Factorisations Of Cunningham Numbers C-(5,n) = 5^n - 1 Canonical Representation Of Factorisations 1. Factorisations are given from smallest to largest factor, with a period '.' separating factors. 2. Multiplicity of factors is indicated with the carat '^' in ascii tradition for the text version of the tables but not the HTML version. 3. 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. Notation Used In The Tables 1. #Fac is the number of (non distinct) prime factors in an expression. 2. A plussed #Fac means that more prime factors exist but they are unknown due to an unfactored composite in the expression. ======================================================================================================================== n #Fac Factorisation 1 2 2^2 2 4 2^3.3 3 3 2^2.31 4 6 2^4.3.13 5 4 2^2.11.71 6 7 2^3.3^2.7.31 7 3 2^2.19531 8 8 2^5.3.13.313 9 5 2^2.19.31.829 10 7 2^3.3.11.71.521 11 3 2^2.12207031 12 10 2^4.3^2.7.13.31.601 13 3 2^2.305175781 14 7 2^3.3.29.449.19531 15 7 2^2.11.31.71.181.1741 16 11 2^6.3.13.17.313.11489 17 4 2^2.409.466344409 18 11 2^3.3^3.7.19.31.829.5167 19 5 2^2.191.6271.3981071 20 11 2^4.3.11.13.41.71.521.9161 21 6 2^2.31.379.19531.519499 22 8 2^3.3.23.67.5281.12207031 23 4 2^2.8971.332207361361 24 13 2^5.3^2.7.13.31.313.601.390001 25 8 2^2.11.71.101.251.401.9384251 26 7 2^3.3.5227.38923.305175781 27 9 2^2.19.31.109.271.829.4159.31051 28 10 2^4.3.13.29.449.19531.234750601 29 5 2^2.59.35671.22125996444329 30 14 2^3.3^2.7.11.31.61.71.181.521.1741.7621 31 4 2^2.1861.625552508473588471 32 14 2^7.3.13.17.313.2593.11489.29423041 33 6 2^2.31.199.12207031.386478495679 34 8 2^3.3.409.3061.41540861.466344409 35 9 2^2.11.71.211.631.4201.19531.85280581 36 16 2^4.3^3.7.13.19.31.37.601.829.5167.6597973 37 5 2^2.149.13971969971.8737481256739 38 10 2^3.3.191.761.6271.19609.213029.3981071 39 6 2^2.31.79.305175781.608459012088799 40 15 2^5.3.11.13.41.71.241.313.521.9161.632133361 41 4 2^2.2238236249.5079304643216687969 42 16 2^3.3^2.7^2.29.31.43.127.379.449.7603.19531.519499 43 4 2^2.1644512641.172827552198815888791 44 12 2^4.3.13.23.67.89.5281.12207031.1030330938209 45 12 2^2.11.19.31.71.181.829.1171.1741.169831.297315901 46 8 2^3.3.47.8971.332207361361.42272797713043 47 3 2^2.177635683940025046467781066894531 48 17 2^6.3^2.7.13.17.31.313.601.11489.390001.152587500001 49 4 2^2.19531.227376585863531112677002031251 50 13 2^3.3.11.71.101.251.401.521.1901.9384251.50150933101 51 8 2^2.31.409.90271.317731.466344409.654652168021 52 12 2^4.3.13^2.53.5227.38923.305175781.83181652304609 53 5 2^2.5960555749.17154094481.27145365052629449 54 19 2^3.3^4.7.19.31.109.163.271.487.829.4159.5167.31051.16018507 55 10 2^2.11^2.71.103511.511831.12207031.65628751.190295821 56 13 2^5.3.13.29.313.449.19531.234750601.59509429687890001 57 7 2^2.31.191.6271.3981071.11735415506748076408140121 58 9 2^3.3.59.35671.5096867.6090817323763.22125996444329 59 4 2^2.21180247636732981.2047572230657338751575051 60 21 2^4.3^2.7.11.13.31.41.61.71.181.521.601.1741.2281.7621.9161.69566521 61 5 2^2.8419.918585913061.140194179307171898833699259 62 9 2^3.3.1303.1861.21207101.28086211607.625552508473588471 63 11 2^2.19.31.379.829.19531.280729.519499.2161279.23792163643711 64 18 2^8.3.13.17.313.641.2593.11489.29423041.75068993.241931001601 65 8 2^2.11.71.131.305175781.1034150930241911.20986207825565581 66 15 2^3.3^2.7.23.31.67.199.5281.595123.12207031.190771747.386478495679 67 7 2^2.269.1609.26399.2454335007529.604088623657497125653141 68 14 2^4.3.13.409.1973.3061.20129.45289.41540861.466344409.12447002677 69 9 2^2.31.139.6211.8971.332207361361.598761682261.8868050880709 70 16 2^3.3.11.29.71.211.449.521.631.4201.19531.15216601.85280581.4698932281 71 4 2^2.569.18607929421228039083223253529869111644362732899 72 22 2^5.3^3.7.13.19.31.37.73.313.601.829.5167.390001.543097.6597973.1503418321 73 5 2^2.4853479.5729041.9519524151770349914726200576714027279 74 10 2^3.3.149.9103.29010221.13971969971.8737481256739.45920153384867 75 16 2^2.11.31.71.101.151.181.251.401.1741.3301.1989151.9384251.49892851.183794551 76 14 2^4.3.13.191.761.6271.19609.213029.3981071.4885168129.2864226125209369 77 7 2^2.19531.12207031.527093491.8090594434231.162715052426691233701 78 14 2^3.3^2.7.31.79.3121.5227.38923.305175781.22735632934561.608459012088799 79 5 2^2.205367807127911.58523123221688392679.344120456368919234899 80 20 2^6.3.11.13.17.41.71.241.313.521.9161.11489.25601.632133361.909456847814334401 81 11 2^2.19.31.109.271.829.4159.4861.31051.11419697846380955982026777206637491 82 10 2^3.3.83.43543.221401.2238236249.9472026608675509.5079304643216687969 83 5 2^2.20515111.1431185706701868962383741.88040095945103834627376781 84 22 2^4.3^2.7^2.13.29.31.43.127.379.449.601.2521.7603.19531.519499.234750601.24587411156281 85 9 2^2.11.71.409.1531.466344409.34563155350221618511.8198241112969626815581 86 10 2^3.3.1549.9547.1644512641.7866608083.1628744948329.172827552198815888791 87 9 2^2.31.59.5569.6961.35671.22125996444329.28870194250662203210437116612769 88 15 2^5.3.13.23.67.89.313.5281.12207031.1030330938209.9080418348371887359375390001 89 8 2^2.179.9807089.14597959.834019001.8157179360521.231669654363683130095909 90 22 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 2^4.3.13.47.8971.332207361361.42272797713043.5465713352000770660547109750601 93 9 2^2.31^2.1861.148429.878851.625552508473588471.172974812463239310024750410929 94 8 2^3.3.2069.15888756269.3602372010909260861.177635683940025046467781066894531 95 11 2^2.11.71.191.2851.6271.3981071.4113691.1245576402371959291.11600321878916922053491 96 22 2^7.3^2.7.13.17.31.97.313.601.2593.11489.390001.29423041.152587500001.240031591394168814433 97 5 2^2.389.264811.153159805660301568024613754993807288151489686913246436306439 98 11 2^3.3.29.449.19531.49105547.1866013003.2481357870461.227376585863531112677002031251 99 12 2^2.19.31.199.829.143551.1731511.12207031.386478495679.22542470482159.153560376376050799 100 20 2^4.3.11.13.41.71.101.251.401.521.1901.9161.239201.9384251.424256201.50150933101.89620825374601 101 5 2^2.5937018283241.3434487311396589821473854121.483593153887747265029536907421 102 18 2^3.3^2.7.31.103.409.3061.8467.90271.317731.528667.41540861.466344409.60119016343.654652168021 103 6 2^2.3709.28429.59117897713198738371603984809.39546955636451768643571562540114219 104 17 2^5.3.13^2.53.313.5227.38923.51169.305175781.537181587281.83181652304609.129044008326199409 105 17 2^2.11.31.71.181.211.379.631.1741.4201.19531.519499.1736701.85280581.119461537021.21226783250214361 106 10 2^3.3.107.5960555749.17154094481.28838378869.27145365052629449.599659003321309822423087 107 7 2^2.6421.5486016363791.35411885288978941.172163150940018661.717433171088016374418821 108 25 2^4.3^4.7.13.19.31.37.109.163.271.487.601.829.4159.5167.31051.6597973.16018507.14551915228363037109375001 109 6 2^2.1091.1007161.1528399.2293559892404294400692399012979688850301546383400890423075969 110 17 2^3.3.11^2.23.67.71.521.5281.103511.511831.12207031.65628751.190295821.10910444855403996246103496881 111 8 2^2.31.149.3109.13971969971.8737481256739.54928520946880307112306785731407655242899973469 112 20 2^6.3.13.17.29.113.313.337.449.11489.19531.234750601.2520917617.59509429687890001.37007700327977836913 113 10 2^2.2939.6329.129499.308491.304247586761.2084303944451.620216264269531.8237123176890810696379 114 16 2^3.3^2.7.31.191.229.761.6271.19609.213029.3981071.75649382555448580095589.11735415506748076408140121 115 14 2^2.11.71.461.691.8971.689081.2855911.29028071.824480311.17223586571.332207361361.100062970166640331 116 12 2^4.3.13.59.35671.5096867.6090817323763.22125996444329.1334402673828313149547634216455312875601 117 10 2^2.19.31.79.829.223963741.305175781.608459012088799.937938782117311845318745554345005320717861 118 10 2^3.3.827.5242462229.3237765225301.2059647179472887.21180247636732981.2047572230657338751575051 119 10 2^2.239.409.1429.4999.19531.466344409.7497182681291140146079.788868477693980100643230089490226571 120 27 2^5.3^2.7.11.13.31.41.61.71.181.241.313.521.601.1741.2281.7621.9161.390001.69566521.632133361.2332031717285\ 1318360001 121 6 2^2.12101.486179.12207031.13094322377956920597215509541997540493466263550896158313340716530769 122 11 2^3.3.367.8419.9029.918585913061.15571335384347.14008364639128540436401.140194179307171898833699259 123 10 2^2.31.739.960139.1785961.2238236249.9025583299.5079304643216687969.5832474690386022428273180864659 124 13 2^4.3.13.1303.1861.21207101.28086211607.625552508473588471.8124604717965111529.102651353523520067851969 125 13 2^2.11.71.101.251.401.3597751.9384251.28707251.4032808198751.767186663625251.24687045214139234043375683501 126 27 2^3.3^3.7^2.19.29.31.43.127.379.449.829.883.5167.7603.19531.280729.406729.519499.2161279.24132781.169241650\ 3.23792163643711 127 3 2^2.14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531 128 22 2^9.3.13.17.313.641.769.2593.11489.29423041.75068993.241931001601.3666499598977.961329567826437419512256640\ 01 129 8 2^2.31.18471511.1644512641.172827552198815888791.43955934961951833386625799.51349797354047205216257689 130 16 2^3.3.11.71.131.521.5227.18461.38923.305175781.15188886343541.1034150930241911.15199221608544481.2098620782\ 5565581 131 7 2^2.2621.23928199.34720241.16815642611861.250805666433416532678429525124977090318975999001796354124089 132 22 2^4.3^2.7.13.23.31.67.89.199.601.1453.5281.595123.12207031.190771747.386478495679.1030330938209.65093871834\ 17404924784917 133 12 2^2.191.6271.9311.19531.65171.281429.3981071.3257947519.152317058321.29090007107767075239783794592001366542\ 871 134 10 2^3.3.269.1609.26399.2454335007529.604088623657497125653141.11293772630057337854244300009061892827351888021 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 2^5.3.13.137.313.409.1973.3061.20129.45289.623017.41540861.466344409.12447002677.938894988049.1361753880209. 4959636586609 137 8 2^2.20551.603349.48102071.121719631478506669.7851027307722624763151.251755028858658462627642052961230751431 138 18 2^3.3^2.7.31.47.139.6211.8971.66163549.253592389.332207361361.598761682261.8868050880709.42272797713043.403\ 316413944121 139 5 2^2.21521602057721.6789441546024769741462601111.24550591546653776667941845268908441565415743319193209001 140 23 2^4.3.11.13.29.41.71.211.281.449.521.631.4201.9161.19531.15216601.85280581.234750601.4698932281.13148832195\ 720299503896018648521 141 5 2^2.31.177635683940025046467781066894531.16286160623917663079467944573580125726889931566772922392814390121 142 9 2^3.3.569.4261.5747338499820296170481.288231038713838413442281.18607929421228039083223253529869111644362732\ 899 143 7 2^2.12207031.305175781.24615836446631.53130566763791958299.460183952753824357170225842292658707895690816315\ 909 144 28 2^6.3^3.7.13.17.19.31.37.73.313.601.829.1297.5167.11489.390001.543097.6597973.1503418321.152587500001.27391\ 77855667309845605995807633 145 10 2^2.11.59.71.35671.1461311.22125996444329.2158365113981511371558358567665231.488654500355218081336311051543\ 759628081 146 10 2^3.3.4853479.5729041.63554310563.777612767772190289.3570677866897550288203.9519524151770349914726200576714\ 027279 147 11 2^2.31.379.19531.519499.24556351.5071357999.2035895040229.203906616815994386234329833781.227376585863531112\ 677002031251 148 15 2^4.3.13.149.9103.9769.40849.29010221.13971969971.8737481256739.45920153384867.5102410950961837579307333639\ 18820917976121 149 3 2^2.35032461608120426773093239582247903282006548546912894293926707097244777067146515037165954709053039550781 150 29 2^3.3^2.7.11.31.61.71.101.151.181.251.401.521.1741.1901.3301.7621.118801.1989151.9384251.20775901.24665701. 49892851.149439601.183794551.50150933101 151 8 2^2.1175989.2237519.389439261961.12799319666401.2843809592323334251225153490677489.234808350683195588203155\ 40345862729 152 19 2^5.3.13.191.313.457.761.6271.19609.213029.3981071.4885168129.2864226125209369.21363981507860375753.2165447\ 2202540732126905077281 153 14 2^2.19.31.409.829.4591.90271.317731.26481241.466344409.654652168021.360143672909416579.28596369159272276742\ 1088565601855215949 154 16 2^3.3.23.29.67.449.5281.19531.12207031.527093491.20828886541.8090594434231.162715052426691233701.4997006151\ 6036179615325895945741 155 13 2^2.11.71.311.1861.11161.257611.5624951.31473312961.625552508473588471.21783999170235219053011.174583335852\ 767865379025002452121 156 24 2^4.3^2.7.13^2.31.53.79.157.601.3121.5227.38923.8684521.305175781.4056854881.22735632934561.83181652304609. 608459012088799.667929705480493 157 7 2^2.32029.5129819.2107089779.8616314452100494153901371725720169.4587548699755676969742331799602074877905422\ 766102260881 158 11 2^3.3.18251687.7897663181.511465533067.205367807127911.58523123221688392679.344120456368919234899.373990955\ 25167136010188229 159 8 2^2.31.5960555749.17154094481.1775305720077559.27145365052629449.223967815154673247771933930986251232800839\ 3109037131818519 160 26 2^7.3.11.13.17.41.71.241.313.521.2593.9161.11489.25601.29423041.131349761.632133361.167597261761.9094568478\ 14334401.24625444126052524088217281 161 6 2^2.8971.19531.332207361361.1469386746678216989397901405448901778556342705433890596470719221994542710855107\ 30718993828121 162 25 2^3.3^5.7.19.31.109.163.271.487.829.1783.4159.4861.5023.5167.31051.16018507.2066067271380136212224701233463. 11419697846380955982026777206637491 163 8 2^2.4599209.40100609.675775181.6582151087844246659.102556399583828574447011133455059.2541462766396986870745\ 222882425433052891 164 16 2^4.3.13.83.43543.193357.221401.6355001.2238236249.1148205782281.9472026608675509.5079304643216687969.56373\ 078952722628530598981268453 165 19 2^2.11^2.31.71.181.199.331.1741.2311.103511.511831.12207031.65628751.190295821.386478495679.986716511563526\ 7180926131.13585095374919980427914311 166 10 2^3.3.167.20515111.1431185706701868962383741.4029666108840585686296627.88040095945103834627376781.256078770\ 2841639767474730913969 167 5 2^2.18371.53441.1361204447657665492151527789766442232666296870678835610403733269298091781079248108419798324\ 52900690680385721 168 29 2^5.3^2.7^2.13.29.31.43.127.313.379.449.601.2521.6553.7603.19531.90217.390001.519499.234750601.245874111562\ 81.59509429687890001.6019022585035590658668001 169 6 2^2.13859.305175781.784646826705980283039372085276899721.10067335901765297228504234600727488967589607275738\ 01229970212800434559 170 18 2^3.3.11.71.409.521.1531.3061.41540861.75752681.247515241.466344409.504156421.34563155350221618511.68795069\ 664507129341.8198241112969626815581 171 11 2^2.19^2.31.191.829.6271.3981071.11735415506748076408140121.16088618804380305453087171930478326510082728281\ 0075925369403839312088918579 172 15 2^4.3.13.173.1549.9547.1644512641.7866608083.1628744948329.2171388367013.172827552198815888791.132331554743\ 163541916284364878460504933118649 173 6 2^2.1039.3461.1708272343265311.3399198310201876309603479571994210993424343866291299248077248995481719050792\ 54114627192212342747249 174 18 2^3.3^2.7.31.59.349.5569.6961.35671.5096867.6090817323763.22125996444329.210390487070809.225003581339659919\ 72941.28870194250662203210437116612769 175 22 2^2.11.71.101.211.251.401.631.4201.12601.19531.28001.50051.200201.8894201.9384251.22661801.85280581.1657309\ 151.38105263380318401.16711449148651875290388101 176 22 2^6.3.13.17.23.67.89.313.5281.11489.13729.929281.12207031.1030330938209.71225159567951317923809.91029014606\ 406186465761.9080418348371887359375390001 177 8 2^2.31.198241.21180247636732981.2047572230657338751575051.340863370420651571324835367261.143656408334378524\ 08745701299256005364862514221 178 13 2^3.3.179.9807089.14597959.834019001.8157179360521.39387996609449861.56522267529181963.23166965436368313009\ 5909.12094715786677995586454978647 179 8 2^2.359.3581.75539.17315029.100894073362387242965129.192314444462213728810818160511138304152610629589418566\ 747969452950500442408719960811 180 34 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