1Factorisations Of Cunningham Numbers C-(7,n) = 7^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 2.3
24 2 5 2^4.3
25 3 4 2.3^2.19
26 4 8 2^5.3.5^2
27 5 3 2.3.2801
28 6 8 2^4.3^2.19.43
29 7 4 2.3.29.4733
30 8 10 2^6.3.5^2.1201
31 9 7 2.3^3.19.37.1063
32 10 8 2^4.3.11.191.2801
33 11 4 2.3.1123.293459
34 12 13 2^5.3^2.5^2.13.19.43.181
35 13 3 2.3.16148168401
36 14 9 2^4.3.29.113.911.4733
37 15 7 2.3^2.19.31.2801.159871
38 16 13 2^7.3.5^2.17.1201.169553
39 17 4 2.3.14009.2767631689
40 18 12 2^4.3^3.19.37.43.1063.117307
41 19 4 2.3.419.4534166740403
42 20 14 2^5.3.5^3.11.191.281.2801.4021
43 21 7 2.3^2.19.29.4733.11898664849
44 22 9 2^4.3.23.1123.293459.10746341
45 23 5 2.3.47.3083.31479823396757
46 24 18 2^6.3^2.5^2.13.19.43.73.181.193.409.1201
47 25 5 2.3.2551.2801.31280679788951
48 26 8 2^4.3.53.228511817.16148168401
49 27 12 2.3^4.19.37.109.811.1063.2377.2583253
50 28 13 2^5.3.5^2.29.113.911.4733.13564461457
51 29 5 2.3.59.127540261.71316922984999
52 30 14 2^4.3^2.11.19.31.43.191.2801.159871.6568801
53 31 5 2.3.311.21143.3999088279399464409
54 32 16 2^8.3.5^2.17.353.1201.169553.47072139617
55 33 9 2.3^2.19.1123.3631.293459.1532917.12323587
56 34 8 2^4.3.14009.2767631689.29078814248401
57 35 7 2.3.29.2801.4733.2127431041.77192844961
58 36 18 2^5.3^3.5^2.13.19.37.43.181.1063.117307.13841169553
59 37 5 2.3.223.2887.4805345109492315767981401
60 38 9 2^4.3.419.351121.4058036683.4534166740403
61 39 8 2.3^2.19.486643.7524739.44975113.16148168401
62 40 18 2^6.3.5^3.11.41.191.281.1201.2801.4021.810221830361
63 41 5 2.3.83.20515909.4362139336229068656094783
64 42 15 2^4.3^2.19.29.43.113.911.4733.51031.309079.11898664849
65 43 4 2.3.166003607842448777.2192537062271178641
66 44 15 2^5.3.5^2.23.661.1123.1409.293459.10746341.83960385389
67 45 12 2.3^3.19.31.37.1063.2801.159871.1527007411.125096112091
68 46 9 2^4.3.47.3083.31479823396757.3421093417510114543
69 47 4 2.3.13722816749522711.63681511996418550459487
70 48 22 2^7.3^2.5^2.13.17.19.43.73.181.193.409.1201.169553.33232924804801
71 49 8 2.3.29.3529.4733.1074473.13473433.6106505825833677713
72 50 11 2^4.3.11.191.2551.2801.31280679788951.79787519018560501
73 51 10 2.3^2.19.103.14009.365773.2316281689.2767631689.10879733611
74 52 13 2^5.3.5^2.53.157.228511817.16148168401.1195857367853217109
75 53 5 2.3.8269.319591.38904276017035188056372051839841219
76 54 18 2^4.3^4.19.37.43.109.811.1063.2377.117307.2583253.1628413557556843
77 55 6 2.3.1123.2801.293459.5457586804596062091175455674392801
78 56 19 2^6.3.5^2.29.113.337.911.1201.2129.4733.517553.515717329.13564461457
79 57 10 2.3^2.19^2.419.19609.879399649.4534166740403.6957533874046531
80 58 9 2^4.3.59.127540261.71316922984999.402488219476647465854701
81 59 6 2.3.459257.134927809.550413361.354639323684545612988577649
82 60 24 2^5.3^2.5^3.11.13.19.31.43.61.181.191.281.2801.4021.159871.6568801.555915824341
83 61 6 2.3.367.4759.177237331.1914662449813727660680530326064591907
84 62 11 2^4.3.311.373.21143.9754399.5420506947192709.3999088279399464409
85 63 11 2.3^3.19.29.37.1063.4733.11898664849.2643999917660728787808396988849
86 64 20 2^9.3.5^2.17.353.1201.169553.7699649.134818753.47072139617.531968664833
87 65 9 2.3.131.2801.157951.787021.16148168401.4446437759531.434502978835771
88 66 17 2^4.3^2.19.23.43.67.1123.3631.293459.1532917.10746341.12323587.1357105535093947
89 67 6 2.3.228337.147300841.206244761.10052011757370829033540932021825161
90 68 14 2^5.3.5^2.137.14009.59361349.2767631689.29078814248401.133088039373662309
91 69 10 2.3^2.19.47.139.3083.402011881627.31479823396757.235169662395069356312233
92 70 18 2^4.3.11.29.71.113.191.421.911.2801.4733.12128131.603926681.2127431041.77192844961
93 71 4 2.3.990643452963163.169002145064468556765676975247413756542145739
94 72 26 2^6.3^3.5^2.13.19.37.43.73.181.193.409.1063.1201.42409.117307.137089.13841169553.32952799801
95 73 7 2.3.439.3675989.359390389.1958423494433591.7222605228105536202757606969
96 74 10 2^4.3.149.223.2887.4805345109492315767981401.15572244900182528777225808449
97 75 11 2.3^2.19.31.2551.2801.29251.159871.31280679788951.217648180992721729506406538251
98 76 13 2^5.3.5^2.419.351121.4058036683.4534166740403.2598696228942460402343442913969
99 77 9 2.3.29.1123.4733.293459.724487149.6809710909.88262612316754526107621113329689
100 78 17 2^4.3^2.19.43.53.79.486643.7524739.23850061.44975113.228511817.16148168401.115868130379
101 79 4 2.3.913242407367610843676812931.1056836588644853738704557482552056406147
102 80 24 2^7.3.5^3.11.17.41.191.281.881.1201.2801.4021.169553.542081.810221830361.2312581841562813841
103 81 17 2.3^5.19.37.109.811.1063.1621.2377.3727.2583253.3368791.70722308812401674174993533367023
104 82 12 2^4.3.83.4849399.8999993.20515909.1636258751.78009515593.4362139336229068656094783
105 83 9 2.3.167.66733.76066181.7685542369.62911130477521.303567967057423.18624275418445601
106 84 22 2^5.3^2.5^2.13.19.29.43.113.181.911.4733.51031.309079.11898664849.13564461457.195489390796456327201
107 85 8 2.3.1531.2801.4931.14009.2767631689.138497973518827432485604572537024087153816681041
108 86 14 2^4.3.947.19867.20899.163573.235211.3799051.4749781.166003607842448777.2192537062271178641
109 87 10 2.3^2.19.59.127540261.2576743207.71316922984999.196915704073465747.358475907408445923469
110 88 20 2^6.3.5^2.23.89.661.1123.1201.1409.8713.293459.10746341.83960385389.8206973609150536446402438593
111 89 5 2.3.1805633.18489605314740987765913.8166146875847876762859119015147004762656450569
112 90 24 2^4.3^3.11.19.31.37.43.191.541.1063.2801.117307.154351.159871.295831.6568801.7777981.1527007411.125096112091
113 91 8 2.3.29.4733.7304123737.16148168401.231410451435538144122809.3565837331172073232378945297
114 92 16 2^5.3.5^2.47.3083.26681.649981.15513961.31479823396757.3421093417510114543.55681942361860463813
115 93 10 2.3^2.19.311.21143.5463751.2211164386353499.3999088279399464409.36148617745189465516342817701
116 94 8 2^4.3.13722816749522711.63681511996418550459487.655417289594537954307682339857743931943
117 95 8 2.3.419.2801.36671.1966385431.4534166740403.83588499889013461558350575326824370345112529401
118 96 28 2^8.3^2.5^2.13.17.19.43.73.97.181.193.353.409.1201.169553.104837857.47072139617.33232924804801.108604397663\
119 266369
120 97 5 2.3.389.971.4160924156784953821413999107825795646911807584554735726748631757909547764679
121 98 20 2^4.3.29.113.197.883.911.3529.3823.4733.161309.1074473.1445599.13473433.19847549.101361401.6106505825833677\
122 713
123 99 15 2.3^3.19.37.199.1063.1123.3631.173647.293459.1532917.12323587.14658652062814508164798530246267135510037033
124 100 22 2^5.3.5^4.11.101.191.281.2551.2801.4021.13001.25301.31280679788951.79787519018560501.38327966300231909291101
125 101 6 2.3.607.809.6263.1226962153072980952980067096888460031879516017670288348423584305043494594529
126 102 18 2^4.3^2.19.43.103.14009.365773.1135261.12192877.2316281689.2767631689.10879733611.29078814248401.9092074664\
127 9833
128 103 4 2.3.17923.10316589882658148664018432412741304154103858145253645339510927287724805842171756259
129 104 18 2^6.3.5^2.53.157.313.1201.85094881.228511817.16148168401.1195857367853217109.1377454635342537460935008154217
130 105 13 2.3^2.19.29.31.2801.4733.159871.2127431041.11898664849.77192844961.42693162668620904426304495389707999425601
131 106 12 2^4.3.107.8269.319591.345449549.35416476134069.58902316970027001503.38904276017035188056372051839841219
132 107 5 2.3.227109283745807808529.1620221568881364582821.1206506689449517154664984054683391885701717268373
133 108 27 2^5.3^4.5^2.13.19.37.43.109.181.811.1063.2377.26893.117307.2583253.13841169553.167039577217.590297313273013.
134 1628413557556843
135 109 5 2.3.14551288401737861.63505707690048880101785428103.23540782932240399632107200158745339309941271547
136 110 19 2^4.3.11^2.23.191.331.1123.2311.2801.38501.293459.2864401.10746341.7840815905526451.54575868045960620911754\
137 55674392801
138 111 11 2.3^2.19.223.2887.6217.177379.56713875643149053038693.4805345109492315767981401.966513020957488728227630485\
139 99
140 112 27 2^7.3.5^2.17.29.113.337.449.673.911.1201.2129.4733.169553.517553.39648001.515717329.13564461457.21535258550\
141 401.142256806230113
142 113 4 2.3.227.230091944348186646613985311030910601771732680858725360845463092718251327185092028815673428363
143 114 19 2^4.3^2.19^2.43.419.457.19609.351121.879399649.4058036683.24006520939.4534166740403.6957533874046531.275430\
144 251632699963
145 115 12 2.3.47.1151.2801.3083.188831.1446701.723461377501.31479823396757.27229507836853201541.323388097576653901216\
146 14112981
147 116 16 2^5.3.5^2.59.233.127540261.136853089.55716067510309.71316922984999.116714640028973541741413.402488219476647\
148 465854701
149 117 16 2.3^3.19.37.1063.1873.322921.486643.2280097.7524739.44975113.7687225261.16148168401.66135384230579134218722\
150 8684843715341
151 118 13 2^4.3.122131.459257.134927809.550413361.4261190159.1187164242679.14683403662888806475673.354639323684545612\
152 988577649
153 119 11 2.3.29.4733.12377.14009.34273.2767631689.305213588009240737.440779823883628367834893.2023356904834733683686\
154 3191403341
155 120 33 2^6.3^2.5^3.11.13.19.31.41.43.61.73.181.191.193.281.409.1201.2801.4021.159871.6568801.12913561.555915824341.
156 810221830361.85560261859655897641
157 121 9 2.3.1123.1453.65099.293459.11795261559086963.58792315124013823398811997.13928884340651233393054864060847158\
158 508075329
159 122 10 2^4.3.367.4759.177237331.1914662449813727660680530326064591907.44451912814717044465691467294568943905088020\
160 9231501
161 123 9 2.3^2.19.83.267403.20515909.4362139336229068656094783.13031612278097596136163934699402177453365619293349843\
162 0337748067
163 124 17 2^5.3.5^2.311.373.21143.9754399.33947629297.5420506947192709.3999088279399464409.74502648768583254173.19684\
164 6325409292090901
165 125 8 2.3.251.2551.2801.31280679788951.2182816753758823696751.590354667835684444020417934211947301188761723956532\
166 3800435501
167 126 25 2^4.3^3.19.29.37.43.113.127.911.1063.4733.9829.51031.117307.309079.20801593.67979647.1506625093.11898664849.
168 2643999917660728787808396988849
169 127 5 2.3.260461507.554351226505275380676162672703.24534164319836858284335214459848074446885004177502212550076704\
170 7213117
171 128 24 2^10.3.5^2.17.353.1201.35969.169553.7699649.134818753.47072139617.531968664833.1110623386241.15266848196793\
172 556098085000332888634369
173 129 10 2.3^2.19.10837.63350976270733.166003607842448777.2192537062271178641.175446584281395198837259.6946231973486\
174 82715265952229891
175 130 18 2^4.3.11.53.131.191.2801.157951.787021.1175071.228511817.16148168401.4446437759531.434502978835771.35695043\
176 869049049222174543845808031
177 131 3 2.3.8505346116479680194953954163954280577066639233068267330253081977410514153169870714693030729025353732044\
178 7270457
179 132 29 2^5.3^2.5^2.13.19.23.43.67.181.661.1123.1409.3631.29569.293459.1532917.2784937.10746341.12323587.678240817.
180 83960385389.116320403133001.1357105535093947
181 133 11 2.3.29.419.4733.401563177.2662276961.4534166740403.373740808373213.897558513407803666357.445657944321249761\
182 45013684073215440137
183 134 12 2^4.3.20771.228337.147300841.206244761.6557750853567755279.383942665465635068312581125821527.10052011757370\
184 829033540932021825161
185 135 21 2.3^4.19.31.37.109.271.811.1063.2377.2801.159871.185221.2583253.1527007411.125096112091.175561876921802311.
186 797937984757981841530188510084780901
187 136 19 2^6.3.5^2.137.1201.14009.20129.94793.59361349.2767631689.29078814248401.133088039373662309.6389917485430821\
188 13037456009420293477766438233
189 137 8 2.3.2741.213721.251533.57162922399254002352124124899.65480203458464902965944539043.181428113215102554427027\
190 51468712154533804561
191 138 18 2^4.3^2.19.43.47.139.277.3083.402011881627.7396787205469.31479823396757.3421093417510114543.850194891513615\
192 5490673.235169662395069356312233
193 139 5 2.3.19739.673039.369071860325105204940905426444784144250426677655115371406716343216852089137589555456819857\
194 19375774106220917
195 140 28 2^5.3.5^3.11.29.71.113.191.281.421.911.2801.4021.4733.12128131.603926681.2127431041.13564461457.77192844961.
196 102314938321.18690488255321.19584845505919961
197 141 9 2.3^2.19.283.5960917.13722816749522711.63681511996418550459487.28591793293072926277385447141879418320873502\
198 6049402141999388275408759
199 142 9 2^4.3.990643452963163.1351405472411521.92914860840816888117372433724419584467881183.16900214506446855676567\
200 6975247413756542145739
201 143 8 2.3.1123.293459.16148168401.528808508322667.376215890379315997311416372784691746214777.11119427897815667812\
202 99747693078700888402223739
203 144 35 2^7.3^3.5^2.13.17.19.37.43.73.181.193.409.1063.1201.42409.117307.129169.137089.169553.25726609.51385969.635\
204 311009.13841169553.32952799801.338325042961.33232924804801
205 145 9 2.3.59.2801.4899841.127540261.71316922984999.277463632645667965008782910911.2822743899874399927030333062466\
206 2217730888039289619786090751
207 146 13 2^4.3.439.3067.279883.3675989.359390389.1958423494433591.7222605228105536202757606969.716764748064350430205\
208 8174754486698790538818746798241
209 147 14 2.3^2.19.29.3529.4733.1074473.13473433.11898664849.4060603391041.6106505825833677713.4247708713399033015675\
210 09.56427334222486513688076273080920621
211 148 14 2^5.3.5^2.149.223.2887.4805345109492315767981401.15572244900182528777225808449.6891042949305882214394659726\
212 647344864958515967158596120016737
213 149 3 2.3.1385022127101034087007743810331355039266633249933176317292277906573251633103418332277759454260526370920\
214 67324133850503035623601
215 150 22 2^4.3^2.11.19.31.43.151.191.2551.2801.29251.159871.6568801.6005492312551.31280679788951.79787519018560501.7\
216 021370289199888801.217648180992721729506406538251
217 151 7 2.3.115356256117.36076003832567.206462520503013793561.2856349001315592319937.276529023162022452344185243512\
218 4159094999555183731339173137659
219 152 20 2^6.3.5^2.419.1201.351121.44118001.700197881.4058036683.1295161807633.4534166740403.1299254811081649.135214\
220 434686939513.2598696228942460402343442913969
221 153 19 2.3^3.19.37.103.307.613.1063.4591.14009.44371.365773.2316281689.2767631689.10879733611.44072862804091655188\
222 147.795000162131334968169163150985614882079420233
223 154 21 2^4.3.23.29.113.463.911.1123.4733.293459.333103.10746341.258576319.724487149.6809710909.32817262777539703.4\
224 43632323630099913.88262612316754526107621113329689
225 155 11 2.3.311.2801.21143.21391.21701.1622982371.9254997611.3999088279399464409.3172801518994677306295492126843582\
226 5250349092899077924422648569887851893731
227 156 27 2^5.3^2.5^2.13^2.19.43.53.79.157.181.486643.7524739.23850061.44975113.228511817.16148168401.115868130379.36\
228 5302616611175569.1195857367853217109.7886422107556319674933
229 157 6 2.3.4397.5653.1039945344901.3088837530933217469974776415779808389101928682917555417651530821177567508549116\
230 4240495874534303554491469173279661
231 158 11 2^4.3.317.2874811.7573763065938754357.913242407367610843676812931.104875706439110156251225614941159441477.1\
232 056836588644853738704557482552056406147
233 159 11 2.3^2.19.8269.32119.319591.1695259.84247682063005850464952755729.38904276017035188056372051839841219.145532\
234 9561052597138348454392994231780317942530389
235 160 30 2^8.3.5^3.11.17.41.191.281.353.881.1201.2801.4021.169553.542081.38470561.47072139617.810221830361.102118777\
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936 192320558859369717.1491795958375513642426565124210730643931478615066871228523778950151875869378196710880709\
937 977712386418670048447341464914847587718695713