
 144    24  2.2.2.2.2.2.5.7.13.17.19.37.41.73.97.193.577.757.769.6481.530713.1418632417.282429005041.56227703611393
 145     7  2.11.11.59.28537.20381027.183349688798536618131199274872809217263632838323547361
 146     9  2.2.2.439.11243.20149.15768033143.9460375336977361.38488154120055537150068589763279
 147    11  2.13.491.1093.4019.8233.47041.51157.131713.368089.254395969103901649521223867932173929
 148    13  2.2.2.2.5.149.18427.107671.953861.13097927.56737873.17189128703.142659759801404920771391593
 149     4  2.7451.177941761.46509804063632583432467217805311362636553293639540930405531
 150    22  2.2.2.7.11.11.13.31.61.151.271.601.2551.4561.8951.9601.26251.119101.391151.1530601.22996651.2098303812601
 151     5  2.1511.6263783.64745079361.905673230703550690601003473107008473103084254587061
 152    17  2.2.2.2.2.5.41.761.1597.2851.31769.101917.363889.3302353.5301533.25480398173.278733912072436804273
 153    10  2.13.757.1871.12853.34511.6213394261.35106034213.99810171997.28090626041813012073462457
 154    13  2.2.2.23.67.547.661.1093.3851.51457561.7151459701.76831835389.56495392933101222275861053369
 155     9  2.11.11.311.683.102673.4404047.3586225081.1078579799806668629607014283525941686969924751
 156    22  2.2.2.2.5.7.13.13.53.73.79.157.313.2887.6553.7333.10141.325729.398581.797161.4795973261.271722723752757889
 157     5  2.9421.3381925092493.9891109125337566719.1283810768507270931382867729773882314783
 158     9  2.2.2.66361.432853009.327220181191.392038110671.145171177264407947.567239060331150635317
 159     7  2.13.107.24169.712550912937217.3747607031112307667.40559607827224525043263763418498193
 160    23  2.2.2.2.2.2.2.5.5.11.11.17.41.61.193.1181.14401.8194721.21523361.42521761.700984481.128653413121.5977474287\
            54241
 161     5  2.47.1093.1001523179.636961216046002471921398696960338364910115196955450597747751689
 162    21  2.2.2.7.13.19.37.109.163.433.757.1297.3889.8209.19441.19927.208657.224209.1190701.5879415781.12557612956332\
            313
 163     4  2.5227348213873.8882811705390167.6351885141964057411259499526611848626072045955243
 164    13  2.2.2.2.5.83.33703.2088869.2526913.110767897.86950696619.270547105429567.574933708017116710865237
 165    13  2.11.11.11.13.23.1321.3851.4561.50821.2413941289.560088668384411.4183739978746243239852385111562221
 166    11  2.2.2.167.499.997.12119.2466097.1036745531.950996059627210897943351.813201725710097952736361977
 167     6  2.58451.88177.1767863.10063060897082377.260551495718621260054268273374657473120059796409
 168    28  2.2.2.2.2.5.7.7.13.29.41.43.73.337.547.673.1009.1093.2269.2857.6481.16493.167329.368089.430697.647753.10968\
            8713.2108826721
 169     5  2.2029.797161.163264150141.814222556753878193601980463083668707558864014894642043902929
 170    16  2.2.2.11.11.61.103.307.1021.1531.1871.34511.224401.2663568851051.862970652262943171.13271362257832586268931
 171    10  2.13.229.757.1597.119701.248749.363889.1824179209.27203787889921135221329070240968055313746007669
 172    13  2.2.2.2.5.173.431.470593.2641485701.55473422113.903239908009.380808546861411923.82064241848634269407
 173     5  2.347.762239.2125048865543.30985428700388045508959018054392810762033149280306907746766819
 174    19  2.2.2.7.13.59.349.523.6091.28537.74821.142159.261697.1383301.5385997.20381027.32234893.37464463.15022412397\
            5857
 175    11  2.11.11.71.1093.8951.109201.391151.2664097031.1430128198787051.11459299580388289258664119605215721251
 176    22  2.2.2.2.2.2.5.17.23.41.67.89.193.661.3851.5501.570461.2382953.6922081.56625998353.15656839738849.1363620137\
            403810529
 177     7  2.13.709.14425532687.489769993189671059.2224898159852613649.9736622508037946817946068730077829
 178     9  2.2.2.179.264331.1125706177.1611479891519807.5042939439565996049162197.2444322641415331355533344283
 179     8  2.359.56207.100957.19510643.291066066130451.6779963644378513811.161868664744491655705858963594331
 180    28  2.2.2.2.5.5.7.11.11.13.19.31.37.61.73.181.271.757.1181.1621.4561.176401.387631.530713.755551.927001.4776336\
            1.452808441334403281
 181     4  2.90863.890159.1412740676235815729693013611798695493926336144083867368022228212267580445753
 182    13  2.2.2.547.1093.8737.398581.595141.797161.4011586307.2354116499281.2452788561133.3745603812007166116831643
 183     8  2.13.733.603901.97806913.2421854958301.105293313660391861035901.7165195867462155138286987098273769
 184    14  2.2.2.2.2.5.41.47.1289.12553493.1001523179.23535794707.70601370627701.7431708463054117564478285049413474811\
            29
 185    13  2.11.11.2221.17761.35521.146891.13097927.228082801.17189128703.49804972211.87841814842081.16542359111967047\
            41
 186    16  2.2.2.7.13.373.683.1117.6883.102673.541447.3058399.4404047.22434744889.88239050462461.262737018440153191448\
            27917
 187     9  2.23.1871.3851.6359.34511.1272753542934479.3411926755457243.527447346649058852221083363397206345775307
 188    14  2.2.2.2.5.1223.16921.21997.256057.5112661.96656723.563838649753.1534179947851.12538428313220526578547784943\
            9329
 189    11  2.13.109.433.757.1093.8209.368089.144542918285300809.49888641454623789553.67775349707440873247475442867753
 190    15  2.2.2.11.11.61.191.1597.2851.39901.101917.363889.29574984661.25349956307509384561.7895808769460932143966013\
            1899631
 191     5  2.383.311713.9593931911.5890868591760365434332005074929710400548909181468214858888800348369500317
 192    27  2.2.2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481.7297.68737.76801.21523361.96948097.24127552321.70613232\
            600577.926510094425921
 193     6  2.6563.29723.2346066378779.218246094772601642186973037.607981469094652492202396647678317419649770543
 194     9  2.2.2.76631.459991849.503803759819.2549755542947.20591603926857377806745611.48845962828028421155731228333
 195    16  2.11.11.13.13.131.313.2341.4561.6553.7333.797161.3701101.39838501.110133112994711.9813992993974897720899455\
            4331725481
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