Factorisations Of Cunningham Numbers C-(5,n) = 5n - 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     4  2.2.2.3
   3     3  2.2.31
   4     6  2.2.2.2.3.13
   5     4  2.2.11.71
   6     7  2.2.2.3.3.7.31
   7     3  2.2.19531
   8     8  2.2.2.2.2.3.13.313
   9     5  2.2.19.31.829
  10     7  2.2.2.3.11.71.521
  11     3  2.2.12207031
  12    10  2.2.2.2.3.3.7.13.31.601
  13     3  2.2.305175781
  14     7  2.2.2.3.29.449.19531
  15     7  2.2.11.31.71.181.1741
  16    11  2.2.2.2.2.2.3.13.17.313.11489
  17     4  2.2.409.466344409
  18    11  2.2.2.3.3.3.7.19.31.829.5167
  19     5  2.2.191.6271.3981071
  20    11  2.2.2.2.3.11.13.41.71.521.9161
  21     6  2.2.31.379.19531.519499
  22     8  2.2.2.3.23.67.5281.12207031
  23     4  2.2.8971.332207361361
  24    13  2.2.2.2.2.3.3.7.13.31.313.601.390001
  25     8  2.2.11.71.101.251.401.9384251
  26     7  2.2.2.3.5227.38923.305175781
  27     9  2.2.19.31.109.271.829.4159.31051
  28    10  2.2.2.2.3.13.29.449.19531.234750601
  29     5  2.2.59.35671.22125996444329
  30    14  2.2.2.3.3.7.11.31.61.71.181.521.1741.7621
  31     4  2.2.1861.625552508473588471
  32    14  2.2.2.2.2.2.2.3.13.17.313.2593.11489.29423041
  33     6  2.2.31.199.12207031.386478495679
  34     8  2.2.2.3.409.3061.41540861.466344409
  35     9  2.2.11.71.211.631.4201.19531.85280581
  36    16  2.2.2.2.3.3.3.7.13.19.31.37.601.829.5167.6597973
  37     5  2.2.149.13971969971.8737481256739
  38    10  2.2.2.3.191.761.6271.19609.213029.3981071
  39     6  2.2.31.79.305175781.608459012088799
  40    15  2.2.2.2.2.3.11.13.41.71.241.313.521.9161.632133361
  41     4  2.2.2238236249.5079304643216687969
  42    16  2.2.2.3.3.7.7.29.31.43.127.379.449.7603.19531.519499
  43     4  2.2.1644512641.172827552198815888791
  44    12  2.2.2.2.3.13.23.67.89.5281.12207031.1030330938209
  45    12  2.2.11.19.31.71.181.829.1171.1741.169831.297315901
  46     8  2.2.2.3.47.8971.332207361361.42272797713043
  47     3  2.2.177635683940025046467781066894531
  48    17  2.2.2.2.2.2.3.3.7.13.17.31.313.601.11489.390001.152587500001
  49     4  2.2.19531.227376585863531112677002031251
  50    13  2.2.2.3.11.71.101.251.401.521.1901.9384251.50150933101
  51     8  2.2.31.409.90271.317731.466344409.654652168021
  52    12  2.2.2.2.3.13.13.53.5227.38923.305175781.83181652304609
  53     5  2.2.5960555749.17154094481.27145365052629449
  54    19  2.2.2.3.3.3.3.7.19.31.109.163.271.487.829.4159.5167.31051.16018507
  55    10  2.2.11.11.71.103511.511831.12207031.65628751.190295821
  56    13  2.2.2.2.2.3.13.29.313.449.19531.234750601.59509429687890001
  57     7  2.2.31.191.6271.3981071.11735415506748076408140121
  58     9  2.2.2.3.59.35671.5096867.6090817323763.22125996444329
  59     4  2.2.21180247636732981.2047572230657338751575051
  60    21  2.2.2.2.3.3.7.11.13.31.41.61.71.181.521.601.1741.2281.7621.9161.69566521
  61     5  2.2.8419.918585913061.140194179307171898833699259
  62     9  2.2.2.3.1303.1861.21207101.28086211607.625552508473588471
  63    11  2.2.19.31.379.829.19531.280729.519499.2161279.23792163643711
  64    18  2.2.2.2.2.2.2.2.3.13.17.313.641.2593.11489.29423041.75068993.241931001601
  65     8  2.2.11.71.131.305175781.1034150930241911.20986207825565581
  66    15  2.2.2.3.3.7.23.31.67.199.5281.595123.12207031.190771747.386478495679
  67     7  2.2.269.1609.26399.2454335007529.604088623657497125653141
  68    14  2.2.2.2.3.13.409.1973.3061.20129.45289.41540861.466344409.12447002677
  69     9  2.2.31.139.6211.8971.332207361361.598761682261.8868050880709
  70    16  2.2.2.3.11.29.71.211.449.521.631.4201.19531.15216601.85280581.4698932281
  71     4  2.2.569.18607929421228039083223253529869111644362732899
  72    22  2.2.2.2.2.3.3.3.7.13.19.31.37.73.313.601.829.5167.390001.543097.6597973.1503418321
  73     5  2.2.4853479.5729041.9519524151770349914726200576714027279
  74    10  2.2.2.3.149.9103.29010221.13971969971.8737481256739.45920153384867
  75    16  2.2.11.31.71.101.151.181.251.401.1741.3301.1989151.9384251.49892851.183794551
  76    14  2.2.2.2.3.13.191.761.6271.19609.213029.3981071.4885168129.2864226125209369
  77     7  2.2.19531.12207031.527093491.8090594434231.162715052426691233701
  78    14  2.2.2.3.3.7.31.79.3121.5227.38923.305175781.22735632934561.608459012088799
  79     5  2.2.205367807127911.58523123221688392679.344120456368919234899
  80    20  2.2.2.2.2.2.3.11.13.17.41.71.241.313.521.9161.11489.25601.632133361.909456847814334401
  81    11  2.2.19.31.109.271.829.4159.4861.31051.11419697846380955982026777206637491
  82    10  2.2.2.3.83.43543.221401.2238236249.9472026608675509.5079304643216687969
  83     5  2.2.20515111.1431185706701868962383741.88040095945103834627376781
  84    22  2.2.2.2.3.3.7.7.13.29.31.43.127.379.449.601.2521.7603.19531.519499.234750601.24587411156281
  85     9  2.2.11.71.409.1531.466344409.34563155350221618511.8198241112969626815581
  86    10  2.2.2.3.1549.9547.1644512641.7866608083.1628744948329.172827552198815888791
  87     9  2.2.31.59.5569.6961.35671.22125996444329.28870194250662203210437116612769
  88    15  2.2.2.2.2.3.13.23.67.89.313.5281.12207031.1030330938209.9080418348371887359375390001
  89     8  2.2.179.9807089.14597959.834019001.8157179360521.231669654363683130095909
  90    22  2.2.2.3.3.3.7.11.19.31.61.71.181.521.829.1171.1741.5167.7621.169831.297315901.60081451169922001
  91     6  2.2.19531.305175781.9680647790568589086355559.17499733663152976533452519
  92    11  2.2.2.2.3.13.47.8971.332207361361.42272797713043.5465713352000770660547109750601
  93     9  2.2.31.31.1861.148429.878851.625552508473588471.172974812463239310024750410929
  94     8  2.2.2.3.2069.15888756269.3602372010909260861.177635683940025046467781066894531
  95    11  2.2.11.71.191.2851.6271.3981071.4113691.1245576402371959291.11600321878916922053491
  96    22  2.2.2.2.2.2.2.3.3.7.13.17.31.97.313.601.2593.11489.390001.29423041.152587500001.240031591394168814433
  97     5  2.2.389.264811.153159805660301568024613754993807288151489686913246436306439
  98    11  2.2.2.3.29.449.19531.49105547.1866013003.2481357870461.227376585863531112677002031251
  99    12  2.2.19.31.199.829.143551.1731511.12207031.386478495679.22542470482159.153560376376050799
 100    20  2.2.2.2.3.11.13.41.71.101.251.401.521.1901.9161.239201.9384251.424256201.50150933101.89620825374601
 101     5  2.2.5937018283241.3434487311396589821473854121.483593153887747265029536907421
 102    18  2.2.2.3.3.7.31.103.409.3061.8467.90271.317731.528667.41540861.466344409.60119016343.654652168021
 103     6  2.2.3709.28429.59117897713198738371603984809.39546955636451768643571562540114219
 104    17  2.2.2.2.2.3.13.13.53.313.5227.38923.51169.305175781.537181587281.83181652304609.129044008326199409
 105    17  2.2.11.31.71.181.211.379.631.1741.4201.19531.519499.1736701.85280581.119461537021.21226783250214361
 106    10  2.2.2.3.107.5960555749.17154094481.28838378869.27145365052629449.599659003321309822423087
 107     7  2.2.6421.5486016363791.35411885288978941.172163150940018661.717433171088016374418821
 108    25  2.2.2.2.3.3.3.3.7.13.19.31.37.109.163.271.487.601.829.4159.5167.31051.6597973.16018507.14551915228363037109\
            375001
 109     6  2.2.1091.1007161.1528399.2293559892404294400692399012979688850301546383400890423075969
 110    17  2.2.2.3.11.11.23.67.71.521.5281.103511.511831.12207031.65628751.190295821.10910444855403996246103496881
 111     8  2.2.31.149.3109.13971969971.8737481256739.54928520946880307112306785731407655242899973469
 112    20  2.2.2.2.2.2.3.13.17.29.113.313.337.449.11489.19531.234750601.2520917617.59509429687890001.37007700327977836\
            913
 113    10  2.2.2939.6329.129499.308491.304247586761.2084303944451.620216264269531.8237123176890810696379
 114    16  2.2.2.3.3.7.31.191.229.761.6271.19609.213029.3981071.75649382555448580095589.11735415506748076408140121
 115    14  2.2.11.71.461.691.8971.689081.2855911.29028071.824480311.17223586571.332207361361.100062970166640331
 116    12  2.2.2.2.3.13.59.35671.5096867.6090817323763.22125996444329.1334402673828313149547634216455312875601
 117    10  2.2.19.31.79.829.223963741.305175781.608459012088799.937938782117311845318745554345005320717861
 118    10  2.2.2.3.827.5242462229.3237765225301.2059647179472887.21180247636732981.2047572230657338751575051
 119    10  2.2.239.409.1429.4999.19531.466344409.7497182681291140146079.788868477693980100643230089490226571
 120    27  2.2.2.2.2.3.3.7.11.13.31.41.61.71.181.241.313.521.601.1741.2281.7621.9161.390001.69566521.632133361.2332031\
            7172851318360001
 121     6  2.2.12101.486179.12207031.13094322377956920597215509541997540493466263550896158313340716530769
 122    11  2.2.2.3.367.8419.9029.918585913061.15571335384347.14008364639128540436401.140194179307171898833699259
 123    10  2.2.31.739.960139.1785961.2238236249.9025583299.5079304643216687969.5832474690386022428273180864659
 124    13  2.2.2.2.3.13.1303.1861.21207101.28086211607.625552508473588471.8124604717965111529.102651353523520067851969
 125    13  2.2.11.71.101.251.401.3597751.9384251.28707251.4032808198751.767186663625251.24687045214139234043375683501
 126    27  2.2.2.3.3.3.7.7.19.29.31.43.127.379.449.829.883.5167.7603.19531.280729.406729.519499.2161279.24132781.16924\
            16503.23792163643711
 127     3  2.2.14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531
 128    22  2.2.2.2.2.2.2.2.2.3.13.17.313.641.769.2593.11489.29423041.75068993.241931001601.3666499598977.9613295678264\
            3741951225664001
 129     8  2.2.31.18471511.1644512641.172827552198815888791.43955934961951833386625799.51349797354047205216257689
 130    16  2.2.2.3.11.71.131.521.5227.18461.38923.305175781.15188886343541.1034150930241911.15199221608544481.20986207\
            825565581
 131     7  2.2.2621.23928199.34720241.16815642611861.250805666433416532678429525124977090318975999001796354124089
 132    22  2.2.2.2.3.3.7.13.23.31.67.89.199.601.1453.5281.595123.12207031.190771747.386478495679.1030330938209.6509387\
            183417404924784917
 133    12  2.2.191.6271.9311.19531.65171.281429.3981071.3257947519.152317058321.29090007107767075239783794592001366542\
            871
 134    10  2.2.2.3.269.1609.26399.2454335007529.604088623657497125653141.112937726300573378542443000090618928273518880\
            21
 135    20  2.2.11.19.31.71.109.181.271.541.829.1171.1741.4159.11071.31051.169831.297315901.1312315694449748688331.2694\
            1244373060650224561
 136    21  2.2.2.2.2.3.13.137.313.409.1973.3061.20129.45289.623017.41540861.466344409.12447002677.938894988049.1361753\
            880209.4959636586609
 137     8  2.2.20551.603349.48102071.121719631478506669.7851027307722624763151.251755028858658462627642052961230751431
 138    18  2.2.2.3.3.7.31.47.139.6211.8971.66163549.253592389.332207361361.598761682261.8868050880709.42272797713043.4\
            03316413944121
 139     5  2.2.21521602057721.6789441546024769741462601111.24550591546653776667941845268908441565415743319193209001
 140    23  2.2.2.2.3.11.13.29.41.71.211.281.449.521.631.4201.9161.19531.15216601.85280581.234750601.4698932281.1314883\
            2195720299503896018648521
 141     5  2.2.31.177635683940025046467781066894531.16286160623917663079467944573580125726889931566772922392814390121
 142     9  2.2.2.3.569.4261.5747338499820296170481.288231038713838413442281.186079294212280390832232535298691116443627\
            32899
 143     7  2.2.12207031.305175781.24615836446631.53130566763791958299.460183952753824357170225842292658707895690816315\
            909
 144    28  2.2.2.2.2.2.3.3.3.7.13.17.19.31.37.73.313.601.829.1297.5167.11489.390001.543097.6597973.1503418321.15258750\
            0001.2739177855667309845605995807633
 145    10  2.2.11.59.71.35671.1461311.22125996444329.2158365113981511371558358567665231.488654500355218081336311051543\
            759628081
 146    10  2.2.2.3.4853479.5729041.63554310563.777612767772190289.3570677866897550288203.95195241517703499147262005767\
            14027279
 147    11  2.2.31.379.19531.519499.24556351.5071357999.2035895040229.203906616815994386234329833781.227376585863531112\
            677002031251
 148    15  2.2.2.2.3.13.149.9103.9769.40849.29010221.13971969971.8737481256739.45920153384867.510241095096183757930733\
            363918820917976121
 149     3  2.2.35032461608120426773093239582247903282006548546912894293926707097244777067146515037165954709053039550781
 150    29  2.2.2.3.3.7.11.31.61.71.101.151.181.251.401.521.1741.1901.3301.7621.118801.1989151.9384251.20775901.2466570\
            1.49892851.149439601.183794551.50150933101
 151     8  2.2.1175989.2237519.389439261961.12799319666401.2843809592323334251225153490677489.234808350683195588203155\
            40345862729
 152    19  2.2.2.2.2.3.13.191.313.457.761.6271.19609.213029.3981071.4885168129.2864226125209369.21363981507860375753.2\
            1654472202540732126905077281
 153    14  2.2.19.31.409.829.4591.90271.317731.26481241.466344409.654652168021.360143672909416579.28596369159272276742\
            1088565601855215949
 154    16  2.2.2.3.23.29.67.449.5281.19531.12207031.527093491.20828886541.8090594434231.162715052426691233701.49970061\
            516036179615325895945741
 155    13  2.2.11.71.311.1861.11161.257611.5624951.31473312961.625552508473588471.21783999170235219053011.174583335852\
            767865379025002452121
 156    24  2.2.2.2.3.3.7.13.13.31.53.79.157.601.3121.5227.38923.8684521.305175781.4056854881.22735632934561.8318165230\
            4609.608459012088799.667929705480493
 157     7  2.2.32029.5129819.2107089779.8616314452100494153901371725720169.4587548699755676969742331799602074877905422\
            766102260881
 158    11  2.2.2.3.18251687.7897663181.511465533067.205367807127911.58523123221688392679.344120456368919234899.3739909\
            5525167136010188229
 159     8  2.2.31.5960555749.17154094481.1775305720077559.27145365052629449.223967815154673247771933930986251232800839\
            3109037131818519
 160    26  2.2.2.2.2.2.2.3.11.13.17.41.71.241.313.521.2593.9161.11489.25601.29423041.131349761.632133361.167597261761.
            909456847814334401.24625444126052524088217281
 161     6  2.2.8971.19531.332207361361.1469386746678216989397901405448901778556342705433890596470719221994542710855107\
            30718993828121
 162    25  2.2.2.3.3.3.3.3.7.19.31.109.163.271.487.829.1783.4159.4861.5023.5167.31051.16018507.20660672713801362122247\
            01233463.11419697846380955982026777206637491
 163     8  2.2.4599209.40100609.675775181.6582151087844246659.102556399583828574447011133455059.2541462766396986870745\
            222882425433052891
 164    16  2.2.2.2.3.13.83.43543.193357.221401.6355001.2238236249.1148205782281.9472026608675509.5079304643216687969.5\
            6373078952722628530598981268453
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 807     0  
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 809     0  
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 811     0  
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 813     0  
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 817     0  
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 819     0  
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 821     0  
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 823     0  
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 827     0  
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 829     0  
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 831     0  
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 833     0  
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 837     0  
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 839     0  
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