- 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 5 2.2.2.2.3
3 4 2.3.3.19
4 8 2.2.2.2.2.3.5.5
5 3 2.3.2801
6 8 2.2.2.2.3.3.19.43
7 4 2.3.29.4733
8 10 2.2.2.2.2.2.3.5.5.1201
9 7 2.3.3.3.19.37.1063
10 8 2.2.2.2.3.11.191.2801
11 4 2.3.1123.293459
12 13 2.2.2.2.2.3.3.5.5.13.19.43.181
13 3 2.3.16148168401
14 9 2.2.2.2.3.29.113.911.4733
15 7 2.3.3.19.31.2801.159871
16 13 2.2.2.2.2.2.2.3.5.5.17.1201.169553
17 4 2.3.14009.2767631689
18 12 2.2.2.2.3.3.3.19.37.43.1063.117307
19 4 2.3.419.4534166740403
20 14 2.2.2.2.2.3.5.5.5.11.191.281.2801.4021
21 7 2.3.3.19.29.4733.11898664849
22 9 2.2.2.2.3.23.1123.293459.10746341
23 5 2.3.47.3083.31479823396757
24 18 2.2.2.2.2.2.3.3.5.5.13.19.43.73.181.193.409.1201
25 5 2.3.2551.2801.31280679788951
26 8 2.2.2.2.3.53.228511817.16148168401
27 12 2.3.3.3.3.19.37.109.811.1063.2377.2583253
28 13 2.2.2.2.2.3.5.5.29.113.911.4733.13564461457
29 5 2.3.59.127540261.71316922984999
30 14 2.2.2.2.3.3.11.19.31.43.191.2801.159871.6568801
31 5 2.3.311.21143.3999088279399464409
32 16 2.2.2.2.2.2.2.2.3.5.5.17.353.1201.169553.47072139617
33 9 2.3.3.19.1123.3631.293459.1532917.12323587
34 8 2.2.2.2.3.14009.2767631689.29078814248401
35 7 2.3.29.2801.4733.2127431041.77192844961
36 18 2.2.2.2.2.3.3.3.5.5.13.19.37.43.181.1063.117307.13841169553
37 5 2.3.223.2887.4805345109492315767981401
38 9 2.2.2.2.3.419.351121.4058036683.4534166740403
39 8 2.3.3.19.486643.7524739.44975113.16148168401
40 18 2.2.2.2.2.2.3.5.5.5.11.41.191.281.1201.2801.4021.810221830361
41 5 2.3.83.20515909.4362139336229068656094783
42 15 2.2.2.2.3.3.19.29.43.113.911.4733.51031.309079.11898664849
43 4 2.3.166003607842448777.2192537062271178641
44 15 2.2.2.2.2.3.5.5.23.661.1123.1409.293459.10746341.83960385389
45 12 2.3.3.3.19.31.37.1063.2801.159871.1527007411.125096112091
46 9 2.2.2.2.3.47.3083.31479823396757.3421093417510114543
47 4 2.3.13722816749522711.63681511996418550459487
48 22 2.2.2.2.2.2.2.3.3.5.5.13.17.19.43.73.181.193.409.1201.169553.33232924804801
49 8 2.3.29.3529.4733.1074473.13473433.6106505825833677713
50 11 2.2.2.2.3.11.191.2551.2801.31280679788951.79787519018560501
51 10 2.3.3.19.103.14009.365773.2316281689.2767631689.10879733611
52 13 2.2.2.2.2.3.5.5.53.157.228511817.16148168401.1195857367853217109
53 5 2.3.8269.319591.38904276017035188056372051839841219
54 18 2.2.2.2.3.3.3.3.19.37.43.109.811.1063.2377.117307.2583253.1628413557556843
55 6 2.3.1123.2801.293459.5457586804596062091175455674392801
56 19 2.2.2.2.2.2.3.5.5.29.113.337.911.1201.2129.4733.517553.515717329.13564461457
57 10 2.3.3.19.19.419.19609.879399649.4534166740403.6957533874046531
58 9 2.2.2.2.3.59.127540261.71316922984999.402488219476647465854701
59 6 2.3.459257.134927809.550413361.354639323684545612988577649
60 24 2.2.2.2.2.3.3.5.5.5.11.13.19.31.43.61.181.191.281.2801.4021.159871.6568801.555915824341
61 6 2.3.367.4759.177237331.1914662449813727660680530326064591907
62 11 2.2.2.2.3.311.373.21143.9754399.5420506947192709.3999088279399464409
63 11 2.3.3.3.19.29.37.1063.4733.11898664849.2643999917660728787808396988849
64 20 2.2.2.2.2.2.2.2.2.3.5.5.17.353.1201.169553.7699649.134818753.47072139617.531968664833
65 9 2.3.131.2801.157951.787021.16148168401.4446437759531.434502978835771
66 17 2.2.2.2.3.3.19.23.43.67.1123.3631.293459.1532917.10746341.12323587.1357105535093947
67 6 2.3.228337.147300841.206244761.10052011757370829033540932021825161
68 14 2.2.2.2.2.3.5.5.137.14009.59361349.2767631689.29078814248401.133088039373662309
69 10 2.3.3.19.47.139.3083.402011881627.31479823396757.235169662395069356312233
70 18 2.2.2.2.3.11.29.71.113.191.421.911.2801.4733.12128131.603926681.2127431041.77192844961
71 4 2.3.990643452963163.169002145064468556765676975247413756542145739
72 26 2.2.2.2.2.2.3.3.3.5.5.13.19.37.43.73.181.193.409.1063.1201.42409.117307.137089.13841169553.32952799801
73 7 2.3.439.3675989.359390389.1958423494433591.7222605228105536202757606969
74 10 2.2.2.2.3.149.223.2887.4805345109492315767981401.15572244900182528777225808449
75 11 2.3.3.19.31.2551.2801.29251.159871.31280679788951.217648180992721729506406538251
76 13 2.2.2.2.2.3.5.5.419.351121.4058036683.4534166740403.2598696228942460402343442913969
77 9 2.3.29.1123.4733.293459.724487149.6809710909.88262612316754526107621113329689
78 17 2.2.2.2.3.3.19.43.53.79.486643.7524739.23850061.44975113.228511817.16148168401.115868130379
79 4 2.3.913242407367610843676812931.1056836588644853738704557482552056406147
80 24 2.2.2.2.2.2.2.3.5.5.5.11.17.41.191.281.881.1201.2801.4021.169553.542081.810221830361.2312581841562813841
81 17 2.3.3.3.3.3.19.37.109.811.1063.1621.2377.3727.2583253.3368791.70722308812401674174993533367023
82 12 2.2.2.2.3.83.4849399.8999993.20515909.1636258751.78009515593.4362139336229068656094783
83 9 2.3.167.66733.76066181.7685542369.62911130477521.303567967057423.18624275418445601
84 22 2.2.2.2.2.3.3.5.5.13.19.29.43.113.181.911.4733.51031.309079.11898664849.13564461457.195489390796456327201
85 8 2.3.1531.2801.4931.14009.2767631689.138497973518827432485604572537024087153816681041
86 14 2.2.2.2.3.947.19867.20899.163573.235211.3799051.4749781.166003607842448777.2192537062271178641
87 10 2.3.3.19.59.127540261.2576743207.71316922984999.196915704073465747.358475907408445923469
88 20 2.2.2.2.2.2.3.5.5.23.89.661.1123.1201.1409.8713.293459.10746341.83960385389.8206973609150536446402438593
89 5 2.3.1805633.18489605314740987765913.8166146875847876762859119015147004762656450569
90 24 2.2.2.2.3.3.3.11.19.31.37.43.191.541.1063.2801.117307.154351.159871.295831.6568801.7777981.1527007411.12509\
6112091
91 8 2.3.29.4733.7304123737.16148168401.231410451435538144122809.3565837331172073232378945297
92 16 2.2.2.2.2.3.5.5.47.3083.26681.649981.15513961.31479823396757.3421093417510114543.55681942361860463813
93 10 2.3.3.19.311.21143.5463751.2211164386353499.3999088279399464409.36148617745189465516342817701
94 8 2.2.2.2.3.13722816749522711.63681511996418550459487.655417289594537954307682339857743931943
95 8 2.3.419.2801.36671.1966385431.4534166740403.83588499889013461558350575326824370345112529401
96 28 2.2.2.2.2.2.2.2.3.3.5.5.13.17.19.43.73.97.181.193.353.409.1201.169553.104837857.47072139617.33232924804801.
108604397663266369
97 5 2.3.389.971.4160924156784953821413999107825795646911807584554735726748631757909547764679
98 20 2.2.2.2.3.29.113.197.883.911.3529.3823.4733.161309.1074473.1445599.13473433.19847549.101361401.610650582583\
3677713
99 15 2.3.3.3.19.37.199.1063.1123.3631.173647.293459.1532917.12323587.14658652062814508164798530246267135510037033
100 22 2.2.2.2.2.3.5.5.5.5.11.101.191.281.2551.2801.4021.13001.25301.31280679788951.79787519018560501.383279663002\
31909291101
101 6 2.3.607.809.6263.1226962153072980952980067096888460031879516017670288348423584305043494594529
102 18 2.2.2.2.3.3.19.43.103.14009.365773.1135261.12192877.2316281689.2767631689.10879733611.29078814248401.909207\
46649833
103 4 2.3.17923.10316589882658148664018432412741304154103858145253645339510927287724805842171756259
104 18 2.2.2.2.2.2.3.5.5.53.157.313.1201.85094881.228511817.16148168401.1195857367853217109.1377454635342537460935\
008154217
105 13 2.3.3.19.29.31.2801.4733.159871.2127431041.11898664849.77192844961.42693162668620904426304495389707999425601
106 12 2.2.2.2.3.107.8269.319591.345449549.35416476134069.58902316970027001503.38904276017035188056372051839841219
107 5 2.3.227109283745807808529.1620221568881364582821.1206506689449517154664984054683391885701717268373
108 27 2.2.2.2.2.3.3.3.3.5.5.13.19.37.43.109.181.811.1063.2377.26893.117307.2583253.13841169553.167039577217.59029\
7313273013.1628413557556843
109 5 2.3.14551288401737861.63505707690048880101785428103.23540782932240399632107200158745339309941271547
110 19 2.2.2.2.3.11.11.23.191.331.1123.2311.2801.38501.293459.2864401.10746341.7840815905526451.545758680459606209\
1175455674392801
111 11 2.3.3.19.223.2887.6217.177379.56713875643149053038693.4805345109492315767981401.966513020957488728227630485\
99
112 27 2.2.2.2.2.2.2.3.5.5.17.29.113.337.449.673.911.1201.2129.4733.169553.517553.39648001.515717329.13564461457.2\
1535258550401.142256806230113
113 4 2.3.227.230091944348186646613985311030910601771732680858725360845463092718251327185092028815673428363
114 19 2.2.2.2.3.3.19.19.43.419.457.19609.351121.879399649.4058036683.24006520939.4534166740403.6957533874046531.2\
75430251632699963
115 12 2.3.47.1151.2801.3083.188831.1446701.723461377501.31479823396757.27229507836853201541.323388097576653901216\
14112981
116 16 2.2.2.2.2.3.5.5.59.233.127540261.136853089.55716067510309.71316922984999.116714640028973541741413.402488219\
476647465854701
117 16 2.3.3.3.19.37.1063.1873.322921.486643.2280097.7524739.44975113.7687225261.16148168401.661353842305791342187\
228684843715341
118 13 2.2.2.2.3.122131.459257.134927809.550413361.4261190159.1187164242679.14683403662888806475673.35463932368454\
5612988577649
119 11 2.3.29.4733.12377.14009.34273.2767631689.305213588009240737.440779823883628367834893.2023356904834733683686\
3191403341
120 33 2.2.2.2.2.2.3.3.5.5.5.11.13.19.31.41.43.61.73.181.191.193.281.409.1201.2801.4021.159871.6568801.12913561.55\
5915824341.810221830361.85560261859655897641
121 9 2.3.1123.1453.65099.293459.11795261559086963.58792315124013823398811997.13928884340651233393054864060847158\
508075329
122 10 2.2.2.2.3.367.4759.177237331.1914662449813727660680530326064591907.4445191281471704446569146729456894390508\
80209231501
123 9 2.3.3.19.83.267403.20515909.4362139336229068656094783.13031612278097596136163934699402177453365619293349843\
0337748067
124 17 2.2.2.2.2.3.5.5.311.373.21143.9754399.33947629297.5420506947192709.3999088279399464409.74502648768583254173.
196846325409292090901
125 8 2.3.251.2551.2801.31280679788951.2182816753758823696751.590354667835684444020417934211947301188761723956532\
3800435501
126 25 2.2.2.2.3.3.3.19.29.37.43.113.127.911.1063.4733.9829.51031.117307.309079.20801593.67979647.1506625093.11898\
664849.2643999917660728787808396988849
127 5 2.3.260461507.554351226505275380676162672703.24534164319836858284335214459848074446885004177502212550076704\
7213117
128 24 2.2.2.2.2.2.2.2.2.2.3.5.5.17.353.1201.35969.169553.7699649.134818753.47072139617.531968664833.1110623386241.
15266848196793556098085000332888634369
129 10 2.3.3.19.10837.63350976270733.166003607842448777.2192537062271178641.175446584281395198837259.6946231973486\
82715265952229891
130 18 2.2.2.2.3.11.53.131.191.2801.157951.787021.1175071.228511817.16148168401.4446437759531.434502978835771.3569\
5043869049049222174543845808031
131 3 2.3.8505346116479680194953954163954280577066639233068267330253081977410514153169870714693030729025353732044\
7270457
132 29 2.2.2.2.2.3.3.5.5.13.19.23.43.67.181.661.1123.1409.3631.29569.293459.1532917.2784937.10746341.12323587.6782\
40817.83960385389.116320403133001.1357105535093947
133 11 2.3.29.419.4733.401563177.2662276961.4534166740403.373740808373213.897558513407803666357.445657944321249761\
45013684073215440137
134 12 2.2.2.2.3.20771.228337.147300841.206244761.6557750853567755279.383942665465635068312581125821527.1005201175\
7370829033540932021825161
135 21 2.3.3.3.3.19.31.37.109.271.811.1063.2377.2801.159871.185221.2583253.1527007411.125096112091.175561876921802\
311.797937984757981841530188510084780901
136 19 2.2.2.2.2.2.3.5.5.137.1201.14009.20129.94793.59361349.2767631689.29078814248401.133088039373662309.63899174\
8543082113037456009420293477766438233
137 8 2.3.2741.213721.251533.57162922399254002352124124899.65480203458464902965944539043.181428113215102554427027\
51468712154533804561
138 18 2.2.2.2.3.3.19.43.47.139.277.3083.402011881627.7396787205469.31479823396757.3421093417510114543.85019489151\
36155490673.235169662395069356312233
139 5 2.3.19739.673039.369071860325105204940905426444784144250426677655115371406716343216852089137589555456819857\
19375774106220917
140 28 2.2.2.2.2.3.5.5.5.11.29.71.113.191.281.421.911.2801.4021.4733.12128131.603926681.2127431041.13564461457.771\
92844961.102314938321.18690488255321.19584845505919961
141 9 2.3.3.19.283.5960917.13722816749522711.63681511996418550459487.28591793293072926277385447141879418320873502\
6049402141999388275408759
142 9 2.2.2.2.3.990643452963163.1351405472411521.92914860840816888117372433724419584467881183.1690021450644685567\
65676975247413756542145739
143 8 2.3.1123.293459.16148168401.528808508322667.376215890379315997311416372784691746214777.11119427897815667812\
99747693078700888402223739
144 35 2.2.2.2.2.2.2.3.3.3.5.5.13.17.19.37.43.73.181.193.409.1063.1201.42409.117307.129169.137089.169553.25726609.
51385969.635311009.13841169553.32952799801.338325042961.33232924804801
145 9 2.3.59.2801.4899841.127540261.71316922984999.277463632645667965008782910911.2822743899874399927030333062466\
2217730888039289619786090751
146 13 2.2.2.2.3.439.3067.279883.3675989.359390389.1958423494433591.7222605228105536202757606969.71676474806435043\
02058174754486698790538818746798241
147 14 2.3.3.19.29.3529.4733.1074473.13473433.11898664849.4060603391041.6106505825833677713.4247708713399033015675\
09.56427334222486513688076273080920621
148 14 2.2.2.2.2.3.5.5.149.223.2887.4805345109492315767981401.15572244900182528777225808449.6891042949305882214394\
659726647344864958515967158596120016737
149 3 2.3.1385022127101034087007743810331355039266633249933176317292277906573251633103418332277759454260526370920\
67324133850503035623601
150 22 2.2.2.2.3.3.11.19.31.43.151.191.2551.2801.29251.159871.6568801.6005492312551.31280679788951.797875190185605\
01.7021370289199888801.217648180992721729506406538251
151 7 2.3.115356256117.36076003832567.206462520503013793561.2856349001315592319937.276529023162022452344185243512\
4159094999555183731339173137659
152 20 2.2.2.2.2.2.3.5.5.419.1201.351121.44118001.700197881.4058036683.1295161807633.4534166740403.129925481108164\
9.135214434686939513.2598696228942460402343442913969
153 19 2.3.3.3.19.37.103.307.613.1063.4591.14009.44371.365773.2316281689.2767631689.10879733611.440728628040916551\
88147.795000162131334968169163150985614882079420233
154 21 2.2.2.2.3.23.29.113.463.911.1123.4733.293459.333103.10746341.258576319.724487149.6809710909.328172627775397\
03.443632323630099913.88262612316754526107621113329689
155 11 2.3.311.2801.21143.21391.21701.1622982371.9254997611.3999088279399464409.3172801518994677306295492126843582\
5250349092899077924422648569887851893731
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