Factorisations Of Cunningham Numbers C-(3,n) = 3^n - 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. #Fac is the number of (non distinct) prime factors in an expression. 2. A plussed #Fac means that more prime factors exist but they are unknown due to an unfactored composite in the expression. ======================================================================================================================== n #Fac Factorisation 1 1 2 2 3 2^3 3 2 2.13 4 5 2^4.5 5 3 2.11^2 6 5 2^3.7.13 7 2 2.1093 8 7 2^5.5.41 9 3 2.13.757 10 6 2^3.11^2.61 11 3 2.23.3851 12 8 2^4.5.7.13.73 13 2 2.797161 14 5 2^3.547.1093 15 5 2.11^2.13.4561 16 10 2^6.5.17.41.193 17 3 2.1871.34511 18 8 2^3.7.13.19.37.757 19 3 2.1597.363889 20 10 2^4.5^2.11^2.61.1181 21 4 2.13.1093.368089 22 7 2^3.23.67.661.3851 23 3 2.47.1001523179 24 11 2^5.5.7.13.41.73.6481 25 5 2.11^2.8951.391151 26 5 2^3.398581.797161 27 6 2.13.109.433.757.8209 28 9 2^4.5.29.547.1093.16493 29 4 2.59.28537.20381027 30 11 2^3.7.11^2.13.31.61.271.4561 31 4 2.683.102673.4404047 32 12 2^7.5.17.41.193.21523361 33 5 2.13.23.3851.2413941289 34 8 2^3.103.307.1021.1871.34511 35 6 2.11^2.71.1093.2664097031 36 12 2^4.5.7.13.19.37.73.757.530713 37 3 2.13097927.17189128703 38 7 2^3.1597.2851.101917.363889 39 7 2.13^2.313.6553.7333.797161 40 13 2^5.5^2.11^2.41.61.1181.42521761 41 4 2.83.2526913.86950696619 42 11 2^3.7^2.13.43.547.1093.2269.368089 43 3 2.431.380808546861411923 44 11 2^4.5.23.67.661.3851.5501.570461 45 9 2.11^2.13.181.757.1621.4561.927001 46 6 2^3.47.1001523179.23535794707 47 5 2.1223.21997.5112661.96656723 48 17 2^6.5.7.13.17.41.73.97.193.577.769.6481 49 7 2.491.1093.4019.8233.51157.131713 50 10 2^3.11^2.61.151.8951.391151.22996651 51 6 2.13.1871.12853.34511.99810171997 52 9 2^4.5.53.398581.797161.4795973261 53 4 2.107.24169.3747607031112307667 54 13 2^3.7.13.19.37.109.433.757.8209.19441.19927 55 8 2.11^3.23.1321.3851.560088668384411 56 13 2^5.5.29.41.547.1093.16493.430697.647753 57 7 2.13.229.1597.248749.363889.1824179209 58 9 2^3.59.523.6091.28537.5385997.20381027 59 3 2.14425532687.489769993189671059 60 17 2^4.5^2.7.11^2.13.31.61.73.271.1181.4561.47763361 61 3 2.603901.105293313660391861035901 62 8 2^3.683.6883.102673.4404047.22434744889 63 6 2.13.757.1093.368089.144542918285300809 64 14 2^8.5.17.41.193.21523361.926510094425921 65 7 2.11^2.131.797161.3701101.110133112994711 66 12 2^3.7.13.23.67.661.3851.25411.176419.2413941289 67 4 2.221101.441019876741.475384700124973 68 12 2^4.5.103.307.1021.1871.34511.956353.1743831169 69 6 2.13.47.277.1001523179.2461243576713869557 70 11 2^3.11^2.61.71.547.1093.2664097031.374857981681 71 2 2.3754733257489862401973357979128773 72 16 2^5.5.7.13.19.37.41.73.757.6481.530713.282429005041 73 5 2.11243.20149.15768033143.9460375336977361 74 8 2^3.18427.107671.13097927.56737873.17189128703 75 10 2.11^2.13.601.4561.8951.9601.391151.2098303812601 76 11 2^4.5.1597.2851.101917.363889.5301533.25480398173 77 7 2.23.1093.3851.51457561.7151459701.76831835389 78 15 2^3.7.13^2.79.157.313.2887.6553.7333.10141.398581.797161 79 4 2.432853009.392038110671.145171177264407947 80 18 2^6.5^2.11^2.17.41.61.193.1181.14401.42521761.128653413121 81 9 2.13.109.433.757.3889.8209.1190701.12557612956332313 82 8 2^3.83.33703.2526913.86950696619.270547105429567 83 5 2.167.12119.1036745531.950996059627210897943351 84 18 2^4.5.7^2.13.29.43.73.547.1093.2269.2857.16493.368089.109688713 85 7 2.11^2.1871.34511.2663568851051.862970652262943171 86 6 2^3.431.380808546861411923.82064241848634269407 87 8 2.13.59.28537.74821.20381027.32234893.150224123975857 88 16 2^5.5.23.41.67.89.661.3851.5501.570461.2382953.56625998353 89 4 2.179.1611479891519807.5042939439565996049162197 90 19 2^3.7.11^2.13.19.31.37.61.181.271.757.1621.4561.387631.755551.927001 91 5 2.1093.797161.4011586307.3745603812007166116831643 92 10 2^4.5.47.12553493.1001523179.23535794707.70601370627701 93 7 2.13.683.1117.102673.4404047.26273701844015319144827917 94 10 2^3.1223.16921.21997.256057.5112661.96656723.1534179947851 95 7 2.11^2.191.1597.363889.78958087694609321439660131899631 96 21 2^7.5.7.13.17.41.73.97.193.577.769.6481.76801.21523361.24127552321 97 4 2.76631.2549755542947.48845962828028421155731228333 98 12 2^3.491.547.1093.4019.8233.51157.131713.857643277.127522693159 99 8 2.13.23.757.3851.3186217.2413941289.12812432238302009985937 100 18 2^4.5^3.11^2.61.101.151.1181.8951.391151.394201.22996651.61070817601 101 4 2.33034273.465092326319.50316775668019759306202964023 102 15 2^3.7.13.103.307.613.1021.1871.12853.30091.34511.129159847.99810171997 103 2 2.6957596529882152968992225251835887181478451547013 104 13 2^5.5.41.53.398581.797161.2093124281.4795973261.37644053098601 105 13 2.11^2.13.71.421.1093.4561.6301.368089.1616161.2664097031.26751945361 106 8 2^3.107.24169.78719947.61557605176233223.3747607031112307667 107 4 2.50077.229837.48965028505045123993421250406516036571557 108 18 2^4.5.7.13.19.37.73.109.433.757.8209.19441.19927.530713.150094634909578633 109 6 2.1091.521402591.3499901929.239789806103.10624346875389299603 110 15 2^3.11^3.23.61.67.661.1321.3851.659671.24472341743191.560088668384411 111 7 2.13.13097927.18702169.119779213.17189128703.6962353413269964253 112 19 2^6.5.17.29.41.113.193.547.1093.16493.19489.430697.647753.36214795668330833 113 5 2.227.1583.2172539.526256453012063980796131127321354599535039 114 15 2^3.7.13.229.1597.2851.3079.53923.101917.248749.363889.1162320517.1824179209 115 8 2.11^2.47.1975931.1001523179.6273542442241.52370346649565455417091 116 13 2^4.5.59.523.6091.12413.28537.5385997.20381027.37945127666529000523013 117 11 2.13^2.313.757.6553.7333.797161.4162861.1846794457.2821964307371847613 118 7 2^3.3187.14425532687.489769993189671059.1108439448677340328268341 119 7 2.239.1093.1871.34511.44626806191326911791.397881837642577477902049 120 24 2^5.5^2.7.11^2.13.31.41.61.73.241.271.1181.4561.6481.298801.26050081.42521761.47763361 121 6 2.23.3851.11617.3981923614021.657890411545272648205502849240259841 122 7 2^3.367.603901.105293313660391861035901.86630432442539925437931403 123 7 2.13.83.51169.2526913.86950696619.1999827817517387044561568810795329 124 13 2^4.5.683.6883.102673.4404047.1403808961.2860659169.9500438809.22434744889 125 10 2.11^2.251.8951.391151.358291751.14781691751.391632555001.989947158849251 126 19 2^3.7^2.13.19.37.43.127.547.757.883.1093.2269.2521.368089.550554229.144542918285300809 127 6 2.5843.681229.21520151.76082653.301515315752300874236564235591357673 128 16 2^9.5.17.41.193.21523361.926510094425921.1716841910146256242328924544641 129 7 2.13.431.4129.2199072289.380808546861411923.912851565662857110894244969 130 12 2^3.11^2.61.131.398581.797161.3701101.110133112994711.105919308797935444986721 131 3 2.263.605199588591144003100881306574406851660288427740394885828171 132 18 2^4.5.7.13.23.67.73.661.3851.5501.25411.176419.570461.2413941289.13490012358249728401 133 6 2.1093.1597.363889.8757948941961838067.257513776243156826379279929309507 134 8 2^3.221101.5390821.441019876741.475384700124973.4299412981246169975118907 135 15 2.11^2.13.109.181.433.541.757.1621.4561.8209.927001.53825041.773618132427345151923061 136 17 2^5.5.41.103.137.307.1021.1871.34511.956353.1743831169.6458150122561.3833564416504313 137 4 2.4933.217629707.108081809773839995188256800499141543684393035450350551 138 15 2^3.7.13.47.139.277.5107.9109.132619.1476463.1001523179.23535794707.2461243576713869557 139 4 2.1669.5430731.115215201111546538317696820901417129607616709798043944747 140 20 2^4.5^2.11^2.29.61.71.547.1093.1181.16493.28596961.32839661.94373861.2664097031.374857981681 141 9 2.13.1223.21997.5112661.96656723.161969595577.2031161085853.165301473942399079669 142 9 2^3.853.2131.82219.3099719989.4052490063499.3754733257489862401973357979128773 143 5 2.23.3851.797161.1198014380856762535048758241151960180137876946928788681521 144 24 2^6.5.7.13.17.19.37.41.73.97.193.577.757.769.6481.530713.1418632417.282429005041.56227703611393 145 7 2.11^2.59.28537.20381027.183349688798536618131199274872809217263632838323547361 146 9 2^3.439.11243.20149.15768033143.9460375336977361.38488154120055537150068589763279 147 11 2.13.491.1093.4019.8233.47041.51157.131713.368089.254395969103901649521223867932173929 148 13 2^4.5.149.18427.107671.953861.13097927.56737873.17189128703.142659759801404920771391593 149 4 2.7451.177941761.46509804063632583432467217805311362636553293639540930405531 150 22 2^3.7.11^2.13.31.61.151.271.601.2551.4561.8951.9601.26251.119101.391151.1530601.22996651.2098303812601 151 5 2.1511.6263783.64745079361.905673230703550690601003473107008473103084254587061 152 17 2^5.5.41.761.1597.2851.31769.101917.363889.3302353.5301533.25480398173.278733912072436804273 153 10 2.13.757.1871.12853.34511.6213394261.35106034213.99810171997.28090626041813012073462457 154 13 2^3.23.67.547.661.1093.3851.51457561.7151459701.76831835389.56495392933101222275861053369 155 9 2.11^2.311.683.102673.4404047.3586225081.1078579799806668629607014283525941686969924751 156 22 2^4.5.7.13^2.53.73.79.157.313.2887.6553.7333.10141.325729.398581.797161.4795973261.271722723752757889 157 5 2.9421.3381925092493.9891109125337566719.1283810768507270931382867729773882314783 158 9 2^3.66361.432853009.327220181191.392038110671.145171177264407947.567239060331150635317 159 7 2.13.107.24169.712550912937217.3747607031112307667.40559607827224525043263763418498193 160 23 2^7.5^2.11^2.17.41.61.193.1181.14401.8194721.21523361.42521761.700984481.128653413121.597747428754241 161 5 2.47.1093.1001523179.636961216046002471921398696960338364910115196955450597747751689 162 21 2^3.7.13.19.37.109.163.433.757.1297.3889.8209.19441.19927.208657.224209.1190701.5879415781.12557612956332313 163 4 2.5227348213873.8882811705390167.6351885141964057411259499526611848626072045955243 164 13 2^4.5.83.33703.2088869.2526913.110767897.86950696619.270547105429567.574933708017116710865237 165 13 2.11^3.13.23.1321.3851.4561.50821.2413941289.560088668384411.4183739978746243239852385111562221 166 11 2^3.167.499.997.12119.2466097.1036745531.950996059627210897943351.813201725710097952736361977 167 6 2.58451.88177.1767863.10063060897082377.260551495718621260054268273374657473120059796409 168 28 2^5.5.7^2.13.29.41.43.73.337.547.673.1009.1093.2269.2857.6481.16493.167329.368089.430697.647753.109688713.2\ 108826721 169 5 2.2029.797161.163264150141.814222556753878193601980463083668707558864014894642043902929 170 16 2^3.11^2.61.103.307.1021.1531.1871.34511.224401.2663568851051.862970652262943171.13271362257832586268931 171 10 2.13.229.757.1597.119701.248749.363889.1824179209.27203787889921135221329070240968055313746007669 172 13 2^4.5.173.431.470593.2641485701.55473422113.903239908009.380808546861411923.82064241848634269407 173 5 2.347.762239.2125048865543.30985428700388045508959018054392810762033149280306907746766819 174 19 2^3.7.13.59.349.523.6091.28537.74821.142159.261697.1383301.5385997.20381027.32234893.37464463.1502241239758\ 57 175 11 2.11^2.71.1093.8951.109201.391151.2664097031.1430128198787051.11459299580388289258664119605215721251 176 22 2^6.5.17.23.41.67.89.193.661.3851.5501.570461.2382953.6922081.56625998353.15656839738849.1363620137403810529 177 7 2.13.709.14425532687.489769993189671059.2224898159852613649.9736622508037946817946068730077829 178 9 2^3.179.264331.1125706177.1611479891519807.5042939439565996049162197.2444322641415331355533344283 179 8 2.359.56207.100957.19510643.291066066130451.6779963644378513811.161868664744491655705858963594331 180 28 2^4.5^2.7.11^2.13.19.31.37.61.73.181.271.757.1181.1621.4561.176401.387631.530713.755551.927001.47763361.452\ 808441334403281 181 4 2.90863.890159.1412740676235815729693013611798695493926336144083867368022228212267580445753 182 13 2^3.547.1093.8737.398581.595141.797161.4011586307.2354116499281.2452788561133.3745603812007166116831643 183 8 2.13.733.603901.97806913.2421854958301.105293313660391861035901.7165195867462155138286987098273769 184 14 2^5.5.41.47.1289.12553493.1001523179.23535794707.70601370627701.743170846305411756447828504941347481129 185 13 2.11^2.2221.17761.35521.146891.13097927.228082801.17189128703.49804972211.87841814842081.1654235911196704741 186 16 2^3.7.13.373.683.1117.6883.102673.541447.3058399.4404047.22434744889.88239050462461.26273701844015319144827\ 917 187 9 2.23.1871.3851.6359.34511.1272753542934479.3411926755457243.527447346649058852221083363397206345775307 188 14 2^4.5.1223.16921.21997.256057.5112661.96656723.563838649753.1534179947851.125384283132205265785477849439329 189 11 2.13.109.433.757.1093.8209.368089.144542918285300809.49888641454623789553.67775349707440873247475442867753 190 15 2^3.11^2.61.191.1597.2851.39901.101917.363889.29574984661.25349956307509384561.7895808769460932143966013189\ 9631 191 5 2.383.311713.9593931911.5890868591760365434332005074929710400548909181468214858888800348369500317 192 27 2^8.5.7.13.17.41.73.97.193.577.769.6481.7297.68737.76801.21523361.96948097.24127552321.70613232600577.92651\ 0094425921 193 6 2.6563.29723.2346066378779.218246094772601642186973037.607981469094652492202396647678317419649770543 194 9 2^3.76631.459991849.503803759819.2549755542947.20591603926857377806745611.48845962828028421155731228333 195 16 2.11^2.13^2.131.313.2341.4561.6553.7333.797161.3701101.39838501.110133112994711.981399299397489772089945543\ 31725481 196 21 2^4.5.29.197.491.547.1093.4019.8233.16493.16661.51157.131713.251325313.857643277.127522693159.426712077457. 34013149495921 197 5 2.9851.741019334164502879.11472574961994477441469621.58733573000937067164211172290216978734891718609 198 22 2^3.7.13.19.23.37.67.199.397.661.757.3851.4357.25411.176419.3186217.337448233.2413941289.378450588583.12812\ 432238302009985937 199 4 2.1360648969.293366430131930353811221418233.110902970953020998760372036298330712066931713186888935429 200 24 2^5.5^3.11^2.41.61.101.151.1181.8951.133201.391151.394201.22996651.42521761.18055139801.61070817601.6145992\ 6512826500975801 201 7 2.13.221101.1089421.441019876741.475384700124973.606888680894320302113812772385855126907748678398622467309 202 8 2^3.379963.33034273.465092326319.50316775668019759306202964023.1017291527198723292208309354658785077827527 203 8 2.59.1093.2843.28537.735673.20381027.45710553733635551271263934571653147487690442652554544220310250384660059 204 23 2^4.5.7.13.73.103.307.409.613.1021.1871.12853.30091.34511.956353.49637281.129159847.1743831169.99810171997. 187668407555352123529 205 9 2.11^2.83.6971.31981.2526913.86950696619.656014262570688827408083292697668196087284247240671872421177502707\ 51 206 7 2^3.619.3661040653.1535090713229126909942383374434289901.6957596529882152968992225251835887181478451547013 207 11 2.13.47.277.757.829.1657.4969.1001523179.2461243576713869557.1347383535369337305525136183495059997240461761\ 85208477 208 20 2^6.5.17.41.53.193.1249.13729.398581.797161.475356961.2093124281.4795973261.37644053098601.7804643378464442\ 96785447886881 209 10 2.23.419.1597.2927.3851.363889.99381983898121.340838185560681043030809047.122248739643995179286707888399612\ 5166979 210 29 2^3.7^2.11^2.13.31.43.61.71.211.271.421.547.1051.1093.2269.4561.6301.24151.368089.1616161.3369031.3454081.2\ 664097031.26751945361.374857981681 211 7 2.2111.962188370639.54046656969013.5676687374958905209.1695949409060064182746451.22260233052088235975354234\ 411 212 14 2^4.5.107.24169.90313.78719947.609422621.1481588501.61557605176233223.3747607031112307667.46074068338167202\ 1327601001 213 8 2.13.5113.22716867932413.115264393627813.3613512804721129.89665588664737776553.3754733257489862401973357979\ 128773 214 9 2^3.643.50077.100153.229837.48965028505045123993421250406516036571557.4375617272295428356111030724847180250\ 451293 215 8 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