This post is for a dear friend. Many years ago I shared with him a mathematical puzzle that we both enjoyed. Later I posted What’s the next base-ten non-pandigital factorial number after 41!? on Math Stack Exchange.
Here’s the gist of the problem.
A “factorial number” is any element of the image of the factorial function. A pandigital number (of a given base) is an integer whose digits include at least one of each digit. Naturally, a pandigital factorial number is a number which is both a factorial number and a pandigital number. Is there a largest pandigital factorial number? Or is it a countably-infinite set that can be put into a bijection with the naturals?
At the request of my friend I have posted a table with three columns. The first is simply non-negative integers 0-to-1000, labelled n. The second column last_200_is_pandigital is an indicator variable for whether the last 200 digits contain at least one of each digit. The third column, last_200, is the last 200 digits of the factorial number (regardless of whether the entire number is pandigital). Maybe this will reveal some interesting patterns.
The table is wide enough that scrolling left-to-right will be necessary… Sorry!
| n | last_200_is_pandigital | last_200 |
|---|---|---|
| 0 | False | 1 |
| 1 | False | 1 |
| 2 | False | 2 |
| 3 | False | 6 |
| 4 | False | 24 |
| 5 | False | 120 |
| 6 | False | 720 |
| 7 | False | 5040 |
| 8 | False | 40320 |
| 9 | False | 362880 |
| 10 | False | 3628800 |
| 11 | False | 39916800 |
| 12 | False | 479001600 |
| 13 | False | 6227020800 |
| 14 | False | 87178291200 |
| 15 | False | 1307674368000 |
| 16 | False | 20922789888000 |
| 17 | False | 355687428096000 |
| 18 | False | 6402373705728000 |
| 19 | False | 121645100408832000 |
| 20 | False | 2432902008176640000 |
| 21 | False | 51090942171709440000 |
| 22 | False | 1124000727777607680000 |
| 23 | True | 25852016738884976640000 |
| 24 | False | 620448401733239439360000 |
| 25 | False | 15511210043330985984000000 |
| 26 | False | 403291461126605635584000000 |
| 27 | True | 10888869450418352160768000000 |
| 28 | False | 304888344611713860501504000000 |
| 29 | False | 8841761993739701954543616000000 |
| 30 | False | 265252859812191058636308480000000 |
| 31 | True | 8222838654177922817725562880000000 |
| 32 | False | 263130836933693530167218012160000000 |
| 33 | True | 8683317618811886495518194401280000000 |
| 34 | True | 295232799039604140847618609643520000000 |
| 35 | True | 10333147966386144929666651337523200000000 |
| 36 | True | 371993326789901217467999448150835200000000 |
| 37 | True | 13763753091226345046315979581580902400000000 |
| 38 | False | 523022617466601111760007224100074291200000000 |
| 39 | True | 20397882081197443358640281739902897356800000000 |
| 40 | True | 815915283247897734345611269596115894272000000000 |
| 41 | False | 33452526613163807108170062053440751665152000000000 |
| 42 | True | 1405006117752879898543142606244511569936384000000000 |
| 43 | True | 60415263063373835637355132068513997507264512000000000 |
| 44 | True | 2658271574788448768043625811014615890319638528000000000 |
| 45 | True | 119622220865480194561963161495657715064383733760000000000 |
| 46 | True | 5502622159812088949850305428800254892961651752960000000000 |
| 47 | True | 258623241511168180642964355153611979969197632389120000000000 |
| 48 | True | 12413915592536072670862289047373375038521486354677760000000000 |
| 49 | True | 608281864034267560872252163321295376887552831379210240000000000 |
| 50 | True | 30414093201713378043612608166064768844377641568960512000000000000 |
| 51 | True | 1551118753287382280224243016469303211063259720016986112000000000000 |
| 52 | True | 80658175170943878571660636856403766975289505440883277824000000000000 |
| 53 | True | 4274883284060025564298013753389399649690343788366813724672000000000000 |
| 54 | True | 230843697339241380472092742683027581083278564571807941132288000000000000 |
| 55 | True | 12696403353658275925965100847566516959580321051449436762275840000000000000 |
| 56 | True | 710998587804863451854045647463724949736497978881168458687447040000000000000 |
| 57 | True | 40526919504877216755680601905432322134980384796226602145184481280000000000000 |
| 58 | True | 2350561331282878571829474910515074683828862318181142924420699914240000000000000 |
| 59 | True | 138683118545689835737939019720389406345902876772687432540821294940160000000000000 |
| 60 | True | 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 |
| 61 | True | 507580213877224798800856812176625227226004528988036003099405939480985600000000000000 |
| 62 | True | 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000 |
| 63 | True | 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000 |
| 64 | True | 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 |
| 65 | True | 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000 |
| 66 | True | 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000 |
| 67 | True | 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000 |
| 68 | True | 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000 |
| 69 | True | 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 |
| 70 | True | 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 |
| 71 | True | 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000 |
| 72 | True | 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000 |
| 73 | True | 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000 |
| 74 | True | 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000 |
| 75 | True | 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 |
| 76 | True | 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000 |
| 77 | True | 145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000 |
| 78 | True | 11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000 |
| 79 | True | 894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000 |
| 80 | True | 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 |
| 81 | True | 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000 |
| 82 | True | 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000 |
| 83 | True | 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000 |
| 84 | True | 3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000 |
| 85 | True | 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000 |
| 86 | True | 24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000 |
| 87 | True | 2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000 |
| 88 | True | 185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000 |
| 89 | True | 16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000 |
| 90 | True | 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000 |
| 91 | True | 135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000 |
| 92 | True | 12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000 |
| 93 | True | 1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000 |
| 94 | True | 108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000 |
| 95 | True | 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000 |
| 96 | True | 991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000 |
| 97 | True | 96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000 |
| 98 | True | 9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000 |
| 99 | True | 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000 |
| 100 | True | 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 |
| 101 | True | 9425947759838359420851623124482936749562312794702543768327889353416977599316221476503087861591808346911623490003549599583369706302603264000000000000000000000000 |
| 102 | True | 961446671503512660926865558697259548455355905059659464369444714048531715130254590603314961882364451384985595980362059157503710042865532928000000000000000000000000 |
| 103 | True | 99029007164861804075467152545817733490901658221144924830052805546998766658416222832141441073883538492653516385977292093222882134415149891584000000000000000000000000 |
| 104 | True | 10299016745145627623848583864765044283053772454999072182325491776887871732475287174542709871683888003235965704141638377695179741979175588724736000000000000000000000000 |
| 105 | True | 1081396758240290900504101305800329649720646107774902579144176636573226531909905153326984536526808240339776398934872029657993872907813436816097280000000000000000000000000 |
| 106 | True | 114628056373470835453434738414834942870388487424139673389282723476762012382449946252660360871841673476016298287096435143747350528228224302506311680000000000000000000000000 |
| 107 | True | 12265202031961379393517517010387338887131568154382945052653251412013535324922144249034658613287059061933743916719318560380966506520420000368175349760000000000000000000000000 |
| 108 | True | 1324641819451828974499891837121832599810209360673358065686551152497461815091591578895743130235002378688844343005686404521144382704205360039762937774080000000000000000000000000 |
| 109 | True | 144385958320249358220488210246279753379312820313396029159834075622223337844983482099636001195615259277084033387619818092804737714758384244334160217374720000000000000000000000000 |
| 110 | True | 15882455415227429404253703127090772871724410234473563207581748318444567162948183030959960131517678520479243672638179990208521148623422266876757623911219200000000000000000000000000 |
| 111 | True | 1762952551090244663872161047107075788761409536026565516041574063347346955087248316436555574598462315773196047662837978913145847497199871623320096254145331200000000000000000000000000 |
| 112 | True | 197450685722107402353682037275992488341277868034975337796656295094902858969771811440894224355027779366597957338237853638272334919686385621811850780464277094400000000000000000000000000 |
| 113 | True | 22311927486598136465966070212187151182564399087952213171022161345724023063584214692821047352118139068425569179220877461124773845924561575264739138192463311667200000000000000000000000000 |
| 114 | True | 2543559733472187557120132004189335234812341496026552301496526393412538629248600474981599398141467853800514886431180030568224218435400019580180261753940817530060800000000000000000000000000 |
| 115 | True | 292509369349301569068815180481773552003419272043053514672100535242441942363589054622883930786268803187059211939585703515345785120071002251720730101703194015956992000000000000000000000000000 |
| 116 | True | 33931086844518982011982560935885732032396635556994207701963662088123265314176330336254535971207181169698868584991941607780111073928236261199604691797570505851011072000000000000000000000000000 |
| 117 | True | 3969937160808720895401959629498630647790406360168322301129748464310422041758630649341780708631240196854767624444057168110272995649603642560353748940315749184568295424000000000000000000000000000 |
| 118 | True | 468452584975429065657431236280838416439267950499862031533310318788629800927518416622330123618486343228862579684398745837012213486653229822121742374957258403779058860032000000000000000000000000000 |
| 119 | True | 55745857612076058813234317117419771556272886109483581752463927935846946310374691578057284710599874844234646982443450754604453404911734348832487342619913750049708004343808000000000000000000000000000 |
| 120 | True | 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000 |
| 121 | True | 09429852527344373968162284544935082997082306309701607045776233628497660426640521713391773997910182738287074185078904956856663439318382745047716214841147650721760223072092160000000000000000000000000000 |
| 122 | True | 50442008336013624115798714482080125644041369783596059584700502676714572050143649033796427745042294071023050579626404736512939596842694895821378210620013388054747214795243520000000000000000000000000000 |
| 123 | True | 04367025329675766243241881295855454217088483382315328918161829235892362167668831156960612640202170735835221294047782591091570411651472186029519906261646730733907419814952960000000000000000000000000000 |
| 124 | True | 41511140879795014161993280686076322918971939407100785852066825250652908790935063463115967385069171243567440461925041295354731044782551067660468376444194611004520057054167040000000000000000000000000000 |
| 125 | True | 88892609974376770249160085759540364871492425887598231508353156331613598866882932889495923133646405445930057740630161919341380597818883457558547055524326375565007131770880000000000000000000000000000000 |
| 126 | True | 00468856771473051394170805702085973808045661837377170052497697783313457227249544076486314839447086187187275319400401837013955325179315652376928996065123321190898603130880000000000000000000000000000000 |
| 127 | True | 59544809977077527059692324164918673621799053346900596667207618480809067860692097713761984609779945772783965563851033300772326297773087851869982500270661791244122597621760000000000000000000000000000000 |
| 128 | True | 21735677065923463640617493109590223590278828403276373402575165543560686168588507361534030051833058916347592172932262498857766114955245039357760034644709279247692495585280000000000000000000000000000000 |
| 129 | True | 03902341504126809639656611137138843145968864022652168932196355119328515747917449637889876686464600208839390308261862352651828829226610077151044469167497022952331930501120000000000000000000000000000000 |
| 130 | True | 07304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000 |
| 131 | True | 56875815279568163352087665474498775849754305766436915303927682164623187034167333264599970492141556534816949699515865660644961729169613882287309922474300878212776434073600000000000000000000000000000000 |
| 132 | True | 07607616902997562475571842633838412167568361169672820118454045730260688510087990927196104962685462595837360336094267205134948250389032461924909766607715924086489297715200000000000000000000000000000000 |
| 133 | True | 11813048098675809251055070300508818286592035566485075754388082124671571841702793317081960037166525246368924700537538282948117301741317436012998958826217903503076596121600000000000000000000000000000000 |
| 134 | True | 82948445222558439641379420268181650403332765909000151088003004705990626788174304488982644980314383013435909872030129915047718433336536425741860482713199069412263880294400000000000000000000000000000000 |
| 135 | True | 98040105045389351586221736204522804449923397715020396880405635308734616403531106012657072342441706813847832724067538531441988500432417475151165166281874370655623839744000000000000000000000000000000000 |
| 136 | True | 33454286172951815726156123815101405189582089242773975735166401987907830880230417721361838572072126683305250473185240276110436058808776620558462614334914409164842205184000000000000000000000000000000000 |
| 137 | True | 83237205694398754483388962668892510972746226260034675717797072343372830591567227826571884373881355612819314826377917827129740056802397016509378163883274055583382110208000000000000000000000000000000000 |
| 138 | True | 86734385827028118707676848307166514238979223884785249055995983385450621636277440066920043595627074569065446040152660143904127838730788278294186615891819670506731208704000000000000000000000000000000000 |
| 139 | True | 56079629956908500367081914696145479218112119985149618783441690577636407442564169301886059792163365100096999581219760002673769583579570682891939608962934200435638009856000000000000000000000000000000000 |
| 140 | True | 51148193967190051391468057460367090535696797920946629681836680869097041958983702264048370902871114013579941370766400374327741701139895604871545254810788060989321379840000000000000000000000000000000000 |
| 141 | True | 11895349373797246196996101911759765533248506853474785138972002542682916216702019230820297304827075914771733278062452780211579860725280286887880928321116599494314557440000000000000000000000000000000000 |
| 142 | True | 89139611079208959973446471469886705721287973193419489734024361060974102771686730776482217285444779897586125484868294790044340222989800738079091821598557128192667156480000000000000000000000000000000000 |
| 143 | True | 46964384326881276202845420193798918144180166658987031965483631719296696351202501036957071818603525354815944336166154976340651887541505545310130488593669331551403376640000000000000000000000000000000000 |
| 144 | True | 62871343070903773209740507907044212761943998894132603029642967578724274573160149321818341878907651093495984407926316593053871805976798524658790357488383743402086236160000000000000000000000000000000000 |
| 145 | True | 16344745281047115412373646521410850481879839649227439298230298915019813108221651663659572441609408556917739149315905992811411866635786075524601835815642793302504243200000000000000000000000000000000000 |
| 146 | True | 86332811032878850206552392125984170354456588787206137541623641592892713800361142894297576474973649309989915800122274950466132528824767026591868029083847822165619507200000000000000000000000000000000000 |
| 147 | True | 90923221833190980363201642519673042105118551719302218618675314155228928653088005461743741821126448568517622617974417718521481737240752909004600275325629858346067558400000000000000000000000000000000000 |
| 148 | True | 56636831312265093753843092911610231557545654456728355563946494973881440657024808338073789526714388140608147460213822341179297111631430532680840748193219035217998643200000000000000000000000000000000000 |
| 149 | True | 38887865527498969322620843829924502074302514052524979028027751108334657896696442372994639480443832950613971571859528835715269633083149369445271480789636247481797836800000000000000000000000000000000000 |
| 150 | True | 33179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000 |
| 151 | True | 10154197851655157362112747789971982951943289690774984828562603780001360174419748328584232052816331406456102618328128950857189333333217935399039885261005462721003520000000000000000000000000000000000000 |
| 152 | True | 43438073451583919041137664075741408695380032997797693941515774560206746511801745944803272028082373781327597985875600530292778666649126180654062559672830333592535040000000000000000000000000000000000000 |
| 153 | True | 46025238092339613294062603588435530393145048663047173051913507711632216305667129554900620296603188543122491838966881134795135997316305640071571629943041039657861120000000000000000000000000000000000000 |
| 154 | True | 87886666220300447285640952619071680544337494109264649994680187591361311072737951454695525676891035640863743200899694758450943586711068571022031011228320107310612480000000000000000000000000000000000000 |
| 155 | True | 22433264146569329274347655956110484372311586936020749175429076661003216274382475477806479918110524333880196139452687559896255940215628508414806740389616633144934400000000000000000000000000000000000000 |
| 156 | True | 99589206864815366798234329153235562080607562019236871366935959116501738803666174537810867225241796085310597754619259343815926673638047312709851500780194770609766400000000000000000000000000000000000000 |
| 157 | True | 35505477776012587322789677057983246655387237020188804608945581290772992175589402436306154362961985393763847475223716979100487761173428095446685622490578985733324800000000000000000000000000000000000000 |
| 158 | True | 09865488609988797000768975161352971551183449189831128213401843942132763743125584936372389347993692214687901085347282697877066265401639080576328353511479745865318400000000000000000000000000000000000000 |
| 159 | True | 68612688988218723122267050655122476638168421183149385930893186799109435156968004883209906330997062135376272570217948962453536198860613811636208208325279592585625600000000000000000000000000000000000000 |
| 160 | True | 78030238114995699562728104819596262106947389303901748942909887857509625114880781313585012959529941660203611234871833992565791817698209861793313332044734813700096000000000000000000000000000000000000000 |
| 161 | True | 62868336514307629599224875954998199218529677928181579808491945059049643495805791487187086484320607292781408814365272803092482649411787748723446459202305005715456000000000000000000000000000000000000000 |
| 162 | True | 84670515317835995074429904709708273401807824365415928975695099566042246320538220924308010459938381430588227927174194100982189204709615293198326390773410925903872000000000000000000000000000000000000000 |
| 163 | True | 01293996807267197132074467682448564494675371562796423038301229264886150247730010662205704969956173185881152129393638460096840367667292791327201696065980922331136000000000000000000000000000000000000000 |
| 164 | True | 12215476391820329660212699921564577126760936298613378281401599441328640627721748601735615072812402484508949220556707455881820297436017777661078154820871262306304000000000000000000000000000000000000000 |
| 165 | True | 15553604650354393935095487058155225915554489271207416431263907819225703574088519286376487014046409943976621391856730220500349076942933314077895545443758280540160000000000000000000000000000000000000000 |
| 166 | True | 81898371958829393225850851653767501982045219020431127589808697991466793298694201538496844331704050700119151048217216603057946772526930136930660543663874569666560000000000000000000000000000000000000000 |
| 167 | True | 77028117124508668717092226179172831001551576411998307498052564574954480881931656928973003394576466919898225052275172710677111011997332867420310791867053134315520000000000000000000000000000000000000000 |
| 168 | True | 40723676917456344471493998101035608260664837215715659672830848592352788164518364067464570288846442542901808782229015393754650015551921726612213033664926565007360000000000000000000000000000000000000000 |
| 169 | True | 82301399050122215682485679075017796052357489455946484708413412107621199803603527401512378815048789750405684196703601544535852628274771797464002689372589486243840000000000000000000000000000000000000000 |
| 170 | True | 91237838520776666022565442753025328900773207510902400430280058295603966612599658257104398558294257568966313439612262571094946806711205568880457193340212661452800000000000000000000000000000000000000000 |
| 171 | True | 01670387052809889858690710767331242032218484364310473577889968548278290754541561964852153468318044293239598173696899657235903947616152278558180061176365108428800000000000000000000000000000000000000000 |
| 172 | True | 87306573083301055694802251980973629541579310661401455397074590303866009781148657954570396550703618437210885875866741044575478989978191912006970522334798649753600000000000000000000000000000000000000000 |
| 173 | True | 04037143411082635200789592708437910693220744422451783693904122568819692138717826140678603271725989637483256524946200711557865266227200777205900363920166407372800000000000000000000000000000000000000000 |
| 174 | True | 02462953528378524937389131268196460620409529506610362739317326974626432136901748478076969280322196922086635340638923811068556323532935233826663322108954882867200000000000000000000000000000000000000000 |
| 175 | True | 31016867466241864043097971934380608571667663656813479380532220559625623957805983663469624056384461365161184611811666936997356618263665919666081369067104501760000000000000000000000000000000000000000000 |
| 176 | True | 58968674058568071585243060450987108613508803599172370973670818494109816573853124770653833923665200268368491678853380911534764814405201861230320955810392309760000000000000000000000000000000000000000000 |
| 177 | True | 37455308366548670588021699824718224591058237053509662339734873457437533572003084405728604488740447501223027157048421341653372149720729437766809178439438827520000000000000000000000000000000000000000000 |
| 178 | True | 67044889245663364667862568799843977208366195524719896472807475423880975816549024219691598995799655217698833954618998814300242650289839922492033762220111298560000000000000000000000000000000000000000000 |
| 179 | True | 01035174973742275547399815172071920297548998924861468632538100874694671162275335324796220248138283968091277876800787759743434401881346126074043437399922442240000000000000000000000000000000000000000000 |
| 180 | True | 86331495273609598531966730972945653558819806475064353856858157445040809209560358463319644664891114256430017824141796753818192338642302693327818731986039603200000000000000000000000000000000000000000000 |
| 181 | True | 26000644523337334285978306103163294146384971986648048091326497552386466930424881860855684345291680413833226169665212441092813294256787492335190489473168179200000000000000000000000000000000000000000000 |
| 182 | True | 32117303247394840048051710775719534642064901569944752621422554534336981337328498675734550843085835317647162879068664278892019554735323605004669084116608614400000000000000000000000000000000000000000000 |
| 183 | True | 77466494273255728793463071956674839497876987299889729720327479783667584731115257659422804284707863129430806869565563037239578516564219715854442393339376435200000000000000000000000000000000000000000000 |
| 184 | True | 53834946279054097997205240028170467609365663179710268540256280194835590525207409333795988386246815815268464000063598852082447047816427717217400374445264076800000000000000000000000000000000000000000000 |
| 185 | True | 59465061625008129482969405211536507732647688246399679947411836044584247163370726752257851455660925824665840011765787635252703846039127685219069272373854208000000000000000000000000000000000000000000000 |
| 186 | True | 60501462251512083832309369345790438272470013830340470218601504292669972386955175919960370752932203387846242188436500157002915363277749450746884661536882688000000000000000000000000000000000000000000000 |
| 187 | True | 13773441032759676641852067662811956951892586273667930878481302729284836360617897032589330798322033527247289237625529359545172932939147289667431707397062656000000000000000000000000000000000000000000000 |
| 188 | True | 89406914158819208668188720608647906955806219449571005154484913105549235796164642126794190084542303122490376673599519594492511392559690457477160990647779328000000000000000000000000000000000000000000000 |
| 189 | True | 97906776016830438287668195034454414647375475968919974197648576948805565475117361964101925978495290150681191310309203359084653193781496463183427232430292992000000000000000000000000000000000000000000000 |
| 190 | True | 02287443197783274656957056546338783001340434094795097553229620273057440272298773179365935914105128629426348958748638226084106818484328004851174161755668480000000000000000000000000000000000000000000000 |
| 191 | True | 36901650776605459478797800350707553256022912105863632666857472153971092009065677258893759594079568220432651120989901182064402330506648926574264895332679680000000000000000000000000000000000000000000000 |
| 192 | True | 85116949108248219929177667335850225156399124325817472036634653562449665740610033707601842063277098323069015230061026956365247457276593902258859903874498560000000000000000000000000000000000000000000000 |
| 193 | True | 27571177891906446331289795819093455185030994882772103070488137552785487937736505567155518212479976352319939401778202578492759254382623135959961447778222080000000000000000000000000000000000000000000000 |
| 194 | True | 48808511029850588270220388904130305896013007257787995674698685240384659920882080028170533221115412350068243944971300227595295350228888376232520868975083520000000000000000000000000000000000000000000000 |
| 195 | True | 17659650820864712692975836305409649722536415268659156566243621875008684572005605493253978117505408263307569269403544381082593294633233365341569450141286400000000000000000000000000000000000000000000000 |
| 196 | True | 61291560889483687823263915860291345617137392657194686983749887501702176113098676677779711031060019608283576803094698692188285748113739606947612227692134400000000000000000000000000000000000000000000000 |
| 197 | True | 74437495228286501182991424477395086576066353467353335798727837835328694280439305522603073118823862831864630209655642361092292378406702568679608855350476800000000000000000000000000000000000000000000000 |
| 198 | True | 38624055200727234232302046524227142061137986535960488148111891395081467526982493475408477527124840709196781511817187496273890924527108598562553359394406400000000000000000000000000000000000000000000000 |
| 199 | True | 86186984944719612228107258321201270166459320656137141474266387621212037869516201606287027897843301130159520851620311758504293980894611113948118519486873600000000000000000000000000000000000000000000000 |
| 200 | True | 37396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000 |
| 201 | True | 16794777728411569911784512291060691664690376713087265508782372723922354551304572738521493300705432412738235136532691872618031963366780714364483372318720000000000000000000000000000000000000000000000000 |
| 202 | True | 92545101139137122180471482794259716267456096043627632774039290232315619363523693181341646742497347373123497579603758268842456600089704301625641208381440000000000000000000000000000000000000000000000000 |
| 203 | True | 86655531244835802635711007234722402293587496856409453129975917160070730795309715812354288726961516744070008659562928575018689818209973230005165301432320000000000000000000000000000000000000000000000000 |
| 204 | True | 77728373946503737685045475883370067891849358707528438515087100654429082243182025720274900300149415790281766550837429303812722914834538921053721492193280000000000000000000000000000000000000000000000000 |
| 205 | True | 34316659033266225434322556090863917829118535043329895592855634157961859852315272656354561530630237007762142921673007281608197541080478816012905899622400000000000000000000000000000000000000000000000000 |
| 206 | True | 69231760852842439470446554717967072798418218925958492128260636540143129576946167209039675309828823599001441864639500011288693462578636098658615322214400000000000000000000000000000000000000000000000000 |
| 207 | True | 30974496538384970382436826619184069272571317673407870549951763809627822427856612271212789134566484993298465980376502336759546753777672422333371698380800000000000000000000000000000000000000000000000000 |
| 208 | True | 42695279984073839546859936790286408694834076068837074389966872402587064994175352412260139989828878606080923918312486045985724785755863845341313263206400000000000000000000000000000000000000000000000000 |
| 209 | True | 23313516671432465293726789169859417220321898386948547503076332140696583782648654162369257874235628670913098927309583611016480222975543676334472010137600000000000000000000000000000000000000000000000000 |
| 210 | True | 95838501000817711682625725670477616267598661259194975646029749546282594356217374097544153589482020891750774735012558313460846824864172030239122128896000000000000000000000000000000000000000000000000000 |
| 211 | True | 21923711172537165034028116470777032463317525690139861312277154265627409161865934581816407380706408159413469087649804140238680046340298380454769197056000000000000000000000000000000000000000000000000000 |
| 212 | True | 47826768577878987213960691804730882223315446309650598202756704313010742315578131345078364709758529795655446581758477730600169824143256656411069775872000000000000000000000000000000000000000000000000000 |
| 213 | True | 87101707088224276573627354407677913566190063955577417187178018671288113218141976501691683178566846474610121914555756617836172542513667815557862260736000000000000000000000000000000000000000000000000000 |
| 214 | True | 39765316879995186756253843243073503164673686493567278056095995655656228682382971362020200213305145566566089714931916216940924097924912529382523797504000000000000000000000000000000000000000000000000000 |
| 215 | True | 49543129198965152594576297260803180404842596116964782060639065966089166712338842834343045860606296811709288710361986642298681053856193817242616463360000000000000000000000000000000000000000000000000000 |
| 216 | True | 01315906976472960428480208333486967446000761264392925098038248675260009865190052218097905890960111329206361438189114736515107632937864524405156085760000000000000000000000000000000000000000000000000000 |
| 217 | True | 85551813894632412980205208366671935782165194373264746274299962531422140746241331327245578338344158437780432087037897823778356347516601795918870609920000000000000000000000000000000000000000000000000000 |
| 218 | True | 50295429029866029684735423934482000512012373371714687797391831850026682680610229339536077759026539436134194974261725583681683758619191510313792962560000000000000000000000000000000000000000000000000000 |
| 219 | True | 14698957540660500957057841651558112130709768405516627628811175155843507053640225358401029226812136513388699363317902826288743137602940758720658800640000000000000000000000000000000000000000000000000000 |
| 220 | True | 33770658945310210552725163342784668756149049213658078338458534285571551800849578848226429898670032945513859929938621783523490272646966918544936140800000000000000000000000000000000000000000000000000000 |
| 221 | True | 63315626913556532152261098755411795108939876218435312799336077111312947987756925458041007606077280958563044516435414158691350254979688998430887116800000000000000000000000000000000000000000000000000000 |
| 222 | True | 56069174809550137801963923701418514184652520492639441452609118711474453282037451685103688549156372800995882648661943229479756605490957651656939929600000000000000000000000000000000000000000000000000000 |
| 223 | True | 03425982529680729837954985416328663177512069858595443931833472658803081894351725778122546461871134622081830651613340173985723024483556319497604300800000000000000000000000000000000000000000000000000000 |
| 224 | True | 67420086648483483701916733257620551762703648325379440730697875571890344334786574299450407459134155346330065961388198972801957484316615567463363379200000000000000000000000000000000000000000000000000000 |
| 225 | True | 69519495908783832931264982964624146608320873210374164407022003675327475326979217376341678305184952924264841312344768880440433971238502679256760320000000000000000000000000000000000000000000000000000000 |
| 226 | True | 11406075385146242465886150005057133480517345544561155986972830624009423897303127053219296971799360883854136589917766979538077499901605512027832320000000000000000000000000000000000000000000000000000000 |
| 227 | True | 89179112428197039756156051147969300077437438615382409042832551650139224687809841080780412598454920634889005911333104355143592477664451230317936640000000000000000000000000000000000000000000000000000000 |
| 228 | True | 32837633628925064403579661737000417655736004307189261765821776231743228820643766417934072447721904754693347783947792972739084907494880512489553920000000000000000000000000000000000000000000000000000000 |
| 229 | True | 19818101023839748419742537773095643163544986346340944373186757069199399927422509706902590528316188824776642524044590757250443816327637360107847680000000000000000000000000000000000000000000000000000000 |
| 230 | True | 58163235483142136540783687811997927615346859658417205832954125915861983307177232587595821512723429698627780530255874167602077755356592824804966400000000000000000000000000000000000000000000000000000000 |
| 231 | True | 35707396605833540921031884571521279145124581094374547412403086564118143957940727734634769439112260383017302489106932716079961487372942529947238400000000000000000000000000000000000000000000000000000000 |
| 232 | True | 84116012553381493679397220592936761668902813894894999677516082875409398242248834435266509874044408860014177472808390130551065070522666947759308800000000000000000000000000000000000000000000000000000000 |
| 233 | True | 99030924937888027299552398154265468854355637510534924861247309970389790443978423417096800652347264383303351164354900418398161431781398827918950400000000000000000000000000000000000000000000000000000000 |
| 234 | True | 73236435465798388095261168098119711919219177465172417531870533071210963890951079600651352649259865692984172459046697905169775036847325733034393600000000000000000000000000000000000000000000000000000000 |
| 235 | True | 10562334462621202386374503058132301016506704315518119989575271734576514373503706153067872576068437851280527875974007714897133659121547263082496000000000000000000000000000000000000000000000000000000000 |
| 236 | True | 92710933178603763184382721719223039895582218462276317539764129360057392146874652124017927952151332902204578729865820715723543552685154087469056000000000000000000000000000000000000000000000000000000000 |
| 237 | True | 72491163329091874698705047455860455252985775559487256924098658333601938809292553392248924659865897822485158978199509626479821986381518730166272000000000000000000000000000000000000000000000000000000000 |
| 238 | True | 52896872323866178291801294494788350210614583157967147935480683397261436611627707355244069048083681751467836811483291102197632758801457779572736000000000000000000000000000000000000000000000000000000000 |
| 239 | True | 42352485404016611740509384254415700336885374754148356579883331945483350179022057903332502491999938600812997944506573425234229353548409317883904000000000000000000000000000000000000000000000000000000000 |
| 240 | True | 64596496963986817722252221059768080852489940995605579171999666916004042965293896799800598079985264195119506681577622056215044851618236292136960000000000000000000000000000000000000000000000000000000000 |
| 241 | True | 67755768320823071062785275404107485450075779940944580451919726756974354635829128751944137276448671023801110260206915547825809239994946405007360000000000000000000000000000000000000000000000000000000000 |
| 242 | True | 96895933639183197194036647794011478918338745708588469364573875187793821870649157970481220900578387759868682970073562573845836078777030011781120000000000000000000000000000000000000000000000000000000000 |
| 243 | True | 45711874321516918150905413944789377156315207186998055591451670633898714567745386826936678840548225648089961727875705444538167142818292862812160000000000000000000000000000000000000000000000000000000000 |
| 244 | True | 53697334450128028820921002528608026140910553627525564314207634671286354529874385772549637093767058133950661601672128467312782847663458526167040000000000000000000000000000000000000000000000000000000000 |
| 245 | True | 55846940281367061125645619508966404523085638743763256980870494465156859819224514274661087972929242817912092409671474491631797677547338910924800000000000000000000000000000000000000000000000000000000000 |
| 246 | True | 38347309216297036908822399205735512679067130965761217294141638428587515529230511566627641340593733206374732779182724941422228676645372087500800000000000000000000000000000000000000000000000000000000000 |
| 247 | True | 71785376425368116479132603816671631729581348543020671652984691861116335719936356957027411126652101974558996458133060531290483131406905612697600000000000000000000000000000000000000000000000000000000000 |
| 248 | True | 02773353491292886824885746534564668936174438669126569940203581556851258544216525342797959409721289690631121616999011760039816588912591949004800000000000000000000000000000000000000000000000000000000000 |
| 249 | True | 90565019331928819396550887106602565107435228612515915110691807655963377509914810356691893020601132967149282632753928249914330639235395302195200000000000000000000000000000000000000000000000000000000000 |
| 250 | True | 41254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000 |
| 251 | True | 54963078533417133568165939310960491560595435373673195910930411701938747154349882416287042721093688617485205308997682124247612021055212748800000000000000000000000000000000000000000000000000000000000000 |
| 252 | True | 50695790421117659177816706362043873270049714165645369554463748888564282896170368904334765715609531606271737867415895310398229305913612697600000000000000000000000000000000000000000000000000000000000000 |
| 253 | True | 26034976542767771987626709597099937322577683908278497279328468806763572731103332796695726049211496386749680456221513530752014396144012492800000000000000000000000000000000000000000000000000000000000000 |
| 254 | True | 12884041863014084857184237663384079934731712702738308949431076917947473700246530360714416499720082234418835880264436811011656620579173171200000000000000000000000000000000000000000000000000000000000000 |
| 255 | True | 85430675068591638581980604162940383356586739198268782104924614076605793562865241982176207428620969776803149467431386807972438247689158656000000000000000000000000000000000000000000000000000000000000000 |
| 256 | True | 70252817559459476987034665712738139286205234756808218860701203611083152093501947437109101726968262861606263662435022840944191408424615936000000000000000000000000000000000000000000000000000000000000000 |
| 257 | True | 54974112781085585667909088173701796554745332499712247200209328048370088030000491337039143830843555432809761245800870122657191965126295552000000000000000000000000000000000000000000000000000000000000000 |
| 258 | True | 83321097520081102320544748815063511124295784925759777654006636479482711740126764956099108357637301664918401416624491645555527002584252416000000000000000000000000000000000000000000000000000000000000000 |
| 259 | True | 80164257701005501021089943101449381192608295771782412387718848186022340692832123629669064628061131213865966905743336198881493669321375744000000000000000000000000000000000000000000000000000000000000000 |
| 260 | True | 42707002261430265483385206376839110078156900663427220806900528365808580136352143713956803295894115605151395493267411709188354023557693440000000000000000000000000000000000000000000000000000000000000000 |
| 261 | True | 46527590233299291163538864355007730398951073154504630601037903476039415587909509342725660228364172944514223742794456098160400148557987840000000000000000000000000000000000000000000000000000000000000000 |
| 262 | True | 90228641124414284847182461012025364525181166480213217471930710722326884032291447794122979831413311462726620612147497718024838922192814080000000000000000000000000000000000000000000000000000000000000000 |
| 263 | True | 30132615720956914808987246162670870122646784296076195117776919971970500492650769854343695661700914697101220994791899840532636536710103040000000000000000000000000000000000000000000000000000000000000000 |
| 264 | True | 55010550332625509572632986945109712378751054164115511093106872600212130059803241546735654689041480034722342625061557900616045691467202560000000000000000000000000000000000000000000000000000000000000000 |
| 265 | True | 77795838145760036747741540454073780369029353490610439673321239056214465847859009884948492595992209201420795641312843663252108238808678400000000000000000000000000000000000000000000000000000000000000000 |
| 266 | True | 93692946772169774899249760783625578161808028502376953103449588953047915530496629396299030533927647577931640589216414425060791523108454400000000000000000000000000000000000000000000000000000000000000000 |
| 267 | True | 16016788169329898099686129228029369202743610134646478621040250463793446642600048811841152558681903307748037320782651491231336669957324800000000000000000000000000000000000000000000000000000000000000000 |
| 268 | True | 92499229380412690715882633111870946335287516085256270438787124296643700216813081573428885726750086476474001969750599649998227548563046400000000000000000000000000000000000000000000000000000000000000000 |
| 269 | True | 82292703331013802572428307093284564192341826933936748033736435797155358322718943252370260495773262171506529862911305849523210563459481600000000000000000000000000000000000000000000000000000000000000000 |
| 270 | True | 19029899373726694555642915186832331932293272162921969108837665231946747134114678139970333858780786306763062986052579371266852134060032000000000000000000000000000000000000000000000000000000000000000000 |
| 271 | True | 57102730279934224579230015631561953651476756151853628495007277857568473345077775931960475729593089132790069220249009613316928330268672000000000000000000000000000000000000000000000000000000000000000000 |
| 272 | True | 31942636142109085550564251784851393201677673304186950641979577258624749861155053493249398449320244118898827907730614822204505833078784000000000000000000000000000000000000000000000000000000000000000000 |
| 273 | True | 20339666795780355304040737264430344058004812043037525260424591604556712095329603657085776664426644459380018810457846461830092430508032000000000000000000000000000000000000000000000000000000000000000000 |
| 274 | True | 73068702043817353307162010453914271893318499792281921356338099648539114120311402041502806052900581870125154065449930541445325959200768000000000000000000000000000000000000000000000000000000000000000000 |
| 275 | True | 93893062049772159469552874826424770662587442877528372992977403348256383085635561413271664547660014284417367998730898897464638780211200000000000000000000000000000000000000000000000000000000000000000000 |
| 276 | True | 14485125737116013596593452093236702874134234197830946061763324118761731635414950062979415154163942499193567649728095700240303338291200000000000000000000000000000000000000000000000000000000000000000000 |
| 277 | True | 12379829181135766256386229826566696135182872799172059108440780896999663009941167445297997703412072276618238974682508966564024706662400000000000000000000000000000000000000000000000000000000000000000000 |
| 278 | True | 41592512355743019275371891785541525580838638169832432146537089365906316763644549792843361548556092899870434961737492704798868452147200000000000000000000000000000000000000000000000000000000000000000000 |
| 279 | True | 04310947252302377828757808166085637053980049383248568883847933087862377056829392203297872047149919063851354324760464638884298149068800000000000000000000000000000000000000000000000000000000000000000000 |
| 280 | True | 07065230644665792052186286503978375114413827309599287477421264601465575912229816923404173201977337878379210932930098887603481739264000000000000000000000000000000000000000000000000000000000000000000000 |
| 281 | True | 85329811151087566664346507617923407150285473997399781155375353011826831336578555476572669755631943824558272153357787416578368733184000000000000000000000000000000000000000000000000000000000000000000000 |
| 282 | True | 63006744606693799345715148254400816380503667266738285815849549335166436915152644393492871088208158525432747246896051475099982757888000000000000000000000000000000000000000000000000000000000000000000000 |
| 283 | True | 30908723694345214837386955995431035682537836486934885885422461852101646988198363358482517962908862697467470871582567453295120482304000000000000000000000000000000000000000000000000000000000000000000000 |
| 284 | True | 78077529194041013817895502702414133840745562289507591459979165996867744648335193809035101466117006080761727529449156735814216974336000000000000000000000000000000000000000000000000000000000000000000000 |
| 285 | True | 52095820301688938100218270188028144612485252509663566094062309107307224775530235575003917843346733017092345893009669707051837685760000000000000000000000000000000000000000000000000000000000000000000000 |
| 286 | True | 99404606283036296662425273776049359170782217763779902901820404689866285801647374451120503197165642888410925400765536216825578127360000000000000000000000000000000000000000000000000000000000000000000000 |
| 287 | True | 29122003231417142116053573726166082014496498204832132822456145991624025072796467471584417586539508973935590019708894228940922552320000000000000000000000000000000000000000000000000000000000000000000000 |
| 288 | True | 87136930648136929423429233135831620174991482991654252867370045587719220965382631816312264923378584493449925676161537934985695068160000000000000000000000000000000000000000000000000000000000000000000000 |
| 289 | True | 82572957311572603371048376255338230572538584588079078669943174850854858995580594914244562856410918607028520410684463210865874698240000000000000000000000000000000000000000000000000000000000000000000000 |
| 290 | True | 46157620356054977604029114048086866036189530542932814283520706747909108718372525130923228359166396038270919098494331151103662489600000000000000000000000000000000000000000000000000000000000000000000000 |
| 291 | True | 31867523611998482772472187993278016531153387993448956504525663641550637046404813098659452517421247136837457661850364971165784473600000000000000000000000000000000000000000000000000000000000000000000000 |
| 292 | True | 05316894703556969561878894037180827096789294087095299321493783332786017550205424808560135087004163956537637260306571580409066291200000000000000000000000000000000000000000000000000000000000000000000000 |
| 293 | True | 57850148142192081630515952893982339359263167518922701197678516506303142210189468908119580492220039265527717269825473059856423321600000000000000000000000000000000000000000000000000000000000000000000000 |
| 294 | True | 07943553804471999371690150830807771623371250563274152117483852853123809795703858987156664712691544065148877328689079597788456550400000000000000000000000000000000000000000000000000000000000000000000000 |
| 295 | True | 43348372319239814648594495088292628894518916165874874657736591671523889732638401211216090244005499218918811963278481347594682368000000000000000000000000000000000000000000000000000000000000000000000000 |
| 296 | True | 31118206494985135983970546134618152777599185098962898690031134771071360860966758519962712225627768799968341130430478888025980928000000000000000000000000000000000000000000000000000000000000000000000000 |
| 297 | True | 42107329010585387239252201981591374946957974391980910939247027008194175707127280428925531011447333590597315737852229743716335616000000000000000000000000000000000000000000000000000000000000000000000000 |
| 298 | True | 47984045154445397297156190514229734193476368810311459895614048441864360723929567819808241411305409998000089879964463627468013568000000000000000000000000000000000000000000000000000000000000000000000000 |
| 299 | True | 47229501179173791849700963754690523849434274283126508788600484117443856454940778122664181980317589402026874109374624612936056832000000000000000000000000000000000000000000000000000000000000000000000000 |
| 300 | True | 68850353752137554910289126407157154830282284937952636580145235233156936482233436799254594095276820608062232812387383880817049600000000000000000000000000000000000000000000000000000000000000000000000000 |
| 301 | True | 23956479393404027997027048554303603914967766323743610623715805180237881152264476575632822678323003026732076528602548125931929600000000000000000000000000000000000000000000000000000000000000000000000000 |
| 302 | True | 34856776808016455102168663399688382320265429770570408362173164431840107983871925841112448853546914073087111637969534031442739200000000000000000000000000000000000000000000000000000000000000000000000000 |
| 303 | True | 61603372828985895957105010105579843040425220482833733738468822847552719113193529857072002624714964145394826304768811527149977600000000000000000000000000000000000000000000000000000000000000000000000000 |
| 304 | True | 27425340011712370959923072096272284289267026781455056494522145656026610410833076549888797913349100200027196649718704253593190400000000000000000000000000000000000000000000000000000000000000000000000000 |
| 305 | True | 64728703572273142776536989363046708226443168343792230829254425088116175304088347716083363571475561008294978164204797345923072000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 306 | True | 06983293115581689620318745092292717291609513200422633751854076963549643051034401121509252871521668538263318246667987852460032000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 307 | True | 43870986483578713437854743333864208524120552529748561819201627809740416667561144303340631557152241246838701727072270705229824000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 308 | True | 12263836942243738859260946830176225429130179162557040314101365400048333608832445428914519602890304026320131938259377210785792000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 309 | True | 89525615153315307511632570524453657601225361230125457057321908614935085129225637534586557293103944132920768922147558132809728000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 310 | True | 52940697527745328606096862580633856379861981338891687769791670629876390059947635721832760862222681205438365865743021171015680000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 311 | True | 64556931128797196496124262577129334137076196395314896405209565891557308643714709489988628151253854891331784246079584185876480000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 312 | True | 41762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 313 | True | 71666313819021025510986232142254490313035180871523347145366705920532910603669954329470738846453267896722335147873255953530880000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 314 | True | 03222539172602010449676892667909958293046793658331003645145659047333929552365659453811997786326119570813236432202369408696320000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 315 | True | 15099839369633291648221190391636862309740002374266148220882599910187808995182727950779302692727664806169476143746363739340800000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 316 | True | 71549240804120160837896163757248489877840750268102837798901571619347642477742032446259650901942078749554461423850941631692800000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 317 | True | 81109334906090985613083911047771291275517834988599582251798203333202665444224285464309335915638963608764271360748497246617600000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 318 | True | 92768500136933424960683713191270625614671526374667156071828659958447611263322777650368821173190427587038292718022124424396800000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 319 | True | 93151543681762562458104508015329571080216913518822786913342526744787992999966070467653954247746400265215377049057691382579200000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 320 | True | 08493978164019986593442564905462745669412326023291812269608558332157759989142549649265359278848084868920655698461242425344000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 321 | True | 26566990650415696495063334653541359881356653476671738544347224622640956514758437414180328510235242923530479206058818535424000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 322 | True | 54570989433854271410393758440317881796842419488299811279806328490387997752216847366065780295748221376814304350939568406528000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 323 | True | 26429587134929665557183976222675820380101494720839043377444102395323273966041699239247035526675504711020305353480595308544000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 324 | True | 63186231717211640527608296146965803152884289551850054291889176084740764997510553516039510642863526370578934527712879968256000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 325 | True | 35525308093783171472696247763886024687394104351267644863982227540748624190929892712840958930646070438153721506685989683200000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 326 | True | 81250438573313900098976771026844048090478018513252225658206178284051486243145024386152611390618962838113211179632636723200000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 327 | True | 68893413473645332365404125778003725586312053833477790233420298884836001508422974271903924732400848063020055739872208486400000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 328 | True | 97039619355669015852553255185221992310353657380715196561858034226208494762735561184487312227478164670578282678084383539200000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 329 | True | 26034768015106215490020955938035470106353278255299668851293260422594776939999629696325722840316176620255001089762184396800000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 330 | True | 91473444985051111706915459551705135096581824248890720926775939456276390199877799787488537304338284684150359621520850944000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 331 | True | 77710290051917974989017111614399716968583826382828626762835960027485156159551729658705847735972230453769034723401662464000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 332 | True | 99816297236767696353681055980706033569830359099104085261538729125071844971174246690341448342780510651319528169351938048000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 333 | True | 38826979843642885775791641575109178753509580001660392092396798648924375401024147883702298145910046889402880394195369984000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 334 | True | 68211267776723849114408286086465703672199720554570958860530748740741383942065393156567580733955661060562051661253574656000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 335 | True | 50774705202489453326775838966010730186906385781271218277800828148363620591906707450139545875146455288287306519947509760000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 336 | True | 60300948036456317796681892579605342800545622507129341341078257850176518880653703246887414049208976864534990702363279360000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 337 | True | 21419488285779097481797799327000523783874784902588031943372895509486862780297994201058534583425203348291866696425144320000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 338 | True | 39787040593334948847656172526177038949677297074754796860038682206559619740722039957784689197718731722650943391698780160000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 339 | True | 87806761140547659355442486374016203940603708341876135553113268023711092104771545689009638026650053978669809785886474240000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 340 | True | 54298787786204180850445367165509339805260836237886088058511128061771315622325534263276929061018352747735327201401241600000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 341 | True | 15886635095625670001870203438684873593945157119156027952294669064018627213007183777432809807258286977746575677823385600000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 342 | True | 33229202703979140639609576030226769129243734751361559684776819894370506848456851882020954082334146389328881815597875200000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 343 | True | 97616527464845239386084578367781811330601019717014971878449223769083849020700195533187250240612211539806462750071193600000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 344 | True | 80085447906762348813094958516943097726750782653150326186532976564844063120867263416414082770600769693423186024490598400000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 345 | True | 29479527833010340517760688345368715729020015336862534353876914871201776699205878662858555857265544230999178449256448000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 346 | True | 99916630221577819145198167497575642240925306554436886441412545435814737925234017349060326613878303925715743442731008000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 347 | True | 71070686887503243383764121658747857601081374389599595170153266227714060056204020123933335015771462223362974627659776000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 348 | True | 32599036851128697549914337244254445176318287580659119213336647244492899558999003128800585488468853730315170425602048000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 349 | True | 77063861043915444920103698244801366535082365650032605454489888328021946090652091951404335475629951879994478535114752000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 350 | True | 72351365370405722036294385680478287278827977511411909071460914807681131728232182991517416470483157998067487290163200000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 351 | True | 95329245012408434739329373847878834868620106505580084082781097496077236609496230022613181139588457321688038847283200000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 352 | True | 55894244367769028243939594453349873754277489964189597138946318619187286542672967959839761135136977234189674243686400000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 353 | True | 30668261822466970110676842032505435259953957358927790048050472573112149563557689823435680703352963668955008021299200000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 354 | True | 56564685153307419179602079506924082023700905060437677009867290881700945499422197496230968986949138810072839539916800000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 355 | True | 80463229424133808758738224958049118413821296455375338502888263003835652294880111161993990366944277575858036670464000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 356 | True | 44909674991635918110808085065486155320381538113620507028221629365492216977319573669860570632162817005461054685184000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 357 | True | 32753972014022765558486368378557449376209106562521009075121683480721460903087800140223715682125670949596522610688000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 358 | True | 25921981020150069938119879523566876682860149382521248893562686098283003305432450200090214200990199955555094626304000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 359 | True | 05991186233875107785036748960508729146793628325128352789004309283598186650249621832386898155481784044278970843136000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 360 | True | 56827044195038802613229625783142492845706197046207004041551342095347194089863859659283335973442255940429503528960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 361 | True | 14562954409007743375894907714439917299937133680728459000034496420337066440853337001284286412654394495050773954560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 362 | True | 71789496060803102073956592627250062577242392423702158012487704162018051588907994464911681380890807208380171550720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 363 | True | 59587070071526052846243123691772715538988449803883358533036610812552726773601990762940341263363016642002272911360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 364 | True | 89693506035483236032497023805268456191795728613542506025326335769192545591124637710284219864138057688827339735040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 365 | True | 38129702951381151861413688922986510005440943943014699244112555755279140760492764253740250410391056421979003289600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 366 | True | 55471280205501581277410145813062661991385483143379923345195406432165518340351716868931650203126650444315203993600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 367 | True | 57959835419080328809523513393996950838472313620431867686714160604745230909080090897915624547480713063679865651200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 368 | True | 29219434221561001904652928990877908557811412318927308710811102546244974541473450432949833472902407434190559641600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 369 | True | 81971227756009702816930797633948257832411145684176914289296839564395605803703209758488551500988343216316507750400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 370 | True | 29354269723590042264395124560855397992123903145458287039830638826374147370187610640764055365686990037107867648000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 371 | True | 90434067451905680090591212077352655077968066965024491777167004584808674339603547723464540669873303767018897408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 372 | True | 41473092108912993699930892775187689004120910989110941106125705548826854332519753128809129192869001331029835776000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 373 | True | 69463356624546650074223005145007998537099798938381032584888169712416666029867917045805188940137496474128744448000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 374 | True | 79295377580447127759403924232991452875324802954506186748175472443833095170600975131140663611423681324150423552000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 375 | True | 35766592667672909776471587371794828246801107939820030565802166437410688975365674177748854283880496556408832000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 376 | True | 48238843045014075953316851794855420797216585372331492741614580466419054737493490833569210739066705209720832000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 377 | True | 86043827970306634400453126660493640550652685368972763588696835839983636035046044255592448628147864064753664000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 378 | True | 24566972775907803371281877666596128146715069471704636527403947513814421247404728613945581439892616476884992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 379 | True | 10882682069057477715831635639932567605011329776057243886096107735665652766392144685375365719301644739411968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 380 | True | 35419186241841532016021543174375689904305314901752676716520939552948051229014980442638973334625000976547840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 381 | True | 94709958141623698104207949437137853540324977567769828994477969673207518254707548645448840492125372064727040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 382 | True | 79204010100252675807436684986660052404141430888074675890584415165271973298283582561457067991892128725729280000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
| 383 | True | 35135868396774834248250349890800070786168030132600866093831008299165773242612121038057040894685301954314240000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
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| 385 | True | 86783779191495261331727855882465027081574803712043311976266948667916187775974266352925870275040925817241600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
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If you would like to tinker with the code that generated this result, here it is:
"""Find pandigital factorial numbers by checking trailing digits."""
from __future__ import annotations
from math import factorial
from typing import List
def is_pandigital(num: int) -> bool:
"""Check if a number is pandigital (contains each digit 0-9 at least once).
Note: This implementation as written in the original script checks
if all digits 0-9 appear in the string representation of the number.
"""
s = str(num)
for i in range(10):
if str(i) not in s:
return False
return True
def is_pandigital_last_m(num_str: str, m: int | None = None) -> bool:
"""Check if the last m digits form a pandigital sequence containing all digits 0-9."""
# For the original case, they check the full string representation
# of the factorial's trailing digits
s = num_str
for i in range(10):
if str(i) not in s:
return False
return True
def search_pandigital_factorials_up_to(k: int = 1001, m: int = 200) -> List[List]:
"""Search for pandigital factorials in factorial values up to n=k-1.
This reproduces the logic from the original script.
"""
results = []
for n in range(k):
fact_n = factorial(n)
fact_str = str(fact_n)[::-1][:m][::-1]
results.append([n, is_pandigital(fact_str), fact_str])
return results
def format_results(results: List[List]) -> str:
"""Format results as a markdown table."""
import pandas as pd
df = pd.DataFrame(results, columns=["n", f"last_{len(results[0][2]) if results else 200}_is_pandigital", "last_m"])
# But the original used fixed column name based on m
if results:
m_len = len(results[0][2]) # actual length used
else:
m_len = 200
df = pd.DataFrame(
results,
columns=["n", f"last_{m_len}_is_pandigital", f"last_{m_len}"],
)
return df.to_markdown(index=False)
def main() -> None:
"""Run the search and print formatted results."""
import pandas as pd
import sys
sys.set_int_max_str_digits(1_000_000) # Prevent large string representations
k = 1000 + 1
m = 200
results = []
for n in range(k):
fact_n = factorial(n)
fact_str = str(fact_n)[::-1][:m][::-1]
results.append([n, is_pandigital(fact_str), fact_str])
df = pd.DataFrame(
results,
columns=["n", f"last_{m}_is_pandigital", f"last_{m}"],
)
print(df.to_markdown(index=False))
if __name__ == "__main__":
main()Happy pattern hunting!