1Factorisations Of Cunningham Numbers C-(11,n) = 11^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 2 2.5
24 2 5 2^3.3.5
25 3 4 2.5.7.19
26 4 7 2^4.3.5.61
27 5 4 2.5^2.3221
28 6 9 2^3.3^2.5.7.19.37
29 7 4 2.5.43.45319
30 8 9 2^5.3.5.61.7321
31 9 5 2.5.7.19.1772893
32 10 8 2^3.3.5^2.3221.13421
33 11 4 2.5.15797.1806113
34 12 13 2^4.3^2.5.7.13.19.37.61.1117
35 13 4 2.5.1093.3158528101
36 14 8 2^3.3.5.43.45319.1623931
37 15 7 2.5^2.7.19.3221.195019441
38 16 12 2^6.3.5.17.61.7321.6304673
39 17 3 2.5.50544702849929377
40 18 12 2^3.3^3.5.7.19.37.590077.1772893
41 19 3 2.5.6115909044841454629
42 20 11 2^4.3.5^2.61.3221.13421.212601841
43 21 10 2.5.7^2.19.43.1723.8527.27763.45319
44 22 11 2^3.3.5.23.89.199.15797.58367.1806113
45 23 5 2.5.829.28878847.3740221981231
46 24 17 2^5.3^2.5.7.13.19.37.61.1117.7321.10657.20113
47 25 8 2.5^3.3001.3221.24151.1856458657451
48 26 10 2^3.3.5.53.911.1093.59583967.3158528101
49 27 6 2.5.7.19.1772893.5559917315850179173
50 28 13 2^4.3.5.29.43.61.1933.45319.1623931.55527473
51 29 4 2.5.523.303309617049998388989376043
52 30 15 2^3.3^2.5^2.7.19.31.37.3221.13421.7537711.195019441
53 31 5 2.5.50159.2428541.157571957584602258799
54 32 15 2^7.3.5.17.61.7321.51329.6304673.447600088289
55 33 9 2.5.7.19.661.1453.15797.1806113.637265428480297
56 34 9 2^3.3.5.71707.264793.2218331.50544702849929377
57 35 8 2.5^2.43.211.3221.45319.42437717969530394595211
58 36 17 2^4.3^3.5.7.13.19.37.61.1117.590077.1772893.3138426605161
59 37 6 2.5.2591.36855109.136151713.2615418118891695851
60 38 10 2^3.3.5.191.229.83791.1390636259.6115909044841454629
61 39 12 2.5.7.19.79.157.547.1093.84631.480091.32508061.3158528101
62 40 15 2^5.3.5^2.41.61.3221.7321.13421.212601841.1120648576818041
63 41 9 2.5.83.1231.27061.509221.14092193.29866451.840139875599
64 42 17 2^3.3^2.5.7^2.19.37.43.1723.8527.27763.45319.1623931.3421169496361
65 43 4 2.5.1416258521793067.42534656091583268045915654719
66 44 15 2^4.3.5.23.61.89.199.15797.58367.251857.1806113.2649263870814793
67 45 9 2.5^2.7.19.3221.1772893.195019441.9842332430037465033595921
68 46 12 2^3.3.5.47.829.1013.241363.28878847.3740221981231.6493405343627
69 47 5 2.5.2069.22666879066355177.18806327041824690595747113889
70 48 24 2^6.3^2.5.7.13.17.19.37.61.97.241.1117.1777.7321.10657.20113.6304673.1106131489
71 49 7 2.5.43.45319.510810301.1065264019.100641220283951395639601683
72 50 14 2^3.3.5^3.3001.3221.13421.24151.46601.1856458657451.14436295738510501
73 51 9 2.5.7.19.10711.457315063.15085812853.25994736109.50544702849929377
74 52 13 2^4.3.5.53.61.911.1093.59583967.3158528101.9768997162071483134919121
75 53 6 2.5.107.351497.6005113.6918082374901313855125397665325977135579
76 54 16 2^3.3^4.5.7.19.37.379.590077.1772893.4889988840047743.5559917315850179173
77 55 10 2.5^2.3221.15797.25301.39161.1806113.643170158708221.645654335737185721
78 56 19 2^5.3.5.29.43.61.113.449.1933.2521.7321.45319.1623931.55527473.77001139434480073
79 57 8 2.5.7.19^2.1047623475541.6115909044841454629.1412900479108654932024439
80 58 10 2^3.3.5.59.523.10979607179423.204064664440913.303309617049998388989376043
81 59 5 2.5.1181.70845409351.33083146850190391025301565142735000331370209599
82 60 21 2^4.3^2.5^2.7.13.19.31.37.61.1117.3221.13421.7537711.195019441.212601841.46329453543600481
83 61 5 2.5.440177.520518327319589.1461808298382111034194027645506019619578037
84 62 12 2^3.3.5.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223
85 63 16 2.5.7^2.19.43.127.1723.8317.8527.27763.45319.867259.1772893.106431697.316825425410373433
86 64 19 2^8.3.5.17.61.193.257.7321.51329.6304673.447600088289.21283620033217629539178799361
87 65 8 2.5^2.131.1093.3221.3158528101.673267426712748387612994804392183645147042355211
88 66 22 2^3.3^2.5.7.19.23.37.67.89.199.661.1453.9439.15797.58367.991651.1806113.1169382127.637265428480297
89 67 6 2.5.15277.2160349.76394148218203559.235335702141939072378977155172505285655211
90 68 15 2^4.3.5.61.137.71707.264793.2218331.2481791513.9598959833.641625222857.50544702849929377
91 69 10 2.5.7.19.139.829.28878847.8209475377.3740221981231.5283012903770196631383821046101707
92 70 19 2^3.3.5^2.43.71^2.211.3221.7561.13421.17011.45319.1623931.1649341.10047871.42437717969530394595211
93 71 7 2.5.1847.64327.159248456569.1273880539247.360426336941693434048414944508078750920763
94 72 24 2^5.3^3.5.7.13.19.37.61.73.1117.7321.10657.20113.40177.590077.1772893.3138426605161.3358335487319458201
95 73 3 2.5.1051153199500053598403188407217590190707671147285551702341089650185945215953
96 74 11 2^3.3.5.2591.36855109.136151713.2615418118891695851.2691614274040036601.10527743181888260981
97 75 15 2.5^3.7.19.151.3001.3221.24151.59302051.195019441.1826934301.1856458657451.27665283091695977275201
98 76 14 2^4.3.5.61.191.229.83791.1390636259.1990415149.6115909044841454629.15403468930064931175264655869
99 77 8 2.5.43.15797.45319.1806113.593554036769.466345922275629775763320748688970211803553256223529
100 78 23 2^3.3^2.5.7.19.37.53.79.157.313.547.911.1093.63649.84631.480091.32508061.59583967.3158528101.53895302396194\
101 3033
102 79 5 2.5.317.185277551100523662054683911.31705898389348622756718888962810730367411163041955447
103 80 20 2^6.3.5^2.17.41.61.3221.5281.7321.13421.6304673.212601841.1120648576818041.399806412551699044818733915681
104 81 9 2.5.7.19.1772893.139026457.5559917315850179173.14010692617072784593.88236431987113771637099217013
105 82 15 2^3.3.5.83.1231.27061.509221.14092193.29866451.711628063.840139875599.1216150172449.479378523680060338823
106 83 7 2.5.167.12119.178057577.52447614013.1442525225996981034595894901431683672700025887063977893738081
107 84 26 2^4.3^2.5.7^2.13.19.29.37.43.61.1117.1723.1933.8527.19069.27763.45319.1623931.55527473.3421169496361.520799\
108 717831587692709
109 85 8 2.5^2.3221.584916791.553393500180551.50544702849929377.12520270706155176007034654722092907499983681
110 86 9 2^3.3.5.5333.1416258521793067.42534656091583268045915654719.9413099125139413690486707432096974989067
111 87 9 2.5.7.19.523.398113.54415717.303309617049998388989376043.873360172275048609080552096817243827525632861
112 88 21 2^5.3.5.23.61.89.199.353.7321.15797.58367.72689.251857.1806113.13585441.2649263870814793.129825679438716999\
113 6154165633
114 89 6 2.5.73111721.2103114787086589.4180235017418376525776333.75144689824702198592013444969850173811994737
115 90 22 2^3.3^3.5^2.7.19.31.37.181.631.3221.13421.590077.1772893.7537711.195019441.86306335830799838011.98423324300\
116 37465033595921
117 91 7 2.5.43.1093.45319.3158528101.868721697058567435824108245607127696076153182930226460514053403127306646961
118 92 18 2^4.3.5.47.61.829.1013.201757.241363.28878847.2004414397.3740221981231.6493405343627.24737721275161.6569432\
119 72596448809
120 93 10 2.5.7.19.2791.3163.50159.2428541.157571957584602258799.3137876238000684620152119068677936364954475597711271\
121 1197
122 94 12 2^3.3.5.2069.844309.549524471.26097456317.22666879066355177.60699948346804199382437.18806327041824690595747\
123 113889
124 95 8 2.5^2.3221.67989221.6115909044841454629.180124441029509240214675551.709366429143448333528137335486039060202\
125 91
126 96 29 2^7.3^2.5.7.13.17.19.37.61.97.241.577.1117.1777.7321.10657.20113.51329.6304673.1106131489.447600088289.3659\
127 233404740477018363752843393
128 97 5 2.5.389.4247091263.6266849507589571978149106488222106980975381364824424072801340422775737133656105189072051
129 98 15 2^3.3.5.43.11467.45319.800171.1623931.176784259.510810301.1065264019.33761096386802842263303497.10064122028\
130 3951395639601683
131 99 14 2.5.7.19.397.661.1453.2377.15797.1772893.1806113.1240500097.637265428480297.2599071362839584231023974669237\
132 98834567695212357
133 100 20 2^4.3.5^3.61.101.3001.3221.13421.24151.46601.212601841.1856458657451.2248313994601.14436295738510501.199309\
134 9906542710819727884501
135 101 5 2.5.341459085477993311443.86408339296208914807632672776254957729.513767785847095403363378495505038747238330\
136 8083
137 102 20 2^3.3^2.5.7.19.37.103.10711.71707.264793.1348033.2218331.457315063.15085812853.25994736109.5054470284992937\
138 7.16576413357576409067287639
139 103 6 2.5.24103.37723802531.995301206162659155091.202677471366153865787391434710952643545087969532720827000553398\
140 46745091
141 104 16 2^5.3.5.53.61.911.1093.7321.59583967.3158528101.9768997162071483134919121.970106078298260708735599372683605\
142 84022789501553441
143 105 21 2.5^2.7^2.19.43.211.421.1723.3221.8527.27763.45319.540751.599551.2598121.126713791.195019441.23731414400247\
144 02184811.42437717969530394595211
145 106 13 2^3.3.5.107.1697.351497.5353637.6005113.17148893.8357265774463208206521728596439861293.69180823749013138551\
146 25397665325977135579
147 107 5 2.5.1276033068038437.304971297664201988898688683700564748747693245597.6900751922429791724019506627192737704\
148 11957106853
149 108 25 2^4.3^4.5.7.13.19.37.61.109.379.541.1117.590077.1772893.388174681.3138426605161.4889988840047743.5559917315\
150 850179173.1350472353550875103121929
151 109 4 2.5.35970728459102446279558069.9033445926510666398384928207099769878625683305416602322341095021068020592318\
152 51745003701
153 110 23 2^3.3.5^2.23.89.199.3221.4951.13421.15797.25301.39161.58367.411841.1806113.21537414911.85480219991.13152598\
154 3711.643170158708221.645654335737185721
155 111 10 2.5.7.19.2591.36855109.136151713.2615418118891695851.651950416864148392635280596760630561.13334983829534655\
156 64843320786357871664401
157 112 26 2^6.3.5.17.29.43.61.113.337.449.1933.2521.7321.45319.394129.1623931.6304673.55527473.77001139434480073.2363\
158 52238647181441.3090443962383595123379137
159 113 7 2.5.227.45902861.20884152591287817709.22455907106840364577416382241618449.973554682812876324986927406779613\
160 27574083833285959459
161 114 20 2^3.3^2.5.7.19^2.37.191.229.6043.75013.83791.1390636259.1047623475541.6115909044841454629.14129004791086549\
162 32024439.74337838382167137728921322559
163 115 12 2.5^2.829.3221.95911.333041.9964291.28878847.3740221981231.17184010031686356151.729842693308300425195832421\
164 6375350400730975973787843051
165 116 16 2^4.3.5.59.61.349.523.16585333.32637413.10979607179423.204064664440913.303309617049998388989376043.10918187\
166 7624126996017801852385627698243261
167 117 16 2.5.7.19.79.157.547.1093.9127.84631.480091.1772893.1810693.32508061.3158528101.5777953519959062358597260246\
168 2371982722687354954780675870640496251
169 118 12 2^3.3.5.1181.22067.70845409351.32833036072593109.59845177539010249.53199025841281128499153.3308314685019039\
170 1025301565142735000331370209599
171 119 9 2.5.43.239.45319.20580793913.50544702849929377.5787647502138040836760695667.3005681893232976654385404271528\
172 23770594407695480022422691549
173 120 29 2^5.3^2.5^2.7.13.19.31.37.41.61.1117.3221.7321.10657.13421.20113.7537711.195019441.212601841.52020741601.11\
174 20648576818041.46329453543600481.40589999671017742452961
175 121 8 2.5.15797.30977.1806113.1595696213.12407691244609.582793661124452623809041107212020076078733754671394043885\
176 9172127240114655549487246036729
177 122 11 2^3.3.5.440177.53320740257.520518327319589.137218978667473446671.38147158686655703132426388314683.146180829\
178 8382111034194027645506019619578037
179 123 15 2.5.7.19.83.1231.27061.174907.509221.14092193.28385941.29866451.840139875599.142971820992006871646588679396\
180 397417.262535239929018061575878552691659119
181 124 16 2^4.3.5.61.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223.4311672901046383796549.
182 70039146133823870629334170297294343364149
183 125 12 2.5^4.3001.3221.24151.1632185486501.1856458657451.27678437808551251.610080895141084967819354988677284050229\
184 269951248774263726574682822715310251
185 126 29 2^3.3^3.5.7^2.19.37.43.127.1723.8317.8527.27763.45319.590077.867259.1623931.1772893.3304981.106431697.46884\
186 3103.71596275661.278853374647.3421169496361.316825425410373433
187 127 6 2.5.2985212831443.6073732108394141.108345618426999904901.91966303295251191104971960132273397364144023351465\
188 750399992554753980589155137853599
189 128 22 2^9.3.5.17.61.193.257.7321.51329.6304673.447600088289.316955440822738177.21283620033217629539178799361.7032\
190 401262704707649518767703756385761576062060673
191 129 12 2.5.7.19.1549.1389891409.2338110553.44012945778511.1416258521793067.3440126314390780951.4253465609158326804\
192 5915654719.3579868931117378066463082728904957
193 130 18 2^3.3.5^2.53.131.911.1093.1301.3221.13421.25741.59583967.3158528101.316032713956951363848523051612091912095\
194 7201.673267426712748387612994804392183645147042355211
195 131 5 2.5.263.7791763956749016154215607697892626144401.1290774032138704646634687668236941308305597514202044201343\
196 330196757304660698533426132941183587
197 132 30 2^4.3^2.5.7.13.19.23.37.61.67.89.199.661.1117.1453.9439.15797.58367.251857.991651.1806113.1169382127.986309\
198 9401.637265428480297.2649263870814793.46266666682081629547022793157801
199 133 9 2.5.43.45319.292601.1889399.4085166784889.6115909044841454629.118907173249316196764766639893383431910454776\
200 99764476320956042082843152214319805595150031
201 134 15 2^3.3.5.269.15277.181303.2160349.2354458793.2778466094669.76388592846687031.76394148218203559.2028834791377\
202 4902979279.235335702141939072378977155172505285655211
203 135 12 2.5^2.7.19.271.3221.1772893.195019441.5559917315850179173.9842332430037465033595921.35261764476828649109379\
204 34141934983258605489440194538631398471107422118591
205 136 22 2^5.3.5.61.137.409.7321.11969.71707.264793.2218331.2481791513.9598959833.641625222857.739755736441.14387579\
206 997041.50544702849929377.85554906358182623545481335980971521
207 137 8 2.5.8221.339761.3677081.136238281.394711476243912154244261783.848433067196473533441008868772447888723971966\
208 6748414214743814637516122598288562123255444499
209 138 24 2^3.3^2.5.7.19.37.47.139.691.829.1013.241363.28878847.394648951.8209475377.18013255921.932225927887.1577386\
210 579003.3740221981231.6493405343627.5283012903770196631383821046101707
211 139 3 2.5.5670002325217957396258282812671713444868053858812175750811496601630462174655445733557105920797699326519\
212 89153833612198334843467861091902034340949
213 140 27 2^4.3.5^2.29.43.61.71^2.211.1933.3221.7561.13421.17011.45319.1623931.1649341.2970941.10047871.55527473.2126\
214 01841.42437717969530394595211.32925268156330499785365829732750601117816501
215 141 11 2.5.7.19.283.2069.64192789.22666879066355177.44682948968412414039336007.18806327041824690595747113889.72052\
216 0357109665867690144695251088293221239815545113983062729
217 142 13 2^3.3.5.1847.64327.149852362577.159248456569.1273880539247.5604196051154865381517.8620302099267300875307522\
218 246691084877239.360426336941693434048414944508078750920763
219 143 11 2.5.1093.3433.15797.1806113.3158528101.3111663528084541.191144869353686249.39087214421959708068637.10560044\
220 15999653050515555650243045564974450864216443757878943069209
221 144 34 2^6.3^3.5.7.13.17.19.37.61.73.97.241.1117.1777.7321.10657.20113.40177.110161.331921.590077.1772893.6304673.
222 1106131489.3138426605161.3358335487319458201.2653299576575651630603169124592864247361
223 145 9 2.5^2.523.3221.38861.303309617049998388989376043.144801130358116982559692328954495371.698722655477495663987\
224 35989506862167022001782100339822496855955029149120537231
225 146 11 2^3.3.5.668243.147031637.51866303408957.9863258277206753.17427450503923264964680282877251.10511531995000535\
226 98403188407217590190707671147285551702341089650185945215953
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