1Factorisations Of Cunningham Numbers C-(6,n) = 6^n - 1
2
3Canonical Representation Of Factorisations
4
51. Factorisations are given from smallest to largest factor, with a period '.'
6 separating factors.
72. Multiplicity of factors is indicated with the carat '^' in ascii tradition
8 for the text version of the tables but not the HTML version.
93. The backslash '\' is used to indicate continuation of a line, the decimal
10 digit representation of the number does not stop but continues on the next
11 line as if no break had occured. This can sometimes make for bad breaks, but
12 such is life.
13
14Notation Used In The Tables
15
161. #Fac is the number of (non distinct) prime factors in an expression.
172. A plussed #Fac means that more prime factors exist but they are unknown due
18 to an unfactored composite in the expression.
19
20========================================================================================================================
21
22 n #Fac Factorisation
23 1 1 5
24 2 2 5.7
25 3 2 5.43
26 4 3 5.7.37
27 5 3 5^2.311
28 6 4 5.7.31.43
29 7 2 5.55987
30 8 4 5.7.37.1297
31 9 4 5.19.43.2467
32 10 6 5^2.7.11.101.311
33 11 3 5.23.3154757
34 12 7 5.7.13.31.37.43.97
35 13 3 5.3433.760891
36 14 6 5.7^2.29.197.55987
37 15 6 5^2.43.311.1171.1201
38 16 6 5.7.17.37.1297.98801
39 17 5 5.239.409.1123.30839
40 18 7 5.7.19.31.43.2467.46441
41 19 3 5.191.638073026189
42 20 9 5^2.7.11.37.101.241.311.6781
43 21 4 5.43.55987.1822428931
44 22 5 5.7.23.3154757.51828151
45 23 5 5.47.139.3221.7505944891
46 24 9 5.7.13.31.37.43.97.1297.1678321
47 25 6 5^3.311.18198701.40185601
48 26 7 5.7.53.937.3433.37571.760891
49 27 6 5.19.43.163.2467.623067280651
50 28 9 5.7^2.29.37.197.421.55987.5030761
51 29 2 5.7369130657357778596659
52 30 11 5^2.7.11.31.43.101.311.1171.1201.1950271
53 31 3 5.5333.49744740983476472807
54 32 9 5.7.17.37.353.1297.1697.98801.4709377
55 33 6 5.23.43.67.3154757.45686117391553
56 34 8 5.7.239.409.1123.30839.190537.12690943
57 35 7 5^2.71.311.55987.37863211.1469029031
58 36 13 5.7.13.19.31.37.43.73.97.541.2467.46441.55117
59 37 6 5.149.7919.12211.2569799.334286825813
60 38 6 5.7.191.1787.48713705333.638073026189
61 39 6 5.43.3433.760891.3143401.1262014275211
62 40 12 5^2.7.11.37.41.101.241.311.1297.6781.68754507401
63 41 3 5.8648131.1854850885886497427178961
64 42 10 5.7^2.29.31.43.197.55987.1822428931.2527867231
65 43 5 5.173.431.7383359.1048953903129961695599
66 44 9 5.7.23.37.58477.70489.863017.3154757.51828151
67 45 11 5^2.19.43.311.1171.1201.2161.2467.112771.19353635731
68 46 8 5.7.47.139.3221.113958101.990000731.7505944891
69 47 4 5.930911329.45110836129.17821718159716147
70 48 13 5.7.13.17.31.37.43.97.1297.5953.98801.1678321.473896897
71 49 5 5.55987.6527977.122694573317.600827908214213
72 50 10 5^3.7.11.101.311.18198701.40185601.3655688315536801
73 51 9 5.43.239.307.409.1123.30839.927037099.23412002806867
74 52 11 5.7.37.53.313.937.2341.3433.37571.760891.6291946695217
75 53 4 5.13781.357293834576449.7091531088740602980647
76 54 11 5.7.19.31.43.163.2467.46441.114967.883383463.623067280651
77 55 7 5^2.23.311.3154757.3675127061.3031462959351050977391
78 56 14 5.7^2.29.37.197.281.337.421.617.1297.55987.5030761.81035189089
79 57 7 5.43.191.47881.820459.638073026189.219815829325921729
80 58 6 5.7.59.32713.2727192763388813.7369130657357778596659
81 59 4 5.4866979762781.29050941569087.11522163007228653937
82 60 20 5^2.7.11.13.31.37.43.61.97.101.181.241.311.1171.1201.3541.6781.74161.1950271
83 61 4 5.42461491.80057377.17252803354297421346943980322273
84 62 5 5.7.5333.49744740983476472807.189491931189200021056951
85 63 10 5.19.43.379.2467.55987.8387947.616332907.1822428931.5239858051
86 64 12 5.7.17.37.353.1297.1697.2753.98801.145601.4709377.19854979505843329
87 65 9 5^2.311.3433.11831.760891.1420901.49398961.22533649654910414281
88 66 12 5.7.23.31.43.67.463.72073.3154757.51828151.127236649.45686117391553
89 67 3 5.904949028329910415467529.3023706637809542222940030043
90 68 11 5.7.37.239.409.1123.30839.190537.934117.12690943.8289713345361373993
91 69 8 5.43.47.139.3221.11731.7505944891.1236385853432057889667843739281
92 70 18 5^2.7^2.11.29.71.101.197.311.631.701.2311.9241.55987.585131.37863211.1469029031
93 71 2 5.3546245297457217493590449191748546458005595187661976371
94 72 18 5.7.13.19.31.37.43.73.97.541.577.1297.2467.3313.46441.55117.1678321.2478750186961
95 73 5 5.44764549877.2436094907761.8439148071138817.138721648424756087
96 74 10 5.7.149.3923.7919.12211.2569799.334286825813.1096762734443.2054788991719
97 75 12 5^3.43.311.601.1171.1201.82051.18198701.40185601.271041511600591342728451
98 76 9 5.7.37.191.1787.48713705333.638073026189.1030762781149.9736145643041809
99 77 6 5.23.55987.3154757.484847574510970082567.84002092056248016278479853
100 78 15 5.7.31.43.53.79.937.3433.9049.37571.760891.868999.3143401.8857759.1262014275211
101 79 4 5.1147240288157.26283825237209622143.197531251446059329471533015409
102 80 17 5^2.7.11.17.37.41.101.241.311.1297.6781.17761.98801.3696985841.68754507401.121206120881
103 81 8 5.19.43.163.2467.27767002339.623067280651.37725805717350619429950429139147
104 82 7 5.7.83.28537.8648131.1854850885886497427178961.4837453663777044375040181
105 83 8 5.167.499.17597.41580677.80781507941.605274844997.2589238104153304205575487
106 84 17 5.7^2.13.29.31.37.43.97.197.421.55987.5030761.804146449.1822428931.2527867231.6055984789
107 85 10 5^2.239.311.409.1123.30839.26807981.20891158391.94260123386979283872547675418641
108 86 7 5.7.173.431.7383359.1048953903129961695599.412482688627178079807598675848631
109 87 7 5.43.2694217.1833921547.4706691035521.1357610070580129.7369130657357778596659
110 88 12 5.7.23.37.89.1297.58477.70489.863017.3154757.51828151.150080764792922988676714149209
111 89 4 5.8011.2064441331.21777198152670085407545228412531133078179560879352228259
112 90 18 5^2.7.11.19.31.43.101.311.1171.1201.2161.2467.46441.112771.1950271.19353635731.4760317816590150361
113 91 6 5.3433.55987.760891.48215910563832798697.1838738460168896001275668872592841923
114 92 13 5.7.37.47.139.3221.6073.2259889.9564781.113958101.990000731.7505944891.128407494947883673
115 93 9 5.43.5333.186187.290869963.659988451.842660004553.1358539033057.49744740983476472807
116 94 6 5.7.930911329.45110836129.17821718159716147.534577564460822791430647883899825591
117 95 11 5^2.191.311.571.1901.825838991.638073026189.1298704628041.25425408247171.2995523312517361
118 96 20 5.7.13.17.31.37.43.97.193.353.1297.1697.5953.8641.98801.1678321.4709377.473896897.688490113.6931400449
119 97 6 5.389.1747.1586365166597.18969653181299397175271.29579867253585988507046633033646287
120 98 12 5.7^3.29.197.55987.6527977.122694573317.600827908214213.762332681442053.90179616936384011
121 99 13 5.19.23.43.67.2467.16633.3154757.18380539.18414001.226407819331.45686117391553.38167293140100433
122 100 16 5^3.7.11.37.101.241.311.6781.343801.18198701.22243201.40185601.3655688315536801.1748016735462726601
123 101 3 5.1275678077.614561277123903327309455926778985780630117744484485521069032496702063
124 102 17 5.7.31.43.103.239.307.409.919.1123.30839.190537.12690943.927037099.980146969.99617785207.23412002806867
125 103 5 5.2473.5563.160681.12767653355301160780822191431160569156710177181791578590824899905497
126 104 15 5.7.37.53.313.937.1297.2341.3433.37571.192193.760891.14090441.6291946695217.8284434950526240125727017
127 105 15 5^2.43.71.211.311.1171.1201.35281.55987.58171.37863211.1469029031.1822428931.61921104791950322094158011
128 106 9 5.7.107.13781.97351567.33685364386033.357293834576449.71080464397105403.7091531088740602980647
129 107 4 5.643.5044140393054571.11277573027736036722713586016689525331842510247329583574661742579
130 108 21 5.7.13.19.31.37.43.73.97.109.163.541.2467.46441.55117.114967.591841.171467713.883383463.623067280651.932461\
131 936453
132 109 3 5.30726149494277.42855656091880208870012451741752392192104225262820633109434962552795607
133 110 15 5^2.7.11^2.23.101.311.1031141.3154757.51828151.3675127061.16336066781.84155540944421.3031462959351050977391
134 111 11 5.43.149.7919.12211.2569799.89728627.187333846633.334286825813.1487716834806007369.3561693323285489089
135 112 20 5.7^2.17.29.37.113.197.281.337.421.617.1297.4817.55987.98801.4048129.5030761.81035189089.101894402390128830\
136 75423169
137 113 5 5.107351.54466954894479739.201436862864351419099.1448915804946152111264738471459190964062624173
138 114 14 5.7.31.43.191.457.1787.47881.137713.820459.48713705333.638073026189.219815829325921729.190324492938225748951
139 115 12 5^2.47.139.311.461.1151.3221.44851.7505944891.257917526307345124973861.40752608049190149321816351186154151
140 116 9 5.7.37.59.349.32713.2727192763388813.7369130657357778596659.105134528469779071670501631159328247729809
141 117 12 5.19.43.2467.3433.6553.760891.3143401.5958157609.1262014275211.39031258670353.69488040914581799577604095001
142 118 6 5.7.4866979762781.29050941569087.11522163007228653937.1163658999540220416412446482708919139658591671
143 119 11 5.239.409.1123.16661.30839.55987.29032062767.103198889691409.12405291558509977.6783899150200555463142339438\
144 01
145 120 26 5^2.7.11.13.31.37.41.43.61.97.101.181.241.311.1171.1201.1297.3541.6781.13441.74161.1678321.1950271.68754507\
146 401.592575109627400042641
147 121 6 5.23.3154757.4163261521.1304380464883.7274439979153836750841469647330331057551053697734443556853774027
148 122 7 5.7.9151.42461491.80057377.17252803354297421346943980322273.4577830180684945360162613198286645069141001
149 123 7 5.43.8648131.25512169.141304123.1854850885886497427178961.41498448376119216462262063079126262444529017073
150 124 7 5.7.37.5333.49744740983476472807.189491931189200021056951.47552767764994953232854569779888803761183529901
151 125 11 5^4.311.18198701.40185601.9536585501.117811792772681609501.105875321588567599765751.10984457678087509039732\
152 51
153 126 20 5.7^2.19.29.31.43.127.197.379.2467.46441.55987.8387947.616332907.1822428931.2527867231.5239858051.154260982\
154 009.528921402377887
155 127 2 5.133733063818254349335501779590081460423013416258060407531857720755181857441961908284738707408499507
156 128 15 5.7.17.37.353.1297.1697.2753.98801.145601.4709377.4926056449.19854979505843329.447183309836853377.287537871\
157 97056661026689
158 129 8 5.43^2.173.431.7383359.1048953903129961695599.4508900190610152350577887323102224338300552415040178248330163\
159 977
160 130 17 5^2.7.11.53.101.131.311.937.3433.11831.37571.760891.1420901.49398961.22533649654910414281.19993078229848352\
161 3040584108028862541
162 131 6 5.263.3931.6551.1284827442574221936870974393373403.19917397922626842334449833677404096613537638684348856178\
163 059
164 132 23 5.7.13.23.31.37.43.67.97.463.3037.58477.70489.72073.96493.622513.863017.3154757.4629769.51828151.127236649.
165 16266405013.45686117391553
166 133 9 5.191.11971.55987.188861.1101773.638073026189.164331230229374083.223393431463263911519708964052259906781762\
167 9985127899
168 134 8 5.7.269.418349.90571543952974835963.191757760647639121941197.904949028329910415467529.302370663780954222294\
169 0030043
170 135 15 5^2.19.43.163.311.1171.1201.2161.2467.112771.175509721.19353635731.623067280651.606162141679902054991801871\
171 110954177324256409961
172 136 16 5.7.37.137.239.409.1123.1297.5849.30839.190537.934117.12690943.1536052010629489.8289713345361373993.5142057\
173 6374811381403609445473
174 137 6 5.6577.25247731.53280671.60042056488501962187.1522214510879021329626941843334490679379355130104242302631442\
175 9342733
176 138 14 5.7.31.43.47.139.3221.11731.113958101.990000731.7505944891.24648570768391.816214079084081564521.12363858534\
177 32057889667843739281
178 139 5 5.557.21407.128159.1904994318294264032001011698767856776424905969372788422268974477324726371768074195193068\
179 08486559
180 140 25 5^2.7^2.11.29.37.71.101.197.241.311.421.631.701.2311.6781.9241.55987.585131.5030761.37863211.1469029031.135\
181 09594555661.1708114263204222806519161
182 141 11 5.43.283.13537.753554761.930911329.45110836129.122320721569.989671414201.17821718159716147.9318249558895921\
183 24612176563793529
184 142 6 5.7.37489.11735704315681.5757417485448059422914748320317168839.35462452974572174935904491917485464580055951\
185 87661976371
186 143 8 5.23.859.3433.760891.3154757.62545486153056268832471.370492708153183538667516076628295958764609620252358691\
187 48795940042759
188 144 23 5.7.13.17.19.31.37.43.73.97.541.577.1297.2467.3313.5953.46441.55117.98801.1678321.473896897.2478750186961.2\
189 2452257707354557235348829785471057921
190 145 7 5^2.311.132241.150433631394488258261.7369130657357778596659.59580423676805748420140957215180302958743471829\
191 183098610333631
192 146 11 5.7.293.439.120855443.1389436303.44764549877.2436094907761.8439148071138817.138721648424756087.422188345937\
193 8030470824476438562257
194 147 9 5.43.55987.6527977.32093041.1822428931.122694573317.600827908214213.721593495645162209494937916430925440485\
195 5094763766767407121
196 148 15 5.7.37^2.149.3923.4441.7919.12211.2569799.334286825813.1096762734443.2054788991719.3300043400835529.1908924\
197 07618022993841069346975403017
198 149 4 5.38538553.1318713554713829548602512956686040272376450743377909.3463541760502538278596775684588153902182357\
199 12359759067327
200 150 22 5^3.7.11.31.43.101.151.311.601.1171.1201.82051.168151.1950271.18198701.40185601.573178201.918628247364601.3\
201 655688315536801.271041511600591342728451
202 151 4 5.2623968964411.4956504421137000338429923175878885954098593563.48723066259314477894157817245533780187559387\
203 828254264047307
204 152 14 5.7.37.191.1297.1787.4561.48713705333.638073026189.1030762781149.355518408146401.9736145643041809.502818748\
205 6478069273.13038313680704041577
206 153 14 5.19.43.239.307.409.1123.2467.30839.927037099.9757142011.23412002806867.12644443230579801886843521019.40670\
207 77533669936706351248605374735249
208 154 12 5.7^2.23.29.197.55987.3154757.51828151.484847574510970082567.84002092056248016278479853.5701908713415125406\
209 1666621717728669167279862151
210 155 8 5^2.311.5333.3559267608341.49744740983476472807.208210289142572055121.2686345232069105360022926492125783168\
211 511035955840811134515391
212 156 26 5.7.13^2.31.37.43.53.79.97.157.313.937.2341.3433.8893.9049.37571.760891.868999.3143401.8857759.126201427521\
213 1.6291946695217.197743936282933.6429178169720749
214 157 6 5.6446107.6423436771.81127299702871294523556776543.8695994904356302134775281276601.101210377513117399538507\
215 3322337706122495245797
216 158 10 5.7.317.5531.2832941.1147240288157.99687312908749681.26283825237209622143.197531251446059329471533015409.85\
217 92319153827988586815914947213
218 159 8 5.43.13781.118721004139.67587459957091.357293834576449.7091531088740602980647.88342645123243360518614293208\
219 997935963729713364951837539
220 160 23 5^2.7.11.17.37.41.101.241.311.353.1297.1697.6781.9601.17761.98801.4709377.3696985841.68754507401.1212061208\
221 81.2810800069601.2347110840158563816028186318246561
222 161 11 5.47.139.3221.10949.55987.593447.7505944891.491787574454982121.3358586137753609961516447641418203949.403733\
223 622730561138499463252012494935013
224 162 16 5.7.19.31.43.163.1783.2467.46441.114967.149862151.883383463.27767002339.623067280651.3920344350409644507093\
225 715799617.37725805717350619429950429139147
226 163 4 5.653.2378523250342970947582043555610171717174452063.888102772526021838488123845334486037375412519645053051\
227 472793437455099303804577
228 164 11 5.7.37.83.28537.4046701.8648131.174521133001.1854850885886497427178961.4837453663777044375040181.2461793762\
229 06361788466441901958293949537091001
230 165 15 5^2.23.43.67.311.331.1171.1201.3154757.3675127061.45686117391553.13724862774476458441.303146295935105097739\
231 1.46975793563298851302025905551105268509881
232 166 13 5.7.167.499.17597.710813.41580677.6547890917.80781507941.605274844997.21608536062644851877771.2589238104153\
233 304205575487.54824363564629401758409941
234 167 7 5.19466857.10301691259.229027359614687.9703107759710968661.2200446540213260920441013.1822952692682777153874\
235 022559086738173481449195038610359
236 168 25 5.7^2.13.29.31.37.43.97.197.281.337.421.617.1297.55987.1678321.5030761.804146449.1822428931.2527867231.6055\
237 984789.81035189089.1176362433121.19100900655540830489319601
238 169 9 5.677.3433.3719.760891.1420277.3066042413300025661761581713.351082413599031251316269147227.6400588768393061\
239 926708979473301321313835119309935933
240 170 18 5^2.7.11.101.239.311.409.1123.30839.190537.12690943.26807981.1383638161.20891158391.72085651321561.74079767\
241 2014674927371043791.94260123386979283872547675418641
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