- 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 2.2
2 4 2.2.2.3
3 3 2.2.31
4 6 2.2.2.2.3.13
5 4 2.2.11.71
6 7 2.2.2.3.3.7.31
7 3 2.2.19531
8 8 2.2.2.2.2.3.13.313
9 5 2.2.19.31.829
10 7 2.2.2.3.11.71.521
11 3 2.2.12207031
12 10 2.2.2.2.3.3.7.13.31.601
13 3 2.2.305175781
14 7 2.2.2.3.29.449.19531
15 7 2.2.11.31.71.181.1741
16 11 2.2.2.2.2.2.3.13.17.313.11489
17 4 2.2.409.466344409
18 11 2.2.2.3.3.3.7.19.31.829.5167
19 5 2.2.191.6271.3981071
20 11 2.2.2.2.3.11.13.41.71.521.9161
21 6 2.2.31.379.19531.519499
22 8 2.2.2.3.23.67.5281.12207031
23 4 2.2.8971.332207361361
24 13 2.2.2.2.2.3.3.7.13.31.313.601.390001
25 8 2.2.11.71.101.251.401.9384251
26 7 2.2.2.3.5227.38923.305175781
27 9 2.2.19.31.109.271.829.4159.31051
28 10 2.2.2.2.3.13.29.449.19531.234750601
29 5 2.2.59.35671.22125996444329
30 14 2.2.2.3.3.7.11.31.61.71.181.521.1741.7621
31 4 2.2.1861.625552508473588471
32 14 2.2.2.2.2.2.2.3.13.17.313.2593.11489.29423041
33 6 2.2.31.199.12207031.386478495679
34 8 2.2.2.3.409.3061.41540861.466344409
35 9 2.2.11.71.211.631.4201.19531.85280581
36 16 2.2.2.2.3.3.3.7.13.19.31.37.601.829.5167.6597973
37 5 2.2.149.13971969971.8737481256739
38 10 2.2.2.3.191.761.6271.19609.213029.3981071
39 6 2.2.31.79.305175781.608459012088799
40 15 2.2.2.2.2.3.11.13.41.71.241.313.521.9161.632133361
41 4 2.2.2238236249.5079304643216687969
42 16 2.2.2.3.3.7.7.29.31.43.127.379.449.7603.19531.519499
43 4 2.2.1644512641.172827552198815888791
44 12 2.2.2.2.3.13.23.67.89.5281.12207031.1030330938209
45 12 2.2.11.19.31.71.181.829.1171.1741.169831.297315901
46 8 2.2.2.3.47.8971.332207361361.42272797713043
47 3 2.2.177635683940025046467781066894531
48 17 2.2.2.2.2.2.3.3.7.13.17.31.313.601.11489.390001.152587500001
49 4 2.2.19531.227376585863531112677002031251
50 13 2.2.2.3.11.71.101.251.401.521.1901.9384251.50150933101
51 8 2.2.31.409.90271.317731.466344409.654652168021
52 12 2.2.2.2.3.13.13.53.5227.38923.305175781.83181652304609
53 5 2.2.5960555749.17154094481.27145365052629449
54 19 2.2.2.3.3.3.3.7.19.31.109.163.271.487.829.4159.5167.31051.16018507
55 10 2.2.11.11.71.103511.511831.12207031.65628751.190295821
56 13 2.2.2.2.2.3.13.29.313.449.19531.234750601.59509429687890001
57 7 2.2.31.191.6271.3981071.11735415506748076408140121
58 9 2.2.2.3.59.35671.5096867.6090817323763.22125996444329
59 4 2.2.21180247636732981.2047572230657338751575051
60 21 2.2.2.2.3.3.7.11.13.31.41.61.71.181.521.601.1741.2281.7621.9161.69566521
61 5 2.2.8419.918585913061.140194179307171898833699259
62 9 2.2.2.3.1303.1861.21207101.28086211607.625552508473588471
63 11 2.2.19.31.379.829.19531.280729.519499.2161279.23792163643711
64 18 2.2.2.2.2.2.2.2.3.13.17.313.641.2593.11489.29423041.75068993.241931001601
65 8 2.2.11.71.131.305175781.1034150930241911.20986207825565581
66 15 2.2.2.3.3.7.23.31.67.199.5281.595123.12207031.190771747.386478495679
67 7 2.2.269.1609.26399.2454335007529.604088623657497125653141
68 14 2.2.2.2.3.13.409.1973.3061.20129.45289.41540861.466344409.12447002677
69 9 2.2.31.139.6211.8971.332207361361.598761682261.8868050880709
70 16 2.2.2.3.11.29.71.211.449.521.631.4201.19531.15216601.85280581.4698932281
71 4 2.2.569.18607929421228039083223253529869111644362732899
72 22 2.2.2.2.2.3.3.3.7.13.19.31.37.73.313.601.829.5167.390001.543097.6597973.1503418321
73 5 2.2.4853479.5729041.9519524151770349914726200576714027279
74 10 2.2.2.3.149.9103.29010221.13971969971.8737481256739.45920153384867
75 16 2.2.11.31.71.101.151.181.251.401.1741.3301.1989151.9384251.49892851.183794551
76 14 2.2.2.2.3.13.191.761.6271.19609.213029.3981071.4885168129.2864226125209369
77 7 2.2.19531.12207031.527093491.8090594434231.162715052426691233701
78 14 2.2.2.3.3.7.31.79.3121.5227.38923.305175781.22735632934561.608459012088799
79 5 2.2.205367807127911.58523123221688392679.344120456368919234899
80 20 2.2.2.2.2.2.3.11.13.17.41.71.241.313.521.9161.11489.25601.632133361.909456847814334401
81 11 2.2.19.31.109.271.829.4159.4861.31051.11419697846380955982026777206637491
82 10 2.2.2.3.83.43543.221401.2238236249.9472026608675509.5079304643216687969
83 5 2.2.20515111.1431185706701868962383741.88040095945103834627376781
84 22 2.2.2.2.3.3.7.7.13.29.31.43.127.379.449.601.2521.7603.19531.519499.234750601.24587411156281
85 9 2.2.11.71.409.1531.466344409.34563155350221618511.8198241112969626815581
86 10 2.2.2.3.1549.9547.1644512641.7866608083.1628744948329.172827552198815888791
87 9 2.2.31.59.5569.6961.35671.22125996444329.28870194250662203210437116612769
88 15 2.2.2.2.2.3.13.23.67.89.313.5281.12207031.1030330938209.9080418348371887359375390001
89 8 2.2.179.9807089.14597959.834019001.8157179360521.231669654363683130095909
90 22 2.2.2.3.3.3.7.11.19.31.61.71.181.521.829.1171.1741.5167.7621.169831.297315901.60081451169922001
91 6 2.2.19531.305175781.9680647790568589086355559.17499733663152976533452519
92 11 2.2.2.2.3.13.47.8971.332207361361.42272797713043.5465713352000770660547109750601
93 9 2.2.31.31.1861.148429.878851.625552508473588471.172974812463239310024750410929
94 8 2.2.2.3.2069.15888756269.3602372010909260861.177635683940025046467781066894531
95 11 2.2.11.71.191.2851.6271.3981071.4113691.1245576402371959291.11600321878916922053491
96 22 2.2.2.2.2.2.2.3.3.7.13.17.31.97.313.601.2593.11489.390001.29423041.152587500001.240031591394168814433
97 5 2.2.389.264811.153159805660301568024613754993807288151489686913246436306439
98 11 2.2.2.3.29.449.19531.49105547.1866013003.2481357870461.227376585863531112677002031251
99 12 2.2.19.31.199.829.143551.1731511.12207031.386478495679.22542470482159.153560376376050799
100 20 2.2.2.2.3.11.13.41.71.101.251.401.521.1901.9161.239201.9384251.424256201.50150933101.89620825374601
101 5 2.2.5937018283241.3434487311396589821473854121.483593153887747265029536907421
102 18 2.2.2.3.3.7.31.103.409.3061.8467.90271.317731.528667.41540861.466344409.60119016343.654652168021
103 6 2.2.3709.28429.59117897713198738371603984809.39546955636451768643571562540114219
104 17 2.2.2.2.2.3.13.13.53.313.5227.38923.51169.305175781.537181587281.83181652304609.129044008326199409
105 17 2.2.11.31.71.181.211.379.631.1741.4201.19531.519499.1736701.85280581.119461537021.21226783250214361
106 10 2.2.2.3.107.5960555749.17154094481.28838378869.27145365052629449.599659003321309822423087
107 7 2.2.6421.5486016363791.35411885288978941.172163150940018661.717433171088016374418821
108 25 2.2.2.2.3.3.3.3.7.13.19.31.37.109.163.271.487.601.829.4159.5167.31051.6597973.16018507.14551915228363037109\
375001
109 6 2.2.1091.1007161.1528399.2293559892404294400692399012979688850301546383400890423075969
110 17 2.2.2.3.11.11.23.67.71.521.5281.103511.511831.12207031.65628751.190295821.10910444855403996246103496881
111 8 2.2.31.149.3109.13971969971.8737481256739.54928520946880307112306785731407655242899973469
112 20 2.2.2.2.2.2.3.13.17.29.113.313.337.449.11489.19531.234750601.2520917617.59509429687890001.37007700327977836\
913
113 10 2.2.2939.6329.129499.308491.304247586761.2084303944451.620216264269531.8237123176890810696379
114 16 2.2.2.3.3.7.31.191.229.761.6271.19609.213029.3981071.75649382555448580095589.11735415506748076408140121
115 14 2.2.11.71.461.691.8971.689081.2855911.29028071.824480311.17223586571.332207361361.100062970166640331
116 12 2.2.2.2.3.13.59.35671.5096867.6090817323763.22125996444329.1334402673828313149547634216455312875601
117 10 2.2.19.31.79.829.223963741.305175781.608459012088799.937938782117311845318745554345005320717861
118 10 2.2.2.3.827.5242462229.3237765225301.2059647179472887.21180247636732981.2047572230657338751575051
119 10 2.2.239.409.1429.4999.19531.466344409.7497182681291140146079.788868477693980100643230089490226571
120 27 2.2.2.2.2.3.3.7.11.13.31.41.61.71.181.241.313.521.601.1741.2281.7621.9161.390001.69566521.632133361.2332031\
7172851318360001
121 6 2.2.12101.486179.12207031.13094322377956920597215509541997540493466263550896158313340716530769
122 11 2.2.2.3.367.8419.9029.918585913061.15571335384347.14008364639128540436401.140194179307171898833699259
123 10 2.2.31.739.960139.1785961.2238236249.9025583299.5079304643216687969.5832474690386022428273180864659
124 13 2.2.2.2.3.13.1303.1861.21207101.28086211607.625552508473588471.8124604717965111529.102651353523520067851969
125 13 2.2.11.71.101.251.401.3597751.9384251.28707251.4032808198751.767186663625251.24687045214139234043375683501
126 27 2.2.2.3.3.3.7.7.19.29.31.43.127.379.449.829.883.5167.7603.19531.280729.406729.519499.2161279.24132781.16924\
16503.23792163643711
127 3 2.2.14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531
128 22 2.2.2.2.2.2.2.2.2.3.13.17.313.641.769.2593.11489.29423041.75068993.241931001601.3666499598977.9613295678264\
3741951225664001
129 8 2.2.31.18471511.1644512641.172827552198815888791.43955934961951833386625799.51349797354047205216257689
130 16 2.2.2.3.11.71.131.521.5227.18461.38923.305175781.15188886343541.1034150930241911.15199221608544481.20986207\
825565581
131 7 2.2.2621.23928199.34720241.16815642611861.250805666433416532678429525124977090318975999001796354124089
132 22 2.2.2.2.3.3.7.13.23.31.67.89.199.601.1453.5281.595123.12207031.190771747.386478495679.1030330938209.6509387\
183417404924784917
133 12 2.2.191.6271.9311.19531.65171.281429.3981071.3257947519.152317058321.29090007107767075239783794592001366542\
871
134 10 2.2.2.3.269.1609.26399.2454335007529.604088623657497125653141.112937726300573378542443000090618928273518880\
21
135 20 2.2.11.19.31.71.109.181.271.541.829.1171.1741.4159.11071.31051.169831.297315901.1312315694449748688331.2694\
1244373060650224561
136 21 2.2.2.2.2.3.13.137.313.409.1973.3061.20129.45289.623017.41540861.466344409.12447002677.938894988049.1361753\
880209.4959636586609
137 8 2.2.20551.603349.48102071.121719631478506669.7851027307722624763151.251755028858658462627642052961230751431
138 18 2.2.2.3.3.7.31.47.139.6211.8971.66163549.253592389.332207361361.598761682261.8868050880709.42272797713043.4\
03316413944121
139 5 2.2.21521602057721.6789441546024769741462601111.24550591546653776667941845268908441565415743319193209001
140 23 2.2.2.2.3.11.13.29.41.71.211.281.449.521.631.4201.9161.19531.15216601.85280581.234750601.4698932281.1314883\
2195720299503896018648521
141 5 2.2.31.177635683940025046467781066894531.16286160623917663079467944573580125726889931566772922392814390121
142 9 2.2.2.3.569.4261.5747338499820296170481.288231038713838413442281.186079294212280390832232535298691116443627\
32899
143 7 2.2.12207031.305175781.24615836446631.53130566763791958299.460183952753824357170225842292658707895690816315\
909
144 28 2.2.2.2.2.2.3.3.3.7.13.17.19.31.37.73.313.601.829.1297.5167.11489.390001.543097.6597973.1503418321.15258750\
0001.2739177855667309845605995807633
145 10 2.2.11.59.71.35671.1461311.22125996444329.2158365113981511371558358567665231.488654500355218081336311051543\
759628081
146 10 2.2.2.3.4853479.5729041.63554310563.777612767772190289.3570677866897550288203.95195241517703499147262005767\
14027279
147 11 2.2.31.379.19531.519499.24556351.5071357999.2035895040229.203906616815994386234329833781.227376585863531112\
677002031251
148 15 2.2.2.2.3.13.149.9103.9769.40849.29010221.13971969971.8737481256739.45920153384867.510241095096183757930733\
363918820917976121
149 3 2.2.35032461608120426773093239582247903282006548546912894293926707097244777067146515037165954709053039550781
150 29 2.2.2.3.3.7.11.31.61.71.101.151.181.251.401.521.1741.1901.3301.7621.118801.1989151.9384251.20775901.2466570\
1.49892851.149439601.183794551.50150933101
151 8 2.2.1175989.2237519.389439261961.12799319666401.2843809592323334251225153490677489.234808350683195588203155\
40345862729
152 19 2.2.2.2.2.3.13.191.313.457.761.6271.19609.213029.3981071.4885168129.2864226125209369.21363981507860375753.2\
1654472202540732126905077281
153 14 2.2.19.31.409.829.4591.90271.317731.26481241.466344409.654652168021.360143672909416579.28596369159272276742\
1088565601855215949
154 16 2.2.2.3.23.29.67.449.5281.19531.12207031.527093491.20828886541.8090594434231.162715052426691233701.49970061\
516036179615325895945741
155 13 2.2.11.71.311.1861.11161.257611.5624951.31473312961.625552508473588471.21783999170235219053011.174583335852\
767865379025002452121
156 24 2.2.2.2.3.3.7.13.13.31.53.79.157.601.3121.5227.38923.8684521.305175781.4056854881.22735632934561.8318165230\
4609.608459012088799.667929705480493
157 7 2.2.32029.5129819.2107089779.8616314452100494153901371725720169.4587548699755676969742331799602074877905422\
766102260881
158 11 2.2.2.3.18251687.7897663181.511465533067.205367807127911.58523123221688392679.344120456368919234899.3739909\
5525167136010188229
159 8 2.2.31.5960555749.17154094481.1775305720077559.27145365052629449.223967815154673247771933930986251232800839\
3109037131818519
160 26 2.2.2.2.2.2.2.3.11.13.17.41.71.241.313.521.2593.9161.11489.25601.29423041.131349761.632133361.167597261761.
909456847814334401.24625444126052524088217281
161 6 2.2.8971.19531.332207361361.1469386746678216989397901405448901778556342705433890596470719221994542710855107\
30718993828121
162 25 2.2.2.3.3.3.3.3.7.19.31.109.163.271.487.829.1783.4159.4861.5023.5167.31051.16018507.20660672713801362122247\
01233463.11419697846380955982026777206637491
163 8 2.2.4599209.40100609.675775181.6582151087844246659.102556399583828574447011133455059.2541462766396986870745\
222882425433052891
164 16 2.2.2.2.3.13.83.43543.193357.221401.6355001.2238236249.1148205782281.9472026608675509.5079304643216687969.5\
6373078952722628530598981268453
165 19 2.2.11.11.31.71.181.199.331.1741.2311.103511.511831.12207031.65628751.190295821.386478495679.98671651156352\
67180926131.13585095374919980427914311
166 10 2.2.2.3.167.20515111.1431185706701868962383741.4029666108840585686296627.88040095945103834627376781.2560787\
702841639767474730913969
167 5 2.2.18371.53441.1361204447657665492151527789766442232666296870678835610403733269298091781079248108419798324\
52900690680385721
168 29 2.2.2.2.2.3.3.7.7.13.29.31.43.127.313.379.449.601.2521.6553.7603.19531.90217.390001.519499.234750601.245874\
11156281.59509429687890001.6019022585035590658668001
169 6 2.2.13859.305175781.784646826705980283039372085276899721.10067335901765297228504234600727488967589607275738\
01229970212800434559
170 18 2.2.2.3.11.71.409.521.1531.3061.41540861.75752681.247515241.466344409.504156421.34563155350221618511.687950\
69664507129341.8198241112969626815581
171 11 2.2.19.19.31.191.829.6271.3981071.11735415506748076408140121.1608861880438030545308717193047832651008272828\
10075925369403839312088918579
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