Factorisations Of Cunningham/Mersenne Numbers C-(2,n) = M(n) = 2^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 1 1 2 1 3 3 1 7 4 2 3.5 5 1 31 6 3 3^2.7 7 1 127 8 3 3.5.17 9 2 7.73 10 3 3.11.31 11 2 23.89 12 5 3^2.5.7.13 13 1 8191 14 3 3.43.127 15 3 7.31.151 16 4 3.5.17.257 17 1 131071 18 6 3^3.7.19.73 19 1 524287 20 6 3.5^2.11.31.41 21 4 7^2.127.337 22 4 3.23.89.683 23 2 47.178481 24 7 3^2.5.7.13.17.241 25 3 31.601.1801 26 3 3.2731.8191 27 3 7.73.262657 28 6 3.5.29.43.113.127 29 3 233.1103.2089 30 7 3^2.7.11.31.151.331 31 1 2147483647 32 5 3.5.17.257.65537 33 4 7.23.89.599479 34 3 3.43691.131071 35 4 31.71.127.122921 36 10 3^3.5.7.13.19.37.73.109 37 2 223.616318177 38 3 3.174763.524287 39 4 7.79.8191.121369 40 8 3.5^2.11.17.31.41.61681 41 2 13367.164511353 42 8 3^2.7^2.43.127.337.5419 43 3 431.9719.2099863 44 7 3.5.23.89.397.683.2113 45 6 7.31.73.151.631.23311 46 4 3.47.178481.2796203 47 3 2351.4513.13264529 48 10 3^2.5.7.13.17.97.241.257.673 49 2 127.4432676798593 50 7 3.11.31.251.601.1801.4051 51 5 7.103.2143.11119.131071 52 7 3.5.53.157.1613.2731.8191 53 3 6361.69431.20394401 54 9 3^4.7.19.73.87211.262657 55 6 23.31.89.881.3191.201961 56 8 3.5.17.29.43.113.127.15790321 57 4 7.32377.524287.1212847 58 6 3.59.233.1103.2089.3033169 59 2 179951.3203431780337 60 13 3^2.5^2.7.11.13.31.41.61.151.331.1321 61 1 2305843009213693951 62 3 3.715827883.2147483647 63 7 7^2.73.127.337.92737.649657 64 7 3.5.17.257.641.65537.6700417 65 3 31.8191.145295143558111 66 9 3^2.7.23.67.89.683.20857.599479 67 2 193707721.761838257287 68 7 3.5.137.953.26317.43691.131071 69 4 7.47.178481.10052678938039 70 9 3.11.31.43.71.127.281.86171.122921 71 3 228479.48544121.212885833 72 14 3^3.5.7.13.17.19.37.73.109.241.433.38737 73 3 439.2298041.9361973132609 74 5 3.223.1777.25781083.616318177 75 7 7.31.151.601.1801.100801.10567201 76 7 3.5.229.457.174763.524287.525313 77 4 23.89.127.581283643249112959 78 8 3^2.7.79.2731.8191.121369.22366891 79 3 2687.202029703.1113491139767 80 10 3.5^2.11.17.31.41.257.61681.4278255361 81 6 7.73.2593.71119.262657.97685839 82 5 3.83.13367.164511353.8831418697 83 2 167.57912614113275649087721 84 14 3^2.5.7^2.13.29.43.113.127.337.1429.5419.14449 85 3 31.131071.9520972806333758431 86 5 3.431.9719.2099863.2932031007403 87 6 7.233.1103.2089.4177.9857737155463 88 10 3.5.17.23.89.353.397.683.2113.2931542417 89 1 618970019642690137449562111 90 13 3^3.7.11.19.31.73.151.331.631.23311.18837001 91 5 127.911.8191.112901153.23140471537 92 9 3.5.47.277.1013.1657.30269.178481.2796203 93 3 7.2147483647.658812288653553079 94 6 3.283.2351.4513.13264529.165768537521 95 5 31.191.524287.420778751.30327152671 96 13 3^2.5.7.13.17.97.193.241.257.673.65537.22253377 97 2 11447.13842607235828485645766393 98 5 3.43.127.4363953127297.4432676798593 99 8 7.23.73.89.199.153649.599479.33057806959 100 14 3.5^3.11.31.41.101.251.601.1801.4051.8101.268501 101 2 7432339208719.341117531003194129 102 11 3^2.7.103.307.2143.2857.6529.11119.43691.131071 103 2 2550183799.3976656429941438590393 104 10 3.5.17.53.157.1613.2731.8191.858001.308761441 105 11 7^2.31.71.127.151.337.29191.106681.122921.152041 106 6 3.107.6361.69431.20394401.28059810762433 107 1 162259276829213363391578010288127 108 15 3^4.5.7.13.19.37.73.109.87211.246241.262657.279073 109 2 745988807.870035986098720987332873 110 12 3.11^2.23.31.89.683.881.2971.3191.201961.48912491 111 6 7.223.321679.26295457.319020217.616318177 112 11 3.5.17.29.43.113.127.257.5153.15790321.54410972897 113 5 3391.23279.65993.1868569.1066818132868207 114 9 3^2.7.571.32377.174763.524287.1212847.160465489 115 6 31.47.14951.178481.4036961.2646507710984041 116 9 3.5.59.233.1103.2089.3033169.107367629.536903681 117 9 7.73.79.937.6553.8191.86113.121369.7830118297 118 6 3.2833.37171.179951.1824726041.3203431780337 119 6 127.239.20231.131071.62983048367.131105292137 120 17 3^2.5^2.7.11.13.17.31.41.61.151.241.331.1321.61681.4562284561 121 4 23.89.727.1786393878363164227858270210279 122 3 3.768614336404564651.2305843009213693951 123 5 7.13367.3887047.164511353.177722253954175633 124 8 3.5.5581.8681.49477.384773.715827883.2147483647 125 5 31.601.1801.269089806001.4710883168879506001 126 14 3^3.7^2.19.43.73.127.337.5419.92737.649657.77158673929 127 1 170141183460469231731687303715884105727 128 9 3.5.17.257.641.65537.274177.6700417.67280421310721 129 5 7.431.9719.2099863.11053036065049294753459639 130 9 3.11.31.131.2731.8191.409891.7623851.145295143558111 131 2 263.10350794431055162386718619237468234569 132 15 3^2.5.7.13.23.67.89.397.683.2113.20857.312709.599479.4327489 133 3 127.524287.163537220852725398851434325720959 134 5 3.7327657.193707721.761838257287.6713103182899 135 10 7.31.73.151.271.631.23311.262657.348031.49971617830801 136 11 3.5.17^2.137.953.26317.43691.131071.354689.2879347902817 137 2 32032215596496435569.5439042183600204290159 138 9 3^2.7.47.139.178481.2796203.168749965921.10052678938039 139 2 5625767248687.123876132205208335762278423601 140 16 3.5^2.11.29.31.41.43.71.113.127.281.86171.122921.7416361.47392381 141 6 7.2351.4513.13264529.4375578271.646675035253258729 142 6 3.228479.48544121.56409643.212885833.13952598148481 143 6 23.89.8191.724153.158822951431.5782172113400990737 144 19 3^3.5.7.13.17.19.37.73.97.109.241.257.433.577.673.38737.487824887233 145 5 31.233.1103.2089.2679895157783862814690027494144991 146 6 3.439.1753.2298041.9361973132609.1795918038741070627 147 7 7^3.127.337.4432676798593.2741672362528725535068727 148 10 3.5.149.223.593.1777.25781083.184481113.231769777.616318177 149 2 86656268566282183151.8235109336690846723986161 150 14 3^2.7.11.31.151.251.331.601.1801.4051.100801.10567201.1133836730401 151 5 18121.55871.165799.2332951.7289088383388253664437433 152 11 3.5.17.229.457.1217.148961.174763.524287.525313.24517014940753 153 8 7.73.103.919.2143.11119.131071.75582488424179347083438319 154 10 3.23.43.89.127.617.683.78233.35532364099.581283643249112959 155 8 31^2.311.11471.73471.2147483647.4649919401.18158209813151 156 18 3^2.5.7.13^2.53.79.157.313.1249.1613.2731.3121.8191.21841.121369.22366891 157 4 852133201.60726444167.1654058017289.2134387368610417 158 5 3.2687.202029703.1113491139767.201487636602438195784363 159 8 7.6361.6679.69431.13960201.20394401.540701761.229890275929 160 13 3.5^2.11.17.31.41.257.61681.65537.414721.4278255361.44479210368001 161 7 47.127.1289.178481.3188767.45076044553.14808607715315782481 162 16 3^5.7.19.73.163.2593.71119.87211.135433.262657.97685839.272010961 163 5 150287.704161.110211473.27669118297.36230454570129675721 164 10 3.5.83.10169.13367.181549.12112549.43249589.164511353.8831418697 165 10 7.23.31.89.151.881.3191.201961.599479.2048568835297380486760231 166 8 3.167.499.1163.2657.155377.13455809771.57912614113275649087721 167 2 2349023.79638304766856507377778616296087448490695649 168 19 3^2.5.7^2.13.17.29.43.113.127.241.337.1429.3361.5419.14449.15790321.88959882481 169 4 4057.8191.6740339310641.3340762283952395329506327023033 170 7 3.11.31.43691.131071.9520972806333758431.26831423036065352611 171 7 7.73.32377.524287.1212847.93507247.3042645634792541312037847 172 10 3.5.173.431.9719.101653.500177.2099863.1759217765581.2932031007403 173 4 730753.1505447.70084436712553223.155285743288572277679887 174 11 3^2.7.59.233.1103.2089.4177.3033169.9857737155463.96076791871613611 175 9 31.71.127.601.1801.39551.122921.60816001.535347624791488552837151 176 14 3.5.17.23.89.257.353.397.683.2113.229153.119782433.2931542417.43872038849 177 6 7.179951.184081.27989941729.3203431780337.9213624084535989031 178 5 3.179.62020897.18584774046020617.618970019642690137449562111 179 3 359.1433.1489459109360039866456940197095433721664951999121 180 24 3^3.5^2.7.11.13.19.31.37.41.61.73.109.151.181.331.631.1321.23311.54001.18837001.29247661 181 4 43441.1164193.7648337.7923871097285295625344647665764672671 182 11 3.43.127.911.2731.8191.224771.1210483.112901153.23140471537.25829691707 183 5 7.367.55633.2305843009213693951.37201708625305146303973352041 184 11 3.5.17.47.277.1013.1657.30269.178481.2796203.291280009243618888211558641 185 5 31.223.616318177.1587855697992791.7248808599285760001152755641 186 8 3^2.7.529510939.715827883.2147483647.2903110321.658812288653553079 187 5 23.89.131071.707983.1032670816743843860998850056278950666491537 188 10 3.5.283.2351.3761.4513.13264529.7484047069.165768537521.140737471578113 189 10 7^2.73.127.337.92737.262657.649657.1560007.207617485544258392970753527 190 10 3.11.31.191.2281.174763.524287.420778751.30327152671.3011347479614249131 191 5 383.7068569257.39940132241.332584516519201.87274497124602996457 192 16 3^2.5.7.13.17.97.193.241.257.641.673.65537.6700417.22253377.18446744069414584321 193 3 13821503.61654440233248340616559.14732265321145317331353282383 194 7 3.971.1553.11447.31817.1100876018364883721.13842607235828485645766393 195 8 7.31.79.151.8191.121369.145295143558111.134304196845099262572814573351 196 11 3.5.29.43.113.127.197.19707683773.4363953127297.4432676798593.4981857697937 197 2 7487.26828803997912886929710867041891989490486893845712448833 198 17 3^3.7.19.23.67.73.89.199.683.5347.20857.153649.599479.33057806959.242099935645987 199 2 164504919713.4884164093883941177660049098586324302977543600799 200 20 3.5^3.11.17.31.41.101.251.401.601.1801.4051.8101.61681.268501.340801.2787601.3173389601 201 6 7.1609.22111.193707721.761838257287.87449423397425857942678833145441 202 4 3.7432339208719.341117531003194129.845100400152152934331135470251 203 7 127.233.1103.2089.136417.121793911.11348055580883272011090856053175361113 204 20 3^2.5.7.13.103.137.307.409.953.2143.2857.3061.6529.11119.13669.26317.43691.131071.1326700741 205 6 31.13367.2940521.164511353.70171342151.3655725065508797181674078959681 206 5 3.2550183799.415141630193.8142767081771726171.3976656429941438590393 207 9 7.47.73.79903.178481.634569679.2232578641663.10052678938039.42166482463639 208 12 3.5.17.53.157.257.1613.2731.8191.858001.308761441.78919881726271091143763623681 209 6 23.89.524287.94803416684681.1512348937147247.5346950541323960232319657 210 22 3^2.7^2.11.31.43.71.127.151.211.281.331.337.5419.29191.86171.106681.122921.152041.664441.1564921 211 3 15193.60272956433838849161.3593875704495823757388199894268773153439 212 10 3.5.107.6361.69431.15358129.20394401.586477649.28059810762433.1801439824104653 213 7 7.66457.228479.48544121.212885833.2849881972114740679.4205268574191396793 214 4 3.643.84115747449047881488635567801.162259276829213363391578010288127 215 8 31.431.1721.9719.2099863.731516431.514851898711.297927289744047764444862191 216 21 3^4.5.7.13.17.19.37.73.109.241.433.38737.87211.246241.262657.279073.33975937.138991501037953 217 6 127.5209.62497.2147483647.6268703933840364033151.378428804431424484082633 218 5 3.104124649.745988807.870035986098720987332873.2077756847362348863128179 219 7 7.439.3943.2298041.9361973132609.671165898617413417.4815314615204347717321 220 19 3.5^2.11^2.23.31.41.89.397.683.881.2113.2971.3191.201961.48912491.415878438361.3630105520141 221 4 1327.8191.131071.2365454398418399772605086209214363458552839866247069233 222 13 3^2.7.223.1777.3331.17539.321679.25781083.26295457.319020217.616318177.107775231312019 223 6 18287.196687.1466449.2916841.1469495262398780123809.596242599987116128415063 224 16 3.5.17.29.43.113.127.257.449.2689.5153.65537.15790321.183076097.54410972897.358429848460993 225 14 7.31.73.151.601.631.1801.23311.100801.115201.617401.10567201.1348206751.13861369826299351 226 10 3.227.3391.23279.48817.65993.1868569.636190001.1066818132868207.491003369344660409 227 2 26986333437777017.7992177738205979626491506950867720953545660121688631 228 17 3^2.5.7.13.229.457.571.32377.131101.160969.174763.524287.525313.1212847.160465489.275415303169 229 4 1504073.20492753.59833457464970183.467795120187583723534280000348743236593 230 12 3.11.31.47.691.14951.178481.2796203.4036961.1884103651.345767385170491.2646507710984041 231 10 7^2.23.89.127.337.463.599479.581283643249112959.4982397651178256151338302204762057 232 12 3.5.17.59.233.1103.2089.59393.3033169.107367629.536903681.82280195167144119832390568177 233 4 1399.135607.622577.116868129879077600270344856324766260085066532853492178431 234 16 3^3.7.19.73.79.937.2731.6553.8191.86113.121369.22366891.7830118297.5302306226370307681801 235 7 31.2351.4513.13264529.2391314881.72296287361.73202300395158005845473537146974751 236 13 3.5.1181.2833.3541.37171.157649.174877.179951.5521693.1824726041.104399276341.3203431780337 237 8 7.1423.2687.49297.202029703.1113491139767.23728823512345609279.31357373417090093431 238 11 3.43.127.239.20231.43691.131071.823679683.62983048367.131105292137.143162553165560959297 239 6 479.1913.5737.176383.134000609.7110008717824458123105014279253754096863768062879 240 23 3^2.5^2.7.11.13.17.31.41.61.97.151.241.257.331.673.1321.61681.394783681.4278255361.4562284561.46908728641 241 2 22000409.160619474372352289412737508720216839225805656328990879953332340439 242 8 3.23.89.683.727.117371.11054184582797800455736061107.1786393878363164227858270210279 243 10 7.73.487.2593.71119.262657.97685839.16753783618801.192971705688577.3712990163251158343 244 9 3.5.733.1709.3456749.368140581013.667055378149.768614336404564651.2305843009213693951 245 7 31.71.127.1471.122921.4432676798593.252359902034571016856214298851708529738525821631 246 12 3^2.7.83.739.13367.165313.3887047.164511353.8831418697.13194317913029593.177722253954175633 247 6 8191.15809.524287.6459570124697.402004106269663.1282816117617265060453496956212169 248 12 3.5.17.5581.8681.49477.290657.384773.715827883.2147483647.3770202641.1141629180401976895873 249 5 7.167.1621324657.57912614113275649087721.8241594690167137359552274418432855740327 250 11 3.11.31.251.601.1801.4051.229668251.269089806001.4710883168879506001.5519485418336288303251 251 5 503.54217.178230287214063289511.61676882198695257501367.12070396178249893039969681 252 24 3^3.5.7^2.13.19.29.37.43.73.109.113.127.337.1429.5419.14449.92737.649657.40388473189.77158673929.1187500983\ 49 253 8 23^2.47.89.178481.4103188409.199957736328435366769577.44667711762797798403039426178361 254 3 3.56713727820156410577229101238628035243.170141183460469231731687303715884105727 255 11 7.31.103.151.2143.11119.106591.131071.949111.9520972806333758431.5702451577639775545838643151 256 11 3.5.17.257.641.65537.274177.6700417.67280421310721.59649589127497217.5704689200685129054721 257 3 535006138814359.1155685395246619182673033.374550598501810936581776630096313181393 258 11 3^2.7.431.1033.9719.2099863.1591582393.2932031007403.15686603697451.11053036065049294753459639 259 5 127.223.616318177.2499285769.21234370960880098806027750185552713706866970578963970119 260 19 3.5^2.11.31.41.53.131.157.521.1613.2731.8191.51481.409891.7623851.34110701.108140989558681.145295143558111 261 8 7.73.233.1103.2089.4177.9857737155463.328017025014102923449988663752960080886511412965881 262 6 3.263.1049.4744297.182331128681207781784391813611.10350794431055162386718619237468234569 263 4 23671.13572264529177.120226360536848498024035943.383725126655170964501315730676446647 264 22 3^2.5.7.13.17.23.67.89.241.353.397.683.2113.7393.20857.312709.599479.4327489.1761345169.2931542417.98618273\ 953 265 7 31.6361.69431.20394401.29324808311.197748738449921.36614110124735294634435619027766763481 266 8 3.43.127.4523.174763.524287.106788290443848295284382097033.163537220852725398851434325720959 267 5 7.78903841.28753302853087.618970019642690137449562111.24124332437713924084267316537353 268 11 3.5.269.7327657.15152453.42875177.193707721.2559066073.761838257287.6713103182899.9739278030221 269 2 13822297.68625988504811774259364670661552948915363901845035416371912463477873783063 270 22 3^4.7.11.19.31.73.151.271.331.631.811.15121.23311.87211.262657.348031.18837001.49971617830801.3858386426478\ 91 271 2 15242475217.248927757868131890277330541567820045256364273970773286542188386932989391 272 15 3.5.17^2.137.257.953.26317.43691.131071.354689.383521.2368179743873.2879347902817.373200722470799764577 273 13 7^2.79.127.337.911.8191.121369.108749551.112901153.23140471537.4093204977277417.86977595801949844993 274 7 3.1097.15619.32127963626435681.105498212027592977.32032215596496435569.5439042183600204290159 275 10 23.31.89.601.881.1801.3191.201961.382027665134363932751.4074891477354886815033308087379995347151 276 17 3^2.5.7.13.47.139.277.1013.1657.30269.178481.2796203.168749965921.5415624023749.10052678938039.703343928238\ 09 277 3 1121297.31133636305610209482201109050392404721.6955979459776540052280934851589652278783 278 5 3.4506937.5625767248687.123876132205208335762278423601.51542639524661795300074174250365699 279 9 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