# Factorisations Of Cunningham Numbers C-(6,n) = 6n - 1

## Canonical Representation Of Factorisations

 Factorisations are given from smallest to largest factor, with a period '.' separating factors. Multiplicity of factors is indicated with the carat '^' in ascii tradition for the text version of the tables but not the HTML version. 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

 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. Prime exponents are coloured orange. C±(b,n) is usually composite in this case too. 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. Unfactored composites are coloured red. No factors for these composites is known. Hyperlinked numbers occur in previous exponents in the same or related table. #Fac is the number of (non distinct) prime factors in the expression. 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  5 [1st Prime]
2     2  5.7
3     2  5.43
4     3  5.7.37
5     3  5.5.311
6     4  5.7.31.43
7     2  5.55987
8     4  5.7.37.1297
9     4  5.19.43.2467
10     6  5.5.7.11.101.311
11     3  5.23.3154757
12     7  5.7.13.31.37.43.97
13     3  5.3433.760891
14     6  5.7.7.29.197.55987
15     6  5.5.43.311.1171.1201
16     6  5.7.17.37.1297.98801
17     5  5.239.409.1123.30839
18     7  5.7.19.31.43.2467.46441
19     3  5.191.638073026189
20     9  5.5.7.11.37.101.241.311.6781
21     4  5.43.55987.1822428931
22     5  5.7.23.3154757.51828151
23     5  5.47.139.3221.7505944891
24     9  5.7.13.31.37.43.97.1297.1678321
25     6  5.5.5.311.18198701.40185601
26     7  5.7.53.937.3433.37571.760891
27     6  5.19.43.163.2467.623067280651
28     9  5.7.7.29.37.197.421.55987.5030761
29     2  5.7369130657357778596659
30    11  5.5.7.11.31.43.101.311.1171.1201.1950271
31     3  5.5333.49744740983476472807
32     9  5.7.17.37.353.1297.1697.98801.4709377
33     6  5.23.43.67.3154757.45686117391553
34     8  5.7.239.409.1123.30839.190537.12690943
35     7  5.5.71.311.55987.37863211.1469029031
36    13  5.7.13.19.31.37.43.73.97.541.2467.46441.55117
37     6  5.149.7919.12211.2569799.334286825813
38     6  5.7.191.1787.48713705333.638073026189
39     6  5.43.3433.760891.3143401.1262014275211
40    12  5.5.7.11.37.41.101.241.311.1297.6781.68754507401
41     3  5.8648131.1854850885886497427178961
42    10  5.7.7.29.31.43.197.55987.1822428931.2527867231
43     5  5.173.431.7383359.1048953903129961695599
44     9  5.7.23.37.58477.70489.863017.3154757.51828151
45    11  5.5.19.43.311.1171.1201.2161.2467.112771.19353635731
46     8  5.7.47.139.3221.113958101.990000731.7505944891
47     4  5.930911329.45110836129.17821718159716147
48    13  5.7.13.17.31.37.43.97.1297.5953.98801.1678321.473896897
49     5  5.55987.6527977.122694573317.600827908214213
50    10  5.5.5.7.11.101.311.18198701.40185601.3655688315536801
51     9  5.43.239.307.409.1123.30839.927037099.23412002806867
52    11  5.7.37.53.313.937.2341.3433.37571.760891.6291946695217
53     4  5.13781.357293834576449.7091531088740602980647
54    11  5.7.19.31.43.163.2467.46441.114967.883383463.623067280651
55     7  5.5.23.311.3154757.3675127061.3031462959351050977391
56    14  5.7.7.29.37.197.281.337.421.617.1297.55987.5030761.81035189089
57     7  5.43.191.47881.820459.638073026189.219815829325921729
58     6  5.7.59.32713.2727192763388813.7369130657357778596659
59     4  5.4866979762781.29050941569087.11522163007228653937
60    20  5.5.7.11.13.31.37.43.61.97.101.181.241.311.1171.1201.3541.6781.74161.1950271
61     4  5.42461491.80057377.17252803354297421346943980322273
62     5  5.7.5333.49744740983476472807.189491931189200021056951
63    10  5.19.43.379.2467.55987.8387947.616332907.1822428931.5239858051
64    12  5.7.17.37.353.1297.1697.2753.98801.145601.4709377.19854979505843329
65     9  5.5.311.3433.11831.760891.1420901.49398961.22533649654910414281
66    12  5.7.23.31.43.67.463.72073.3154757.51828151.127236649.45686117391553
67     3  5.904949028329910415467529.3023706637809542222940030043
68    11  5.7.37.239.409.1123.30839.190537.934117.12690943.8289713345361373993
69     8  5.43.47.139.3221.11731.7505944891.1236385853432057889667843739281
70    18  5.5.7.7.11.29.71.101.197.311.631.701.2311.9241.55987.585131.37863211.1469029031
71     2  5.3546245297457217493590449191748546458005595187661976371
72    18  5.7.13.19.31.37.43.73.97.541.577.1297.2467.3313.46441.55117.1678321.2478750186961
73     5  5.44764549877.2436094907761.8439148071138817.138721648424756087
74    10  5.7.149.3923.7919.12211.2569799.334286825813.1096762734443.2054788991719
75    12  5.5.5.43.311.601.1171.1201.82051.18198701.40185601.271041511600591342728451
76     9  5.7.37.191.1787.48713705333.638073026189.1030762781149.9736145643041809
77     6  5.23.55987.3154757.484847574510970082567.84002092056248016278479853
78    15  5.7.31.43.53.79.937.3433.9049.37571.760891.868999.3143401.8857759.1262014275211
79     4  5.1147240288157.26283825237209622143.197531251446059329471533015409
80    17  5.5.7.11.17.37.41.101.241.311.1297.6781.17761.98801.3696985841.68754507401.121206120881
81     8  5.19.43.163.2467.27767002339.623067280651.37725805717350619429950429139147
82     7  5.7.83.28537.8648131.1854850885886497427178961.4837453663777044375040181
83     8  5.167.499.17597.41580677.80781507941.605274844997.2589238104153304205575487
84    17  5.7.7.13.29.31.37.43.97.197.421.55987.5030761.804146449.1822428931.2527867231.6055984789
85    10  5.5.239.311.409.1123.30839.26807981.20891158391.94260123386979283872547675418641
86     7  5.7.173.431.7383359.1048953903129961695599.412482688627178079807598675848631
87     7  5.43.2694217.1833921547.4706691035521.1357610070580129.7369130657357778596659
88    12  5.7.23.37.89.1297.58477.70489.863017.3154757.51828151.150080764792922988676714149209
89     4  5.8011.2064441331.21777198152670085407545228412531133078179560879352228259
90    18  5.5.7.11.19.31.43.101.311.1171.1201.2161.2467.46441.112771.1950271.19353635731.4760317816590150361
91     6  5.3433.55987.760891.48215910563832798697.1838738460168896001275668872592841923
92    13  5.7.37.47.139.3221.6073.2259889.9564781.113958101.990000731.7505944891.128407494947883673
93     9  5.43.5333.186187.290869963.659988451.842660004553.1358539033057.49744740983476472807
94     6  5.7.930911329.45110836129.17821718159716147.534577564460822791430647883899825591
95    11  5.5.191.311.571.1901.825838991.638073026189.1298704628041.25425408247171.2995523312517361
96    20  5.7.13.17.31.37.43.97.193.353.1297.1697.5953.8641.98801.1678321.4709377.473896897.688490113.6931400449
97     6  5.389.1747.1586365166597.18969653181299397175271.29579867253585988507046633033646287
98    12  5.7.7.7.29.197.55987.6527977.122694573317.600827908214213.762332681442053.90179616936384011
99    13  5.19.23.43.67.2467.16633.3154757.18380539.18414001.226407819331.45686117391553.38167293140100433
100    16  5.5.5.7.11.37.101.241.311.6781.343801.18198701.22243201.40185601.3655688315536801.1748016735462726601
101     3  5.1275678077.614561277123903327309455926778985780630117744484485521069032496702063
102    17  5.7.31.43.103.239.307.409.919.1123.30839.190537.12690943.927037099.980146969.99617785207.23412002806867
103     5  5.2473.5563.160681.12767653355301160780822191431160569156710177181791578590824899905497
104    15  5.7.37.53.313.937.1297.2341.3433.37571.192193.760891.14090441.6291946695217.8284434950526240125727017
105    15  5.5.43.71.211.311.1171.1201.35281.55987.58171.37863211.1469029031.1822428931.61921104791950322094158011
106     9  5.7.107.13781.97351567.33685364386033.357293834576449.71080464397105403.7091531088740602980647
107     4  5.643.5044140393054571.11277573027736036722713586016689525331842510247329583574661742579
108    21  5.7.13.19.31.37.43.73.97.109.163.541.2467.46441.55117.114967.591841.171467713.883383463.623067280651.932461\
936453
109     3  5.30726149494277.42855656091880208870012451741752392192104225262820633109434962552795607
110    15  5.5.7.11.11.23.101.311.1031141.3154757.51828151.3675127061.16336066781.84155540944421.3031462959351050977391
111    11  5.43.149.7919.12211.2569799.89728627.187333846633.334286825813.1487716834806007369.3561693323285489089
112    20  5.7.7.17.29.37.113.197.281.337.421.617.1297.4817.55987.98801.4048129.5030761.81035189089.101894402390128830\
75423169
113     5  5.107351.54466954894479739.201436862864351419099.1448915804946152111264738471459190964062624173
114    14  5.7.31.43.191.457.1787.47881.137713.820459.48713705333.638073026189.219815829325921729.190324492938225748951
115    12  5.5.47.139.311.461.1151.3221.44851.7505944891.257917526307345124973861.40752608049190149321816351186154151
116     9  5.7.37.59.349.32713.2727192763388813.7369130657357778596659.105134528469779071670501631159328247729809
117    12  5.19.43.2467.3433.6553.760891.3143401.5958157609.1262014275211.39031258670353.69488040914581799577604095001
118     6  5.7.4866979762781.29050941569087.11522163007228653937.1163658999540220416412446482708919139658591671
119    11  5.239.409.1123.16661.30839.55987.29032062767.103198889691409.12405291558509977.6783899150200555463142339438\
01
120    26  5.5.7.11.13.31.37.41.43.61.97.101.181.241.311.1171.1201.1297.3541.6781.13441.74161.1678321.1950271.68754507\
401.592575109627400042641
121     6  5.23.3154757.4163261521.1304380464883.7274439979153836750841469647330331057551053697734443556853774027
122     7  5.7.9151.42461491.80057377.17252803354297421346943980322273.4577830180684945360162613198286645069141001
123     7  5.43.8648131.25512169.141304123.1854850885886497427178961.41498448376119216462262063079126262444529017073
124     7  5.7.37.5333.49744740983476472807.189491931189200021056951.47552767764994953232854569779888803761183529901
125    11  5.5.5.5.311.18198701.40185601.9536585501.117811792772681609501.105875321588567599765751.1098445767808750903\
973251
126    20  5.7.7.19.29.31.43.127.197.379.2467.46441.55987.8387947.616332907.1822428931.2527867231.5239858051.154260982\
009.528921402377887
127     2  5.133733063818254349335501779590081460423013416258060407531857720755181857441961908284738707408499507
128    15  5.7.17.37.353.1297.1697.2753.98801.145601.4709377.4926056449.19854979505843329.447183309836853377.287537871\
97056661026689
129     8  5.43.43.173.431.7383359.1048953903129961695599.450890019061015235057788732310222433830055241504017824833016\
3977
130    17  5.5.7.11.53.101.131.311.937.3433.11831.37571.760891.1420901.49398961.22533649654910414281.19993078229848352\
3040584108028862541
131     6  5.263.3931.6551.1284827442574221936870974393373403.19917397922626842334449833677404096613537638684348856178\
059
132    23  5.7.13.23.31.37.43.67.97.463.3037.58477.70489.72073.96493.622513.863017.3154757.4629769.51828151.127236649.
16266405013.45686117391553
133     9  5.191.11971.55987.188861.1101773.638073026189.164331230229374083.223393431463263911519708964052259906781762\
9985127899
134     8  5.7.269.418349.90571543952974835963.191757760647639121941197.904949028329910415467529.302370663780954222294\
0030043
135    15  5.5.19.43.163.311.1171.1201.2161.2467.112771.175509721.19353635731.623067280651.606162141679902054991801871\
110954177324256409961
136    16  5.7.37.137.239.409.1123.1297.5849.30839.190537.934117.12690943.1536052010629489.8289713345361373993.5142057\
6374811381403609445473
137     6  5.6577.25247731.53280671.60042056488501962187.1522214510879021329626941843334490679379355130104242302631442\
9342733
138    14  5.7.31.43.47.139.3221.11731.113958101.990000731.7505944891.24648570768391.816214079084081564521.12363858534\
32057889667843739281
139     5  5.557.21407.128159.1904994318294264032001011698767856776424905969372788422268974477324726371768074195193068\
08486559
140    25  5.5.7.7.11.29.37.71.101.197.241.311.421.631.701.2311.6781.9241.55987.585131.5030761.37863211.1469029031.135\
09594555661.1708114263204222806519161
141    11  5.43.283.13537.753554761.930911329.45110836129.122320721569.989671414201.17821718159716147.9318249558895921\
24612176563793529
142     6  5.7.37489.11735704315681.5757417485448059422914748320317168839.35462452974572174935904491917485464580055951\
87661976371
143     8  5.23.859.3433.760891.3154757.62545486153056268832471.370492708153183538667516076628295958764609620252358691\
48795940042759
144    23  5.7.13.17.19.31.37.43.73.97.541.577.1297.2467.3313.5953.46441.55117.98801.1678321.473896897.2478750186961.2\
2452257707354557235348829785471057921
145     7  5.5.311.132241.150433631394488258261.7369130657357778596659.59580423676805748420140957215180302958743471829\
183098610333631
146    11  5.7.293.439.120855443.1389436303.44764549877.2436094907761.8439148071138817.138721648424756087.422188345937\
8030470824476438562257
147     9  5.43.55987.6527977.32093041.1822428931.122694573317.600827908214213.721593495645162209494937916430925440485\
5094763766767407121
148    15  5.7.37.37.149.3923.4441.7919.12211.2569799.334286825813.1096762734443.2054788991719.3300043400835529.190892\
407618022993841069346975403017
149     4  5.38538553.1318713554713829548602512956686040272376450743377909.3463541760502538278596775684588153902182357\
12359759067327
150    22  5.5.5.7.11.31.43.101.151.311.601.1171.1201.82051.168151.1950271.18198701.40185601.573178201.918628247364601.
3655688315536801.271041511600591342728451
151     4  5.2623968964411.4956504421137000338429923175878885954098593563.48723066259314477894157817245533780187559387\
828254264047307
152    14  5.7.37.191.1297.1787.4561.48713705333.638073026189.1030762781149.355518408146401.9736145643041809.502818748\
6478069273.13038313680704041577
153    14  5.19.43.239.307.409.1123.2467.30839.927037099.9757142011.23412002806867.12644443230579801886843521019.40670\
77533669936706351248605374735249
154    12  5.7.7.23.29.197.55987.3154757.51828151.484847574510970082567.84002092056248016278479853.5701908713415125406\
1666621717728669167279862151
155     8  5.5.311.5333.3559267608341.49744740983476472807.208210289142572055121.2686345232069105360022926492125783168\
511035955840811134515391
156    26  5.7.13.13.31.37.43.53.79.97.157.313.937.2341.3433.8893.9049.37571.760891.868999.3143401.8857759.12620142752\
11.6291946695217.197743936282933.6429178169720749
157     6  5.6446107.6423436771.81127299702871294523556776543.8695994904356302134775281276601.101210377513117399538507\
3322337706122495245797
158    10  5.7.317.5531.2832941.1147240288157.99687312908749681.26283825237209622143.197531251446059329471533015409.85\
92319153827988586815914947213
159     8  5.43.13781.118721004139.67587459957091.357293834576449.7091531088740602980647.88342645123243360518614293208\
997935963729713364951837539
160    23  5.5.7.11.17.37.41.101.241.311.353.1297.1697.6781.9601.17761.98801.4709377.3696985841.68754507401.1212061208\
81.2810800069601.2347110840158563816028186318246561
161    11  5.47.139.3221.10949.55987.593447.7505944891.491787574454982121.3358586137753609961516447641418203949.403733\
622730561138499463252012494935013
162    16  5.7.19.31.43.163.1783.2467.46441.114967.149862151.883383463.27767002339.623067280651.3920344350409644507093\
715799617.37725805717350619429950429139147
163     4  5.653.2378523250342970947582043555610171717174452063.888102772526021838488123845334486037375412519645053051\
472793437455099303804577
164    11  5.7.37.83.28537.4046701.8648131.174521133001.1854850885886497427178961.4837453663777044375040181.2461793762\
06361788466441901958293949537091001
165    15  5.5.23.43.67.311.331.1171.1201.3154757.3675127061.45686117391553.13724862774476458441.303146295935105097739\
1.46975793563298851302025905551105268509881
166    13  5.7.167.499.17597.710813.41580677.6547890917.80781507941.605274844997.21608536062644851877771.2589238104153\
304205575487.54824363564629401758409941
167     7  5.19466857.10301691259.229027359614687.9703107759710968661.2200446540213260920441013.1822952692682777153874\
022559086738173481449195038610359
168    25  5.7.7.13.29.31.37.43.97.197.281.337.421.617.1297.55987.1678321.5030761.804146449.1822428931.2527867231.6055\
984789.81035189089.1176362433121.19100900655540830489319601
169     9  5.677.3433.3719.760891.1420277.3066042413300025661761581713.351082413599031251316269147227.6400588768393061\
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```