Factorisations Of Cunningham Numbers C-(7,n) = 7^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 2 2.3 2 5 2^4.3 3 4 2.3^2.19 4 8 2^5.3.5^2 5 3 2.3.2801 6 8 2^4.3^2.19.43 7 4 2.3.29.4733 8 10 2^6.3.5^2.1201 9 7 2.3^3.19.37.1063 10 8 2^4.3.11.191.2801 11 4 2.3.1123.293459 12 13 2^5.3^2.5^2.13.19.43.181 13 3 2.3.16148168401 14 9 2^4.3.29.113.911.4733 15 7 2.3^2.19.31.2801.159871 16 13 2^7.3.5^2.17.1201.169553 17 4 2.3.14009.2767631689 18 12 2^4.3^3.19.37.43.1063.117307 19 4 2.3.419.4534166740403 20 14 2^5.3.5^3.11.191.281.2801.4021 21 7 2.3^2.19.29.4733.11898664849 22 9 2^4.3.23.1123.293459.10746341 23 5 2.3.47.3083.31479823396757 24 18 2^6.3^2.5^2.13.19.43.73.181.193.409.1201 25 5 2.3.2551.2801.31280679788951 26 8 2^4.3.53.228511817.16148168401 27 12 2.3^4.19.37.109.811.1063.2377.2583253 28 13 2^5.3.5^2.29.113.911.4733.13564461457 29 5 2.3.59.127540261.71316922984999 30 14 2^4.3^2.11.19.31.43.191.2801.159871.6568801 31 5 2.3.311.21143.3999088279399464409 32 16 2^8.3.5^2.17.353.1201.169553.47072139617 33 9 2.3^2.19.1123.3631.293459.1532917.12323587 34 8 2^4.3.14009.2767631689.29078814248401 35 7 2.3.29.2801.4733.2127431041.77192844961 36 18 2^5.3^3.5^2.13.19.37.43.181.1063.117307.13841169553 37 5 2.3.223.2887.4805345109492315767981401 38 9 2^4.3.419.351121.4058036683.4534166740403 39 8 2.3^2.19.486643.7524739.44975113.16148168401 40 18 2^6.3.5^3.11.41.191.281.1201.2801.4021.810221830361 41 5 2.3.83.20515909.4362139336229068656094783 42 15 2^4.3^2.19.29.43.113.911.4733.51031.309079.11898664849 43 4 2.3.166003607842448777.2192537062271178641 44 15 2^5.3.5^2.23.661.1123.1409.293459.10746341.83960385389 45 12 2.3^3.19.31.37.1063.2801.159871.1527007411.125096112091 46 9 2^4.3.47.3083.31479823396757.3421093417510114543 47 4 2.3.13722816749522711.63681511996418550459487 48 22 2^7.3^2.5^2.13.17.19.43.73.181.193.409.1201.169553.33232924804801 49 8 2.3.29.3529.4733.1074473.13473433.6106505825833677713 50 11 2^4.3.11.191.2551.2801.31280679788951.79787519018560501 51 10 2.3^2.19.103.14009.365773.2316281689.2767631689.10879733611 52 13 2^5.3.5^2.53.157.228511817.16148168401.1195857367853217109 53 5 2.3.8269.319591.38904276017035188056372051839841219 54 18 2^4.3^4.19.37.43.109.811.1063.2377.117307.2583253.1628413557556843 55 6 2.3.1123.2801.293459.5457586804596062091175455674392801 56 19 2^6.3.5^2.29.113.337.911.1201.2129.4733.517553.515717329.13564461457 57 10 2.3^2.19^2.419.19609.879399649.4534166740403.6957533874046531 58 9 2^4.3.59.127540261.71316922984999.402488219476647465854701 59 6 2.3.459257.134927809.550413361.354639323684545612988577649 60 24 2^5.3^2.5^3.11.13.19.31.43.61.181.191.281.2801.4021.159871.6568801.555915824341 61 6 2.3.367.4759.177237331.1914662449813727660680530326064591907 62 11 2^4.3.311.373.21143.9754399.5420506947192709.3999088279399464409 63 11 2.3^3.19.29.37.1063.4733.11898664849.2643999917660728787808396988849 64 20 2^9.3.5^2.17.353.1201.169553.7699649.134818753.47072139617.531968664833 65 9 2.3.131.2801.157951.787021.16148168401.4446437759531.434502978835771 66 17 2^4.3^2.19.23.43.67.1123.3631.293459.1532917.10746341.12323587.1357105535093947 67 6 2.3.228337.147300841.206244761.10052011757370829033540932021825161 68 14 2^5.3.5^2.137.14009.59361349.2767631689.29078814248401.133088039373662309 69 10 2.3^2.19.47.139.3083.402011881627.31479823396757.235169662395069356312233 70 18 2^4.3.11.29.71.113.191.421.911.2801.4733.12128131.603926681.2127431041.77192844961 71 4 2.3.990643452963163.169002145064468556765676975247413756542145739 72 26 2^6.3^3.5^2.13.19.37.43.73.181.193.409.1063.1201.42409.117307.137089.13841169553.32952799801 73 7 2.3.439.3675989.359390389.1958423494433591.7222605228105536202757606969 74 10 2^4.3.149.223.2887.4805345109492315767981401.15572244900182528777225808449 75 11 2.3^2.19.31.2551.2801.29251.159871.31280679788951.217648180992721729506406538251 76 13 2^5.3.5^2.419.351121.4058036683.4534166740403.2598696228942460402343442913969 77 9 2.3.29.1123.4733.293459.724487149.6809710909.88262612316754526107621113329689 78 17 2^4.3^2.19.43.53.79.486643.7524739.23850061.44975113.228511817.16148168401.115868130379 79 4 2.3.913242407367610843676812931.1056836588644853738704557482552056406147 80 24 2^7.3.5^3.11.17.41.191.281.881.1201.2801.4021.169553.542081.810221830361.2312581841562813841 81 17 2.3^5.19.37.109.811.1063.1621.2377.3727.2583253.3368791.70722308812401674174993533367023 82 12 2^4.3.83.4849399.8999993.20515909.1636258751.78009515593.4362139336229068656094783 83 9 2.3.167.66733.76066181.7685542369.62911130477521.303567967057423.18624275418445601 84 22 2^5.3^2.5^2.13.19.29.43.113.181.911.4733.51031.309079.11898664849.13564461457.195489390796456327201 85 8 2.3.1531.2801.4931.14009.2767631689.138497973518827432485604572537024087153816681041 86 14 2^4.3.947.19867.20899.163573.235211.3799051.4749781.166003607842448777.2192537062271178641 87 10 2.3^2.19.59.127540261.2576743207.71316922984999.196915704073465747.358475907408445923469 88 20 2^6.3.5^2.23.89.661.1123.1201.1409.8713.293459.10746341.83960385389.8206973609150536446402438593 89 5 2.3.1805633.18489605314740987765913.8166146875847876762859119015147004762656450569 90 24 2^4.3^3.11.19.31.37.43.191.541.1063.2801.117307.154351.159871.295831.6568801.7777981.1527007411.125096112091 91 8 2.3.29.4733.7304123737.16148168401.231410451435538144122809.3565837331172073232378945297 92 16 2^5.3.5^2.47.3083.26681.649981.15513961.31479823396757.3421093417510114543.55681942361860463813 93 10 2.3^2.19.311.21143.5463751.2211164386353499.3999088279399464409.36148617745189465516342817701 94 8 2^4.3.13722816749522711.63681511996418550459487.655417289594537954307682339857743931943 95 8 2.3.419.2801.36671.1966385431.4534166740403.83588499889013461558350575326824370345112529401 96 28 2^8.3^2.5^2.13.17.19.43.73.97.181.193.353.409.1201.169553.104837857.47072139617.33232924804801.108604397663\ 266369 97 5 2.3.389.971.4160924156784953821413999107825795646911807584554735726748631757909547764679 98 20 2^4.3.29.113.197.883.911.3529.3823.4733.161309.1074473.1445599.13473433.19847549.101361401.6106505825833677\ 713 99 15 2.3^3.19.37.199.1063.1123.3631.173647.293459.1532917.12323587.14658652062814508164798530246267135510037033 100 22 2^5.3.5^4.11.101.191.281.2551.2801.4021.13001.25301.31280679788951.79787519018560501.38327966300231909291101 101 6 2.3.607.809.6263.1226962153072980952980067096888460031879516017670288348423584305043494594529 102 18 2^4.3^2.19.43.103.14009.365773.1135261.12192877.2316281689.2767631689.10879733611.29078814248401.9092074664\ 9833 103 4 2.3.17923.10316589882658148664018432412741304154103858145253645339510927287724805842171756259 104 18 2^6.3.5^2.53.157.313.1201.85094881.228511817.16148168401.1195857367853217109.1377454635342537460935008154217 105 13 2.3^2.19.29.31.2801.4733.159871.2127431041.11898664849.77192844961.42693162668620904426304495389707999425601 106 12 2^4.3.107.8269.319591.345449549.35416476134069.58902316970027001503.38904276017035188056372051839841219 107 5 2.3.227109283745807808529.1620221568881364582821.1206506689449517154664984054683391885701717268373 108 27 2^5.3^4.5^2.13.19.37.43.109.181.811.1063.2377.26893.117307.2583253.13841169553.167039577217.590297313273013. 1628413557556843 109 5 2.3.14551288401737861.63505707690048880101785428103.23540782932240399632107200158745339309941271547 110 19 2^4.3.11^2.23.191.331.1123.2311.2801.38501.293459.2864401.10746341.7840815905526451.54575868045960620911754\ 55674392801 111 11 2.3^2.19.223.2887.6217.177379.56713875643149053038693.4805345109492315767981401.966513020957488728227630485\ 99 112 27 2^7.3.5^2.17.29.113.337.449.673.911.1201.2129.4733.169553.517553.39648001.515717329.13564461457.21535258550\ 401.142256806230113 113 4 2.3.227.230091944348186646613985311030910601771732680858725360845463092718251327185092028815673428363 114 19 2^4.3^2.19^2.43.419.457.19609.351121.879399649.4058036683.24006520939.4534166740403.6957533874046531.275430\ 251632699963 115 12 2.3.47.1151.2801.3083.188831.1446701.723461377501.31479823396757.27229507836853201541.323388097576653901216\ 14112981 116 16 2^5.3.5^2.59.233.127540261.136853089.55716067510309.71316922984999.116714640028973541741413.402488219476647\ 465854701 117 16 2.3^3.19.37.1063.1873.322921.486643.2280097.7524739.44975113.7687225261.16148168401.66135384230579134218722\ 8684843715341 118 13 2^4.3.122131.459257.134927809.550413361.4261190159.1187164242679.14683403662888806475673.354639323684545612\ 988577649 119 11 2.3.29.4733.12377.14009.34273.2767631689.305213588009240737.440779823883628367834893.2023356904834733683686\ 3191403341 120 33 2^6.3^2.5^3.11.13.19.31.41.43.61.73.181.191.193.281.409.1201.2801.4021.159871.6568801.12913561.555915824341. 810221830361.85560261859655897641 121 9 2.3.1123.1453.65099.293459.11795261559086963.58792315124013823398811997.13928884340651233393054864060847158\ 508075329 122 10 2^4.3.367.4759.177237331.1914662449813727660680530326064591907.44451912814717044465691467294568943905088020\ 9231501 123 9 2.3^2.19.83.267403.20515909.4362139336229068656094783.13031612278097596136163934699402177453365619293349843\ 0337748067 124 17 2^5.3.5^2.311.373.21143.9754399.33947629297.5420506947192709.3999088279399464409.74502648768583254173.19684\ 6325409292090901 125 8 2.3.251.2551.2801.31280679788951.2182816753758823696751.590354667835684444020417934211947301188761723956532\ 3800435501 126 25 2^4.3^3.19.29.37.43.113.127.911.1063.4733.9829.51031.117307.309079.20801593.67979647.1506625093.11898664849. 2643999917660728787808396988849 127 5 2.3.260461507.554351226505275380676162672703.24534164319836858284335214459848074446885004177502212550076704\ 7213117 128 24 2^10.3.5^2.17.353.1201.35969.169553.7699649.134818753.47072139617.531968664833.1110623386241.15266848196793\ 556098085000332888634369 129 10 2.3^2.19.10837.63350976270733.166003607842448777.2192537062271178641.175446584281395198837259.6946231973486\ 82715265952229891 130 18 2^4.3.11.53.131.191.2801.157951.787021.1175071.228511817.16148168401.4446437759531.434502978835771.35695043\ 869049049222174543845808031 131 3 2.3.8505346116479680194953954163954280577066639233068267330253081977410514153169870714693030729025353732044\ 7270457 132 29 2^5.3^2.5^2.13.19.23.43.67.181.661.1123.1409.3631.29569.293459.1532917.2784937.10746341.12323587.678240817. 83960385389.116320403133001.1357105535093947 133 11 2.3.29.419.4733.401563177.2662276961.4534166740403.373740808373213.897558513407803666357.445657944321249761\ 45013684073215440137 134 12 2^4.3.20771.228337.147300841.206244761.6557750853567755279.383942665465635068312581125821527.10052011757370\ 829033540932021825161 135 21 2.3^4.19.31.37.109.271.811.1063.2377.2801.159871.185221.2583253.1527007411.125096112091.175561876921802311. 797937984757981841530188510084780901 136 19 2^6.3.5^2.137.1201.14009.20129.94793.59361349.2767631689.29078814248401.133088039373662309.6389917485430821\ 13037456009420293477766438233 137 8 2.3.2741.213721.251533.57162922399254002352124124899.65480203458464902965944539043.181428113215102554427027\ 51468712154533804561 138 18 2^4.3^2.19.43.47.139.277.3083.402011881627.7396787205469.31479823396757.3421093417510114543.850194891513615\ 5490673.235169662395069356312233 139 5 2.3.19739.673039.369071860325105204940905426444784144250426677655115371406716343216852089137589555456819857\ 19375774106220917 140 28 2^5.3.5^3.11.29.71.113.191.281.421.911.2801.4021.4733.12128131.603926681.2127431041.13564461457.77192844961. 102314938321.18690488255321.19584845505919961 141 9 2.3^2.19.283.5960917.13722816749522711.63681511996418550459487.28591793293072926277385447141879418320873502\ 6049402141999388275408759 142 9 2^4.3.990643452963163.1351405472411521.92914860840816888117372433724419584467881183.16900214506446855676567\ 6975247413756542145739 143 8 2.3.1123.293459.16148168401.528808508322667.376215890379315997311416372784691746214777.11119427897815667812\ 99747693078700888402223739 144 35 2^7.3^3.5^2.13.17.19.37.43.73.181.193.409.1063.1201.42409.117307.129169.137089.169553.25726609.51385969.635\ 311009.13841169553.32952799801.338325042961.33232924804801 145 9 2.3.59.2801.4899841.127540261.71316922984999.277463632645667965008782910911.2822743899874399927030333062466\ 2217730888039289619786090751 146 13 2^4.3.439.3067.279883.3675989.359390389.1958423494433591.7222605228105536202757606969.716764748064350430205\ 8174754486698790538818746798241 147 14 2.3^2.19.29.3529.4733.1074473.13473433.11898664849.4060603391041.6106505825833677713.4247708713399033015675\ 09.56427334222486513688076273080920621 148 14 2^5.3.5^2.149.223.2887.4805345109492315767981401.15572244900182528777225808449.6891042949305882214394659726\ 647344864958515967158596120016737 149 3 2.3.1385022127101034087007743810331355039266633249933176317292277906573251633103418332277759454260526370920\ 67324133850503035623601 150 22 2^4.3^2.11.19.31.43.151.191.2551.2801.29251.159871.6568801.6005492312551.31280679788951.79787519018560501.7\ 021370289199888801.217648180992721729506406538251 151 7 2.3.115356256117.36076003832567.206462520503013793561.2856349001315592319937.276529023162022452344185243512\ 4159094999555183731339173137659 152 20 2^6.3.5^2.419.1201.351121.44118001.700197881.4058036683.1295161807633.4534166740403.1299254811081649.135214\ 434686939513.2598696228942460402343442913969 153 19 2.3^3.19.37.103.307.613.1063.4591.14009.44371.365773.2316281689.2767631689.10879733611.44072862804091655188\ 147.795000162131334968169163150985614882079420233 154 21 2^4.3.23.29.113.463.911.1123.4733.293459.333103.10746341.258576319.724487149.6809710909.32817262777539703.4\ 43632323630099913.88262612316754526107621113329689 155 11 2.3.311.2801.21143.21391.21701.1622982371.9254997611.3999088279399464409.3172801518994677306295492126843582\ 5250349092899077924422648569887851893731 156 27 2^5.3^2.5^2.13^2.19.43.53.79.157.181.486643.7524739.23850061.44975113.228511817.16148168401.115868130379.36\ 5302616611175569.1195857367853217109.7886422107556319674933 157 6 2.3.4397.5653.1039945344901.3088837530933217469974776415779808389101928682917555417651530821177567508549116\ 4240495874534303554491469173279661 158 11 2^4.3.317.2874811.7573763065938754357.913242407367610843676812931.104875706439110156251225614941159441477.1\ 056836588644853738704557482552056406147 159 11 2.3^2.19.8269.32119.319591.1695259.84247682063005850464952755729.38904276017035188056372051839841219.145532\ 9561052597138348454392994231780317942530389 160 30 2^8.3.5^3.11.17.41.191.281.353.881.1201.2801.4021.169553.542081.38470561.47072139617.810221830361.102118777\ 045028801.2312581841562813841.310484866091676781304919233441 161 10 2.3.29.47.3083.4733.4406588677.31479823396757.4615185796935334098258901.15055781938825018473753891500648508\ 6145065087672198550975239193637571002600137 162 27 2^4.3^5.19.37.43.109.163.487.811.1063.1621.2377.3727.15877.117307.2583253.3368791.1628413557556843.70722308\ 812401674174993533367023.3426171911854086574033958308360873411 163 8 2.3.653.9781.1260643.962207945014470392304193.1648536343690282975764489383562678396141955057.73548403576963\ 48186997141461981606470291584313584199443 164 18 2^5.3.5^2.83.4849399.8999993.20515909.33842057.1636258751.78009515593.5449628176194898649.43621393362290686\ 56094783.215399976956807881972039163130016444991137 165 17 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2^4.3^2.11.19.29.31.43.71.113.191.211.421.911.2801.4733.51031.159871.309079.6568801.12128131.603926681.2127\ 431041.11898664849.77192844961.338640865331157691.450798894542150330401.42693162668620904426304495389707999\ 425601 211 5 2.3.141793.25901828181222890897428585774179766860170863299438695413795254930505191880636307.938750071762380\ 696516440050300186170396791830893409813886026297637087471612609007080078230307 212 18 2^5.3.5^2.107.8269.15053.319591.7627549.345449549.35416476134069.58902316970027001503.389042760170351880563\ 72051839841219.66284833432285160162590803535350777411419371011803789028357303049568916086249 213 10 2.3^2.19.968299.582053568181.990643452963163.169002145064468556765676975247413756542145739.1274759667849259\ 732505774376326193816317726317.24640304627535595210208716854848978157699652842397850563 214 11 2^4.3.1499.82413922847.227109283745807808529.1620221568881364582821.120650668944951715466498405468339188570\ 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