- 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 2 2.5
2 5 2.2.2.3.5
3 4 2.5.7.19
4 7 2.2.2.2.3.5.61
5 4 2.5.5.3221
6 9 2.2.2.3.3.5.7.19.37
7 4 2.5.43.45319
8 9 2.2.2.2.2.3.5.61.7321
9 5 2.5.7.19.1772893
10 8 2.2.2.3.5.5.3221.13421
11 4 2.5.15797.1806113
12 13 2.2.2.2.3.3.5.7.13.19.37.61.1117
13 4 2.5.1093.3158528101
14 8 2.2.2.3.5.43.45319.1623931
15 7 2.5.5.7.19.3221.195019441
16 12 2.2.2.2.2.2.3.5.17.61.7321.6304673
17 3 2.5.50544702849929377
18 12 2.2.2.3.3.3.5.7.19.37.590077.1772893
19 3 2.5.6115909044841454629
20 11 2.2.2.2.3.5.5.61.3221.13421.212601841
21 10 2.5.7.7.19.43.1723.8527.27763.45319
22 11 2.2.2.3.5.23.89.199.15797.58367.1806113
23 5 2.5.829.28878847.3740221981231
24 17 2.2.2.2.2.3.3.5.7.13.19.37.61.1117.7321.10657.20113
25 8 2.5.5.5.3001.3221.24151.1856458657451
26 10 2.2.2.3.5.53.911.1093.59583967.3158528101
27 6 2.5.7.19.1772893.5559917315850179173
28 13 2.2.2.2.3.5.29.43.61.1933.45319.1623931.55527473
29 4 2.5.523.303309617049998388989376043
30 15 2.2.2.3.3.5.5.7.19.31.37.3221.13421.7537711.195019441
31 5 2.5.50159.2428541.157571957584602258799
32 15 2.2.2.2.2.2.2.3.5.17.61.7321.51329.6304673.447600088289
33 9 2.5.7.19.661.1453.15797.1806113.637265428480297
34 9 2.2.2.3.5.71707.264793.2218331.50544702849929377
35 8 2.5.5.43.211.3221.45319.42437717969530394595211
36 17 2.2.2.2.3.3.3.5.7.13.19.37.61.1117.590077.1772893.3138426605161
37 6 2.5.2591.36855109.136151713.2615418118891695851
38 10 2.2.2.3.5.191.229.83791.1390636259.6115909044841454629
39 12 2.5.7.19.79.157.547.1093.84631.480091.32508061.3158528101
40 15 2.2.2.2.2.3.5.5.41.61.3221.7321.13421.212601841.1120648576818041
41 9 2.5.83.1231.27061.509221.14092193.29866451.840139875599
42 17 2.2.2.3.3.5.7.7.19.37.43.1723.8527.27763.45319.1623931.3421169496361
43 4 2.5.1416258521793067.42534656091583268045915654719
44 15 2.2.2.2.3.5.23.61.89.199.15797.58367.251857.1806113.2649263870814793
45 9 2.5.5.7.19.3221.1772893.195019441.9842332430037465033595921
46 12 2.2.2.3.5.47.829.1013.241363.28878847.3740221981231.6493405343627
47 5 2.5.2069.22666879066355177.18806327041824690595747113889
48 24 2.2.2.2.2.2.3.3.5.7.13.17.19.37.61.97.241.1117.1777.7321.10657.20113.6304673.1106131489
49 7 2.5.43.45319.510810301.1065264019.100641220283951395639601683
50 14 2.2.2.3.5.5.5.3001.3221.13421.24151.46601.1856458657451.14436295738510501
51 9 2.5.7.19.10711.457315063.15085812853.25994736109.50544702849929377
52 13 2.2.2.2.3.5.53.61.911.1093.59583967.3158528101.9768997162071483134919121
53 6 2.5.107.351497.6005113.6918082374901313855125397665325977135579
54 16 2.2.2.3.3.3.3.5.7.19.37.379.590077.1772893.4889988840047743.5559917315850179173
55 10 2.5.5.3221.15797.25301.39161.1806113.643170158708221.645654335737185721
56 19 2.2.2.2.2.3.5.29.43.61.113.449.1933.2521.7321.45319.1623931.55527473.77001139434480073
57 8 2.5.7.19.19.1047623475541.6115909044841454629.1412900479108654932024439
58 10 2.2.2.3.5.59.523.10979607179423.204064664440913.303309617049998388989376043
59 5 2.5.1181.70845409351.33083146850190391025301565142735000331370209599
60 21 2.2.2.2.3.3.5.5.7.13.19.31.37.61.1117.3221.13421.7537711.195019441.212601841.46329453543600481
61 5 2.5.440177.520518327319589.1461808298382111034194027645506019619578037
62 12 2.2.2.3.5.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223
63 16 2.5.7.7.19.43.127.1723.8317.8527.27763.45319.867259.1772893.106431697.316825425410373433
64 19 2.2.2.2.2.2.2.2.3.5.17.61.193.257.7321.51329.6304673.447600088289.21283620033217629539178799361
65 8 2.5.5.131.1093.3221.3158528101.673267426712748387612994804392183645147042355211
66 22 2.2.2.3.3.5.7.19.23.37.67.89.199.661.1453.9439.15797.58367.991651.1806113.1169382127.637265428480297
67 6 2.5.15277.2160349.76394148218203559.235335702141939072378977155172505285655211
68 15 2.2.2.2.3.5.61.137.71707.264793.2218331.2481791513.9598959833.641625222857.50544702849929377
69 10 2.5.7.19.139.829.28878847.8209475377.3740221981231.5283012903770196631383821046101707
70 19 2.2.2.3.5.5.43.71.71.211.3221.7561.13421.17011.45319.1623931.1649341.10047871.42437717969530394595211
71 7 2.5.1847.64327.159248456569.1273880539247.360426336941693434048414944508078750920763
72 24 2.2.2.2.2.3.3.3.5.7.13.19.37.61.73.1117.7321.10657.20113.40177.590077.1772893.3138426605161.335833548731945\
8201
73 3 2.5.1051153199500053598403188407217590190707671147285551702341089650185945215953
74 11 2.2.2.3.5.2591.36855109.136151713.2615418118891695851.2691614274040036601.10527743181888260981
75 15 2.5.5.5.7.19.151.3001.3221.24151.59302051.195019441.1826934301.1856458657451.27665283091695977275201
76 14 2.2.2.2.3.5.61.191.229.83791.1390636259.1990415149.6115909044841454629.15403468930064931175264655869
77 8 2.5.43.15797.45319.1806113.593554036769.466345922275629775763320748688970211803553256223529
78 23 2.2.2.3.3.5.7.19.37.53.79.157.313.547.911.1093.63649.84631.480091.32508061.59583967.3158528101.538953023961\
943033
79 5 2.5.317.185277551100523662054683911.31705898389348622756718888962810730367411163041955447
80 20 2.2.2.2.2.2.3.5.5.17.41.61.3221.5281.7321.13421.6304673.212601841.1120648576818041.399806412551699044818733\
915681
81 9 2.5.7.19.1772893.139026457.5559917315850179173.14010692617072784593.88236431987113771637099217013
82 15 2.2.2.3.5.83.1231.27061.509221.14092193.29866451.711628063.840139875599.1216150172449.479378523680060338823
83 7 2.5.167.12119.178057577.52447614013.1442525225996981034595894901431683672700025887063977893738081
84 26 2.2.2.2.3.3.5.7.7.13.19.29.37.43.61.1117.1723.1933.8527.19069.27763.45319.1623931.55527473.3421169496361.52\
0799717831587692709
85 8 2.5.5.3221.584916791.553393500180551.50544702849929377.12520270706155176007034654722092907499983681
86 9 2.2.2.3.5.5333.1416258521793067.42534656091583268045915654719.9413099125139413690486707432096974989067
87 9 2.5.7.19.523.398113.54415717.303309617049998388989376043.873360172275048609080552096817243827525632861
88 21 2.2.2.2.2.3.5.23.61.89.199.353.7321.15797.58367.72689.251857.1806113.13585441.2649263870814793.129825679438\
7169996154165633
89 6 2.5.73111721.2103114787086589.4180235017418376525776333.75144689824702198592013444969850173811994737
90 22 2.2.2.3.3.3.5.5.7.19.31.37.181.631.3221.13421.590077.1772893.7537711.195019441.86306335830799838011.9842332\
430037465033595921
91 7 2.5.43.1093.45319.3158528101.868721697058567435824108245607127696076153182930226460514053403127306646961
92 18 2.2.2.2.3.5.47.61.829.1013.201757.241363.28878847.2004414397.3740221981231.6493405343627.24737721275161.656\
943272596448809
93 10 2.5.7.19.2791.3163.50159.2428541.157571957584602258799.3137876238000684620152119068677936364954475597711271\
1197
94 12 2.2.2.3.5.2069.844309.549524471.26097456317.22666879066355177.60699948346804199382437.188063270418246905957\
47113889
95 8 2.5.5.3221.67989221.6115909044841454629.180124441029509240214675551.709366429143448333528137335486039060202\
91
96 29 2.2.2.2.2.2.2.3.3.5.7.13.17.19.37.61.97.241.577.1117.1777.7321.10657.20113.51329.6304673.1106131489.4476000\
88289.3659233404740477018363752843393
97 5 2.5.389.4247091263.6266849507589571978149106488222106980975381364824424072801340422775737133656105189072051
98 15 2.2.2.3.5.43.11467.45319.800171.1623931.176784259.510810301.1065264019.33761096386802842263303497.100641220\
283951395639601683
99 14 2.5.7.19.397.661.1453.2377.15797.1772893.1806113.1240500097.637265428480297.2599071362839584231023974669237\
98834567695212357
100 20 2.2.2.2.3.5.5.5.61.101.3001.3221.13421.24151.46601.212601841.1856458657451.2248313994601.14436295738510501.
1993099906542710819727884501
101 5 2.5.341459085477993311443.86408339296208914807632672776254957729.513767785847095403363378495505038747238330\
8083
102 20 2.2.2.3.3.5.7.19.37.103.10711.71707.264793.1348033.2218331.457315063.15085812853.25994736109.50544702849929\
377.16576413357576409067287639
103 6 2.5.24103.37723802531.995301206162659155091.202677471366153865787391434710952643545087969532720827000553398\
46745091
104 16 2.2.2.2.2.3.5.53.61.911.1093.7321.59583967.3158528101.9768997162071483134919121.970106078298260708735599372\
68360584022789501553441
105 21 2.5.5.7.7.19.43.211.421.1723.3221.8527.27763.45319.540751.599551.2598121.126713791.195019441.23731414400247\
02184811.42437717969530394595211
106 13 2.2.2.3.5.107.1697.351497.5353637.6005113.17148893.8357265774463208206521728596439861293.691808237490131385\
5125397665325977135579
107 5 2.5.1276033068038437.304971297664201988898688683700564748747693245597.6900751922429791724019506627192737704\
11957106853
108 25 2.2.2.2.3.3.3.3.5.7.13.19.37.61.109.379.541.1117.590077.1772893.388174681.3138426605161.4889988840047743.55\
59917315850179173.1350472353550875103121929
109 4 2.5.35970728459102446279558069.9033445926510666398384928207099769878625683305416602322341095021068020592318\
51745003701
110 23 2.2.2.3.5.5.23.89.199.3221.4951.13421.15797.25301.39161.58367.411841.1806113.21537414911.85480219991.131525\
983711.643170158708221.645654335737185721
111 10 2.5.7.19.2591.36855109.136151713.2615418118891695851.651950416864148392635280596760630561.13334983829534655\
64843320786357871664401
112 26 2.2.2.2.2.2.3.5.17.29.43.61.113.337.449.1933.2521.7321.45319.394129.1623931.6304673.55527473.77001139434480\
073.236352238647181441.3090443962383595123379137
113 7 2.5.227.45902861.20884152591287817709.22455907106840364577416382241618449.973554682812876324986927406779613\
27574083833285959459
114 20 2.2.2.3.3.5.7.19.19.37.191.229.6043.75013.83791.1390636259.1047623475541.6115909044841454629.14129004791086\
54932024439.74337838382167137728921322559
115 12 2.5.5.829.3221.95911.333041.9964291.28878847.3740221981231.17184010031686356151.729842693308300425195832421\
6375350400730975973787843051
116 16 2.2.2.2.3.5.59.61.349.523.16585333.32637413.10979607179423.204064664440913.303309617049998388989376043.1091\
81877624126996017801852385627698243261
117 16 2.5.7.19.79.157.547.1093.9127.84631.480091.1772893.1810693.32508061.3158528101.5777953519959062358597260246\
2371982722687354954780675870640496251
118 12 2.2.2.3.5.1181.22067.70845409351.32833036072593109.59845177539010249.53199025841281128499153.33083146850190\
391025301565142735000331370209599
119 9 2.5.43.239.45319.20580793913.50544702849929377.5787647502138040836760695667.3005681893232976654385404271528\
23770594407695480022422691549
120 29 2.2.2.2.2.3.3.5.5.7.13.19.31.37.41.61.1117.3221.7321.10657.13421.20113.7537711.195019441.212601841.52020741\
601.1120648576818041.46329453543600481.40589999671017742452961
121 8 2.5.15797.30977.1806113.1595696213.12407691244609.582793661124452623809041107212020076078733754671394043885\
9172127240114655549487246036729
122 11 2.2.2.3.5.440177.53320740257.520518327319589.137218978667473446671.38147158686655703132426388314683.1461808\
298382111034194027645506019619578037
123 15 2.5.7.19.83.1231.27061.174907.509221.14092193.28385941.29866451.840139875599.142971820992006871646588679396\
397417.262535239929018061575878552691659119
124 16 2.2.2.2.3.5.61.311.1303.10789.50159.2428541.157571957584602258799.3658524738455131951223.431167290104638379\
6549.70039146133823870629334170297294343364149
125 12 2.5.5.5.5.3001.3221.24151.1632185486501.1856458657451.27678437808551251.61008089514108496781935498867728405\
0229269951248774263726574682822715310251
126 29 2.2.2.3.3.3.5.7.7.19.37.43.127.1723.8317.8527.27763.45319.590077.867259.1623931.1772893.3304981.106431697.4\
68843103.71596275661.278853374647.3421169496361.316825425410373433
127 6 2.5.2985212831443.6073732108394141.108345618426999904901.91966303295251191104971960132273397364144023351465\
750399992554753980589155137853599
128 22 2.2.2.2.2.2.2.2.2.3.5.17.61.193.257.7321.51329.6304673.447600088289.316955440822738177.21283620033217629539\
178799361.7032401262704707649518767703756385761576062060673
129 12 2.5.7.19.1549.1389891409.2338110553.44012945778511.1416258521793067.3440126314390780951.4253465609158326804\
5915654719.3579868931117378066463082728904957
130 18 2.2.2.3.5.5.53.131.911.1093.1301.3221.13421.25741.59583967.3158528101.3160327139569513638485230516120919120\
957201.673267426712748387612994804392183645147042355211
131 5 2.5.263.7791763956749016154215607697892626144401.1290774032138704646634687668236941308305597514202044201343\
330196757304660698533426132941183587
132 30 2.2.2.2.3.3.5.7.13.19.23.37.61.67.89.199.661.1117.1453.9439.15797.58367.251857.991651.1806113.1169382127.98\
63099401.637265428480297.2649263870814793.46266666682081629547022793157801
133 9 2.5.43.45319.292601.1889399.4085166784889.6115909044841454629.118907173249316196764766639893383431910454776\
99764476320956042082843152214319805595150031
134 15 2.2.2.3.5.269.15277.181303.2160349.2354458793.2778466094669.76388592846687031.76394148218203559.20288347913\
774902979279.235335702141939072378977155172505285655211
135 12 2.5.5.7.19.271.3221.1772893.195019441.5559917315850179173.9842332430037465033595921.35261764476828649109379\
34141934983258605489440194538631398471107422118591
136 22 2.2.2.2.2.3.5.61.137.409.7321.11969.71707.264793.2218331.2481791513.9598959833.641625222857.739755736441.14\
387579997041.50544702849929377.85554906358182623545481335980971521
137 8 2.5.8221.339761.3677081.136238281.394711476243912154244261783.848433067196473533441008868772447888723971966\
6748414214743814637516122598288562123255444499
138 24 2.2.2.3.3.5.7.19.37.47.139.691.829.1013.241363.28878847.394648951.8209475377.18013255921.932225927887.15773\
86579003.3740221981231.6493405343627.5283012903770196631383821046101707
139 3 2.5.5670002325217957396258282812671713444868053858812175750811496601630462174655445733557105920797699326519\
89153833612198334843467861091902034340949
140 27 2.2.2.2.3.5.5.29.43.61.71.71.211.1933.3221.7561.13421.17011.45319.1623931.1649341.2970941.10047871.55527473.
212601841.42437717969530394595211.32925268156330499785365829732750601117816501
141 11 2.5.7.19.283.2069.64192789.22666879066355177.44682948968412414039336007.18806327041824690595747113889.72052\
0357109665867690144695251088293221239815545113983062729
142 13 2.2.2.3.5.1847.64327.149852362577.159248456569.1273880539247.5604196051154865381517.86203020992673008753075\
22246691084877239.360426336941693434048414944508078750920763
143 11 2.5.1093.3433.15797.1806113.3158528101.3111663528084541.191144869353686249.39087214421959708068637.10560044\
15999653050515555650243045564974450864216443757878943069209
144 34 2.2.2.2.2.2.3.3.3.5.7.13.17.19.37.61.73.97.241.1117.1777.7321.10657.20113.40177.110161.331921.590077.177289\
3.6304673.1106131489.3138426605161.3358335487319458201.2653299576575651630603169124592864247361
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