Factorisations Of Cunningham Numbers C-(7,n) = 7n - 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  2.3
   2     5  2.2.2.2.3
   3     4  2.3.3.19
   4     8  2.2.2.2.2.3.5.5
   5     3  2.3.2801
   6     8  2.2.2.2.3.3.19.43
   7     4  2.3.29.4733
   8    10  2.2.2.2.2.2.3.5.5.1201
   9     7  2.3.3.3.19.37.1063
  10     8  2.2.2.2.3.11.191.2801
  11     4  2.3.1123.293459
  12    13  2.2.2.2.2.3.3.5.5.13.19.43.181
  13     3  2.3.16148168401
  14     9  2.2.2.2.3.29.113.911.4733
  15     7  2.3.3.19.31.2801.159871
  16    13  2.2.2.2.2.2.2.3.5.5.17.1201.169553
  17     4  2.3.14009.2767631689
  18    12  2.2.2.2.3.3.3.19.37.43.1063.117307
  19     4  2.3.419.4534166740403
  20    14  2.2.2.2.2.3.5.5.5.11.191.281.2801.4021
  21     7  2.3.3.19.29.4733.11898664849
  22     9  2.2.2.2.3.23.1123.293459.10746341
  23     5  2.3.47.3083.31479823396757
  24    18  2.2.2.2.2.2.3.3.5.5.13.19.43.73.181.193.409.1201
  25     5  2.3.2551.2801.31280679788951
  26     8  2.2.2.2.3.53.228511817.16148168401
  27    12  2.3.3.3.3.19.37.109.811.1063.2377.2583253
  28    13  2.2.2.2.2.3.5.5.29.113.911.4733.13564461457
  29     5  2.3.59.127540261.71316922984999
  30    14  2.2.2.2.3.3.11.19.31.43.191.2801.159871.6568801
  31     5  2.3.311.21143.3999088279399464409
  32    16  2.2.2.2.2.2.2.2.3.5.5.17.353.1201.169553.47072139617
  33     9  2.3.3.19.1123.3631.293459.1532917.12323587
  34     8  2.2.2.2.3.14009.2767631689.29078814248401
  35     7  2.3.29.2801.4733.2127431041.77192844961
  36    18  2.2.2.2.2.3.3.3.5.5.13.19.37.43.181.1063.117307.13841169553
  37     5  2.3.223.2887.4805345109492315767981401
  38     9  2.2.2.2.3.419.351121.4058036683.4534166740403
  39     8  2.3.3.19.486643.7524739.44975113.16148168401
  40    18  2.2.2.2.2.2.3.5.5.5.11.41.191.281.1201.2801.4021.810221830361
  41     5  2.3.83.20515909.4362139336229068656094783
  42    15  2.2.2.2.3.3.19.29.43.113.911.4733.51031.309079.11898664849
  43     4  2.3.166003607842448777.2192537062271178641
  44    15  2.2.2.2.2.3.5.5.23.661.1123.1409.293459.10746341.83960385389
  45    12  2.3.3.3.19.31.37.1063.2801.159871.1527007411.125096112091
  46     9  2.2.2.2.3.47.3083.31479823396757.3421093417510114543
  47     4  2.3.13722816749522711.63681511996418550459487
  48    22  2.2.2.2.2.2.2.3.3.5.5.13.17.19.43.73.181.193.409.1201.169553.33232924804801
  49     8  2.3.29.3529.4733.1074473.13473433.6106505825833677713
  50    11  2.2.2.2.3.11.191.2551.2801.31280679788951.79787519018560501
  51    10  2.3.3.19.103.14009.365773.2316281689.2767631689.10879733611
  52    13  2.2.2.2.2.3.5.5.53.157.228511817.16148168401.1195857367853217109
  53     5  2.3.8269.319591.38904276017035188056372051839841219
  54    18  2.2.2.2.3.3.3.3.19.37.43.109.811.1063.2377.117307.2583253.1628413557556843
  55     6  2.3.1123.2801.293459.5457586804596062091175455674392801
  56    19  2.2.2.2.2.2.3.5.5.29.113.337.911.1201.2129.4733.517553.515717329.13564461457
  57    10  2.3.3.19.19.419.19609.879399649.4534166740403.6957533874046531
  58     9  2.2.2.2.3.59.127540261.71316922984999.402488219476647465854701
  59     6  2.3.459257.134927809.550413361.354639323684545612988577649
  60    24  2.2.2.2.2.3.3.5.5.5.11.13.19.31.43.61.181.191.281.2801.4021.159871.6568801.555915824341
  61     6  2.3.367.4759.177237331.1914662449813727660680530326064591907
  62    11  2.2.2.2.3.311.373.21143.9754399.5420506947192709.3999088279399464409
  63    11  2.3.3.3.19.29.37.1063.4733.11898664849.2643999917660728787808396988849
  64    20  2.2.2.2.2.2.2.2.2.3.5.5.17.353.1201.169553.7699649.134818753.47072139617.531968664833
  65     9  2.3.131.2801.157951.787021.16148168401.4446437759531.434502978835771
  66    17  2.2.2.2.3.3.19.23.43.67.1123.3631.293459.1532917.10746341.12323587.1357105535093947
  67     6  2.3.228337.147300841.206244761.10052011757370829033540932021825161
  68    14  2.2.2.2.2.3.5.5.137.14009.59361349.2767631689.29078814248401.133088039373662309
  69    10  2.3.3.19.47.139.3083.402011881627.31479823396757.235169662395069356312233
  70    18  2.2.2.2.3.11.29.71.113.191.421.911.2801.4733.12128131.603926681.2127431041.77192844961
  71     4  2.3.990643452963163.169002145064468556765676975247413756542145739
  72    26  2.2.2.2.2.2.3.3.3.5.5.13.19.37.43.73.181.193.409.1063.1201.42409.117307.137089.13841169553.32952799801
  73     7  2.3.439.3675989.359390389.1958423494433591.7222605228105536202757606969
  74    10  2.2.2.2.3.149.223.2887.4805345109492315767981401.15572244900182528777225808449
  75    11  2.3.3.19.31.2551.2801.29251.159871.31280679788951.217648180992721729506406538251
  76    13  2.2.2.2.2.3.5.5.419.351121.4058036683.4534166740403.2598696228942460402343442913969
  77     9  2.3.29.1123.4733.293459.724487149.6809710909.88262612316754526107621113329689
  78    17  2.2.2.2.3.3.19.43.53.79.486643.7524739.23850061.44975113.228511817.16148168401.115868130379
  79     4  2.3.913242407367610843676812931.1056836588644853738704557482552056406147
  80    24  2.2.2.2.2.2.2.3.5.5.5.11.17.41.191.281.881.1201.2801.4021.169553.542081.810221830361.2312581841562813841
  81    17  2.3.3.3.3.3.19.37.109.811.1063.1621.2377.3727.2583253.3368791.70722308812401674174993533367023
  82    12  2.2.2.2.3.83.4849399.8999993.20515909.1636258751.78009515593.4362139336229068656094783
  83     9  2.3.167.66733.76066181.7685542369.62911130477521.303567967057423.18624275418445601
  84    22  2.2.2.2.2.3.3.5.5.13.19.29.43.113.181.911.4733.51031.309079.11898664849.13564461457.195489390796456327201
  85     8  2.3.1531.2801.4931.14009.2767631689.138497973518827432485604572537024087153816681041
  86    14  2.2.2.2.3.947.19867.20899.163573.235211.3799051.4749781.166003607842448777.2192537062271178641
  87    10  2.3.3.19.59.127540261.2576743207.71316922984999.196915704073465747.358475907408445923469
  88    20  2.2.2.2.2.2.3.5.5.23.89.661.1123.1201.1409.8713.293459.10746341.83960385389.8206973609150536446402438593
  89     5  2.3.1805633.18489605314740987765913.8166146875847876762859119015147004762656450569
  90    24  2.2.2.2.3.3.3.11.19.31.37.43.191.541.1063.2801.117307.154351.159871.295831.6568801.7777981.1527007411.12509\
            6112091
  91     8  2.3.29.4733.7304123737.16148168401.231410451435538144122809.3565837331172073232378945297
  92    16  2.2.2.2.2.3.5.5.47.3083.26681.649981.15513961.31479823396757.3421093417510114543.55681942361860463813
  93    10  2.3.3.19.311.21143.5463751.2211164386353499.3999088279399464409.36148617745189465516342817701
  94     8  2.2.2.2.3.13722816749522711.63681511996418550459487.655417289594537954307682339857743931943
  95     8  2.3.419.2801.36671.1966385431.4534166740403.83588499889013461558350575326824370345112529401
  96    28  2.2.2.2.2.2.2.2.3.3.5.5.13.17.19.43.73.97.181.193.353.409.1201.169553.104837857.47072139617.33232924804801.
            108604397663266369
  97     5  2.3.389.971.4160924156784953821413999107825795646911807584554735726748631757909547764679
  98    20  2.2.2.2.3.29.113.197.883.911.3529.3823.4733.161309.1074473.1445599.13473433.19847549.101361401.610650582583\
            3677713
  99    15  2.3.3.3.19.37.199.1063.1123.3631.173647.293459.1532917.12323587.14658652062814508164798530246267135510037033
 100    22  2.2.2.2.2.3.5.5.5.5.11.101.191.281.2551.2801.4021.13001.25301.31280679788951.79787519018560501.383279663002\
            31909291101
 101     6  2.3.607.809.6263.1226962153072980952980067096888460031879516017670288348423584305043494594529
 102    18  2.2.2.2.3.3.19.43.103.14009.365773.1135261.12192877.2316281689.2767631689.10879733611.29078814248401.909207\
            46649833
 103     4  2.3.17923.10316589882658148664018432412741304154103858145253645339510927287724805842171756259
 104    18  2.2.2.2.2.2.3.5.5.53.157.313.1201.85094881.228511817.16148168401.1195857367853217109.1377454635342537460935\
            008154217
 105    13  2.3.3.19.29.31.2801.4733.159871.2127431041.11898664849.77192844961.42693162668620904426304495389707999425601
 106    12  2.2.2.2.3.107.8269.319591.345449549.35416476134069.58902316970027001503.38904276017035188056372051839841219
 107     5  2.3.227109283745807808529.1620221568881364582821.1206506689449517154664984054683391885701717268373
 108    27  2.2.2.2.2.3.3.3.3.5.5.13.19.37.43.109.181.811.1063.2377.26893.117307.2583253.13841169553.167039577217.59029\
            7313273013.1628413557556843
 109     5  2.3.14551288401737861.63505707690048880101785428103.23540782932240399632107200158745339309941271547
 110    19  2.2.2.2.3.11.11.23.191.331.1123.2311.2801.38501.293459.2864401.10746341.7840815905526451.545758680459606209\
            1175455674392801
 111    11  2.3.3.19.223.2887.6217.177379.56713875643149053038693.4805345109492315767981401.966513020957488728227630485\
            99
 112    27  2.2.2.2.2.2.2.3.5.5.17.29.113.337.449.673.911.1201.2129.4733.169553.517553.39648001.515717329.13564461457.2\
            1535258550401.142256806230113
 113     4  2.3.227.230091944348186646613985311030910601771732680858725360845463092718251327185092028815673428363
 114    19  2.2.2.2.3.3.19.19.43.419.457.19609.351121.879399649.4058036683.24006520939.4534166740403.6957533874046531.2\
            75430251632699963
 115    12  2.3.47.1151.2801.3083.188831.1446701.723461377501.31479823396757.27229507836853201541.323388097576653901216\
            14112981
 116    16  2.2.2.2.2.3.5.5.59.233.127540261.136853089.55716067510309.71316922984999.116714640028973541741413.402488219\
            476647465854701
 117    16  2.3.3.3.19.37.1063.1873.322921.486643.2280097.7524739.44975113.7687225261.16148168401.661353842305791342187\
            228684843715341
 118    13  2.2.2.2.3.122131.459257.134927809.550413361.4261190159.1187164242679.14683403662888806475673.35463932368454\
            5612988577649
 119    11  2.3.29.4733.12377.14009.34273.2767631689.305213588009240737.440779823883628367834893.2023356904834733683686\
            3191403341
 120    33  2.2.2.2.2.2.3.3.5.5.5.11.13.19.31.41.43.61.73.181.191.193.281.409.1201.2801.4021.159871.6568801.12913561.55\
            5915824341.810221830361.85560261859655897641
 121     9  2.3.1123.1453.65099.293459.11795261559086963.58792315124013823398811997.13928884340651233393054864060847158\
            508075329
 122    10  2.2.2.2.3.367.4759.177237331.1914662449813727660680530326064591907.4445191281471704446569146729456894390508\
            80209231501
 123     9  2.3.3.19.83.267403.20515909.4362139336229068656094783.13031612278097596136163934699402177453365619293349843\
            0337748067
 124    17  2.2.2.2.2.3.5.5.311.373.21143.9754399.33947629297.5420506947192709.3999088279399464409.74502648768583254173.
            196846325409292090901
 125     8  2.3.251.2551.2801.31280679788951.2182816753758823696751.590354667835684444020417934211947301188761723956532\
            3800435501
 126    25  2.2.2.2.3.3.3.19.29.37.43.113.127.911.1063.4733.9829.51031.117307.309079.20801593.67979647.1506625093.11898\
            664849.2643999917660728787808396988849
 127     5  2.3.260461507.554351226505275380676162672703.24534164319836858284335214459848074446885004177502212550076704\
            7213117
 128    24  2.2.2.2.2.2.2.2.2.2.3.5.5.17.353.1201.35969.169553.7699649.134818753.47072139617.531968664833.1110623386241.
            15266848196793556098085000332888634369
 129    10  2.3.3.19.10837.63350976270733.166003607842448777.2192537062271178641.175446584281395198837259.6946231973486\
            82715265952229891
 130    18  2.2.2.2.3.11.53.131.191.2801.157951.787021.1175071.228511817.16148168401.4446437759531.434502978835771.3569\
            5043869049049222174543845808031
 131     3  2.3.8505346116479680194953954163954280577066639233068267330253081977410514153169870714693030729025353732044\
            7270457
 132    29  2.2.2.2.2.3.3.5.5.13.19.23.43.67.181.661.1123.1409.3631.29569.293459.1532917.2784937.10746341.12323587.6782\
            40817.83960385389.116320403133001.1357105535093947
 133    11  2.3.29.419.4733.401563177.2662276961.4534166740403.373740808373213.897558513407803666357.445657944321249761\
            45013684073215440137
 134    12  2.2.2.2.3.20771.228337.147300841.206244761.6557750853567755279.383942665465635068312581125821527.1005201175\
            7370829033540932021825161
 135    21  2.3.3.3.3.19.31.37.109.271.811.1063.2377.2801.159871.185221.2583253.1527007411.125096112091.175561876921802\
            311.797937984757981841530188510084780901
 136    19  2.2.2.2.2.2.3.5.5.137.1201.14009.20129.94793.59361349.2767631689.29078814248401.133088039373662309.63899174\
            8543082113037456009420293477766438233
 137     8  2.3.2741.213721.251533.57162922399254002352124124899.65480203458464902965944539043.181428113215102554427027\
            51468712154533804561
 138    18  2.2.2.2.3.3.19.43.47.139.277.3083.402011881627.7396787205469.31479823396757.3421093417510114543.85019489151\
            36155490673.235169662395069356312233
 139     5  2.3.19739.673039.369071860325105204940905426444784144250426677655115371406716343216852089137589555456819857\
            19375774106220917
 140    28  2.2.2.2.2.3.5.5.5.11.29.71.113.191.281.421.911.2801.4021.4733.12128131.603926681.2127431041.13564461457.771\
            92844961.102314938321.18690488255321.19584845505919961
 141     9  2.3.3.19.283.5960917.13722816749522711.63681511996418550459487.28591793293072926277385447141879418320873502\
            6049402141999388275408759
 142     9  2.2.2.2.3.990643452963163.1351405472411521.92914860840816888117372433724419584467881183.1690021450644685567\
            65676975247413756542145739
 143     8  2.3.1123.293459.16148168401.528808508322667.376215890379315997311416372784691746214777.11119427897815667812\
            99747693078700888402223739
 144    35  2.2.2.2.2.2.2.3.3.3.5.5.13.17.19.37.43.73.181.193.409.1063.1201.42409.117307.129169.137089.169553.25726609.
            51385969.635311009.13841169553.32952799801.338325042961.33232924804801
 145     9  2.3.59.2801.4899841.127540261.71316922984999.277463632645667965008782910911.2822743899874399927030333062466\
            2217730888039289619786090751
 146    13  2.2.2.2.3.439.3067.279883.3675989.359390389.1958423494433591.7222605228105536202757606969.71676474806435043\
            02058174754486698790538818746798241
 147    14  2.3.3.19.29.3529.4733.1074473.13473433.11898664849.4060603391041.6106505825833677713.4247708713399033015675\
            09.56427334222486513688076273080920621
 148    14  2.2.2.2.2.3.5.5.149.223.2887.4805345109492315767981401.15572244900182528777225808449.6891042949305882214394\
            659726647344864958515967158596120016737
 149     3  2.3.1385022127101034087007743810331355039266633249933176317292277906573251633103418332277759454260526370920\
            67324133850503035623601
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