- 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 2.3
2 2 2.13
3 4 2.3.3.7
4 2 2.313
5 3 2.3.521
6 3 2.13.601
7 4 2.3.29.449
8 3 2.17.11489
9 6 2.3.3.3.7.5167
10 4 2.13.41.9161
11 5 2.3.23.67.5281
12 3 2.313.390001
13 4 2.3.5227.38923
14 3 2.13.234750601
15 7 2.3.3.7.61.521.7621
16 3 2.2593.29423041
17 4 2.3.3061.41540861
18 5 2.13.37.601.6597973
19 5 2.3.761.19609.213029
20 4 2.241.313.632133361
21 10 2.3.3.7.7.29.43.127.449.7603
22 4 2.13.89.1030330938209
23 4 2.3.47.42272797713043
24 4 2.17.11489.152587500001
25 5 2.3.521.1901.50150933101
26 5 2.13.13.53.83181652304609
27 10 2.3.3.3.3.7.163.487.5167.16018507
28 3 2.313.59509429687890001
29 4 2.3.5096867.6090817323763
30 7 2.13.41.601.2281.9161.69566521
31 5 2.3.1303.21207101.28086211607
32 4 2.641.75068993.241931001601
33 9 2.3.3.7.23.67.5281.595123.190771747
34 6 2.13.1973.20129.45289.12447002677
35 7 2.3.29.449.521.15216601.4698932281
36 6 2.73.313.390001.543097.1503418321
37 5 2.3.9103.29010221.45920153384867
38 4 2.13.4885168129.2864226125209369
39 8 2.3.3.7.3121.5227.38923.22735632934561
40 5 2.17.11489.25601.909456847814334401
41 6 2.3.83.43543.221401.9472026608675509
42 6 2.13.601.2521.234750601.24587411156281
43 6 2.3.1549.9547.7866608083.1628744948329
44 3 2.313.9080418348371887359375390001
45 10 2.3.3.3.7.61.521.5167.7621.60081451169922001
46 3 2.13.5465713352000770660547109750601
47 5 2.3.2069.15888756269.3602372010909260861
48 5 2.97.2593.29423041.240031591394168814433
49 7 2.3.29.449.49105547.1866013003.2481357870461
50 7 2.13.41.9161.239201.424256201.89620825374601
51 10 2.3.3.7.103.3061.8467.528667.41540861.60119016343
52 5 2.313.51169.537181587281.129044008326199409
53 5 2.3.107.28838378869.599659003321309822423087
54 6 2.13.37.601.6597973.14551915228363037109375001
55 7 2.3.23.67.521.5281.10910444855403996246103496881
56 7 2.17.113.337.11489.2520917617.37007700327977836913
57 9 2.3.3.7.229.761.19609.213029.75649382555448580095589
58 3 2.13.1334402673828313149547634216455312875601
59 6 2.3.827.5242462229.3237765225301.2059647179472887
60 6 2.241.313.390001.632133361.23320317172851318360001
61 6 2.3.367.9029.15571335384347.14008364639128540436401
62 4 2.13.8124604717965111529.102651353523520067851969
63 16 2.3.3.3.7.7.29.43.127.449.883.5167.7603.406729.24132781.1692416503
64 4 2.769.3666499598977.96132956782643741951225664001
65 8 2.3.521.5227.18461.38923.15188886343541.15199221608544481
66 7 2.13.89.601.1453.1030330938209.6509387183417404924784917
67 3 2.3.11293772630057337854244300009061892827351888021
68 7 2.137.313.623017.938894988049.1361753880209.4959636586609
69 9 2.3.3.7.47.66163549.253592389.42272797713043.403316413944121
70 7 2.13.41.281.9161.234750601.13148832195720299503896018648521
71 5 2.3.4261.5747338499820296170481.288231038713838413442281
72 6 2.17.1297.11489.152587500001.2739177855667309845605995807633
73 5 2.3.63554310563.777612767772190289.3570677866897550288203
74 5 2.13.9769.40849.510241095096183757930733363918820917976121
75 13 2.3.3.7.61.521.1901.7621.118801.20775901.24665701.149439601.50150933101
76 5 2.313.457.21363981507860375753.21654472202540732126905077281
77 9 2.3.23.29.67.449.5281.20828886541.49970061516036179615325895945741
78 10 2.13.13.53.157.601.8684521.4056854881.83181652304609.667929705480493
79 6 2.3.18251687.7897663181.511465533067.37399095525167136010188229
80 6 2.2593.29423041.131349761.167597261761.24625444126052524088217281
81 14 2.3.3.3.3.3.7.163.487.1783.5023.5167.16018507.2066067271380136212224701233463
82 6 2.13.193357.6355001.1148205782281.56373078952722628530598981268453
83 5 2.3.167.4029666108840585686296627.2560787702841639767474730913969
84 7 2.313.6553.90217.390001.59509429687890001.6019022585035590658668001
85 9 2.3.521.3061.41540861.75752681.247515241.504156421.68795069664507129341
86 5 2.13.173.2171388367013.132331554743163541916284364878460504933118649
87 9 2.3.3.7.349.5096867.6090817323763.210390487070809.22500358133965991972941
88 7 2.17.11489.13729.929281.71225159567951317923809.91029014606406186465761
89 5 2.3.39387996609449861.56522267529181963.12094715786677995586454978647
90 12 2.13.37.41.601.2281.9161.6597973.20478961.69566521.6794091374761.25535754811081
91 8 2.3.29.449.5227.38923.15887476811320661.15994146485373751289418997754783021
92 4 2.313.150220315444217.214752088491462210591995581828628861192144614553
93 10 2.3.3.7.1303.21207101.258065887.28086211607.75005167927.53345671490722200466369
94 6 2.13.5077.12409.329573417220613.935213864500231208652603316429973471246089
95 9 2.3.521.761.4561.19609.213029.179763436784239734042181.309828362361188845069741
96 7 2.193.641.75068993.241931001601.5207826497153857.539344757336151926206665601
97 7 2.3.29683.261707.547663.90130760102421063383.27430239803369083066006288929529
98 7 2.13.197.234750601.164204573839769.74535675530760254357.21441970593484574539001
99 12 2.3.3.3.7.23.67.5167.5281.595123.190771747.874300184250616439267985523227691404297001
100 8 2.241.313.4001.132001.776401.632133361.201729070811027930976007420652223887947601
101 3 2.3.6573840876841765045097738044023218580610053625908525039752324422200521
102 12 2.13.601.1973.6733.20129.45289.4613053.19724557.34288117.12447002677.26837241260899651321
103 3 2.3.164346021921044126127443451100580464515251340647713125993808110555013021
104 8 2.17.11489.247161617.825256433.2220784177.31308249137777.889988147002015336570560929
105 18 2.3.3.7.7.29.43.61.127.421.449.521.7603.7621.5236141.15216601.4698932281.1354224218968567573270561
106 4 2.13.8871726015923707071209.534366212823606171881874993300544219189772104182089
107 4 2.3.643.159745355677531226795726527119537776550594226912629399294136965936054647
108 11 2.73.313.73009.390001.543097.1853281.3314953.1503418321.36280398313.13012873776055827785521
109 5 2.3.19403.4046322895447485867367.32707684672709516281678338357373622217207225350621
110 10 2.13.41.89.9161.245521.1458601.1030330938209.2802204291103029121.85725237432926769781584361
111 13 2.3.3.7.223.5107.9103.668221.13844587.29010221.107903101.45920153384867.221746234901611997486023
112 8 2.2593.271489.1149569.10922689.29423041.465314420407473281.7957141013471106527440814723329
113 6 2.3.227.1387189.12249784663.416072767607140626504228216362738974973739625245422473584889
114 9 2.13.601.22573.53590717.4885168129.2108505761893.2864226125209369.86336058161143199543775877
115 7 2.3.47.521.73141.42272797713043.529958401900871889532705668013589387152384352866888324141
116 8 2.233.313.929.33409.397823386118610689.1547355341777494553.431947226814793053965448991778881
117 13 2.3.3.3.7.3121.5167.5227.38923.40483.43236180703.22735632934561.121949664589584488031947458631250949
118 3 2.13.1157409822348098469384602128957288052006070702052516944254770910797210840078500601
119 10 2.3.29.449.2381.3061.25229.4172141.41540861.60433492605929799024858062086345509864222351309382109
120 8 2.17.11489.25601.2172116161.152587500001.909456847814334401.249573426944146284704352710315893441
121 10 2.3.23.67.5281.374499841.304639362281.11449313571047243.4600715686162128721.12819112747383653095727
122 7 2.13.733.61001.19811275733.26933356951273517.30319589876521738837586350091112786441985691445677
123 10 2.3.3.7.83.43543.221401.9472026608675509.30970420211207224741561.3179610795566616049227976098726121
124 3 2.313.751114601164400963558298106851275193494354988352771579238818981647550964507812890001
125 8 2.3.521.1901.3001.50150933101.51204738027593108331001.51336267539863487576798868866296350032791001
126 11 2.13.37.601.2521.6597973.234750601.4661402165281.24587411156281.147053007410401.308942475257273345172721
127 6 2.3.509.2287.2735581.3076137716865400512817630590222174947182195052472086065321936995866231846027
128 4 2.257.23653200983830003298459393.24171717725330873572798545219226642215966994254472458802413313
129 12 2.3.3.7.1549.9547.327845761.558801427.1420986601.7866608083.1628744948329.236419892853700126919767791480523
130 10 2.13.13.41.53.9161.87881.14402441.83181652304609.10371047328004711415976187888122003157511900197790591281
131 4 2.3.263.23278959735865959837783914314445613074672559346722265555860894056527591481597100222820867
132 7 2.313.390001.331660297.112835047682166217.9080418348371887359375390001.2213895710934906295050485076049
133 10 2.3.29.449.761.2129.19609.213029.354047.4905684062582720880172275280025711696216945281088701822552533098887
134 4 2.13.20369.8670367881621696201246383264395739338019619427601080980701370016748806481465099715917129
135 18 2.3.3.3.3.7.61.163.487.521.5167.7621.164701.16018507.31472682400981.182517282870121.60081451169922001.22382\
3944168266601
136 6 2.17.17.11489.999329.17298244498006001776733260622470717119751907722059351560259725074404263356882341457
137 8 2.3.823.2741.22469.7642530702770043710321.61562630761411218787053569.4011366712134698762723279325243498287
138 9 2.13.277.601.70942489.22600337281.66988220431117.1129448349501082362870332521.54657133520007706605471097506\
01
139 6 2.3.172694671812043.417786018853823.2459716746919477501.13476012762896826693076454784079583396699156093189
140 7 2.241.313.632133361.59509429687890001.514845603025661988644048801.24554874798220986864643786538129965751201
141 12 2.3.3.7.283.1129.2069.15888756269.24048335089.37516308093487.3602372010909260861.83401839008933340130657770\
875911981
142 9 2.13.853.72497533.8367932201.200771218157.554474665573.1095832589179957.10928221322658064610359890149344296\
10237
143 12 2.3.23.67.5227.5281.38923.2010581.2253938672701.567618483045329.3028704600213534236926361.11587897416475392\
7617074729
144 6 2.97.2593.29423041.240031591394168814433.126217744835361888865876570445245761220576241612434387207031250000\
01
145 9 2.3.521.5096867.98047293061.3532907090761.6090817323763.17149742984461.388917369321230148861862121856409329\
475801
146 7 2.13.293.27133517.84128413.772557938155429260697128053.8344490393750630749901287104215820511970406163545961\
8689
147 16 2.3.3.7.7.7.29.43.127.449.7603.49105547.1866013003.9887502829.2481357870461.7469667363102313097848984703627\
87834256167309467
148 6 2.313.3257.3542233.10044059578457.3863510929006128731397775997106278623741777873312669722258159878450119598\
00953
149 8 2.3.85229.4394309.12703371381749.1084802496290323.864203844381482464122519761.52361917935772260201994833743\
50559063
150 13 2.13.41.601.2281.9161.14401.239201.69566521.424256201.89620825374601.299541552154912341601.1917567520615207\
7061206122104001
151 4 2.3.43367201.1346350114076627740439648525400870859446925821002870129660381936156650470599755601672561817284\
1821
152 8 2.17.11489.14897.4189729.11524380579073027969.101284922414513827611672455293249.615506112662870422746709179\
075698731217
153 17 2.3.3.3.7.103.307.3061.5167.6427.8467.528667.6297787.41540861.45618058027.60119016343.224444666262772711206\
28423571194332041248441
154 9 2.13.89.8009.40987409.234750601.1030330938209.74353801974761.3205545310095322669335676987039639070961467094\
8349354111761
155 10 2.3.521.1303.21701.21207101.28086211607.108674992710961.145475949458129109023753501.26305238718580315281455\
86480948032725521
156 8 2.313.51169.390001.537181587281.129044008326199409.319143533738738955692755921.3961217425535388935161067587\
3223022522481
157 5 2.3.1585387.223975620462535382927.2569232394939842779680495564023980943892727812972458042294041029133650710\
2459744229
158 7 2.13.317.41081.72997.10390269663517.10657497440017967338967647718253054242742650521015293652487517794112636\
89062240801237
159 10 2.3.3.7.107.5407.1725469.28838378869.599659003321309822423087.629126000698440176948173290025536367961358687\
591029988395118907
160 6 2.641.75068993.241931001601.46957667265666758402894952584920394200961.6258266324069263267587145223441885541\
709510944641
161 8 2.3.29.47.449.116243.42272797713043.18960485330630458608726423548435017513366985359855739634899671100737360\
80198781935695267
162 9 2.13.37.601.6597973.503731168597.14551915228363037109375001.720314410420100602530036001.8492577938450345455\
181723282785204933
163 6 2.3.1981740926993660561.286075553470422974507.721493104094461397911450801.348497483550115442544224379540353\
249271092076223
164 7 2.313.2953.811755457273.46964872205858855033.2211877372577215640856618933593.274336455529883240823514187708\
17073340037603441
165 16 2.3.3.7.23.61.67.521.661.5281.7621.595123.9651181.190771747.10910444855403996246103496881.10895236801197932\
042869534022823840857626381681
166 6 2.13.997.4649.99006230951147470700089.896045657712933264240211729388605474603462200808101295164294346037293\
2436601305246853
167 5 2.3.4978061451403.50902967640396173052637279626869845515838501.35158967909030207343496611675401197018177156\
4516376842044907
168 11 2.17.113.337.11489.12433.2520917617.152587500001.37007700327977836913.44763922656823409574575008753.2267866\
3531006893220213039493696449
169 6 2.3.5227.38923.493481.2218453039442110882133181987181140975254661304315275239985248150354057020847251976922\
5708903579067059921
170 14 2.13.41.1361.1973.9161.14281.20129.45289.14239201.87393601.12447002677.1972618762904267665190337601.6405730\
905595298015162543537765377017161
171 14 2.3.3.3.7.229.761.5167.19609.213029.60272250820183.75649382555448580095589.6267476427578502461453809.822262\
8300623099463003315779263154383
172 6 2.313.18233.30185745097.2646713294612838233.183189037749367561353160052737923198105661589251022209827163406\
2217297884703623956697
173 5 2.3.347.42794294406607.937441455241963094607957706948612301160760445304907763236810669171892433701043108759\
79970232855261687349
174 8 2.13.601.382801.506670253.146817720340602448117.1334402673828313149547634216455312875601.703346099946949634\
05747806474103032308808001
175 13 2.3.29.449.521.701.1901.2801.15216601.4698932281.50150933101.6309154245455368301.60748729625391012923689977\
527382296073385364682787107908201
176 10 2.353.2593.1827937.2704769.29423041.1800750547615213217.609201485490930587260897.830940907997357679202561.4\
300806813670912100945629926401
177 15 2.3.3.7.709.827.1063.347629.5242462229.49987218529.3237765225301.2059647179472887.130325543183670643.504583\
856881942565107.1663887084465861537223
178 4 2.13.20365288294844141313970353677.492943178875032482640838985113395959050145702649364199012184405675798010\
53361633437921664941413
179 8 2.3.21320258969.12021304420747747.227138023883511049.20324346366468227562461.9711234996179070876201114229.1\
893017204291990900535319125287
180 14 2.73.241.313.8641.390001.440641.543097.632133361.1503418321.356646293281.50735307557193841.2332031717285131\
8360001.183199167868426942613978977201
181 6 2.3.1087.28961.101723.1698076598320997975868223540073977077839321323584898520172503381664545593585083705639\
04333431096051133215931383061
182 9 2.13.13.53.234750601.3640732369.83181652304609.141437955091157453.90564759861751060627735545502572941779870\
922788399250312667071190788497493
183 13 2.3.3.7.367.9029.17203.11833147.2880471241.15571335384347.1117197595048793563.14008364639128540436401.13671\
72296621765608583209862989093193371834027
184 7 2.17.11489.14966561.7323187654220815881445121.36153673470666026958084532869022033.2634784118655786958605265\
74080287248856096438703401625137
185 9 2.3.521.2221.3701.9103.29010221.45920153384867.654418058067838415738219243693599843014730577527147788290112\
2358940971377123359179724468647761
186 10 2.13.373.601.1117.1489.10269119521.8124604717965111529.102651353523520067851969.122805029678209774239568680\
554379023530649238353837445060117108769
187 11 2.3.23.67.1123.3061.5281.12343.41540861.17871635646349095375983368709164224334356049680569.3314493287892012\
3499901728500119115510249577864305170741
188 8 2.313.90617.755009.951281.12795134934601897.4760594190627487654169124325931441.1027093115067605645962209945\
69542246072758985784591096622629841
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