- 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 3.3
2 3 3.3.11
3 4 3.3.3.37
4 4 3.3.11.101
5 4 3.3.41.271
6 7 3.3.3.7.11.13.37
7 4 3.3.239.4649
8 6 3.3.11.73.101.137
9 6 3.3.3.3.37.333667
10 6 3.3.11.41.271.9091
11 4 3.3.21649.513239
12 9 3.3.3.7.11.13.37.101.9901
13 5 3.3.53.79.265371653
14 6 3.3.11.239.4649.909091
15 8 3.3.3.31.37.41.271.2906161
16 8 3.3.11.17.73.101.137.5882353
17 4 3.3.2071723.5363222357
18 11 3.3.3.3.7.11.13.19.37.52579.333667
19 3 3.3.1111111111111111111
20 9 3.3.11.41.101.271.3541.9091.27961
21 9 3.3.3.37.43.239.1933.4649.10838689
22 9 3.3.11.11.23.4093.8779.21649.513239
23 3 3.3.11111111111111111111111
24 12 3.3.3.7.11.13.37.73.101.137.9901.99990001
25 7 3.3.41.271.21401.25601.182521213001
26 8 3.3.11.53.79.859.265371653.1058313049
27 9 3.3.3.3.3.37.757.333667.440334654777631
28 10 3.3.11.29.101.239.281.4649.909091.121499449
29 7 3.3.3191.16763.43037.62003.77843839397
30 15 3.3.3.7.11.13.31.37.41.211.241.271.2161.9091.2906161
31 5 3.3.2791.6943319.57336415063790604359
32 13 3.3.11.17.73.101.137.353.449.641.1409.69857.5882353
33 8 3.3.3.37.67.21649.513239.1344628210313298373
34 8 3.3.11.103.4013.2071723.5363222357.21993833369
35 9 3.3.41.71.239.271.4649.123551.102598800232111471
36 14 3.3.3.3.7.11.13.19.37.101.9901.52579.333667.999999000001
37 5 3.3.2028119.247629013.2212394296770203368013
38 5 3.3.11.909090909090909091.1111111111111111111
39 8 3.3.3.37.53.79.265371653.900900900900990990990991
40 13 3.3.11.41.73.101.137.271.3541.9091.27961.1676321.5964848081
41 6 3.3.83.1231.538987.201763709900322803748657942361
42 17 3.3.3.7.7.11.13.37.43.127.239.1933.2689.4649.459691.909091.10838689
43 6 3.3.173.1527791.1963506722254397.2140992015395526641
44 13 3.3.11.11.23.89.101.4093.8779.21649.513239.1052788969.1056689261
45 12 3.3.3.3.31.37.41.271.238681.333667.2906161.4185502830133110721
46 8 3.3.11.47.139.2531.549797184491917.11111111111111111111111
47 4 3.3.35121409.316362908763458525001406154038726382279
48 15 3.3.3.7.11.13.17.37.73.101.137.9901.5882353.99990001.9999999900000001
49 6 3.3.239.4649.505885997.1976730144598190963568023014679333
50 12 3.3.11.41.251.271.5051.9091.21401.25601.182521213001.78875943472201
51 10 3.3.3.37.613.210631.2071723.52986961.5363222357.13168164561429877
52 11 3.3.11.53.79.101.521.859.265371653.1058313049.1900381976777332243781
53 6 3.3.107.1659431.1325815267337711173.47198858799491425660200071
54 16 3.3.3.3.3.7.11.13.19.37.757.52579.333667.70541929.14175966169.440334654777631
55 10 3.3.41.271.1321.21649.62921.513239.83251631.1300635692678058358830121
56 14 3.3.11.29.73.101.137.239.281.4649.7841.909091.121499449.127522001020150503761
57 8 3.3.3.37.21319.10749631.1111111111111111111.3931123022305129377976519
58 10 3.3.11.59.3191.16763.43037.62003.77843839397.154083204930662557781201849
59 4 3.3.2559647034361.4340876285657460212144534289928559826755746751
60 22 3.3.3.7.11.13.31.37.41.61.101.211.241.271.2161.3541.9091.9901.27961.2906161.4188901.39526741
61 9 3.3.733.4637.329401.974293.1360682471.106007173861643.7061709990156159479
62 7 3.3.11.2791.6943319.57336415063790604359.909090909090909090909090909091
63 16 3.3.3.3.37.43.239.1933.4649.10837.23311.45613.333667.10838689.45121231.1921436048294281
64 17 3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.834427406578561
65 9 3.3.41.53.79.271.265371653.162503518711.5538396997364024056286510640780600481
66 17 3.3.3.7.11.11.13.23.37.67.4093.8779.21649.513239.599144041.183411838171.1344628210313298373
67 5 3.3.493121.79863595778924342083.28213380943176667001263153660999177245677
68 12 3.3.11.101.103.4013.2071723.28559389.1491383821.5363222357.21993833369.2324557465671829
69 8 3.3.3.37.277.203864078068831.11111111111111111111111.1595352086329224644348978893
70 14 3.3.11.41.71.239.271.4649.9091.123551.909091.4147571.102598800232111471.265212793249617641
71 4 3.3.241573142393627673576957439049.45994811347886846310221728895223034301839
72 20 3.3.3.3.7.11.13.19.37.73.101.137.3169.9901.52579.98641.333667.99990001.999999000001.3199044596370769
73 5 3.3.12171337159.1855193842151350117.49207341634646326934001739482502131487446637
74 9 3.3.11.7253.2028119.247629013.422650073734453.296557347313446299.2212394296770203368013
75 14 3.3.3.31.37.41.151.271.4201.21401.25601.2906161.182521213001.15763985553739191709164170940063151
76 8 3.3.11.101.722817036322379041.909090909090909091.1111111111111111111.1369778187490592461
77 10 3.3.239.4649.5237.21649.42043.513239.29920507.136614668576002329371496447555915740910181043
78 18 3.3.3.7.11.13.13.37.53.79.157.859.6397.216451.265371653.1058313049.388847808493.900900900900990990990991
79 8 3.3.317.6163.10271.307627.49172195536083790769.3660574762725521461527140564875080461079917
80 17 3.3.11.17.41.73.101.137.271.3541.9091.27961.1676321.5070721.5882353.5964848081.19721061166646717498359681
81 15 3.3.3.3.3.3.37.163.757.9397.333667.2462401.440334654777631.676421558270641.130654897808007778425046117
82 9 3.3.11.83.1231.538987.2670502781396266997.3404193829806058997303.201763709900322803748657942361
83 5 3.3.3367147378267.9512538508624154373682136329.346895716385857804544741137394505425384477
84 24 3.3.3.7.7.11.13.29.37.43.101.127.239.281.1933.2689.4649.9901.226549.459691.909091.10838689.121499449.445819\
2223320340849
85 9 3.3.41.271.2071723.262533041.5363222357.8119594779271.4222100119405530170179331190291488789678081
86 10 3.3.11.173.1527791.57009401.2182600451.1963506722254397.2140992015395526641.7306116556571817748755241
87 12 3.3.3.37.3191.4003.16763.43037.62003.72559.77843839397.310170251658029759045157793237339498342763245483
88 17 3.3.11.11.23.73.89.101.137.617.4093.8779.21649.513239.1052788969.1056689261.1620583484601296758492708265640\
2106953
89 7 3.3.497867.103733951.104984505733.5078554966026315671444089.403513310222809053284932818475878953159
90 24 3.3.3.3.7.11.13.19.31.37.41.211.241.271.2161.9091.29611.52579.238681.333667.2906161.3762091.8985695684401.4\
185502830133110721
91 14 3.3.53.79.239.547.4649.14197.17837.4262077.265371653.43442141653.316877365766624209.11074218647053005429131\
8013
92 12 3.3.11.47.101.139.1289.2531.18371524594609.549797184491917.11111111111111111111111.418100330007166986793265\
8901
93 8 3.3.3.37.2791.6943319.57336415063790604359.900900900900900900900900900900990990990990990990990990990991
94 8 3.3.11.6299.35121409.4855067598095567.297262705009139006771611927.316362908763458525001406154038726382279
95 10 3.3.41.191.271.59281.63841.1111111111111111111.1289981231950849543985493631.9651946171216407914560703479517\
51
96 24 3.3.3.7.11.13.17.37.73.97.101.137.353.449.641.1409.9901.69857.206209.5882353.99990001.66554101249.751183130\
82913.9999999900000001
97 5 3.3.12004721.846035731396919233767211537899097169.109399846855370537540339266842070119107662296580348039
98 10 3.3.11.197.239.4649.909091.505885997.1976730144598190963568023014679333.50761416243655329949187817263959390\
35533
99 14 3.3.3.3.37.67.199.397.21649.34849.333667.513239.1344628210313298373.362853724342990469324766235474268869786\
311886053883
100 19 3.3.11.41.101.251.271.3541.5051.9091.21401.25601.27961.60101.7019801.182521213001.14103673319201.7887594347\
2201.1680588011350901
101 5 3.3.4531530181816613234555190841.129063282232848961951985354966759.18998088572819375252842078421374368604969
102 18 3.3.3.7.11.13.37.103.613.4013.210631.2071723.52986961.5363222357.21993833369.291078844423.13168164561429877.
377526955309799110357
103 5 3.3.1031.7034077.153211620887015423991278431667808361439217294295901387715486473457925534859044796980526236\
853
104 15 3.3.11.53.73.79.101.137.521.859.1580801.265371653.1058313049.1900381976777332243781.63252744020215074509062\
2412245443923049201
105 19 3.3.3.31.37.41.43.71.239.271.1933.4649.123551.2906161.10838689.30703738801.625437743071.102598800232111471.
57802050308786191965409441
106 8 3.3.11.107.1659431.1325815267337711173.47198858799491425660200071.90909090909090909090909090909090909090909\
09090909091
107 10 3.3.643.999809.9885089.215257037.2386760191.511399538427507881.646826950155548399.1028807946722253879130231\
1556310051849
108 22 3.3.3.3.3.7.11.13.19.37.101.109.757.9901.52579.153469.333667.70541929.14175966169.999999000001.440334654777\
631.59779577156334533866654838281
109 6 3.3.1192679.712767480971213008079.5295275348767234696493.24682974398435543596240839091037821853728210515008\
6881669547
110 20 3.3.11.11.23.41.271.331.1321.4093.5171.8779.9091.21649.62921.513239.83251631.20163494891.318727841165674579\
776721.1300635692678058358830121
111 11 3.3.3.37.37.2028119.247629013.30557051518647307.2212394296770203368013.8845981170865629119271997.9007781439\
6055017938257237117
112 19 3.3.11.17.29.73.101.113.137.239.281.4649.7841.909091.5882353.121499449.73765755896403138401.127522001020150\
503761.119968369144846370226083377
113 5 3.3.227.908191467191.53895712312217719065267103426685397298498705173449226555003346881878523705781079015749\
721646701723
114 14 3.3.3.7.11.13.37.21319.1458973.10749631.909090909090909091.1111111111111111111.3931123022305129377976519.75\
3201806271328462547977919407
115 10 3.3.41.271.31511.19707665921.20414137203567631.11111111111111111111111.5799951513941382144830754391.1224035\
69491783662720773144041
116 15 3.3.11.59.101.349.3191.16763.38861.43037.62003.618049.77843839397.154083204930662557781201849.1181180637520\
1836408679635736258669583187541
117 14 3.3.3.3.37.53.79.333667.265371653.240396841140769.537947698126879.3352825314499987.900900900900990990990991.
2304017384484085131816292573
118 8 3.3.11.1889.2559647034361.1090805842068098677837.4411922770996074109644535362851087.43408762856574602121445\
34289928559826755746751
119 10 3.3.239.4649.923441.2071723.5363222357.3924966376871.768736559421401249042753476963.32301294214856275165081\
4544437350454640448842187
120 28 3.3.3.7.11.13.31.37.41.61.73.101.137.211.241.271.2161.3541.9091.9901.27961.1676321.2906161.4188901.39526741.
99990001.5964848081.100009999999899989999000000010001
121 8 3.3.15973.21649.38237.274187.513239.59714917620953041236079539149765734015994342199250253823083148168223296\
9649167277637825641074323
122 12 3.3.11.733.4637.81131.329401.974293.1360682471.106007173861643.7061709990156159479.112052225301168368553215\
28257890437575145023592596037161
123 12 3.3.3.37.83.1231.538987.1811791.626920594693.9425856976319889649.201763709900322803748657942361.84146400034\
65161203119978906558054839526493
124 10 3.3.11.101.2791.2049349.6943319.57336415063790604359.909090909090909090909090909091.48312854955451223730555\
4588359039822397307149685578249
125 11 3.3.41.271.751.21401.25601.1797655751.182521213001.176144543406001.4205177580495630455981085900830581997519\
9677041099230574273451704628125001
126 28 3.3.3.3.7.7.11.13.19.37.43.127.239.1933.2689.4649.10837.23311.45613.52579.333667.459691.909091.5274739.1083\
8689.45121231.1921436048294281.189772422673235585874485732659
127 5 3.3.18797.90679.6518718497852438209581196842331429821705369381473495010499558754235443718885196321031597538\
36519854149224951224466197
128 20 3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.1265011073.834427406578561.1534316\
8188889137818369.515217525265213267447869906815873
129 11 3.3.3.37.173.1527791.210769832431.1963506722254397.2140992015395526641.407429732767505248479163.10490974994\
611747848197172839956039870723832569747
130 15 3.3.11.41.53.79.131.271.859.9091.265371653.1058313049.162503518711.5538396997364024056286510640780600481.83\
96862596258693901610602298557167100076327481
131 11 3.3.80173.109517.141811693.446790173.7370364319027.15594845538029429933.7317723970031057677693.131758351065\
116151205213.180222062287834025451247081
132 25 3.3.3.7.11.11.13.23.37.67.89.101.4093.8779.9901.21649.513239.599144041.1052788969.1056689261.5419170769.183\
411838171.789390798020221.2361000305507449.1344628210313298373
133 8 3.3.239.1597.4649.2021015460335957.1111111111111111111.2788482998620431437549076793905857765163930062352097\
86029420958416508667488018611321233079
134 7 3.3.11.493121.79863595778924342083.28213380943176667001263153660999177245677.909090909090909090909090909090\
909090909090909090909090909090909091
135 20 3.3.3.3.3.31.37.41.271.757.238681.333667.1577071.2906161.16357951.310362841.258360989311.440334654777631.41\
85502830133110721.483418418597220677238517353915231961831
136 16 3.3.11.73.101.103.137.4013.2071723.28559389.152533657.1491383821.5363222357.21993833369.2324557465671829.65\
552746171882583264230070868884366877803237222654400793
137 7 3.3.2467.2535528323.1029879756928762117455431.140175894162990609843314797.123043880137417667485877804096702\
26810319992722055173127328805633899245853
138 18 3.3.3.7.11.13.37.47.139.277.2531.31051.143574021480139.203864078068831.549797184491917.11111111111111111111\
111.24649445347649059192745899.1595352086329224644348978893
139 4 3.3.119124859925363.932728157504043594282003041661807385390618120638384597314097345431032571052315101287361\
4569275960380714495413018734336834397
140 25 3.3.11.29.41.71.101.239.271.281.421.3541.4649.9091.27961.123551.909091.3471301.4147571.13489841.121499449.6\
0368344121.102598800232111471.265212793249617641.848654483879497562821
141 9 3.3.3.37.283.35121409.721030498171501831.316362908763458525001406154038726382279.44150634648836004848211413\
5141919313523563714948107161215664533500695867
142 7 3.3.11.290249.241573142393627673576957439049.45994811347886846310221728895223034301839.31321069464181068355\
415209323405389541706979493156189716729115659
143 11 3.3.53.79.21649.513239.2823679.180523201.265371653.47428676444591705727929369346443.37226581283489953701472\
184267606576037130878873797366013283473311751294203
144 25 3.3.3.3.7.11.13.17.19.37.73.101.137.3169.8929.9901.52579.98641.333667.5882353.99990001.999999000001.3199044\
596370769.9999999900000001.111994624258035614290513943330720125433979169
145 13 3.3.41.271.3191.16763.43037.62003.9605671.77843839397.15589280974996818911.80684370001269698853996151670133\
742711.744909731145732233993613931089059528977143716201
146 9 3.3.11.293.12171337159.1855193842151350117.10826684964539959837294043117.2865788889761949979999225923309086\
02103011.49207341634646326934001739482502131487446637
147 16 3.3.3.37.43.239.1933.4649.63799.4715467.10838689.505885997.267652966241599.2603941883787374089.197673014459\
8190963568023014679333.4769337181464959147997704753876850429427
148 16 3.3.11.101.149.3109.7253.111149.2028119.247629013.708840373781.422650073734453.296557347313446299.669031686\
661427842829.2212394296770203368013.40548140514062774758071840361
149 5 3.3.12517.535596779200919.165736926794133651958901299355714006989136499208236553470054888445255175718613765\
5887808209563554371273008938334507277118593589757
150 25 3.3.3.7.11.13.31.37.41.151.211.241.251.271.2161.4201.5051.9091.21401.25601.2906161.182521213001.78875943472\
201.15763985553739191709164170940063151.10000099999999989999899999000000000100001
151 7 3.3.907.429360649.29877981480806017715604631.28656552837574546515657117360191971140211910788651135283.33323\
66532260724652058380106533605034666939213869789759449
152 14 3.3.11.73.101.137.457.1403417.722817036322379041.909090909090909091.1111111111111111111.1369778187490592461.
5240808656722481737.297478330786365628414805305290302483555043017
153 18 3.3.3.3.37.307.613.18973.210631.333667.2071723.11910133.52986961.5363222357.25332185271529.1316816456142987\
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