- 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 7 [1st Prime]
2 1 37 [2nd Prime]
3 2 7.31
4 1 1297 [3rd Prime]
5 3 7.11.101
6 3 13.37.97
7 4 7.7.29.197
8 2 17.98801
9 3 7.31.46441
10 3 37.241.6781
11 2 7.51828151
12 2 1297.1678321
13 4 7.53.937.37571
14 3 37.421.5030761
15 5 7.11.31.101.1950271
16 3 353.1697.4709377
17 3 7.190537.12690943
18 6 13.37.73.97.541.55117
19 3 7.1787.48713705333
20 3 41.1297.68754507401
21 6 7.7.29.31.197.2527867231
22 4 37.58477.70489.863017
23 3 7.113958101.990000731
24 4 17.5953.98801.473896897
25 4 7.11.101.3655688315536801
26 4 37.313.2341.6291946695217
27 5 7.31.46441.114967.883383463
28 5 281.337.617.1297.81035189089
29 4 7.59.32713.2727192763388813
30 9 13.37.61.97.181.241.3541.6781.74161
31 2 7.189491931189200021056951
32 3 2753.145601.19854979505843329
33 6 7.31.463.72073.51828151.127236649
34 3 37.934117.8289713345361373993
35 11 7.7.11.29.101.197.631.701.2311.9241.585131
36 5 577.1297.3313.1678321.2478750186961
37 4 7.3923.1096762734443.2054788991719
38 3 37.1030762781149.9736145643041809
39 9 7.31.53.79.937.9049.37571.868999.8857759
40 5 17.17761.98801.3696985841.121206120881
41 4 7.83.28537.4837453663777044375040181
42 7 13.37.97.421.5030761.804146449.6055984789
43 2 7.412482688627178079807598675848631
44 3 89.1297.150080764792922988676714149209
45 7 7.11.31.101.46441.1950271.4760317816590150361
46 5 37.6073.2259889.9564781.128407494947883673
47 2 7.534577564460822791430647883899825591
48 7 193.353.1697.8641.4709377.688490113.6931400449
49 7 7.7.7.29.197.762332681442053.90179616936384011
50 6 37.241.6781.343801.22243201.1748016735462726601
51 8 7.31.103.919.190537.12690943.980146969.99617785207
52 4 1297.192193.14090441.8284434950526240125727017
53 5 7.107.97351567.33685364386033.71080464397105403
54 10 13.37.73.97.109.541.55117.591841.171467713.932461936453
55 8 7.11.11.101.1031141.51828151.16336066781.84155540944421
56 6 17.113.4817.98801.4048129.10189440239012883075423169
57 7 7.31.457.1787.137713.48713705333.190324492938225748951
58 3 37.349.105134528469779071670501631159328247729809
59 2 7.1163658999540220416412446482708919139658591671
60 6 41.1297.13441.1678321.68754507401.592575109627400042641
61 3 7.9151.4577830180684945360162613198286645069141001
62 2 37.47552767764994953232854569779888803761183529901
63 10 7.7.29.31.127.197.46441.2527867231.154260982009.528921402377887
64 3 4926056449.447183309836853377.28753787197056661026689
65 8 7.11.53.101.131.937.37571.199930782298483523040584108028862541
66 11 13.37.97.3037.58477.70489.96493.622513.863017.4629769.16266405013
67 5 7.269.418349.90571543952974835963.191757760647639121941197
68 5 137.1297.5849.1536052010629489.51420576374811381403609445473
69 6 7.31.113958101.990000731.24648570768391.816214079084081564521
70 7 37.241.421.6781.5030761.13509594555661.1708114263204222806519161
71 4 7.37489.11735704315681.5757417485448059422914748320317168839
72 5 17.5953.98801.473896897.22452257707354557235348829785471057921
73 6 7.293.439.120855443.1389436303.4221883459378030470824476438562257
74 5 37.37.4441.3300043400835529.190892407618022993841069346975403017
75 10 7.11.31.101.151.168151.1950271.573178201.918628247364601.3655688315536801
76 5 1297.4561.355518408146401.5028187486478069273.13038313680704041577
77 6 7.7.29.197.51828151.57019087134151254061666621717728669167279862151
78 11 13.13.37.97.157.313.2341.8893.6291946695217.197743936282933.6429178169720749
79 6 7.317.5531.2832941.99687312908749681.8592319153827988586815914947213
80 6 353.1697.9601.4709377.2810800069601.2347110840158563816028186318246561
81 8 7.31.1783.46441.114967.149862151.883383463.3920344350409644507093715799617
82 4 37.4046701.174521133001.246179376206361788466441901958293949537091001
83 5 7.710813.6547890917.21608536062644851877771.54824363564629401758409941
84 8 281.337.617.1297.1678321.81035189089.1176362433121.19100900655540830489319601
85 8 7.11.101.190537.12690943.1383638161.72085651321561.740797672014674927371043791
86 5 37.1033.6501601.2914764989376043020733.11510167124054813592781820845997449
87 11 7.31.59.32713.68209.92569.1439329.380675809.519258631.24378360481.2727192763388813
88 4 17.98801.9307950433.19197545705142827447183881455518760379441910619182497
89 3 7.179.1437176850540020021056024701236917910178773041847685459251313907949
90 16 13.37.61.73.97.181.241.541.3541.6781.9001.55117.74161.211501.2106930961.5597780112726834061
91 12 7.7.29.53.197.937.2003.2549.36947.37571.52769627.12468702878009806771287543538567443817
92 4 1297.14537.433176829049.47625006826357122080464279208098880721125912766130417
93 5 7.31.31.189491931189200021056951.1830855782835393620827906093040965051783187521
94 5 37.1693.1029538544148223697293.30585762365533687252981.7098996031830910703530849
95 10 7.11.101.1787.6271.2666738161.37260330001.48713705333.61671024221.3229504809106404383981
96 4 2753.145601.19854979505843329.63340286662973277706162278988150776663495577436161
97 4 7.7449708398813963.6571212276076854019883.8826499007361715764052964663075774479
98 5 37.421.5030761.288628033.802354924671793395266725600744864562917483072464133108417
99 10 7.31.199.463.46441.72073.110881.51828151.127236649.2225208714917658550195227627861513418879
100 8 41.1297.4801.5801.224401.68754507401.1006795824867486182291801.28398752673271140825020401
101 5 7.607.82013.3866281.2909467055506170519577044616632832452708657352232253233553601781
102 8 13.37.97.934117.1785001.8289713345361373993.12346985995648844989.2953728137900959095135649
103 4 7.7211.135025379.20704743230318258100890022657208522727453596408722228548650415542999
104 5 17.98801.36265841.141365953.98327998682892050307547688538841853424435944546993755800017
105 16 7.7.11.29.31.101.197.631.701.2311.9241.71191.585131.1950271.2527867231.271613602977153099649378586566681
106 4 37.26713.175436926004647658810244613736479118917.175787157418305877173455355755546870641
107 2 7.26126771741159407024154726661022582007126551676422442131468770568230221685230103991
108 9 433.577.1297.3313.1678321.115963921.2478750186961.8781208996949976153601.241282001155985351966017
109 3 7.9661979.97346908193625617781778470000484678372469642125201050088483502236579895347349
110 8 37.241.6781.58477.70489.863017.423852369601.433295951605870884187046138704268693683498331456101
111 9 7.31.223.3923.7993.142969.1096762734443.2054788991719.484813024945269068265878512515024013260506641
112 5 353.1697.4709377.490972383553.1026745888453552697436968844848917190436254094111712318750754497
113 6 7.227.8363.586471.5043448999988542328333.217085653849206214541602569383859982900289160186960917
114 11 13.37.97.229.25309.43321.2197693.1030762781149.300537265358917.9736145643041809.659334264781883756771821
115 7 7.11.101.113958101.990000731.23126990778420152651.15138465280223101464931287568892526939099241284821
116 7 233.1297.250793.4916777.6198809.9008169903032260803977.88574437255173019150535038179441097901397209
117 12 7.31.53.79.937.1873.9049.37571.46441.868999.8857759.57063471642936858295625494275761490859413610922514697
118 3 37.554971222573.3231285690411251549937535803579175660890272281294966380800039383396486737158017
119 9 7.7.29.197.190537.12690943.22885730141.2681104713967.9584881019626035133999258735515025036249902934797053
120 11 17.5953.17761.55201.98801.122401.21027841.473896897.3696985841.121206120881.4458139843615061052376640769667\
21
121 5 7.727.51828151.15186641018595718629290023681.3578008788069105048042400002837961114116977849537973223
122 5 37.60757.348433.558416270857.196597122477434001699939656151715927005493674652801355438654544438291553
123 8 7.31.83.1231.28537.4837453663777044375040181.268313928259442786323996685119.628260227263749127899296330959
124 5 1297.106179166897.1062529732255153.505430595651453051641.41857485802028381142383903037144206683835077721
125 9 7.11.101.251.751.5501.3655688315536801.2694730860384999001.233805293126289020639202084597666844981225400241\
001
126 15 13.37.73.97.421.541.1009.17389.55117.5030761.10339309.804146449.6055984789.48129311534221.12185192600132570\
384611238029
127 5 7.509.2287.6557252639250807127523.12514251972598061031154549270275982573061110378811783176435900357554799
128 7 257.763649.50307329.3191106049.2339340566463317436161.2983028405608735541756929.182477700970213219240171852\
81
129 5 7.31.2322118361887.412482688627178079807598675848631.115814113322099366440280889676998813124941173548805953
130 10 37.241.313.2341.6781.425101.571140885901.6291946695217.1095110988527465328644161.19486136423472309637684929\
35356381
131 7 7.118766959.5620905557.18059147791.1519139468453.137286124588876043259567675817.492370801281846683336965699\
07047
132 9 89.1297.602977.1678321.87917281.1581003091009.332526664667473.6416538652864923578689.1500807647929229886767\
14149209
133 10 7.7.29.197.1787.1050169.48713705333.27838508435875439051.6110613202111672866319.716622317368928663955050025\
3057030611
134 3 37.4021.1258148065662933435127171073866560143872261293533825733911764685311660688307770984681658280416519961
135 12 7.11.31.101.271.46441.114967.1950271.883383463.2195738619437791.4760317816590150361.17878872997028128383097\
2402140920212721
136 5 17.17.98801.2376897969771200667937073.992888154555208408072359969200446002102251441040253906228951529060955\
38881
137 4 7.51480217.4582965162279152779295741463389.2448140495278291042529241912014354378530513227666594553134296023\
8107
138 12 13.37.97.277.6073.2259889.9564781.12344559539431993.14030036355387001.23027140435639321.128407494947883673.
279219519230141641
139 3 7.478404033683.43464123950634007416896270274528229077877085950620143478550278600897682734201302908605111172\
4237
140 9 41.281.337.617.1297.68754507401.81035189089.123099618068232205681.40982486632742791332750143162242392858449\
31775661062561
141 5 7.31.1129.534577564460822791430647883899825591.400093872648315443061680477735172345044266448557214947007104\
507237639
142 5 37.4485781.33571579633135513.969155837815909463425781176679854621.58220022739632174549950127401919425992936\
844184277
143 8 7.53.937.2861.37571.3712567.51828151.2623642616266140731907940608862422310623338001684178975972736179031671\
72733704458773
144 10 193.353.1697.8641.115777.4709377.31057921.688490113.6931400449.14019268835179638724593328298903017364203886\
8198120943575131073
145 10 7.11.59.101.32713.168491.35969851301.2727192763388813.71188611917485018014870131.38450776123542785985187808\
85281690026242583211
146 5 37.877.16658893.20007314401.3767439640217533991679971417792901973000703933565811241566664111171375550309696\
7184005923301
147 12 7.7.7.29.31.197.32670457.1152319183.2527867231.762332681442053.90179616936384011.61514653542036838838300629\
06173218740292621286631
148 4 1297.12950593.10742681826196124641.812910461537597351789277337708911744048426523234607657015392944064157118\
19759159724497
149 4 7.17808481.3908095969.1806534126100647194097596047551632860649143589145163864525913101120410386931607948881\
33552030773239
150 15 13.37.61.97.181.241.3541.6781.74161.343801.22243201.38149201.1748016735462726601.340800981614130538049401.1\
3744019238016248925287701988601
151 4 7.1877258342367076264555657.57719839964417489988525624247.4177260955133929558960631779921813101873322007065\
786779841904569
152 6 17.98801.417827633.505981859041.26836193435793601023998323852801.199492594262551677559234014856976616560844\
8716213725436669937
153 13 7.31.103.919.46441.147799.190537.12690943.980146969.99617785207.29274753335383.1888411753890127.61981850959\
910422285012731307171469066599
154 8 37.421.58477.70489.863017.5030761.40590776689.6048141008071456596259776949311257916837567558165203557375479\
4818786652644638545909
155 6 7.11.101.189491931189200021056951.73925704213704945236169449354196288841.3769168199699790684839649519999144\
5129214809531978987311
156 7 1297.192193.1678321.14090441.816213379522588431707233.8284434950526240125727017.618089408508629562797739046\
557629942711588422796977
157 6 7.1571.53381.259993.32577356503.297308882243938865484453677008309867648571856224118520242496051040995144993\
90913563956124405913479
158 3 37.10429.22985458387524760396049933956519941247062829865007890151235623482849657962098495040918310213730329\
73033904327664158129
159 9 7.31.107.97351567.33685364386033.71080464397105403.79850963147627239.886629624220623485114684453959.1388827\
9563077823030315573706460911
160 7 2753.82241.145601.19854979505843329.15954097282309262360999041.4903626466768570999224738379365121.623565458\
885624857143366973953113921
161 9 7.7.29.197.231841.113958101.990000731.3091531661.8463428877114283334832841135980685094133787815940779201328\
511354558563105269202500000131
162 13 13.37.73.97.109.541.55117.591841.171467713.932461936453.39661919912737.26411543817830547235357966561.104753\
2535514129255363516988891792003940353
163 7 7.11411.1712959177.52108050586547.417317792492527332337.390331841336302929436994813.59385353538185533999095\
22760027592696327594011870339
164 3 1297.90823862327833086800386352513067248343828857.351289460623725010305581894540945828444787270943557773540\
836771459982767560667193
165 15 7.11.11.31.101.463.72073.1031141.1950271.51828151.127236649.16336066781.84155540944421.661982172984001.2324\
70996817349914740909949038496736983636813951
166 9 37.997.778873.3020869.13852369.161184670755001.437801891817492814657.62492225855662442512009.28097049972396\
2289858902531662958021839590057517
167 4 7.2339.24362285875922356868655021961427.2240848611344433471047519923958679743088526810022077124471576209605\
7091569159815413649881516047
168 11 17.113.673.4817.5953.98801.4048129.473896897.10189440239012883075423169.3276974780364284482799810397121.228\
576791406017659230547997507603024201377
169 8 7.53.937.4057.37571.116720070342348721.3378307227685242623713508116989468524398534111.154008740494680898484\
89148387594553074912242007981896423
170 10 37.241.1021.6781.934117.8289713345361373993.372810476994982432801.2244807299700346905001.418196746744415875\
29015061.115394656437025419824224817341
171 10 7.31.457.1787.46441.137713.48713705333.62174327387790051073.190324492938225748951.1773086345556501045721501\
5481519172763685683806181388676488969177
172 7 1297.1721.1904729.5993513377.3449220534377.2400135849956129030979293221108376113.32947522230532454787172792\
7490276948774179783794853789837408297
173 3 7.347.17168754933680641828885328290196243178419334128667815027099365404387446550489987693378776240078242722\
7477447336436457634084029167573
174 9 13.37.97.349.104485957.3347320129.298589131777670304546904897.105134528469779071670501631159328247729809.13\
995898620078159024779789479094697362727841
175 17 7.7.11.29.101.197.631.701.2311.3851.9241.12601.585131.1305192701.66631795301.3655688315536801.5660713977589\
80021514503314913468700952468138140520705435915823851
176 5 353.1697.4709377.2653655703600055300471675940271611363631320368111914433.1203248936190203022591615664116879\
4191545029882930365976044832157368897
177 4 7.31.1163658999540220416412446482708919139658591671.2140355196559238331144625485410513513288018960171608816\
987390371347305662078691899857664991
178 3 37.92874768913720582900858911299754687243149941868501755733246139460861.94367640856532298427984430638051386\
2900179721637307961334427437498481
179 8 7.16111.3490859.317649821.2164201732799819.1890213088140761141.684015593168267521517.5560295209693432842899\
5125419832794157001481770390335287600383493
180 10 41.577.1297.3313.13441.1678321.68754507401.2478750186961.592575109627400042641.5041038763890442425806052840\
72981501250037549130936744429106198676798115841
181 8 7.1087.13757.13952929.632269201.33644936669.1032407342933.2183668889401877470795251342807832111594626152381\
2158000579569801581127896122389639630377479533
182 9 37.313.421.1093.2341.5030761.8955493.6291946695217.11884190856613849521822323092626049163425224374408127276\
17705020621304105675607013522505083016934528589
183 8 7.31.367.9151.1676281.1882477437757002169.4577830180684945360162613198286645069141001.239523531668585297595\
7381489000500459401666829178525583973937481377
184 7 17.98801.118593079873.364095314695155207401455201.160021185991868323844533898916209.29122545034054978745227\
82767870577.4476499706959521340159489111133569
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