- 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.
- 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.
n #Fac Factorisation
1 1 2 [1st Prime]
2 3 2.2.2
3 2 2.13
4 5 2.2.2.2.5
5 3 2.11.11
6 5 2.2.2.7.13
7 2 2.1093
8 7 2.2.2.2.2.5.41
9 3 2.13.757
10 6 2.2.2.11.11.61
11 3 2.23.3851
12 8 2.2.2.2.5.7.13.73
13 2 2.797161
14 5 2.2.2.547.1093
15 5 2.11.11.13.4561
16 10 2.2.2.2.2.2.5.17.41.193
17 3 2.1871.34511
18 8 2.2.2.7.13.19.37.757
19 3 2.1597.363889
20 10 2.2.2.2.5.5.11.11.61.1181
21 4 2.13.1093.368089
22 7 2.2.2.23.67.661.3851
23 3 2.47.1001523179
24 11 2.2.2.2.2.5.7.13.41.73.6481
25 5 2.11.11.8951.391151
26 5 2.2.2.398581.797161
27 6 2.13.109.433.757.8209
28 9 2.2.2.2.5.29.547.1093.16493
29 4 2.59.28537.20381027
30 11 2.2.2.7.11.11.13.31.61.271.4561
31 4 2.683.102673.4404047
32 12 2.2.2.2.2.2.2.5.17.41.193.21523361
33 5 2.13.23.3851.2413941289
34 8 2.2.2.103.307.1021.1871.34511
35 6 2.11.11.71.1093.2664097031
36 12 2.2.2.2.5.7.13.19.37.73.757.530713
37 3 2.13097927.17189128703
38 7 2.2.2.1597.2851.101917.363889
39 7 2.13.13.313.6553.7333.797161
40 13 2.2.2.2.2.5.5.11.11.41.61.1181.42521761
41 4 2.83.2526913.86950696619
42 11 2.2.2.7.7.13.43.547.1093.2269.368089
43 3 2.431.380808546861411923
44 11 2.2.2.2.5.23.67.661.3851.5501.570461
45 9 2.11.11.13.181.757.1621.4561.927001
46 6 2.2.2.47.1001523179.23535794707
47 5 2.1223.21997.5112661.96656723
48 17 2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481
49 7 2.491.1093.4019.8233.51157.131713
50 10 2.2.2.11.11.61.151.8951.391151.22996651
51 6 2.13.1871.12853.34511.99810171997
52 9 2.2.2.2.5.53.398581.797161.4795973261
53 4 2.107.24169.3747607031112307667
54 13 2.2.2.7.13.19.37.109.433.757.8209.19441.19927
55 8 2.11.11.11.23.1321.3851.560088668384411
56 13 2.2.2.2.2.5.29.41.547.1093.16493.430697.647753
57 7 2.13.229.1597.248749.363889.1824179209
58 9 2.2.2.59.523.6091.28537.5385997.20381027
59 3 2.14425532687.489769993189671059
60 17 2.2.2.2.5.5.7.11.11.13.31.61.73.271.1181.4561.47763361
61 3 2.603901.105293313660391861035901
62 8 2.2.2.683.6883.102673.4404047.22434744889
63 6 2.13.757.1093.368089.144542918285300809
64 14 2.2.2.2.2.2.2.2.5.17.41.193.21523361.926510094425921
65 7 2.11.11.131.797161.3701101.110133112994711
66 12 2.2.2.7.13.23.67.661.3851.25411.176419.2413941289
67 4 2.221101.441019876741.475384700124973
68 12 2.2.2.2.5.103.307.1021.1871.34511.956353.1743831169
69 6 2.13.47.277.1001523179.2461243576713869557
70 11 2.2.2.11.11.61.71.547.1093.2664097031.374857981681
71 2 2.3754733257489862401973357979128773
72 16 2.2.2.2.2.5.7.13.19.37.41.73.757.6481.530713.282429005041
73 5 2.11243.20149.15768033143.9460375336977361
74 8 2.2.2.18427.107671.13097927.56737873.17189128703
75 10 2.11.11.13.601.4561.8951.9601.391151.2098303812601
76 11 2.2.2.2.5.1597.2851.101917.363889.5301533.25480398173
77 7 2.23.1093.3851.51457561.7151459701.76831835389
78 15 2.2.2.7.13.13.79.157.313.2887.6553.7333.10141.398581.797161
79 4 2.432853009.392038110671.145171177264407947
80 18 2.2.2.2.2.2.5.5.11.11.17.41.61.193.1181.14401.42521761.128653413121
81 9 2.13.109.433.757.3889.8209.1190701.12557612956332313
82 8 2.2.2.83.33703.2526913.86950696619.270547105429567
83 5 2.167.12119.1036745531.950996059627210897943351
84 18 2.2.2.2.5.7.7.13.29.43.73.547.1093.2269.2857.16493.368089.109688713
85 7 2.11.11.1871.34511.2663568851051.862970652262943171
86 6 2.2.2.431.380808546861411923.82064241848634269407
87 8 2.13.59.28537.74821.20381027.32234893.150224123975857
88 16 2.2.2.2.2.5.23.41.67.89.661.3851.5501.570461.2382953.56625998353
89 4 2.179.1611479891519807.5042939439565996049162197
90 19 2.2.2.7.11.11.13.19.31.37.61.181.271.757.1621.4561.387631.755551.927001
91 5 2.1093.797161.4011586307.3745603812007166116831643
92 10 2.2.2.2.5.47.12553493.1001523179.23535794707.70601370627701
93 7 2.13.683.1117.102673.4404047.26273701844015319144827917
94 10 2.2.2.1223.16921.21997.256057.5112661.96656723.1534179947851
95 7 2.11.11.191.1597.363889.78958087694609321439660131899631
96 21 2.2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481.76801.21523361.24127552321
97 4 2.76631.2549755542947.48845962828028421155731228333
98 12 2.2.2.491.547.1093.4019.8233.51157.131713.857643277.127522693159
99 8 2.13.23.757.3851.3186217.2413941289.12812432238302009985937
100 18 2.2.2.2.5.5.5.11.11.61.101.151.1181.8951.391151.394201.22996651.61070817601
101 4 2.33034273.465092326319.50316775668019759306202964023
102 15 2.2.2.7.13.103.307.613.1021.1871.12853.30091.34511.129159847.99810171997
103 2 2.6957596529882152968992225251835887181478451547013
104 13 2.2.2.2.2.5.41.53.398581.797161.2093124281.4795973261.37644053098601
105 13 2.11.11.13.71.421.1093.4561.6301.368089.1616161.2664097031.26751945361
106 8 2.2.2.107.24169.78719947.61557605176233223.3747607031112307667
107 4 2.50077.229837.48965028505045123993421250406516036571557
108 18 2.2.2.2.5.7.13.19.37.73.109.433.757.8209.19441.19927.530713.150094634909578633
109 6 2.1091.521402591.3499901929.239789806103.10624346875389299603
110 15 2.2.2.11.11.11.23.61.67.661.1321.3851.659671.24472341743191.560088668384411
111 7 2.13.13097927.18702169.119779213.17189128703.6962353413269964253
112 19 2.2.2.2.2.2.5.17.29.41.113.193.547.1093.16493.19489.430697.647753.36214795668330833
113 5 2.227.1583.2172539.526256453012063980796131127321354599535039
114 15 2.2.2.7.13.229.1597.2851.3079.53923.101917.248749.363889.1162320517.1824179209
115 8 2.11.11.47.1975931.1001523179.6273542442241.52370346649565455417091
116 13 2.2.2.2.5.59.523.6091.12413.28537.5385997.20381027.37945127666529000523013
117 11 2.13.13.313.757.6553.7333.797161.4162861.1846794457.2821964307371847613
118 7 2.2.2.3187.14425532687.489769993189671059.1108439448677340328268341
119 7 2.239.1093.1871.34511.44626806191326911791.397881837642577477902049
120 24 2.2.2.2.2.5.5.7.11.11.13.31.41.61.73.241.271.1181.4561.6481.298801.26050081.42521761.47763361
121 6 2.23.3851.11617.3981923614021.657890411545272648205502849240259841
122 7 2.2.2.367.603901.105293313660391861035901.86630432442539925437931403
123 7 2.13.83.51169.2526913.86950696619.1999827817517387044561568810795329
124 13 2.2.2.2.5.683.6883.102673.4404047.1403808961.2860659169.9500438809.22434744889
125 10 2.11.11.251.8951.391151.358291751.14781691751.391632555001.989947158849251
126 19 2.2.2.7.7.13.19.37.43.127.547.757.883.1093.2269.2521.368089.550554229.144542918285300809
127 6 2.5843.681229.21520151.76082653.301515315752300874236564235591357673
128 16 2.2.2.2.2.2.2.2.2.5.17.41.193.21523361.926510094425921.1716841910146256242328924544641
129 7 2.13.431.4129.2199072289.380808546861411923.912851565662857110894244969
130 12 2.2.2.11.11.61.131.398581.797161.3701101.110133112994711.105919308797935444986721
131 3 2.263.605199588591144003100881306574406851660288427740394885828171
132 18 2.2.2.2.5.7.13.23.67.73.661.3851.5501.25411.176419.570461.2413941289.13490012358249728401
133 6 2.1093.1597.363889.8757948941961838067.257513776243156826379279929309507
134 8 2.2.2.221101.5390821.441019876741.475384700124973.4299412981246169975118907
135 15 2.11.11.13.109.181.433.541.757.1621.4561.8209.927001.53825041.773618132427345151923061
136 17 2.2.2.2.2.5.41.103.137.307.1021.1871.34511.956353.1743831169.6458150122561.3833564416504313
137 4 2.4933.217629707.108081809773839995188256800499141543684393035450350551
138 15 2.2.2.7.13.47.139.277.5107.9109.132619.1476463.1001523179.23535794707.2461243576713869557
139 4 2.1669.5430731.115215201111546538317696820901417129607616709798043944747
140 20 2.2.2.2.5.5.11.11.29.61.71.547.1093.1181.16493.28596961.32839661.94373861.2664097031.374857981681
141 9 2.13.1223.21997.5112661.96656723.161969595577.2031161085853.165301473942399079669
142 9 2.2.2.853.2131.82219.3099719989.4052490063499.3754733257489862401973357979128773
143 5 2.23.3851.797161.1198014380856762535048758241151960180137876946928788681521
144 24 2.2.2.2.2.2.5.7.13.17.19.37.41.73.97.193.577.757.769.6481.530713.1418632417.282429005041.56227703611393
145 7 2.11.11.59.28537.20381027.183349688798536618131199274872809217263632838323547361
146 9 2.2.2.439.11243.20149.15768033143.9460375336977361.38488154120055537150068589763279
147 11 2.13.491.1093.4019.8233.47041.51157.131713.368089.254395969103901649521223867932173929
148 13 2.2.2.2.5.149.18427.107671.953861.13097927.56737873.17189128703.142659759801404920771391593
149 4 2.7451.177941761.46509804063632583432467217805311362636553293639540930405531
150 22 2.2.2.7.11.11.13.31.61.151.271.601.2551.4561.8951.9601.26251.119101.391151.1530601.22996651.2098303812601
151 5 2.1511.6263783.64745079361.905673230703550690601003473107008473103084254587061
152 17 2.2.2.2.2.5.41.761.1597.2851.31769.101917.363889.3302353.5301533.25480398173.278733912072436804273
153 10 2.13.757.1871.12853.34511.6213394261.35106034213.99810171997.28090626041813012073462457
154 13 2.2.2.23.67.547.661.1093.3851.51457561.7151459701.76831835389.56495392933101222275861053369
155 9 2.11.11.311.683.102673.4404047.3586225081.1078579799806668629607014283525941686969924751
156 22 2.2.2.2.5.7.13.13.53.73.79.157.313.2887.6553.7333.10141.325729.398581.797161.4795973261.271722723752757889
157 5 2.9421.3381925092493.9891109125337566719.1283810768507270931382867729773882314783
158 9 2.2.2.66361.432853009.327220181191.392038110671.145171177264407947.567239060331150635317
159 7 2.13.107.24169.712550912937217.3747607031112307667.40559607827224525043263763418498193
160 23 2.2.2.2.2.2.2.5.5.11.11.17.41.61.193.1181.14401.8194721.21523361.42521761.700984481.128653413121.5977474287\
54241
161 5 2.47.1093.1001523179.636961216046002471921398696960338364910115196955450597747751689
162 21 2.2.2.7.13.19.37.109.163.433.757.1297.3889.8209.19441.19927.208657.224209.1190701.5879415781.12557612956332\
313
163 4 2.5227348213873.8882811705390167.6351885141964057411259499526611848626072045955243
164 13 2.2.2.2.5.83.33703.2088869.2526913.110767897.86950696619.270547105429567.574933708017116710865237
165 13 2.11.11.11.13.23.1321.3851.4561.50821.2413941289.560088668384411.4183739978746243239852385111562221
166 11 2.2.2.167.499.997.12119.2466097.1036745531.950996059627210897943351.813201725710097952736361977
167 6 2.58451.88177.1767863.10063060897082377.260551495718621260054268273374657473120059796409
168 28 2.2.2.2.2.5.7.7.13.29.41.43.73.337.547.673.1009.1093.2269.2857.6481.16493.167329.368089.430697.647753.10968\
8713.2108826721
169 5 2.2029.797161.163264150141.814222556753878193601980463083668707558864014894642043902929
170 16 2.2.2.11.11.61.103.307.1021.1531.1871.34511.224401.2663568851051.862970652262943171.13271362257832586268931
171 10 2.13.229.757.1597.119701.248749.363889.1824179209.27203787889921135221329070240968055313746007669
172 13 2.2.2.2.5.173.431.470593.2641485701.55473422113.903239908009.380808546861411923.82064241848634269407
173 5 2.347.762239.2125048865543.30985428700388045508959018054392810762033149280306907746766819
174 19 2.2.2.7.13.59.349.523.6091.28537.74821.142159.261697.1383301.5385997.20381027.32234893.37464463.15022412397\
5857
175 11 2.11.11.71.1093.8951.109201.391151.2664097031.1430128198787051.11459299580388289258664119605215721251
176 22 2.2.2.2.2.2.5.17.23.41.67.89.193.661.3851.5501.570461.2382953.6922081.56625998353.15656839738849.1363620137\
403810529
177 7 2.13.709.14425532687.489769993189671059.2224898159852613649.9736622508037946817946068730077829
178 9 2.2.2.179.264331.1125706177.1611479891519807.5042939439565996049162197.2444322641415331355533344283
179 8 2.359.56207.100957.19510643.291066066130451.6779963644378513811.161868664744491655705858963594331
180 28 2.2.2.2.5.5.7.11.11.13.19.31.37.61.73.181.271.757.1181.1621.4561.176401.387631.530713.755551.927001.4776336\
1.452808441334403281
181 4 2.90863.890159.1412740676235815729693013611798695493926336144083867368022228212267580445753
182 13 2.2.2.547.1093.8737.398581.595141.797161.4011586307.2354116499281.2452788561133.3745603812007166116831643
183 8 2.13.733.603901.97806913.2421854958301.105293313660391861035901.7165195867462155138286987098273769
184 14 2.2.2.2.2.5.41.47.1289.12553493.1001523179.23535794707.70601370627701.7431708463054117564478285049413474811\
29
185 13 2.11.11.2221.17761.35521.146891.13097927.228082801.17189128703.49804972211.87841814842081.16542359111967047\
41
186 16 2.2.2.7.13.373.683.1117.6883.102673.541447.3058399.4404047.22434744889.88239050462461.262737018440153191448\
27917
187 9 2.23.1871.3851.6359.34511.1272753542934479.3411926755457243.527447346649058852221083363397206345775307
188 14 2.2.2.2.5.1223.16921.21997.256057.5112661.96656723.563838649753.1534179947851.12538428313220526578547784943\
9329
189 11 2.13.109.433.757.1093.8209.368089.144542918285300809.49888641454623789553.67775349707440873247475442867753
190 15 2.2.2.11.11.61.191.1597.2851.39901.101917.363889.29574984661.25349956307509384561.7895808769460932143966013\
1899631
191 5 2.383.311713.9593931911.5890868591760365434332005074929710400548909181468214858888800348369500317
192 27 2.2.2.2.2.2.2.2.5.7.13.17.41.73.97.193.577.769.6481.7297.68737.76801.21523361.96948097.24127552321.70613232\
600577.926510094425921
193 6 2.6563.29723.2346066378779.218246094772601642186973037.607981469094652492202396647678317419649770543
194 9 2.2.2.76631.459991849.503803759819.2549755542947.20591603926857377806745611.48845962828028421155731228333
195 16 2.11.11.13.13.131.313.2341.4561.6553.7333.797161.3701101.39838501.110133112994711.9813992993974897720899455\
4331725481
196 21 2.2.2.2.5.29.197.491.547.1093.4019.8233.16493.16661.51157.131713.251325313.857643277.127522693159.426712077\
457.34013149495921
197 5 2.9851.741019334164502879.11472574961994477441469621.58733573000937067164211172290216978734891718609
198 22 2.2.2.7.13.19.23.37.67.199.397.661.757.3851.4357.25411.176419.3186217.337448233.2413941289.378450588583.128\
12432238302009985937
199 4 2.1360648969.293366430131930353811221418233.110902970953020998760372036298330712066931713186888935429
200 24 2.2.2.2.2.5.5.5.11.11.41.61.101.151.1181.8951.133201.391151.394201.22996651.42521761.18055139801.6107081760\
1.61459926512826500975801
201 7 2.13.221101.1089421.441019876741.475384700124973.606888680894320302113812772385855126907748678398622467309
202 8 2.2.2.379963.33034273.465092326319.50316775668019759306202964023.1017291527198723292208309354658785077827527
203 8 2.59.1093.2843.28537.735673.20381027.45710553733635551271263934571653147487690442652554544220310250384660059
204 23 2.2.2.2.5.7.13.73.103.307.409.613.1021.1871.12853.30091.34511.956353.49637281.129159847.1743831169.99810171\
997.187668407555352123529
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