478129952425125
478,129,952,425,125 is an odd composite number composed of seven prime numbers multiplied together.
478129952425125 is an odd composite number. It is composed of seven distinct prime numbers multiplied together. It has a total of two thousand, three hundred four divisors.
Prime factorization of 478129952425125:
3 × 53 × 73 × 112 × 132 × 173 × 37
(3 × 5 × 5 × 5 × 7 × 7 × 7 × 11 × 11 × 13 × 13 × 17 × 17 × 17 × 37)See below for interesting mathematical facts about the number 478129952425125 from the Numbermatics database.
Names of 478129952425125
- Cardinal: 478129952425125 can be written as Four hundred seventy-eight trillion, one hundred twenty-nine billion, nine hundred fifty-two million, four hundred twenty-five thousand, one hundred twenty-five.
Scientific notation
- Scientific notation: 4.78129952425125 × 1014
Factors of 478129952425125
Divisors of 478129952425125
- Number of divisors d(n): 2304
-
Complete list of divisors:
1 3 5 7 11 13 15 17 21 25 33 35 37 39 49 51 55 65 75 77 85 91 105 111 119 121 125 143 147 165 169 175 185 187 195 221 231 245 255 259 273 275 289 325 343 357 363 375 385 407 425 429 455 481 507 525 539 555 561 595 605 629 637 663 715 735 777 825 833 845 847 867 875 925 935 975 1001 1029 1105 1155 1183 1221 1225 1275 1295 1309 1365 1375 1443 1445 1547 1573 1617 1625 1715 1785 1813 1815 1859 1887 1911 1925 2023 2035 2057 2125 2145 2275 2405 2431 2499 2535 2541 2625 2695 2775 2805 2849 2873 2975 3003 3025 3145 3179 3185 3315 3367 3549 3575 3675 3757 3773 3885 3927 4125 4165 4225 4235 4335 4403 4459 4477 4625 4641 4675 4719 4875 4913 5005 5145 5291 5439 5525 5577 5775 5831 5915 5929 6069 6105 6125 6171 6253 6375 6475 6545 6825 6919 7007 7215 7225 7293 7735 7865 8085 8177 8281 8547 8575 8619 8925 9065 9075 9163 9295 9435 9537 9555 9625 10101 10115 10175 10285 10693 10725 10829 11011 11271 11319 11375 12025 12155 12495 12675 12691 12705 13013 13209 13377 13431 13475 13875 14025 14161 14245 14365 14399 14739 14875 15015 15125 15725 15873 15895 15925 16575 16835 17017 17493 17745 17787 17875 18375 18759 18785 18865 19425 19635 19943 20111 20449 20757 20825 21021 21125 21175 21675 22015 22253 22295 22385 23205 23375 23569 23595 24531 24565 24843 25025 25725 26299 26455 26741 27195 27489 27625 27885 28875 29155 29575 29645 30345 30525 30821 30855 31265 31339 31603 32079 32375 32487 32725 33033 34125 34391 34595 34969 35035 36075 36125 36465 37037 38073 38675 39039 39325 40425 40885 41327 41405 41503 42483 42735 42875 43095 43197 43771 44625 45325 45375 45815 46475 47175 47685 47775 48433 48841 49049 50505 50575 50875 51051 51425 53465 53625 54043 54145 55055 56355 56595 57239 57967 58201 59829 60125 60333 60775 61347 62475 63375 63455 63525 63869 64141 65065 66045 66759 66885 67155 67375 68783 70125 70707 70805 71225 71825 71995 73695 74851 75075 75803 76109 77077 78625 78897 79365 79475 79625 80223 82875 84175 85085 87465 88725 88935 89947 91091 92463 93795 93925 94017 94325 94809 97125 98175 99127 99715 100555 100793 102245 103173 103785 104125 104907 105105 105875 106301 108375 110075 111111 111265 111475 111925 116025 117623 117845 117975 119119 122655 122825 123981 124215 124509 125125 128625 131313 131495 132275 133705 135975 137445 139009 139425 139601 140777 143143 145299 145775 146523 147147 147875 148225 151725 152625 154105 154275 155771 156325 156695 158015 160395 162129 162435 163625 164983 165165 171717 171955 172975 173901 174603 174845 175175 180375 181781 182325 184093 185185 187187 190365 191607 192423 193375 195195 196625 202125 204425 206349 206635 207025 207515 212415 213675 215475 215747 215985 218855 219373 221221 224553 226625 227409 228327 229075 231231 232375 235875 238425 238875 240737 242165 244205 244783 245245 252525 252875 255255 257125 259259 267325 269841 270215 270725 273273 275275 281775 282975 286195 289289 289835 291005 297381 299145 301665 302379 303875 306397 306735 312375 317275 317625 318903 319345 320705 325325 330225 333795 334425 335775 339031 341887 343915 347633 352869 353535 354025 356125 357357 359125 359975 368475 374255 375375 378301 379015 380545 385385 394485 396825 397375 400673 401115 407407 417027 418803 420875 422331 425425 429429 437325 443625 444675 447083 449735 454597 455455 462315 467313 468975 469625 470085 471625 474045 481481 490875 494949 495635 498575 502775 503965 511225 515865 518925 523957 524535 525525 531505 532763 537251 539539 545343 550375 552279 555555 556325 557375 559625 561561 580125 588115 589225 589875 594473 595595 613275 614125 619905 621075 622545 629629 637637 647241 656565 657475 658119 661375 663663 668525 679875 687225 695045 697125 698005 702559 703885 705551 715715 722211 726495 728875 732615 734349 735735 741125 744107 756613 758625 770525 771375 777777 778855 781625 783475 790075 801975 810645 812175 823361 824915 825825 830297 833833 858585 859775 864875 867867 869505 873015 874225 875875 908905 911625 919191 920465 925925 935935 951825 958035 962115 973063 975975 985439 989417 1002001 1017093 1022125 1025661 1031745 1033175 1035125 1037575 1042899 1062075 1068375 1077375 1078735 1079925 1090397 1094275 1096865 1106105 1122765 1134903 1137045 1141635 1145375 1156155 1169311 1192125 1202019 1203685 1210825 1221025 1222221 1223915 1226225 1262625 1272467 1276275 1288651 1293853 1296295 1310309 1336625 1341249 1349205 1351075 1353625 1363791 1366365 1376375 1408875 1414875 1430975 1444443 1446445 1449175 1455025 1486905 1495725 1508325 1511895 1529099 1531985 1533675 1535611 1548547 1571871 1586375 1594515 1596725 1598289 1603525 1611753 1618617 1626625 1651125 1668975 1672125 1678875 1685159 1695155 1709435 1713481 1719575 1738165 1764345 1767675 1770125 1783419 1786785 1799875 1807117 1814813 1842375 1871275 1888887 1891505 1895075 1902725 1912911 1926925 1972425 1984125 1999591 2003365 2005575 2025023 2037035 2085135 2094015 2107677 2111655 2116653 2127125 2144779 2147145 2186625 2223375 2232321 2235415 2248675 2269839 2272985 2277275 2311575 2336565 2344875 2350425 2363153 2370225 2373217 2393209 2407405 2433431 2470083 2474745 2478175 2490891 2492875 2501499 2513875 2519825 2556125 2579325 2594625 2619785 2622675 2627625 2648107 2657525 2663815 2686255 2697695 2726715 2761395 2777775 2781625 2804711 2807805 2851849 2919189 2940575 2946125 2956317 2968251 2972365 2977975 3006003 3066375 3099525 3105375 3112725 3129581 3148145 3182179 3188185 3236205 3271191 3282825 3287375 3290595 3318315 3342625 3370367 3436125 3475225 3490025 3507933 3512795 3519425 3527755 3578575 3611055 3632475 3663075 3667699 3671745 3678675 3720535 3729341 3760757 3783065 3817401 3852625 3865953 3881559 3888885 3894275 3917375 3930927 3950375 4009875 4053225 4060875 4116805 4124575 4129125 4151485 4161311 4169165 4292925 4298875 4339335 4347525 4365075 4371125 4407403 4544525 4587297 4595955 4602325 4606833 4629625 4645641 4679675 4759125 4790175 4810575 4865315 4879875 4917913 4927195 4947085 5010005 5055477 5085465 5128305 5140443 5158725 5165875 5187875 5208749 5214495 5296291 5310375 5393675 5399625 5421351 5444439 5451985 5471375 5484325 5530525 5613825 5674515 5685225 5708175 5763527 5780775 5812079 5846555 5909761 5998773 6010095 6018425 6054125 6075069 6105125 6111105 6119575 6131125 6362335 6381375 6434337 6443255 6469265 6481475 6551545 6706245 6746025 6755375 6811441 6818955 6831825 6925919 7014007 7089459 7119651 7154875 7179627 7222215 7232225 7245875 7275125 7300293 7434525 7478625 7541625 7559475 7645495 7659925 7668375 7678055 7728149 7742735 7859355 7944321 7972575 7983625 7991445 8017625 8058765 8093085 8185177 8344875 8414133 8425795 8475775 8547175 8555547 8567405 8597875 8690825 8821725 8838375 8907269 8917095 8933925 9035585 9056971 9074065 9133267 9172163 9356375 9388743 9444435 9457525 9475375 9513625 9546537 9564555 9634625 9862125 9997955 10016825 10027875 10111101 10125115 10185175 10425675 10470075 10538385 10558275 10583265 10703693 10723895 10735725 10839829 11003097 11161605 11177075 11188023 11243375 11282271 11349195 11364925 11386375 11557875 11682825 11752125 11815765 11851125 11866085 11966045 11994367 12037025 12167155 12350415 12373725 12390875 12454455 12483933 12507495 12599125 12649819 12862421 12896625 13098925 13113375 13222209 13240535 13287625 13319075 13431275 13488475 13633575 13806975 13888875 13997137 14023555 14039025 14175161 14259245 14595945 14702875 14753739 14781585 14841255 14861825 14889875 15030015 15497625 15563625 15626247 15647905 15740725 15888873 15910895 15940925 16181025 16355955 16414125 16452975 16542071 16591575 16752463 16820089 16851835 17034017 17290581 17376125 17436237 17450125 17539665 17563975 17597125 17638775 17729283 17892875 18055275 18162375 18315375 18338495 18358725 18393375 18536749 18602675 18646705 18803785 18915325 19087005 19329765 19407795 19444425 19471375 19654635 19878287 19962943 20266125 20434323 20584025 20622875 20757425 20777757 20806555 20845825 21042021 21464625 21696675 21737625 21825375 21907067 21995501 22037015 22275253 22722625 22936485 22979775 23011625 23034165 23184447 23228205 23398375 23592569 23950875 24052875 24326575 24555531 24589565 24635975 24735425 25050025 25277385 25427325 25641525 25702215 25793625 25994683 26043745 26072475 26105387 26325299 26481455 26721807 26968375 27106755 27170913 27222195 27259925 27399801 27421625 27516489 27652625 28069125 28372575 28426125 28540875 28817635 28903875 29060395 29129177 29232775 29548805 29993865 30050475 30092125 30375345 30555525 30597875 30720989 30851821 31811675 32111079 32171685 32216275 32346325 32407375 32519487 32757725 33531225 33730125 34057205 34094775 34159125 34425391 34629595 35070035 35447295 35598255 35898135 35983101 36111075 36161125 36461243 36501465 37074037 37172625 37797375 37949457 38227475 38299625 38390275 38587263 38640745 38713675 39296775 39721605 39862875 39957225 40293825 40344689 40465425 40684553 40925885 41368327 41991411 42070665 42128975 42378875 42525483 42735875 42777735 42837025 43454125 44108625 44536345 44585475 44669625 45177925 45284855 45370325 45666335 45860815 46943715 47222175 47287625 47680087 47732685 47822775 48481433 49626213 49989775 50084125 50257389 50460267 50555505 50625575 50925875 51102051 52128375 52350375 52691925 52791375 52916325 53518465 53619475 53678625 54097043 54199145 55015485 55610247 55808025 55885375 55940115 56411355 56745975 56824625 57296239 58414125 59078825 59330425 59634861 59830225 59888829 59971835 60185125 60835775 61752075 61868625 62272275 62350883 62419665 62537475 63249095 63398797 63932869 64312105 65494625 65721201 65986503 66111045 66202675 66595375 66825759 67156375 67442375 68167875 69034875 69985685 70117775 70195125 70777707 70875805 71296225 72979725 73768695 73907925 74206275 74309125 74925851 75150075 77984049 78131235 78239525 78316161 78703625 78975897 79444365 79554475 79704625 80905125 81779775 82264875 82710355 82957875 83762315 84100445 84259175 85170085 86452905 87181185 87387531 87698325 87819875 88193875 88548733 88646415 90036947 90276375 91692475 91793625 92162967 92555463 92683745 93013375 93233525 94018925 94576625 95435025 96648825 97038975 97222125 97979959 98273175 99391435 99814715 100465937 102171615 102920125 103276173 103787125 103888785 104032775 104229125 105210105 108483375 109383729 109535335 109977505 110185075 111222111 111376265 114682425 114898875 115170825 115794497 115922235 116141025 117740623 117962845 119238119 121034067 121632875 122053659 122777655 122947825 123179875 123677125 124104981 125250125 126386925 127136625 128207625 128511075 129973415 130218725 130362375 130526935 131626495 132407275 133609035 135533775 135854565 136110975 136299625 136999005 137582445 139148009 141862875 143040261 144088175 145301975 145444299 145645885 146163875 147744025 149969325 150252375 151876725 152777625 153604945 153968507 154259105 155926771 159058375 160555395 160858425 161081375 161731625 162291129 162597435 163788625 167656125 170286025 170473875 171888717 172126955 173147975 175350175 177236475 177991275 179490675 179915505 180555375 181962781 182306215 182507325 184277093 185370185 187052649 189747285 190196391 191137375 191798607 191951375 192936315 193203725 193568375 196483875 198608025 199786125 201469125 201723445 202327125 203422765 203904239 204629425 206841635 209957055 210353325 210644875 212627415 213888675 214185125 215046923 218661157 222681725 222927375 224777553 225889625 226424275 226851625 228331675 229304075 234718575 236110875 238400435 238663425 239113875 240977737 242407165 248131065 249948875 251286945 252301335 252777525 253127875 255510255 259518259 263459625 264581625 265646199 267592325 268097375 270110841 270485215 270995725 275077425 278051235 279040125 279700575 282056775 283729875 284791871 285941513 286481195 289578289 293939877 295394125 296652125 298174305 299151125 299444145 299859175 301397811 304178875 308760375 311361375 311754415 312098325 312687375 316245475 316993985 319664345 321560525 328606005 329932515 330555225 331013375 334128795 337930879 339370031 347383491 349928425 350588875 353221869 353888535 354379025 356481125 357714357 364898625 368843475 369539625 371031375 374629255 375750375 378679301 389920245 390656175 391197625 391580805 394879485 397221825 397772375 401073673 408898875 413551775 417444027 418811575 420502225 421295875 425850425 432264525 435905925 436937655 438491625 442743665 443232075 443791579 447530083 450184735 458462375 460814835 461905521 462777315 463418725 466167625 467780313 470094625 477175125 483244125 485194875 489899795 491365875 496957175 499073575 502329685 510858075 516380865 519443925 520163875 524480957 526050525 545888343 546918645 547676675 549887525 550925375 552831279 556110555 556881325 573412125 575854125 578972485 579611175 580705125 588703115 589814225 596190595 605170335 610268295 611712717 613888275 614739125 619841131 620524905 630258629 631934625 642555375 645140769 649867075 651093625 652634675 655983471 658132475 662036375 668045175 677668875 679272825 680554875 684995025 685859713 687912225 695740045 703261559 715201305 720440875 722933211 726509875 727221495 728229425 738720125 749846625 759383625 768024725 769842535 771295525 778554777 779633855 802776975 804292125 810561479 811455645 812987175 824184361 851430125 854375613 857824539 859443585 860634775 865739875 868734867 876750875 886182375 889956375 897453375 899577525 909813905 911531075 912536625 921385465 926850925 935263245 948736425 950981955 958993035 964681575 966018625 974036063 993040125 1008617225 1013792637 1017113825 1018110093 1019521195 1023147125 1034208175 1049785275 1051766625 1063137075 1069443375 1075234615 1077779549 1093305785 1113408625 1123887765 1132121375 1136037903 1141658375 1146520375 1173592875 1192002175 1193317125 1203221019 1204888685 1212035825 1240655325 1256434725 1261506675 1263887625 1273739467 1277551275 1297591295 1328230995 1331374737 1337961625 1342590249 1350554205 1352426075 1354978625 1375387125 1390256175 1398502875 1410283875 1423959355 1429707565 1432405975 1447891445 1469699385 1490871525 1497220725 1499295875 1505328461 1506989055 1530628099 1558772075 1560491625 1573442871 1581227375 1584969925 1598321725 1607802625 1643030025 1649662575 1652776125 1670643975 1689654395 1696850155 1736917455 1749642125 1766109345 1769442675 1771895125 1788571785 1844217375 1859523393 1873146275 1890775887 1893396505 1949601225 1953280875 1957904025 1974397425 1986109125 2001590591 2005368365 2027048023 2057579139 2067758875 2087220135 2094057875 2102511125 2109784677 2129252125 2161322625 2179529625 2184688275 2213718325 2216160375 2218957895 2237650415 2250923675 2304074175 2309527605 2313886575 2317093625 2338901565 2365516153 2431684437 2449498975 2472553083 2484785875 2495367875 2511648425 2554290375 2581904325 2597219625 2622404785 2630252625 2650755107 2729441715 2734593225 2738383375 2749437625 2764156395 2780552775 2784406625 2894862425 2898055875 2922108189 2943515575 2949071125 2980952975 3025851675 3051341475 3058563585 3069441375 3099205655 3102624525 3132710581 3151293145 3225703845 3233338647 3249335375 3263173375 3279917355 3290662375 3340225875 3396364125 3424975125 3429298565 3439561125 3478700225 3516307795 3576006525 3614666055 3636107475 3641147125 3717239669 3821218401 3840123625 3849212675 3856477625 3892773885 3898169275 4013884875 4052807395 4057278225 4064935875 4120921805 4271878065 4289122695 4297217925 4303173875 4343674335 4411810403 4497887625 4515985383 4549069525 4557655375 4591884297 4606927325 4634254625 4676316225 4743682125 4754909775 4794965175 4823407875 4870180315 4922830913 5043086125 5068963185 5085569125 5090550465 5097605975 5171040875 5248926375 5315685375 5376173075 5388897745 5466528925 5619438825 5680189515 5769290527 5960010875 6004771773 6016105095 6024443425 6060179125 6081144069 6203276625 6282173625 6307533375 6368697335 6387756375 6487956475 6641154975 6656873685 6712951245 6752771025 6762130375 6818252441 6951280875 7096548459 7119796775 7148537825 7162029875 7239457225 7348496925 7454357625 7486103625 7526642305 7534945275 7544456843 7653140495 7793860375 7867214355 7924849625 7952265321 7991608625 8215150125 8248312875 8353219875 8448271975 8484250775 8684587275 8830546725 8847213375 8916176269 8942858925 9297616965 9365731375 9398131743 9453879435 9466982525 9748006125 9789520125 9871987125 10007952955 10026841825 10135240115 10287895695 10436100675 10537299227 10548923385 10714396693 10923441375 11068591625 11094789475 11151719007 11188252075 11254618375 11520370875 11547638025 11569432875 11694507825 11827580765 12158422185 12247494875 12362765415 12558242125 12909521625 13112023925 13235431209 13253775535 13647208575 13672966125 13820781975 13902763875 14011134137 14474312125 14610540945 14717577875 14768492739 14904764875 15129258375 15256707375 15292817925 15496028275 15513122625 15663552905 15756465725 16128519225 16166693235 16399586775 16558613071 17146492825 17307871581 17393501125 17581538975 17880032625 18073330275 18180537375 18586198345 19106092005 19246063375 19463869425 19490846375 20264036975 20286391125 20454757323 20604609025 21359390325 21445613475 21486089625 21718371675 22059052015 22579926915 22633370529 22745347625 22959421485 23034636625 23381581125 23774548875 23974825875 24350901575 24614154565 25344815925 25452752325 25488029875 26020677683 26748528807 26880865375 26944488725 27332644625 28097194125 28400947575 28846452635 30023858865 30080525475 30122217125 30405720345 31611897681 31843486675 32143190079 32439782375 33205774875 33284368425 33564756225 33763855125 34091262205 34459816391 35482742295 35598983875 35742689125 36197286125 36742484625 37633211525 37674726375 37722284215 38265702475 39336071775 39761326605 42033402411 42241359875 42421253875 43422936375 44152733625 44580881345 44714294625 46488084825 46990658715 47269397175 47334912625 49675839213 50039764775 50134209125 50676200575 51439478475 52180503375 52686496135 52744616925 53571983465 55473947375 55758595035 55941260375 57738190125 58472539125 59137903825 60792110925 61813827075 65560119625 66177156045 66268877675 68236042875 69103909875 70055670685 73052704725 73842463695 75000776851 76464089625 77480141375 78062033049 78317764525 78782328625 80642596125 80833466175 81997933875 82793065355 85732464125 86539357905 87907694875 90366651375 92930991725 95530460025 97319347125 98077938959 101320184875 102273786615 103023045125 103379449173 106796951625 107228067375 108591858375 110295260075 112899634575 113166852645 114797107425 115910291497 121754507875 123070772825 126724079625 127263761625 130103388415 133742644035 134722443625 142004737875 144232263175 150119294325 150402627375 152028601725 158059488405 159217433375 160715950395 166421842125 167823781125 170456311025 172299081955 177413711475 182144743781 188166057625 188611421075 191328512375 196680358875 198806633025 210167012055 222904406725 225002330553 232440424125 234953293575 236346985875 248379196065 250198823875 253381002875 257197392375 263432480675 263723084625 267859917325 278792975175 294233816877 295689519125 303960554625 309069135375 330885780225 331344388375 347730874491 350278353425 365263523625 369212318475 375003884255 390310165245 391588822625 404167330875 413965326775 432696789525 464654958625 477652300125 490389694795 511368933075 516897245865 546434231343 551476300375 564498172875 565834263225 573985537125 579551457485 615353864125 650516942075 668713220175 721161315875 750596471625 760143008625 790297442025 803579751975 852281555125 861495409775 887068557375 910723718905 943057105375 994033165125 1050835060275 1114522033625 1125011652765 1174766467875 1241895980325 1275013206467 1317162403375 1339299586625 1393964875875 1471169084385 1654428901125 1738654372455 1751391767125 1846061592375 1875019421275 1951550826225 2069826633875 2163483947625 2451948473975 2556844665375 2584486229325 2732171156715 2829171316125 2897757287425 3252584710375 3343566100875 3825039619401 3951487210125 4017898759875 4307477048875 4553618594525 5254175301375 5625058263825 6209479901625 6375066032335 7355845421925 8693271862275 9375097106375 9757754131125 12259742369875 12922431146625 13660855783575 14488786437125 19125198097005 22768092972625 28125291319125 31875330161675 36779227109625 43466359311375 68304278917875 95625990485025 159376650808375 478129952425125
- Sum of all divisors σ(n): 1205039856384000
- Sum of proper divisors (its aliquot sum) s(n): 726909903958875
- 478129952425125 is an abundant number, because the sum of its proper divisors (726909903958875) is greater than itself. Its abundance is 248779951533750
Bases of 478129952425125
- Binary: 11011001011011011010011011111100010000100101001012
- Hexadecimal: 0x1B2DB4DF884A5
- Base-36: 4PHDV8Q2SL
Squares and roots of 478129952425125
- 478129952425125 squared (4781299524251252) is 228608251406052295868731265625
- 478129952425125 cubed (4781299524251253) is 109304452368766799612204260615374879298828125
-
The
square root of 478129952425125 is 21866182.8498968927 -
The
cube root of 478129952425125 is 78195.5400910313
Scales and comparisons
How big is 478129952425125?- 478,129,952,425,125 seconds is equal to 15,203,053 years, 27 weeks, 5 days, 9 hours, 38 minutes, 45 seconds.
-
To count from 1 to 478,129,952,425,125 would take you about thirty-eight million, seven thousand, six hundred thirty-three years!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
- A cube with a volume of 478129952425125 cubic inches would be around 6516.3 feet tall.
Recreational maths with 478129952425125
- 478129952425125 backwards is 521524259921874
- The number of decimal digits it has is: 15
- The sum of 478129952425125's digits is 66
- More coming soon!
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The information we have on file for 478129952425125 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
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