- 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 3 2.2.3
2 2 2.61
3 5 2.2.3.3.37
4 2 2.7321
5 4 2.2.3.13421
6 4 2.13.61.1117
7 4 2.2.3.1623931
8 3 2.17.6304673
9 7 2.2.3.3.3.37.590077
10 3 2.61.212601841
11 7 2.2.3.23.89.199.58367
12 4 2.7321.10657.20113
13 6 2.2.3.53.911.59583967
14 5 2.29.61.1933.55527473
15 8 2.2.3.3.31.37.13421.7537711
16 3 2.51329.447600088289
17 6 2.2.3.71707.264793.2218331
18 5 2.13.61.1117.3138426605161
19 7 2.2.3.191.229.83791.1390636259
20 4 2.41.7321.1120648576818041
21 7 2.2.3.3.37.1623931.3421169496361
22 4 2.61.251857.2649263870814793
23 7 2.2.3.47.1013.241363.6493405343627
24 7 2.17.97.241.1777.6304673.1106131489
25 6 2.2.3.13421.46601.14436295738510501
26 3 2.61.9768997162071483134919121
27 10 2.2.3.3.3.3.37.379.590077.4889988840047743
28 6 2.113.449.2521.7321.77001139434480073
29 6 2.2.3.59.10979607179423.204064664440913
30 6 2.13.61.1117.212601841.46329453543600481
31 7 2.2.3.311.1303.10789.3658524738455131951223
32 4 2.193.257.21283620033217629539178799361
33 13 2.2.3.3.23.37.67.89.199.9439.58367.991651.1169382127
34 6 2.61.137.2481791513.9598959833.641625222857
35 11 2.2.3.71.71.7561.13421.17011.1623931.1649341.10047871
36 7 2.73.7321.10657.20113.40177.3358335487319458201
37 5 2.2.3.2691614274040036601.10527743181888260981
38 4 2.61.1990415149.15403468930064931175264655869
39 11 2.2.3.3.37.53.313.911.63649.59583967.538953023961943033
40 5 2.17.5281.6304673.399806412551699044818733915681
41 6 2.2.3.711628063.1216150172449.479378523680060338823
42 9 2.13.29.61.1117.1933.19069.55527473.520799717831587692709
43 5 2.2.3.5333.9413099125139413690486707432096974989067
44 6 2.353.7321.72689.13585441.1298256794387169996154165633
45 13 2.2.3.3.3.31.37.181.631.13421.590077.7537711.86306335830799838011
46 6 2.61.201757.2004414397.24737721275161.656943272596448809
47 7 2.2.3.844309.549524471.26097456317.60699948346804199382437
48 5 2.577.51329.447600088289.3659233404740477018363752843393
49 8 2.2.3.11467.800171.1623931.176784259.33761096386802842263303497
50 6 2.61.101.212601841.2248313994601.1993099906542710819727884501
51 11 2.2.3.3.37.103.71707.264793.1348033.2218331.16576413357576409067287639
52 3 2.7321.97010607829826070873559937268360584022789501553441
53 7 2.2.3.1697.5353637.17148893.8357265774463208206521728596439861293
54 9 2.13.61.109.541.1117.388174681.3138426605161.1350472353550875103121929
55 13 2.2.3.23.89.199.4951.13421.58367.411841.21537414911.85480219991.131525983711
56 7 2.17.337.394129.6304673.236352238647181441.3090443962383595123379137
57 12 2.2.3.3.37.191.229.6043.75013.83791.1390636259.74337838382167137728921322559
58 6 2.61.349.16585333.32637413.109181877624126996017801852385627698243261
59 7 2.2.3.22067.32833036072593109.59845177539010249.53199025841281128499153
60 8 2.41.7321.10657.20113.52020741601.1120648576818041.40589999671017742452961
61 6 2.2.3.53320740257.137218978667473446671.38147158686655703132426388314683
62 4 2.61.4311672901046383796549.70039146133823870629334170297294343364149
63 13 2.2.3.3.3.37.590077.1623931.3304981.468843103.71596275661.278853374647.3421169496361
64 3 2.316955440822738177.7032401262704707649518767703756385761576062060673
65 10 2.2.3.53.911.1301.13421.25741.59583967.3160327139569513638485230516120919120957201
66 8 2.13.61.1117.251857.9863099401.2649263870814793.46266666682081629547022793157801
67 9 2.2.3.269.181303.2354458793.2778466094669.76388592846687031.20288347913774902979279
68 7 2.409.7321.11969.739755736441.14387579997041.85554906358182623545481335980971521
69 14 2.2.3.3.37.47.691.1013.241363.394648951.18013255921.932225927887.1577386579003.6493405343627
70 8 2.29.61.1933.2970941.55527473.212601841.32925268156330499785365829732750601117816501
71 6 2.2.3.149852362577.5604196051154865381517.8620302099267300875307522246691084877239
72 10 2.17.97.241.1777.110161.331921.6304673.1106131489.2653299576575651630603169124592864247361
73 8 2.2.3.668243.147031637.51866303408957.9863258277206753.17427450503923264964680282877251
74 8 2.61.149.243595717.254246981.3275634569.5555901630889277.5643352212924479303509278380689
75 13 2.2.3.3.31.37.751.13421.46601.299401.7537711.14436295738510501.2012875525822725447651340174136551
76 6 2.457.7321.35613601.52215193.1124384093561211759006825448167193716190524720926622040561
77 12 2.2.3.23.89.199.58367.1623931.23577401.43037232701.160418704149053207551.2040583524866430994330651
78 12 2.13.13.61.1117.7177.26833.225889.21493057.11771471409361.683665316878909.9768997162071483134919121
79 7 2.2.3.7901.681676939.3238766178025207268898109882481893.88961197883605801425821968775222633
80 10 2.641.2081.4001.51329.232961.447600088289.295090738600481.1037593750081121.11710273559942897538241
81 14 2.2.3.3.3.3.3.37.163.379.590077.5705803.4889988840047743.61599809118365596724303287493080398613594222813
82 5 2.61.2789.57073.1276324589909496813251127403760180491964358075504668934093870861051689695133
83 6 2.2.3.325440677.47433880332031195178437273.1471807913921722283799977862411158403048843176734891
84 11 2.113.449.2521.7321.10657.20113.201407641.70107576001.77001139434480073.6871280144418624289685328789001
85 9 2.2.3.13421.34511.71707.264793.2218331.140915955794291381596090868811368536501646742211013295518273711
86 5 2.61.173.11862832433.1449361076647763556046480383311898979520917866579543803095034909526729197869
87 12 2.2.3.3.37.59.13399.7596493.1727522113.10979607179423.204064664440913.1289269224782205219032537855117489670\
91
88 8 2.17.3169.269281.6304673.2224106369.1409524185566665684709841121.76570022386531005372870206494246296641
89 10 2.2.3.179.188606309.5089163291.75893828851.23510589261592841.371848407757843241773.353082502532286628861787
90 11 2.13.61.1117.9001.16921.22501.212601841.3138426605161.46329453543600481.28309390942693823829766228460785185\
421
91 9 2.2.3.53.911.1623931.59583967.12343942084000822751.84451621887581647750880682185194110642059749383888588911
92 5 2.7321.34961.324599369.3868967792250098248450110086386343042895409814136698442863741267447980557520249
93 11 2.2.3.3.37.311.1303.10789.237843323473654847623.3658524738455131951223.139550866104193032581962716205911186\
7514287
94 7 2.61.1693.6678701.181894150853.1823151514157.170044315788568839331192444262564794666488196032760463244957137
95 10 2.2.3.191.229.13421.83791.1390636259.125391374277955216479795494641.831364610304896938076192434596656578992\
2617921
96 9 2.193.257.2689.850177.7746049.13928006777524033.21283620033217629539178799361.18074341630577348555429415775\
408321
97 6 2.2.3.3881.200924352971689432250644561.11064530571690714453730400924822089371846415813484128967094900415848\
041
98 8 2.29.61.197.1933.55527473.33976720793233.448061744850569765386528729635682996109461034777276693515627127364\
615221
99 18 2.2.3.3.3.23.37.67.89.199.9439.58367.590077.991651.95885659.1169382127.166222146279939538766671.19118100293\
995567795177984039909
100 9 2.41.401.7321.2254601.5931105001.69084589801.1120648576818041.552947563691215268017880199633798414702158479\
175508601
101 7 2.2.3.20201.228104057.1732951869588220873.15819311422790435215889409528474122189791416412562996715979130823\
153947141
102 11 2.13.61.137.1117.2481791513.9598959833.641625222857.382645993638157.563620766036953.20841161015828740030207\
016250006151501
103 8 2.2.3.1237.51396929137.3842537250772226605747.128288938117946418355541.487698205182785810835005539128131683\
672275286097
104 5 2.17.6304673.86759222313428390812218077095850708048977.1084881048536374706129613998429729484098346115257905\
77216753
105 19 2.2.3.3.31.37.71.71.7561.13421.17011.1623931.1649341.7537711.10047871.275310421.137031343051.3421169496361.
2359101627084759668315785103671
106 7 2.61.410982353.23746234974173.22250800656016001.72744498860303958101.12667796019109754352066411884939323800\
6955092974209
107 5 2.2.3.841021.2660904118831225069351374903323531548627122700620087587591802861308909203624886230993288676031\
12602644211
108 10 2.73.433.7321.8209.10657.20113.40177.3358335487319458201.26884080018278857826967012292458876502681409920482\
9048549907077238513
109 6 2.2.3.11119.14389.16924860328413141214365629650474864848331631667162621285647949533748464809147546574145776\
6540635771648351
110 10 2.61.251857.1327481.212601841.36318547582241.110374378040081.2649263870814793.136371262802069831801.2846042\
33173679136521738352001
111 10 2.2.3.3.37.37.223.2691614274040036601.10527743181888260981.126249345637608650029153686851973084319021976823\
501721176605898316609411
112 8 2.10529.15233.51329.132833.447600088289.7782479531201887486913.56767692210863509237921611739434366077435616\
458970709176918840577
113 5 2.2.3.909877.4357220014122675184259919179380668633668941449742142981468187554807931862519633084677616319104\
58201865781422893
114 9 2.13.61.1117.1990415149.37820720459377.308673703543834165513.15403468930064931175264655869.8253119172808086\
9985969416771354049347961
115 11 2.2.3.47.1013.2531.13421.241363.6493405343627.558956737278445325461.338588199387527746331211270897090075844\
65813794083046310289193779151
116 7 2.233.7321.287681.60604269272032563100609.1502477990708696255525449.708553482774634872757217319786870088342\
38471892366559611974577
117 14 2.2.3.3.3.37.53.313.911.63649.590077.59583967.538953023961943033.956311769100660490503396992656891206874453\
285835048997148999317765990784561
118 6 2.61.1291321673.1013563312793953470363741024001073.64838817747578095323592827914385846481.74004240886932111\
404174666525790714071569
119 14 2.2.3.71707.264793.1623931.2218331.110917283.124214819.69796946717.256644509902201.63063653308203311.209145\
6376138057349.315440418833726113081631
120 14 2.17.97.241.1777.3121.5281.114001.6304673.1106131489.1698371041.12658046117876244394801.5828142647817387837\
02162161.399806412551699044818733915681
121 14 2.2.3.23.89.199.727.58367.122453.2095721.103569468207767.1663628038071022183838437.156316328176791781343592\
9194983.71132117849274411458479346616793
122 9 2.61.61.733.15373.19042493.615339081285269009.166945076296840267580084657135863728824204737.683822526820172\
81321628552285946936349023283521
123 9 2.2.3.3.37.711628063.1216150172449.479378523680060338823.22329407744580303934513868394925085808679300359256\
5432816290249576309086373241746401
124 8 2.1489.6449.7321.11161.5721113.92247817.1638950174786153691075952022215074731727187702580869943406736485973\
251947792384699431022645116667161
125 10 2.2.3.251.13421.46601.559001.14436295738510501.30877424283969568616368678353563069501.318083501938831797291\
23443891378924908549472843225872344251
126 14 2.13.29.61.1117.1933.2017.19069.21673.55527473.3138426605161.520799717831587692709.154021704779757520440774\
8160801193.14192755503084386685349267103378497
127 7 2.2.3.509.2140352083.4402640625848258016840688846660358437130425243742595514279.313887145284264795998540992\
87726722553699547881667856766300787
128 6 2.15361.111489577217.574341646346402207998363393.4018529583345312964042058778793458689.25138679918373623167\
15332574077411130744618580176804609
129 9 2.2.3.3.37.1291.5333.9413099125139413690486707432096974989067.253233817806661680794126682548488134256292565\
2085779577235728569623852917746014092331
130 6 2.61.521.212601841.9768997162071483134919121.18215223829103119871143009754672266047822632092109688566278477\
058449896401786143420694541075159161
131 6 2.2.3.9858799.119235724375228558113076040277225949839796708740043.18751244767116478769561770254758588183459\
21167310635558927494336192342549513443
132 11 2.353.7321.10657.20113.72689.13585441.57563039928769.504278350263601.1298256794387169996154165633.705716757\
4674010261807047699037084178851570547276172529
133 10 2.2.3.191.229.83791.1623931.1390636259.23204027016899114504903.13887854992134150485504500896345190378108653\
21432371174936304520406104501526956813520954447
134 6 2.61.47271776033.555596265747977.5653530366032833.194347524816188063157344917316163731510839472419689280815\
3799712458776309964218037475956185945937
135 19 2.2.3.3.3.3.31.37.181.379.631.13421.283771.590077.7537711.861465705211.4889988840047743.8630633583079983801\
1.3909014919478257067611647254311892076465398578584589934681
136 6 2.17.17.6304673.29584734433.3951364572165740533499223885379274688932880605900690343904021732819435255040666\
3629632980855979005749712409762411371230481
137 9 2.2.3.823.2467.12932527.666751384702583.33702237384570719055067.6618225834843701910882465020377513146074534\
519708431589347550012959904179170066334607874103
138 11 2.13.61.277.1117.201757.6128029.2004414397.24737721275161.656943272596448809.260813416520010869997945696781\
73937248173282084703143498940836604277367886736092977
139 7 2.2.3.48560832383207.23835478071413231.226911237770389320465096194749609274682969829.1799020021420670793955\
452910062648782329345676350070250930470021301187
140 11 2.41.113.281.449.2521.7321.1120648576818041.77001139434480073.7406965671094607547812305361.4522523011641833\
124254190467380698665648996274963293418051231917039641
141 11 2.2.3.3.37.2539.844309.549524471.26097456317.60699948346804199382437.27601121268595702663499475964138228754\
9960710026365311501070014837044470192630725201808980699
142 5 2.61.192553.6896695512898403271082223952161993974407591311981.465811407486640028940330582024245866580550375\
64653708522157973308108576026344096114825014757
143 20 2.2.3.23.53.89.199.859.911.2003.23167.36037.58367.59583967.2008696691.172626755159.303798181831.61915142248\
6169.784071823409769959923.1376758841851098858192561441291859498245379
144 8 2.577.3457.51329.114500564929.447600088289.3659233404740477018363752843393.23778845560226372843327820636243\
112457967210053130898985010753129117249420547694635777
145 9 2.2.3.59.13421.54521.10979607179423.204064664440913.8653719005168933795819192954442052944398178101271333803\
063467458016405399722313222353196657036509056155169947241
146 7 2.61.293.877.10851207624233.1642924373932604240398418631306800170146224088997.19770121700484944588827152871\
7782524432344168525454840257403895055137223757102073861
147 14 2.2.3.3.37.11467.800171.1623931.176784259.54447297367.3421169496361.593567588238393763.33761096386802842263\
303497.92798096943647997760409196962615760375999913293276053417701
148 5 2.1481.7321.10170146161160624507589185121238262249266667161256127057415217.60622626428062749376619618807622\
668011972562662106003547080399907358442197151548735273
149 7 2.2.3.1193.1530827.775322709138856254112793450158954494201167319485721463.865525327060749392778837283153902\
5466268936040995557086831408002731188838672182099838786137
150 11 2.13.61.101.1117.212601841.2248313994601.46329453543600481.7884604271247668072701.1993099906542710819727884\
501.25979746658107161913187074671032833320672752745552382077035701
151 8 2.2.3.907.3323.255421785001.372781462691737543021989945244913.516730790696110151347975686092076212041433557\
4957069856125009544580377375533922662140211511462475018258507
152 6 2.17.13681.6304673.1077214649569.61962162575073047547441022812017657107747598240691544804534029908829317210\
002521690237365440376265162862693661729168926665388807254289
153 17 2.2.3.3.3.37.103.2143.71707.264793.590077.1348033.2218331.70740970147.16576413357576409067287639.1840706193\
591427502373477305882643135847.33755635467861578498080914222269606335643433763
154 12 2.29.61.617.1933.99793.251857.55527473.28785963361.2649263870814793.65808672978228777210147008368433.801396\
672655716252884113843317517700515501139590143917044530149262225615817
155 13 2.2.3.311.1303.10789.13421.25111.668671.3658524738455131951223.1945899780650862081973056361.251539498252379\
73485338723920570841.123056604485215768770111502151330349856185113277226921
156 10 2.1873.7321.10657.20113.24337.332327331649.341226120551908708215217157918113.182101820899247346556088181826\
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