> load "tut6data.txt";
Loading "L:\win\Magma\MATH2068\tut6data.txt"
> time Factorial(10000);
28462596809170545189064132121198688901480514017027992307941799942744113400037644437729907\
86757784775815884062142317528830042339940153518739052421161382716174819824199827592418289\
25978789812425312059465996259867065601615720360323979263287367170557419759620994797203461\
53698119897092611277500484198845410475544642442136573303076703628825803548967461117097369\
57860367019107151273058728104115864056128116538532596842582599558468814643042558983664931\
70592517172042765974074461334000541940524623034368691540594040662278282483715120383221786\
44627183822923899638992827221879702459387693803094627332292570555459690027875282242544348\
02112755901916942542902891690721909708369053987374745248337289952180236328274121704026808\
67692104515558405671725553720158521328290342799898184493136106403814893044996215999993596\
70892980190336998484404665419236258424947163178961192041233108268651071354516845540936033\
00960721034694437798234943078062606942230268188522759205702923084312618849760656074258627\
94488271559568315334405344254466484168945804257094616736131876052349822863264529215294234\
79870603344290737158688499178932580691483168854251956006172372636323974420786924642956012\
30628872012265295296409150830133663098273380635397290150658182257429547589439976511386554\
12081257886837042392087644847615690012648892715907063064096616280387840444851916437908071\
86112370622133415415065991843875961023926713276546986163657706626438638029848051952769536\
19525924093090861447190739076858575593478698172073437209310482547562856777769408156407496\
22752549933841128092896375169902198704924056175317863469397980246197370790418683299310165\
54150742308393176878366923694849025999607729684293977427536263119825416681531891763234839\
19082100014717893218422780513518173492190114624687576983537344145601312261522139117875968\
83673640872079370029920382791980387023720780391403123689976081528403060511167094847222248\
70389199993442071395836983063962232079115624044250808919914319837120445598344047556759489\
21210149815245454359428541439084356441998422485547853216362403009844285533182925315420655\
12370797058163934602962476970103887422064415366267337154287007891227493406843364428898471\
00840641600093623935261248037975293343928764398316390312776450722479267851700826669598389\
52615075900734921519759265919270887320259406638211880198885474826604834225645770574397312\
22597006719360617635135795298217942907977053272832675014880244435286816450261656628375465\
19006171873442260438919298506071515390031106684727360135816706437861756757439184376479658\
13610059963868955233464878174614324357322486432679848198145843270303589550842053478849336\
45824825920332880890257823882332657702052489709370472102142484133424652682068067323142144\
83854074182139621846870108359582946965235632764870475718351616879235068366271743711915723\
36114307012112076760869785155972184648598591864364171685089962551682091079357023111851817\
47750108046225855213147648974906607528770828976675149510096823296897320006223928880566580\
36140311285465929084078033974900664953205873164948093883816198658850827382468034897864757\
11667989042356801830350413387573197263089790943571068779730163391808786847494363353389337\
35869064058484178280651962758264344292580584222129476494029486226707618329882290040723904\
03733168207417413251656688443079339447019208905620788387585342512820957359307018197708340\
16381763827856253951682542664461494104471157953326237281546879408042371858742302620026422\
18226941886262121072977766574010183761822801368575864421858630115398437122991070100940619\
29413223202773193959467006713695377097897778118288242442920864816134179562017471831609687\
66104314049795819823644580736820940402221118153005143338707660706314961610777111744805955\
27643483333857440402127570318515272983774359218785585527955910286644579173620072218581433\
09977294778923720717942857756271300923982397921957581197264742642878266682353915687857271\
62014619224426626670840076566562580710947439874011077281166991880626872662656558334566500\
78903090506560746330780271585308176912237728135105845273265916262196476205714348802156308\
15259005343721141000303039242866457207328473481712034168186328968865048287367933398443971\
23673508452734019630942769765268417017499075694798275782583522999431563332210743913155012\
44590053247026803129123922979790304175878233986223735350546426469135025039510092392865851\
08682088070662734733200354995720397086488066040929854607006339409885836349865466136727880\
74876470070245879011804651829611127709060901615202211146154315831766995706097461808535939\
04000678928785488278509386373537039040494126846189912728715626550012708330399502578799317\
05431882752659225814948950746639976007316927310831735883056612614782997663188070063044632\
42911226069193127888156622159152327045769586751282199093894268660196390448971891859747292\
53103224802105438410443258284728305842978041624051081103269140019005687843963415026965210\
48920272140232160234898588827371428695339681755106287470907473718188014223487248498558198\
43909465170836436899430618965024328835327966719018452762055108570762620424450962332320474\
47078311904344993514426255017017710173795511247461594717318627015655712662958551250777117\
38338208419705893367323724453280456537178514960308802580284067847809414641838659226652806\
86797884325066053794304625028710510492934726747126749989263462735816714693506049511034075\
54046581703934810467584856259677679597682994093340263872693783653209122877180774511526226\
42548771835461108886360843272806227776643097283879056728618036048633464893371439415250259\
45965250152095953615797713559579496572977565090269442808847976127666484700361964890604376\
19346942704440702153179435838310514049154626087284866787505416741467316489993563813128669\
31427616863537305634586626957894568275065810235950814888778955073939365341937365700848318\
50447568221544406759920313807707353997803633926733454954929666875992253089389808643060653\
29617931640296124926730806380318739125961511318903593512664808185683667702865377423907465\
82390910955517179770580797789289752490230737801753142680363914244720257728891784950078117\
88933662975043680421466819782427298069757939174222945668318581567681628879787062453124665\
17276227582954934214836588689192995874020956960002435603052898298663868920769928340305497\
10266514322306125231915131843876903823706205399206933943716880466429711476743564486375026\
84769814885310535406332884506201217330263067648132293156104355194176105071244902487327727\
31120919458651374931909651624976916575538121985664322079786663003989386602386073578581143\
94715872800893374165033792965832618436073133327526023605115524227228447251463863269369763\
76251019671438012569122778442842699944082915221590469443728249865808520518657629299277550\
88331286726384187132777808744466438753526447335624411394476287809746506839529821081749679\
58836452273344694873793471790710064978236466016680572034297929207446822322848665839522211\
44685957285840386337727803022759153049786587391951365024627419589908837438733159428737202\
97706202071202130385721759332111624133304227737424163535535879770653096476858860773014327\
78290328894795818404378858567772932094476778669357537460048142376741194182671636870481056\
91115621561435751629052735122435008060465366891745819654948260861226075029306276147881326\
89552807361490225258196828150510333181321296596649581590304212387756459909732967280666838\
49166257949747922905361845563741034791430771561168650484292490281102992529678735298767829\
26904078877848026247922275073594840581743908625187794689004594206016860514277224448627246\
99111462001498806627235388378093806285443847630532350701320280294883920081321354464500561\
34987017834271106158177289819290656498688081045562233703067254251277277330283498433595772\
57595622470370779338714659303308862969944031833266579751467650271734629888377739784821870\
07180267412659971587280354404784324786749071279216728985235884869435466922551013376063779\
15164597254257116968477339951158998349081888281263984400505546210066988792614558214565319\
69690982725393451576040861347625877816586729441077535882416231577908253805474693354058246\
97176743245234514984830271703965438877376373581917365824542733474904242629460112998819165\
63713847111849156915054768140411749801454265712394204425441028075806001388198650613759288\
53903892264432294799028648284009959867596358099911269536760152717308685275657214758350712\
22982965295649178350717508357413622825450556202709694174767992592297748886274113145876761\
47531456895328093117052696486410187407673296986649236437382565475022816471926815559883196\
62984830777666684062231431588438491051905828181674076446303330011971029303645586659465186\
90744752508378419876229904159117936827997606541860887216266548864923443910309232569106337\
75969739051781122764668486791736049404393703339351900609387268397299246478483727274770977\
46669359978485712015678900024194726922097498412732314740154998092038145982141648117635714\
78015542315996678385348544864069364105569135313352311840535813489409381918218986948253839\
60989942822027599339635206217705343572073396250574216769465101608495601439303244304271576\
09952730868460920442222610315422998444480211009816133382482737521899873820531516492713449\
81059501599748005715919122021544877487501034732461906339413030308923994119850062259021841\
64409988173214324422108554248620896250260604398180189026317781146617454999771440665232863\
84636384700165561815386109818811118173419130550502486034585675558563751172977429932907494\
42365796683327009183673389773479017592488856603799527715405690830173117238941403261596122\
92912225191095948743805673381278538616491842786938417556898047100859868372033615175158097\
02256627520016095619222992540175987852203854591377178397638981119848580329104875166692119\
51045148966777615982494687274206634375932078526189226872855276713248832677941529128391654\
07968344190239094803676688707838011367042753971396201424784935196735301444404037823526674\
43755674088302522574527380620998045123318810272901204299798900542312621796813523775804116\
25114591759932791341765072928267622368972919605282896752235214252342172478418693173974604\
11877634604625637135309801590617736758715336803958559054827361876112151384673432884325090\
04564535818668190510873179134621573033954058098717201384437709927953279767553109938136584\
04035567957318941419765114363255262706397431465263481200327200967556677019262425850577706\
17893798231096986788448546659527327061670308918277206432551919393673591346037757083193180\
84592956515887524459760172945572050559508592917550651011566507552163514231815354817688419\
60320850508714962704940176841839805825940381825939864612602759542474333762262562871539160\
69025098985070798660621732200163593938611475394561406635675718526617031471453516753007499\
21386520776852382488460062373589660805495165240648054729586991869435881119783368014148807\
83212134571523601240659222085089129569078353705767346716678637809088112834503957848122121\
01117250718383359083886187574661201317298217131072944737656265172310694884425498369514147\
38389247774232094020783120080723532628805390626601818605042493878867787249550325542428422\
65962710506926460717674675023378056718934501107373770341193461133740338653646751367336613\
94731550211457104671161445253324850197901083431641989998414045044901130163759520675715567\
50948524358026910407763721099867162425479538531285288993095657072921867352321666609787498\
96353626105298214725694827999962208257758409884584842503911894476087296851849839763679182\
42266571167166580157914500811657192200233759765317495922397884982814705506190689275625210\
46218566130580025560797460972671503332703231002527464042875555654688376583880254322740350\
74316842786206376970547917264843781744463615205709332285872843156907562555693055588188226\
03590006739339952504379887470935079276181116276309771257983975996526612120317495882059435\
75488386228250840140888572058399240097121921254807409775297427877591256602644348271364723\
18491251808662787086261166999896348124058036847945873648201246536632288890116365722708877\
57736152003450102268890189101673572058661410011723664762657835396364297819011647056170279\
63192233229422873930923333074825893762619899759653008413538324112589963962944512908280202\
32254989366275064995308389256322467946959606690469066862926450062197401217828998729797048\
59021775060092893328957272392019589994471945147360850770400725717439318148461909406269545\
28503052634100056502222615230936488288712204645426770057714899433514716250425236517371026\
60686472534581201866832739536825474565365535975466857887000569883602866864507402569930874\
83441094086086303707908295240576731684941855810482475304758923392801571302824106234999945\
93239052140985655956566134600339615051516475885274221473251799954897799284952274602985566\
67008118712008561550164574004841702103030389963392533374665568178244107374093369192941046\
32307731994759826307383499600770372410446285414648704116273895649834555162165685114551383\
82204700548399667170624646756610129138204890912111722938624425315891306698746204558724480\
60528293781483026221645422804217577607623654598282230708155034694049383177550533050946989\
99476119419231280721807216964378433313606760676965187138394338772485493689061845700572043\
69666646508073449581449596630624669867983287258630006421522021017181391732527517367226262\
14549454685060063346927138383117158497530926432524869602200590998026637653862254632651684\
14963306369548086551101256757717890616694758344043486218485369591602172030456183497524162\
03992644133165188476860683064200485855792447334029014258887640371251864222901633369158506\
32737271995963629127833447862188878710095337535510546889802363782637149269132895643394408\
99470121452134572117715657591451734895195016800621353927175419843876163543479806920886666\
22709951237170624192491428257645312576993973534167304686458518197966823201569379268492699\
99839924135719414968822737040228208051718080034004806152617920139789451862952905584407037\
38300533552421153903385185829366779190610116306233673144419202893857201855569596330833615\
45029042482230929708712478800201738307206048268015667539759378993179351579995892956215630\
73384162945999002767308328277165950642179665231904392505432267537318117553154767807394703\
38931185107297724318378972674957455778183345495942317353558291046967315391275975687281861\
69116108315633723263996888149054394326119718227499679117662855340186019831580962998179110\
72088049922920160620590672712735994618716349457749958053379471871054564525793960242102591\
36415528398395201773012712514892051061708228008339985665786646920737114269682301770416324\
82947940955869469908937916519100630518535210234518979812761914306186436270308197712499275\
10567329094812020577471006877033797089342292071839037441675034938188363422292849467906602\
85674293251642569044363473087656797056595677285291081242733154406580199802711579126254172\
79745286257486592193329380591523952473551888711986039131965428757629019050396408356024627\
75343144091556421817294599415960619796226332427158634259779473486820748020215387347297079\
99753332987785531053820162169791880380753006334350766147737135939362651905222242528141084\
74704529568864775791350216092204034844914995077874310718965572549265128269348951579507548\
61723413946103651766167503299486422440396595118822649813159250801851263866353086222234910\
94629059317829408195640484702456538305432056506924422671863255307640761872086780391711356\
36350126952509129102049604282323262899650275895105284436817741573094187489442806542756143\
09758281276981249369933130289466705604140843089422311409127222381484703643410196304136307\
36771060038159590829746410114421358321042574358350220737173219745089035573187350445827238\
77072827140616299791962935722410447715505165253586754410939507921836901526113844038268005\
41509243465117114364778994445539936536677275895657139875055429908245856095100369346631006\
73714708029927656933435500927189854050109917474979991554392031908961967615444686048175400\
69568947146392824538380701044418104550617130516058435581752103233846582920107103006112428\
34074586070060601948305513648670210203647084708074227043718937069656887956179287130452245\
16842027402021966415605280335061293558739079393524404092584248380607177444609964035221891\
02296190903256904238137449249490689231433088422439963139639154585406528632646880758114874\
83714082841764552263863135202648940162624948023885682315991029526203371264492799019382111\
34518446387544516391239377974190576649911764237637722282802318465738050121277809680315691\
47726491025750350875879224811022354452441087244856570075518713214659209354850455282917074\
95967754044507794948363717560623269257574128131102419103733380804343253108846948315557294\
02265394972913817581338619457057799561808755951413644907613109617155928376585840036489374\
07682225752393598873108168966768828740383719282769043151410699767830381908569071309193134\
08460195111474827663507246765349220400586266776329355166319396224989799127080044659822648\
99125226813124300528104995058595676527123591494442612554437618645029202881358582871789577\
22411638081516183160312972879698748013982862164562919615309635833731361972477333235302546\
65711969026112373806290302429042757945490300226608474465131617416919168517464649454596960\
05330885252792083472495235473110674109099223541055506299687642153951249355986311346661725\
11689078563332893556915044948518911348830187636510063850256591643302192856559626391438289\
50683248387271656165601115315170552229557659449724547888155323164174532671679788611411653\
55597588331979638070962998880767303616940317736448140427867784251232449974693421348217179\
59519069820460299717200117485730388971920559741474245301113586976625660777097022563326170\
11084637847955552585045780588794407560649741279745309184184052075585264622088214836467546\
52237609210787539190454684852349759986044943322828073120679922402477507514105890774627334\
31909125545135222532927591384204738460305616315423655293531227838975944651578733734346317\
22800010313804254814040220905804050560038609374034350688630814346838489007089385650500275\
69059678069404698435184535134141031615133683043714786642925389717165978629010728400758939\
70038831774264816372511327736992682770946534258359611188195509246206215397812119724476262\
37715344520480698190825249439639622511138311774289785358255908324904804975160471042575697\
53442551515779815600370847230603484753977513688390404316017486248871339311818523029425425\
67620248568839397083674878845378917257414515591791903539853507720090059497935293945963121\
34455033682606900598287177235333752219419155473037420623432628929683970150588921911120492\
49864792053410872349115430987182160055762209075732304626106597744947658346313025598636315\
02995967235247694397546253020678819330437228480020930535415564066483856937814460313869756\
34592002334626069959555134847541478911808303298164215874529229526789379256477520290526753\
49356673744293182673374571642465407748267901046778759085408130531447176455869894169668940\
43648995246524744398834958387120629648541335755381341950049874381336906270397387458660429\
68715958207157665998266073170056244655417630245013491595672889426197461444969086716558597\
82729228702723774835097362901019130417812735773037781804081589136005207315806941034305003\
18434934236026924473306001386111978177447266960892832105254311649603342010203260386367253\
28896483334058622048436165753620014684054766496664735669795729533948091382637033242209308\
39366954980688240491622063147911494642042500022450413425558561937442905257252436320054487\
44152430730521507049102043407657247686509575117412541372953164452176557723534860182156683\
33525205328300001083440087622668438170232356056451582569541773591978136499755596019125677\
44942717986360045847405209290089397315276024304951653864431388147876977541478757432610159\
87970975885562580676619797309847246076948482112794842797653660705505163910441502255442032\
97212920330093533566872945959123279658863764868941884336405484940095749657916576872139273\
30153555097865114767947399690623184878377515462613823651665956337209345708208301840482797\
00572807143292572757743622958704736164160973181724159420427036606640408974024552153072522\
73886372418596464552236732604111645984640200102169208233151553888210715271912678765317950\
71908204525100447821291318544054814494151867114207103693891129125012750853466337717749376\
01654345469639004271112982925509683042066572536427947220002083531388370878164995718971762\
93387948542712768826520037663259245616148687448974715193662192756658524621144574070106753\
80427564184440834805203838265052601698584060084788422421887856927897751810442805474427229\
45516742033568646060997797312495043332142520505367579049952078359765041537900113257953604\
06551726548790221735954441511394292316489506631778130390574620824491719213118641296337046\
61406456900178942356738775523130952785912774533241855442484484493664210731348819180640189\
22231730215664581347318644999790578166209146987071803938888578128074022636360229411435486\
98714021435720559477308928086536789202019351026053615679244832767494761178583160718657103\
10842200560259545115191391309119544447844361032741876102338843391687589233423790859841968\
26652561062875123757231849147495194598572889793498179176182265248040823712810979077263886\
42860679170822885758527034708397145616199262478447946927949968459456323827022973641735034\
30783194115698247820013290851202878474805860188960045901745974055630732714487679085288867\
97880997069524068100662561144001498341358088973724684406494885707416768791641322420537365\
40673301863924979109154747859591638655975070905811759248995022147992509456355825143158144\
64060134283490422798357939659258985200763845646681640732681928346007767285876284900068874\
56463927496441590403403367233781449159703294178729415506105412951540015939385166392932567\
74295575494800466582735796539909402335436446493768272725418736275475329768081903253361410\
86433084237771738995221536763095302045902438694632702895293994483013577589081214884558493\
81987450592091406720952246909626307694175334098369885936370031497372897799636001862650017\
49292900879311899978229637123066422979961635825726001122889836476514180459757700421208339\
49364659647336464289044499325396227091907373705772051322815957863227591912786054297862953\
18861555980472816071086413280358540016005557568685579178597789919790265659262128300722535\
14015259735693007290153922111168685047404021721744420517380002513610004945341193243316683\
44243125963098812396962202358858395587831685194833126653577353244379935683215269177042249\
03457453485891381258268136690892947680905263556063811966130606393693841181771354592988431\
72329122362624588683942028899816935611698654298847765131182276625267399788088160104706515\
42335015671353744817086234314662531190291040152262927104099285072418843329007277794754111\
63755217656358931632663604938121840183751281888477116897547948376766408484275362307401954\
21832179854962606665903479258163423926709478399070629231665350372850197513248138038370708\
94638925470887039085723581006130628646664710006104352115778926613432214655311411882596942\
92628452210902668841497576334155492113558125461655807827347011581400600834576213313038998\
78432706537199567095708473857860926491888583787392391655542635773012922436416040625517368\
92335636568854365851646207821875741724364525814143487632761341752707376754922276287782264\
76515431534158571377352273033540337636420425803425726474968621782366695135341067737842113\
13711319873732228918052750628122777164124944124012071259543199917465747458925826137128255\
55535080404143944557295994554635608487251339462936358940832098964801619583130429720964794\
12853938899626536892826380767716875958850221646458243094016500968879736615773356031683671\
03868952282709415095452227440027354992536702147159940565448138421863801287999008209335763\
20736369405991424263718294000613741900579513096298545330748197802568301089672873802234820\
48886297313036968988264065790478156238977848536502569106423179573602533090876327178491118\
97484322468680863403839641761276057886465744722848249326874430625512205069551684646694771\
83681911432873544815836350548146411099960143390595799766290646881295025039150923633011076\
07063286331739337814969338024758003505278978275575092860403942050634293932706463616103182\
28792481526793068627492372756318522256542660085568494977202859091509304954259674736483314\
37236349555448901598668408362176913559656039519670425368863482369587129462524759031776813\
18497758827657674048255813650210364958550570325921995767533426422378372358605850940358397\
71034766706447886408311096503025652156074640196527169997323734652371734565955145594930981\
66644006211599349133180135150528651842178828026343325934755850761168697709125580056185683\
71054085608124951940314806461871940257766328526701969838756756152469675902810686489686929\
33159543520976875271372016161609311742501997092896849400346962423256884106651133043774122\
56176258658941236728171145526423894512631717834790276921171452887352955019336759218908006\
04863373778672818061025478257043678844950351892578749983669478590861297554308412267706095\
43476121337174331567837901620123372370233383164147064285921859776101582327219979150628718\
68186750981665537745013020880333904353639770263363809098526494532628146558065546504823486\
42949539061325740049691288834051822293364447668385503796797580961998357580702775953596878\
82261946596122230445492756002749551685835425822953360428344263184780688253954507466918778\
97765406038432512843812811316856204608617289408229658626174420766920297427930088129519854\
67871354862323661041321658127926715154596159435259345675744599230788920551954008231640971\
95912500254552375031067356397488355424804496813830306718519314913357892021236053081999520\
20584503423499932150962634977812456658304680581824563524814625849331926195406884818446445\
24842948606301616947666324262523147632237110969536948382448231641039622450767540561428746\
82678357237048956069906527926884558445120466548533785340266466450423396384882577198749536\
11300494215593735545211926186721478265416885604094928290056616883807637656690510740892510\
54916522296887867696863165251491770149990006663734454612026278070192569870622554092894519\
47187780043061300218282874258670487484808269485734447782440787341027108248702695238308049\
10960482013901294024631244800159336670212658317677879752965963472576894326540435889267293\
95068786083062626626328739208732730254791009993211338897780781433672879144876837368646774\
85287777374035474728716442177678207129645062708809786379281440711925051411480049070556080\
97229299792441471062852247029870699869227676341773513258602908903875707454368077876422385\
33370069208961635100923358730398654390607188095255755338036472589500730677212252807817947\
10564811713785574510576910443229254290241494335883960936793213616969542512997310310328044\
36954501929843820842383121265825740594509426942777307124802176915781835720087170538773256\
01798713300550591137782384179164028084140962382084763739301393077842855454522236755982466\
62506087542848761041456613622276424059143044555808563181809352304077938916149021162924005\
15074914068443203230365609954878620999194306564455332547135557365318516011700321550690787\
71675206288152788589714941032098698408304896652435103050244467993177914765910342894912905\
41203616016956712221408063694059403045521862128799330928562310224184463652890974446401519\
86623183881962444822590783585914043686193019041458962693878907034982169868696934448086213\
99053459179282665430479820721963413475564652548314377115667845907779719651077246800029358\
15462676463102242790073136313525220670629511259358744731341864924972827847966445854489629\
32905262058065248588707020879389134476083344653170939242408249328008915731319541348311820\
92775248688054873394331586756266612217935505119060999291137944563499562739189845902902171\
31557060962678816733029401984642373904450980280309489759812592520558509735374365568257803\
13681902007151675693827281818824587541710721180806556448039122504537089422695358382192535\
07569283409563985926559974039131670929004399627597683037521750336087902829567306886226307\
77297335338536826687345190357097096873223237383004940901232392743187590465263270951784062\
67264828893646896593219169521106361729757074376148061601331104911692271318609404145014842\
86642363471698289241818048436523053886455980983927383649068548082301426780314393744043180\
78226787794940062064891512489525165430056344483750467517542070433133724868706332375616452\
32360481932024377596890914783372179553676992603235715185513391098402739063753280702313301\
75575426939620262942391094532353791012594896494181256367299296708425066759980345627345559\
85596285122814145825560248417833056452405084500659887559875186013358606249327844877720068\
42296591945516539562982960591610046578907214842054861830418175604559815168088031783080261\
44599444467791801243214640098361067868341297487259672925878680622308011582202628901436445\
90023016458236667092655712645599257906223047452356255751117707915120027893809757754685461\
21017307522799241407026308137792971909461413145802081087738121624539858769697371425881836\
15260506938092691771208732191500583197711332279357238507194061276129187257209940493025027\
77481566140213274347438819664133300526342290829064009279449248085561311834401618048013570\
32507836323938921567643159620442612809700944107776130638909071294456394056601559246025454\
20477118614042015523337127050137712103457000957800938926532938572047857650877714966340300\
35623805957571916093821713122228104658583889435071764319399730126615914238371702844001203\
99485880996231859472474858776584355077006934099220340378772192728370301380838144394114984\
97173076616296134205910501481428394970069595167693904155790285635691105554731268457149744\
96353205546779407751840566676372229690903461287068298871042787610900909991604438217945117\
63620835379716161833124364431267855435550800507986124664397724135502128238026726719914989\
72724851298128728369748927642079286866697017725979440785815590933250855413129994658111852\
76916524647908191193842332758976995730120981030091710016957187916169422700795289151919125\
21053891838538959315167400505723817401030621004380243011187977704252328073236575129609372\
45605368003751659616423614770933039122440975287173206797612812042802673925655730567593151\
26457500478757565318548258214115740304731474925119108356157657320025461096867018903076485\
31373832912682481741181359032826625082549313211431478953352317043989053928534946642886074\
26837182490249809247948722663368682379958087563704080865564932190548963778554953116739793\
52707994704523991532975343586905141058640965345141828964744393671828527118435607992858959\
78176543950113088848419163516673213692860830956744502801800373716458009168082972708715609\
18503865405343666004550498562468737602255704159580025017409536183928764345800367086495405\
79417200851363571271637683234931342307038212744845014405295416953743819454594565331651409\
90993722722801019654652726227831512103467686166826131471843610025517863247950150022953695\
46631773958934413148148583469437452398115995466607120599779436344018507836089910894807341\
96339392593189739409431100421167291201997226266098719270140241058055153151001098049960441\
47291039451030312664114726736839973315035036742741546992633165270432940675237449075056739\
50892967477911580086439999256481720884742925082154627985607912776861194608621034940553585\
01344721902445438245210892844094981327170106739664711149318967899776615954881861931769001\
75027901783824624387873831483279500879026433992577026588005849778984624295660321276945810\
82434812969084097255067105473247131725499719190103955330584704072808169315862609388601914\
76899441376736214320836073751315743763167546664791867538965715551008506268100051198274868\
07780592667765654100834778571024250133253391587384761024129794736751001163498977803745930\
02545760987067109215359711517825201428121664754303407512860024029703842861598428981660214\
34298490889173596821922844691230359043298772318433099141872646746075583187257131388323560\
15809009594182530207799397648462597901883341793830920965841463574411985878296475850943053\
00814834182174782660377376225299770346875290351731079208322003808080921216434658681798981\
05042743753857867891863505177175016065318264069288832501359195171785376878658817523664215\
34010961295763074762648070312757365787762352859057153932484576503944390496668087711899192\
49893389652485239553679582753061416713175791575638660600483999417954870586820920119515495\
20312945624513154225065748586291616065237966430101726939502822946674896817468211639967949\
50294284013099235901278250437428192557634533217576162292751110598368271567229778620053722\
93231408288705874944406011623652162771755850301345147145276584186427707176996843549962025\
75474318119948833858067596923595806221658324640920953506483579358177429030183153512900143\
21495518177456908388719320697769695657771754499149911431368950836160692539606469893374870\
94293321918560129910856447025625716350550862068924029758968471428367868473545553358347765\
25361565781899969830686546717364459963431364681954274204904724330646750014426975083223690\
13083895492637066778406531328664886080129513771720847581157719491012345141774941482773580\
04143266733237961771696569858278583230050526588350224786805064820144457059319734338292386\
00726016965109032589809099128376522753814935298450994149669338628155680313069810645251927\
03818515872648691762563239441425216118427769145067718411735714396681005615483952443154944\
86423838429890039982611332246896334652210469254513796927600971964533895533210558424564018\
74486110509591117668289427116400540105037704203460525213182280458929986379035723506651087\
82350043349942391285236308896510989246641056331584171142885304143772286629832318970869030\
40030132595147677423751615884091583805915167350451913117819394342848292227230406142258207\
80278291480704267616293025392283210849177599842005951053121647318184094931398004440728473\
25902609169730998153853939031280878823902948001579008000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000000000000000000000000000000000
Time: 0.375
> time x:=Factorial(10000);
Time: 0.078
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <47, 1>, <521, 1>, <11971, 1>, <146976729866361139984771977632029750499087, 1> ]
Time: 0.094
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <11, 1>, <13, 1>, <41, 1>, <101, 1>, 
<62191520171334603393100024998897920572521409, 1> ]
Time: 0.016
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <5, 1>, <31, 1>, <103, 1>, <9739, 1>, <13349569, 1>, <57555851, 1>, <72102983581, 1>, 
<10918452866208583, 1> ]
Time: 0.156
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <283988713744407138993829, 1>, <177051125449666623562829641, 1> ]
Time: 11.063
> /*
> I was unlucky that time! The random number magma chose happened to be
> the product of two large primes, and therefore hard to factorize.
> The probability of such a number being chosen at random is very low
> but it can happen (and just did!).
> */
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <3, 1>, <13, 1>, <103, 1>, <7151, 1>, <76308814817, 1>, 
<14926895122842960837706321680041, 1> ]
Time: 0.219
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <5, 1>, <11, 1>, <47, 1>, <159017, 1>, <12291989, 1>, <624315813301, 1>, 
<18662103564324631392473, 1> ]
Time: 0.141
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <2496031, 1>, <4839994934087205088499778908289926409982717, 1> ]
Time: 0.063
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <229, 1>, <20143037029, 1>, <4453336765935120925969911866776365973, 1> ]
Time: 0.094
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <32183, 1>, <120454945189, 1>, <15088894611899, 1>, <1603818470152504178687, 1> ]
Time: 0.406
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <3, 1>, <4003, 1>, <1562381, 1>, <4318153884384681528224360123447559473959, 1> ]
Time: 0.016
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <3, 2>, <19, 1>, <149, 1>, <3313, 1>, <74143, 1>, <493721, 1>, <51863228107, 1>, 
<451132425231970120591, 1> ]
Time: 0.281
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <79, 1>, <105543019871, 1>, <6119599549297321808949713041902222253, 1> ]
Time: 0.359
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <5130641, 1>, <81132991, 1>, <171992182774651, 1>, <637508900754690142579, 1> ]
Time: 0.984
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 3>, <3, 1>, <23, 1>, <47, 1>, <3121, 1>, <770981, 1>, <3739762686803639, 1>, 
<130510355417404229549, 1> ]
Time: 0.234
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <3, 1>, <41, 1>, <163, 1>, <61553, 1>, <113171, 1>, <39208163283672109, 1>, 
<6533469495944036533, 1> ]
Time: 1.578
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <93249855134091645863843320108167690728153771314661, 1> ]
Time: 0.063
> /*
> This randomly chosen number happened to be prime. Magma would have tried
> dividing it by all the prime numbers up to about 10000, and when it found
> that none of them were divisors of the number it would have started wondering
> if the number was prime. So it would have computed Modexp(2,n-1,n), the residue
> of 2^(n-1) mod n. On finding that the residue is 1, magma would really start
> believing that n is prime, and so it would apply the IsPrime function.
> When IsPrime(n) returns "true", magma can print out the factorization
> of n as <n,1> (the prime n raised to the power 1).
> */
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 2>, <3, 1>, <7, 1>, <181, 1>, <88801, 1>, <380975964816586787, 1>, 
<61875630369410317271353, 1> ]
Time: 2.844
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 4>, <3, 2>, <5, 1>, <619, 1>, <107012463781, 1>, <283197900380148918512132419524209,
1> ]
Time: 0.141
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 1>, <3, 2>, <7, 1>, <2106819219077, 1>, <25865954892529919, 1>, 
<5714838101870745739, 1> ]
Time: 0.984
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <3, 1>, <17, 1>, <29130474168673, 1>, <26998442788400201248665462680851477, 1> ]
Time: 1.031
> n:=Random(10^49,10^50);
> time Factorization(n);
[ <2, 2>, <5, 1>, <11, 1>, <262322316410162437890889, 1>, <279329593346715717086807, 1> ]
Time: 6.344
> /*
> That one was quite hard. But, as you can see from the times taken, most
> randomly chosen numbers of this size are easy enough to factorize. Of course,
> the situation gets worse as the numbers get bigger, because a rather big number
> is quite likely to have two rather big prime factors.
> */
> n:=Random(10^49,10^50);
> time NextPrime(n);
29408715011374148661393738021666435467858408279339
Time: 0.094
> n:=Random(10^49,10^50);
> time NextPrime(n);
12307829156967985782824243194574860140431079517189
Time: 0.094
> n:=Random(10^49,10^50);
> time NextPrime(n);
79076555710673124290597045253865324789202659349863
Time: 0.094
> n:=Random(10^49,10^50);
> time NextPrime(n);
33433819172517223276749760698091210787352312690599
Time: 0.125
> n:=Random(10^49,10^50);
> time NextPrime(n);
93587944941348989115336038018908186681888498294633
Time: 0.125
> n:=Random(10^49,10^50);
> time NextPrime(n);
64795742789103237552711531208618028914083839209121
Time: 0.016
> n:=Random(10^49,10^50);
> time NextPrime(n);
16552398532448275026425957576088262085414186616071
Time: 0.109
> /*
> I suppose that it just applies the IsPrime function to the numbers 
> n, n+1, n+2, etc. until one of them returns "true". Or, more likely,
> it would use the faster IsProbablyPrime function, and only apply
> the rigorous IsPrime test when IsProbablyPrime returns "true".
> Anyway, for numbers of this size, Magma probably doesn't have to
> do the IsProbablyPrime test all that many times before it encounters
> a prime. I guess we can see that by looking at the value of n
> and the value of NextPrime(n):
> */
> n;
16552398532448275026425957576088262085414186616032
> /*
> So in fact it only had to do the IsProbablyPrime test 39 times.
> */
> n:=Random(10^49,10^50);
> n;
14051922835603050588900280312782279967707852891771
> time NextPrime(n);
14051922835603050588900280312782279967707852891803
Time: 0.016
> /*
> So 32 numbers were tested that time.
> */
> n:=Random(10^49,10^50);
> n;
99558325194737616335487008227117113952359909963600
> time NextPrime(n);
99558325194737616335487008227117113952359909964081
Time: 0.078
> /*
> 481 IsProbablyPrime tests this time, i.e. about 15 times as
> many IsProbablyPrime tests as in the previous example, when
> only 32 tests were needed. That is why it took a little longer.
> I guess that it can actually reduce the number of IsProbablyPrime
> tests that it has to do by skipping past even numbers, and multiples
> of 3, and multiples of 5, ... though how far it should go with this
> idea is not so clear to me.
> /*
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <3469908625475731843497959, 1>, <9346317789147021290021903, 1> ]
Time: 8.250
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <3419657768858205194147231, 1>, <8096209709040099088311907, 1> ]
Time: 10.203
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <2326981970060335477862173, 1>, <2798290475518754830113163, 1> ]
Time: 0.844
> /*
> Occasionally the factorization algorithm gets lucky, and comes
> across the factors fairly soon. But it is unpredictable.
> */
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <6285609767571758142783911, 1>, <7838901727517224176481483, 1> ]
Time: 10.219
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <7594694272182961135857799, 1>, <9589951625001389331376801, 1> ]
Time: 12.719
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <5915730180576115463519041, 1>, <8565349682979399822330853, 1> ]
Time: 12.109
> p:=NextPrime(Random(10^24,10^25));
> q:=NextPrime(Random(10^24,10^25));
> n:=p*q;
> time Factorization(n);
[ <4782869582130519464898869, 1>, <5329753279081895619971891, 1> ]
Time: 10.766
> /*
> OK, now lets make the numbers a bit bigger:
> */
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <23760820779152283087024431, 1>, <39345426106152095632075049, 1> ]
Time: 12.313
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <13572533977198623503681161, 1>, <91459137302283424372295563, 1> ]
Time: 14.375
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <44424008328764005066033409, 1>, <76633657908466414218675673, 1> ]
Time: 18.828
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <24803415093275135418191107, 1>, <34798523263593319657076917, 1> ]
Time: 12.375
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <72385212070641664943695229, 1>, <95959461269789745155579911, 1> ]
Time: 15.797
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <18963145521911078091762181, 1>, <70678292603918705992919371, 1> ]
Time: 11.703
> p:=NextPrime(Random(10^25,10^26));
> q:=NextPrime(Random(10^25,10^26));
> n:=p*q;
> time Factorization(n);
[ <46406719043783225808681233, 1>, <84321464994577211618017531, 1> ]
Time: 13.953
> /*
> The time varies quite a bit, but it is slower than it was when
> we were choosing numbers between 10^24 and 10^25. Maybe 20% slower?
> Let's increase the numbers again:
> */
> p:=NextPrime(Random(10^26,10^27));
> q:=NextPrime(Random(10^26,10^27));
> n:=p*q;
> time Factorization(n);
[ <331969608524193582256575089, 1>, <948010275834168082520404117, 1> ]
Time: 17.344
> p:=NextPrime(Random(10^26,10^27));
> q:=NextPrime(Random(10^26,10^27));
> n:=p*q;
> time Factorization(n);
[ <476286267725009618751663689, 1>, <644854380238690110928171147, 1> ]
Time: 17.750
> /*
> And increase them again:
> */
> p:=NextPrime(Random(10^27,10^28));
> q:=NextPrime(Random(10^27,10^28));
> n:=p*q;
> time Factorization(n);
[ <4049448687359574729426954041, 1>, <6140575664624903584144405909, 1> ]
Time: 31.672
> p:=NextPrime(Random(10^27,10^28));
> q:=NextPrime(Random(10^27,10^28));
> n:=p*q;
> time Factorization(n);
[ <4131750132539095352613463819, 1>, <8228330197842944372608687771, 1> ]
Time: 29.578
> p:=NextPrime(Random(10^27,10^28));
> q:=NextPrime(Random(10^27,10^28));
> n:=p*q;
> time Factorization(n);
[ <3943120139627725854113351389, 1>, <6690908727917000906689103551, 1> ]
Time: 28.313
> /*
> It is getting a lot slower.
> Increase the numbers again:
> */
> p:=NextPrime(Random(10^28,10^29));
> q:=NextPrime(Random(10^28,10^29));
> n:=p*q;
> time Factorization(n);
[ <12930758374167982529184081319, 1>, <33068255481840812222331020699, 1> ]
Time: 35.313
> p:=NextPrime(Random(10^28,10^29));
> q:=NextPrime(Random(10^28,10^29));
> n:=p*q;
> time Factorization(n);
[ <15257236264441814597929491961, 1>, <33404434439821901770043914477, 1> ]
Time: 43.703
> p:=NextPrime(Random(10^28,10^29));
> q:=NextPrime(Random(10^28,10^29));
> n:=p*q;
> time Factorization(n);
[ <85701188558340984766965206497, 1>, <88252682685932515981183289881, 1> ]
Time: 45.500
> /*
> Increasing again:
> */
> p:=NextPrime(Random(10^29,10^30));
> q:=NextPrime(Random(10^29,10^30));
> n:=p*q;
> time Factorization(n);
[ <289149324482612450872489878097, 1>, <417739360385110273641071182831, 1> ]
Time: 68.578
> p:=NextPrime(Random(10^30,10^31));
> q:=NextPrime(Random(10^30,10^31));
> n:=p*q;
> time Factorization(n);
[ <1587785972975265104249175184769, 1>, <6686281181602839790395533454461, 1> ]
Time: 118.250
> n;
10616383471517470208168640134168690005039298709051640522304509
> /*
> Here we had a 62 digit number and it took Magma a couple of minutes to
> factorize it. Previously we had a 60 digit number and it took about a minute.
> Let me try a 64 digit number:
> */
> p:=NextPrime(Random(10^31,10^32));
> q:=NextPrime(Random(10^31,10^32));
> n:=p*q;
> time Factorization(n);
[ <27577426773880947601388028051559, 1>, <28181691730126697731684181343071, 1> ]
Time: 197.766
> /*
> Over 3 minutes now. Maybe we can say that increasing the number of digits
> by 6 typically multiplies the factorization time by 3. (I think it is actually
> a lot worse than this.) If so then 70 digit numbers will take about 10 minutes,
> 76 digit numbers about a half an hour, 82 digit numbers about one and a half hours,
> 88 digit numbers about 4 and a half hours, 94 digit numbers 13.5 hours,
> 100 digit numbers over a day, 118 digit numbers a month,, 124 digit numbers 
> would take 3 months, and you certainly wouldn't want to try to factorize
> difficult 1000 digit numbers.
> */
> p:=NextPrime(Random(10^32,10^33));
> q:=NextPrime(Random(10^32,10^33));
> n:=p*q;
> time Factorization(n);
zfecm on 421113686551
(12 digits)
attempting to factor with zsquf: 421113686551
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 145503125939
(12 digits)
attempting to factor with zsquf: 145503125939
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 3955757132797
(13 digits)
attempting to factor with zsquf: 3955757132797
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 1324322855699
(13 digits)
attempting to factor with zsquf: 1324322855699
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 93765981373
(11 digits)
attempting to factor with zsquf: 93765981373
failed to factor with zsquf
1-th zfecm trial with bound 100
no success,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 356769779153
(12 digits)
attempting to factor with zsquf: 356769779153
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 50391199487
(11 digits)
attempting to factor with zsquf: 50391199487
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 69281655407
(11 digits)
attempting to factor with zsquf: 69281655407
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 85698538451
(11 digits)
attempting to factor with zsquf: 85698538451
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 66380053451
(11 digits)
attempting to factor with zsquf: 66380053451
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 4575012668087
(13 digits)
attempting to factor with zsquf: 4575012668087
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 56817285229
(11 digits)
attempting to factor with zsquf: 56817285229
failed to factor with zsquf
1-th zfecm trial with bound 100
no success,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 2037547600219
(13 digits)
attempting to factor with zsquf: 2037547600219
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 527577783653
(12 digits)
attempting to factor with zsquf: 527577783653
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.031 seconds
zfecm on 60675857027
(11 digits)
attempting to factor with zsquf: 60675857027
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 64861098989
(11 digits)
attempting to factor with zsquf: 64861098989
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 58030634677
(11 digits)
attempting to factor with zsquf: 58030634677
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 245091693053
(12 digits)
attempting to factor with zsquf: 245091693053
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.031 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.047 seconds
zfecm on 2337694130509
(13 digits)
attempting to factor with zsquf: 2337694130509
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 2623494907661
(13 digits)
attempting to factor with zsquf: 2623494907661
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.031 seconds
zfecm on 363820679077
(12 digits)
attempting to factor with zsquf: 363820679077
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 58222129619
(11 digits)
attempting to factor with zsquf: 58222129619
failed to factor with zsquf
1-th zfecm trial with bound 100
no success,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 92114045117
(11 digits)
attempting to factor with zsquf: 92114045117
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 124632213347
(12 digits)
attempting to factor with zsquf: 124632213347
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 189217361909
(12 digits)
attempting to factor with zsquf: 189217361909
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 523302349477
(12 digits)
attempting to factor with zsquf: 523302349477
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 549168534389
(12 digits)
attempting to factor with zsquf: 549168534389
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 165148404419
(12 digits)
attempting to factor with zsquf: 165148404419
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 225711028421
(12 digits)
attempting to factor with zsquf: 225711028421
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 1082667644497
(13 digits)
attempting to factor with zsquf: 1082667644497
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 887658762829
(12 digits)
attempting to factor with zsquf: 887658762829
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 4207207917019
(13 digits)
attempting to factor with zsquf: 4207207917019
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 211848878827
(12 digits)
attempting to factor with zsquf: 211848878827
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 995348016191
(12 digits)
attempting to factor with zsquf: 995348016191
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.031 seconds
zfecm on 41352460631
(11 digits)
attempting to factor with zsquf: 41352460631
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 271838141299
(12 digits)
attempting to factor with zsquf: 271838141299
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 199875703523
(12 digits)
attempting to factor with zsquf: 199875703523
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 312754918981
(12 digits)
attempting to factor with zsquf: 312754918981
failed to factor with zsquf
1-th zfecm trial with bound 100
no success,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 813692994749
(12 digits)
attempting to factor with zsquf: 813692994749
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 463198832093
(12 digits)
attempting to factor with zsquf: 463198832093
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 39595079677
(11 digits)
attempting to factor with zsquf: 39595079677
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 140738432227
(12 digits)
attempting to factor with zsquf: 140738432227
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 47875015373
(11 digits)
attempting to factor with zsquf: 47875015373
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 150330359551
(12 digits)
attempting to factor with zsquf: 150330359551
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 2737908750667
(13 digits)
attempting to factor with zsquf: 2737908750667
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 1187325838583
(13 digits)
attempting to factor with zsquf: 1187325838583
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 2911013918053
(13 digits)
attempting to factor with zsquf: 2911013918053
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 843077505503
(12 digits)
attempting to factor with zsquf: 843077505503
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 90650711663
(11 digits)
attempting to factor with zsquf: 90650711663
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 1296360762341
(13 digits)
attempting to factor with zsquf: 1296360762341
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 73433795819
(11 digits)
attempting to factor with zsquf: 73433795819
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 340756162847
(12 digits)
attempting to factor with zsquf: 340756162847
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 1769952873631
(13 digits)
attempting to factor with zsquf: 1769952873631
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 1237925114731
(13 digits)
attempting to factor with zsquf: 1237925114731
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 4375948449137
(13 digits)
attempting to factor with zsquf: 4375948449137
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 2743388488843
(13 digits)
attempting to factor with zsquf: 2743388488843
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 2198542802003
(13 digits)
attempting to factor with zsquf: 2198542802003
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 3046025082857
(13 digits)
attempting to factor with zsquf: 3046025082857
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 62779542431
(11 digits)
attempting to factor with zsquf: 62779542431
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 1880995977323
(13 digits)
attempting to factor with zsquf: 1880995977323
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 867698877047
(12 digits)
attempting to factor with zsquf: 867698877047
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 1712765789627
(13 digits)
attempting to factor with zsquf: 1712765789627
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 397476685169
(12 digits)
attempting to factor with zsquf: 397476685169
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 217163215799
(12 digits)
attempting to factor with zsquf: 217163215799
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.031 seconds
zfecm on 1185365204237
(13 digits)
attempting to factor with zsquf: 1185365204237
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 15228816107
(11 digits)
attempting to factor with zsquf: 15228816107
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 88572722621
(11 digits)
attempting to factor with zsquf: 88572722621
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 330296895713
(12 digits)
attempting to factor with zsquf: 330296895713
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 288153318653
(12 digits)
attempting to factor with zsquf: 288153318653
failed to factor with zsquf
1-th zfecm trial with bound 100
no success,    0.016 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.031 seconds
zfecm on 374500808069
(12 digits)
attempting to factor with zsquf: 374500808069
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 3596092231813
(13 digits)
attempting to factor with zsquf: 3596092231813
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 1239625652593
(13 digits)
attempting to factor with zsquf: 1239625652593
failed to factor with zsquf
1-th zfecm trial with bound 100
trivial factor in zfecm,    0.031 seconds
2-th zfecm trial with bound 100
factor in phase 2,    0.047 seconds
zfecm on 1002695191637
(13 digits)
attempting to factor with zsquf: 1002695191637
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.016 seconds
zfecm on 208335202511
(12 digits)
attempting to factor with zsquf: 208335202511
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 4566917146741
(13 digits)
attempting to factor with zsquf: 4566917146741
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 70946814413
(11 digits)
attempting to factor with zsquf: 70946814413
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 18672816077
(11 digits)
attempting to factor with zsquf: 18672816077
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 4087157595743
(13 digits)
attempting to factor with zsquf: 4087157595743
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 543027740729
(12 digits)
attempting to factor with zsquf: 543027740729
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 135043137443
(12 digits)
attempting to factor with zsquf: 135043137443
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
zfecm on 1334772044357
(13 digits)
attempting to factor with zsquf: 1334772044357
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 50282923321
(11 digits)
attempting to factor with zsquf: 50282923321
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 588801422263
(12 digits)
attempting to factor with zsquf: 588801422263
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.000 seconds
zfecm on 598048591493
(12 digits)
attempting to factor with zsquf: 598048591493
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 2,    0.016 seconds
zfecm on 133348419301
(12 digits)
attempting to factor with zsquf: 133348419301
failed to factor with zsquf
1-th zfecm trial with bound 100
factor in phase 1,    0.000 seconds
[ <714118422612876377097480831404573, 1>, <799545904334723846102946768348343, 1> ]
Time: 342.391
> /*
> Nearly 6 minutes. I think that the estimates in my previous comment
> were way too optimistic.
> */
> testrandom:=procedure(~n,N)
procedure> i:=0;
procedure> repeat
procedure|repeat> i,"random numbers tested and found to be composite";
procedure|repeat> n:=Random(N);
procedure|repeat> i:=i+1;
procedure|repeat> a:=2+Random(n-3);
procedure|repeat> until Modexp(a,n-1,n) eq 1;
procedure> end procedure;
> testrandom(~n,10^100);
0 random numbers tested and found to be composite
1 random numbers tested and found to be composite
2 random numbers tested and found to be composite
3 random numbers tested and found to be composite
4 random numbers tested and found to be composite
5 random numbers tested and found to be composite
6 random numbers tested and found to be composite
7 random numbers tested and found to be composite
8 random numbers tested and found to be composite
9 random numbers tested and found to be composite
10 random numbers tested and found to be composite
11 random numbers tested and found to be composite
12 random numbers tested and found to be composite
13 random numbers tested and found to be composite
14 random numbers tested and found to be composite
15 random numbers tested and found to be composite
16 random numbers tested and found to be composite
17 random numbers tested and found to be composite
18 random numbers tested and found to be composite
19 random numbers tested and found to be composite
20 random numbers tested and found to be composite
21 random numbers tested and found to be composite
22 random numbers tested and found to be composite
23 random numbers tested and found to be composite
24 random numbers tested and found to be composite
25 random numbers tested and found to be composite
26 random numbers tested and found to be composite
27 random numbers tested and found to be composite
28 random numbers tested and found to be composite
29 random numbers tested and found to be composite
30 random numbers tested and found to be composite
31 random numbers tested and found to be composite
32 random numbers tested and found to be composite
33 random numbers tested and found to be composite
34 random numbers tested and found to be composite
35 random numbers tested and found to be composite
36 random numbers tested and found to be composite
37 random numbers tested and found to be composite
38 random numbers tested and found to be composite
39 random numbers tested and found to be composite
40 random numbers tested and found to be composite
41 random numbers tested and found to be composite
42 random numbers tested and found to be composite
43 random numbers tested and found to be composite
44 random numbers tested and found to be composite
45 random numbers tested and found to be composite
46 random numbers tested and found to be composite
47 random numbers tested and found to be composite
48 random numbers tested and found to be composite
49 random numbers tested and found to be composite
50 random numbers tested and found to be composite
51 random numbers tested and found to be composite
52 random numbers tested and found to be composite
53 random numbers tested and found to be composite
54 random numbers tested and found to be composite
55 random numbers tested and found to be composite
56 random numbers tested and found to be composite
57 random numbers tested and found to be composite
58 random numbers tested and found to be composite
59 random numbers tested and found to be composite
60 random numbers tested and found to be composite
61 random numbers tested and found to be composite
62 random numbers tested and found to be composite
63 random numbers tested and found to be composite
64 random numbers tested and found to be composite
65 random numbers tested and found to be composite
66 random numbers tested and found to be composite
67 random numbers tested and found to be composite
68 random numbers tested and found to be composite
69 random numbers tested and found to be composite
70 random numbers tested and found to be composite
71 random numbers tested and found to be composite
72 random numbers tested and found to be composite
73 random numbers tested and found to be composite
74 random numbers tested and found to be composite
75 random numbers tested and found to be composite
76 random numbers tested and found to be composite
77 random numbers tested and found to be composite
78 random numbers tested and found to be composite
79 random numbers tested and found to be composite
80 random numbers tested and found to be composite
81 random numbers tested and found to be composite
82 random numbers tested and found to be composite
83 random numbers tested and found to be composite
84 random numbers tested and found to be composite
85 random numbers tested and found to be composite
86 random numbers tested and found to be composite
87 random numbers tested and found to be composite
88 random numbers tested and found to be composite
89 random numbers tested and found to be composite
90 random numbers tested and found to be composite
91 random numbers tested and found to be composite
92 random numbers tested and found to be composite
93 random numbers tested and found to be composite
94 random numbers tested and found to be composite
95 random numbers tested and found to be composite
96 random numbers tested and found to be composite
97 random numbers tested and found to be composite
98 random numbers tested and found to be composite
99 random numbers tested and found to be composite
100 random numbers tested and found to be composite
101 random numbers tested and found to be composite
102 random numbers tested and found to be composite
103 random numbers tested and found to be composite
104 random numbers tested and found to be composite
105 random numbers tested and found to be composite
106 random numbers tested and found to be composite
107 random numbers tested and found to be composite
108 random numbers tested and found to be composite
109 random numbers tested and found to be composite
110 random numbers tested and found to be composite
111 random numbers tested and found to be composite
112 random numbers tested and found to be composite
113 random numbers tested and found to be composite
114 random numbers tested and found to be composite
115 random numbers tested and found to be composite
116 random numbers tested and found to be composite
117 random numbers tested and found to be composite
118 random numbers tested and found to be composite
119 random numbers tested and found to be composite
120 random numbers tested and found to be composite
121 random numbers tested and found to be composite
122 random numbers tested and found to be composite
123 random numbers tested and found to be composite
124 random numbers tested and found to be composite
125 random numbers tested and found to be composite
126 random numbers tested and found to be composite
127 random numbers tested and found to be composite
> n;
12888582683476494357728896215025130558281417143194370368099154824707815021719533699704686\
54434893913
> IsPrime(n);
true
> testrandom(~n,10^100);
0 random numbers tested and found to be composite
1 random numbers tested and found to be composite
2 random numbers tested and found to be composite
3 random numbers tested and found to be composite
4 random numbers tested and found to be composite
5 random numbers tested and found to be composite
6 random numbers tested and found to be composite
7 random numbers tested and found to be composite
8 random numbers tested and found to be composite
9 random numbers tested and found to be composite
10 random numbers tested and found to be composite
11 random numbers tested and found to be composite
12 random numbers tested and found to be composite
13 random numbers tested and found to be composite
14 random numbers tested and found to be composite
15 random numbers tested and found to be composite
16 random numbers tested and found to be composite
17 random numbers tested and found to be composite
18 random numbers tested and found to be composite
19 random numbers tested and found to be composite
20 random numbers tested and found to be composite
21 random numbers tested and found to be composite
22 random numbers tested and found to be composite
23 random numbers tested and found to be composite
24 random numbers tested and found to be composite
25 random numbers tested and found to be composite
26 random numbers tested and found to be composite
27 random numbers tested and found to be composite
28 random numbers tested and found to be composite
29 random numbers tested and found to be composite
30 random numbers tested and found to be composite
31 random numbers tested and found to be composite
32 random numbers tested and found to be composite
33 random numbers tested and found to be composite
34 random numbers tested and found to be composite
35 random numbers tested and found to be composite
36 random numbers tested and found to be composite
37 random numbers tested and found to be composite
38 random numbers tested and found to be composite
39 random numbers tested and found to be composite
40 random numbers tested and found to be composite
41 random numbers tested and found to be composite
42 random numbers tested and found to be composite
43 random numbers tested and found to be composite
44 random numbers tested and found to be composite
45 random numbers tested and found to be composite
46 random numbers tested and found to be composite
47 random numbers tested and found to be composite
48 random numbers tested and found to be composite
49 random numbers tested and found to be composite
50 random numbers tested and found to be composite
51 random numbers tested and found to be composite
52 random numbers tested and found to be composite
53 random numbers tested and found to be composite
54 random numbers tested and found to be composite
55 random numbers tested and found to be composite
56 random numbers tested and found to be composite
57 random numbers tested and found to be composite
58 random numbers tested and found to be composite
59 random numbers tested and found to be composite
60 random numbers tested and found to be composite
61 random numbers tested and found to be composite
62 random numbers tested and found to be composite
63 random numbers tested and found to be composite
64 random numbers tested and found to be composite
65 random numbers tested and found to be composite
66 random numbers tested and found to be composite
67 random numbers tested and found to be composite
68 random numbers tested and found to be composite
69 random numbers tested and found to be composite
70 random numbers tested and found to be composite
71 random numbers tested and found to be composite
72 random numbers tested and found to be composite
73 random numbers tested and found to be composite
74 random numbers tested and found to be composite
75 random numbers tested and found to be composite
76 random numbers tested and found to be composite
77 random numbers tested and found to be composite
78 random numbers tested and found to be composite
79 random numbers tested and found to be composite
80 random numbers tested and found to be composite
81 random numbers tested and found to be composite
82 random numbers tested and found to be composite
83 random numbers tested and found to be composite
84 random numbers tested and found to be composite
85 random numbers tested and found to be composite
86 random numbers tested and found to be composite
87 random numbers tested and found to be composite
88 random numbers tested and found to be composite
89 random numbers tested and found to be composite
90 random numbers tested and found to be composite
91 random numbers tested and found to be composite
92 random numbers tested and found to be composite
93 random numbers tested and found to be composite
94 random numbers tested and found to be composite
95 random numbers tested and found to be composite
96 random numbers tested and found to be composite
97 random numbers tested and found to be composite
98 random numbers tested and found to be composite
99 random numbers tested and found to be composite
100 random numbers tested and found to be composite
101 random numbers tested and found to be composite
102 random numbers tested and found to be composite
103 random numbers tested and found to be composite
104 random numbers tested and found to be composite
105 random numbers tested and found to be composite
106 random numbers tested and found to be composite
107 random numbers tested and found to be composite
108 random numbers tested and found to be composite
109 random numbers tested and found to be composite
> n;
95238306211873812622453227526078033022250557608183305829099121425102534774466218207051478\
15072927047
> IsPrime(n);
true
> testrandom(~n,10^100);
0 random numbers tested and found to be composite
1 random numbers tested and found to be composite
2 random numbers tested and found to be composite
3 random numbers tested and found to be composite
4 random numbers tested and found to be composite
5 random numbers tested and found to be composite
6 random numbers tested and found to be composite
7 random numbers tested and found to be composite
8 random numbers tested and found to be composite
9 random numbers tested and found to be composite
10 random numbers tested and found to be composite
11 random numbers tested and found to be composite
12 random numbers tested and found to be composite
13 random numbers tested and found to be composite
14 random numbers tested and found to be composite
15 random numbers tested and found to be composite
16 random numbers tested and found to be composite
17 random numbers tested and found to be composite
> n;
73066716840504671838529187302127960649240455096621429926350420481296256428228294109180070\
77931430539
> IsPrime(n);
true
> testrandom(~n,10^100);
0 random numbers tested and found to be composite
1 random numbers tested and found to be composite
2 random numbers tested and found to be composite
3 random numbers tested and found to be composite
4 random numbers tested and found to be composite
5 random numbers tested and found to be composite
6 random numbers tested and found to be composite
7 random numbers tested and found to be composite
8 random numbers tested and found to be composite
9 random numbers tested and found to be composite
10 random numbers tested and found to be composite
11 random numbers tested and found to be composite
12 random numbers tested and found to be composite
13 random numbers tested and found to be composite
14 random numbers tested and found to be composite
15 random numbers tested and found to be composite
16 random numbers tested and found to be composite
17 random numbers tested and found to be composite
18 random numbers tested and found to be composite
19 random numbers tested and found to be composite
20 random numbers tested and found to be composite
21 random numbers tested and found to be composite
22 random numbers tested and found to be composite
23 random numbers tested and found to be composite
24 random numbers tested and found to be composite
25 random numbers tested and found to be composite
26 random numbers tested and found to be composite
27 random numbers tested and found to be composite
28 random numbers tested and found to be composite
29 random numbers tested and found to be composite
30 random numbers tested and found to be composite
31 random numbers tested and found to be composite
32 random numbers tested and found to be composite
33 random numbers tested and found to be composite
34 random numbers tested and found to be composite
35 random numbers tested and found to be composite
36 random numbers tested and found to be composite
37 random numbers tested and found to be composite
38 random numbers tested and found to be composite
39 random numbers tested and found to be composite
40 random numbers tested and found to be composite
41 random numbers tested and found to be composite
42 random numbers tested and found to be composite
43 random numbers tested and found to be composite
44 random numbers tested and found to be composite
45 random numbers tested and found to be composite
46 random numbers tested and found to be composite
47 random numbers tested and found to be composite
48 random numbers tested and found to be composite
49 random numbers tested and found to be composite
50 random numbers tested and found to be composite
51 random numbers tested and found to be composite
52 random numbers tested and found to be composite
53 random numbers tested and found to be composite
54 random numbers tested and found to be composite
55 random numbers tested and found to be composite
56 random numbers tested and found to be composite
57 random numbers tested and found to be composite
58 random numbers tested and found to be composite
59 random numbers tested and found to be composite
60 random numbers tested and found to be composite
61 random numbers tested and found to be composite
62 random numbers tested and found to be composite
63 random numbers tested and found to be composite
64 random numbers tested and found to be composite
65 random numbers tested and found to be composite
66 random numbers tested and found to be composite
67 random numbers tested and found to be composite
68 random numbers tested and found to be composite
69 random numbers tested and found to be composite
70 random numbers tested and found to be composite
71 random numbers tested and found to be composite
72 random numbers tested and found to be composite
73 random numbers tested and found to be composite
74 random numbers tested and found to be composite
75 random numbers tested and found to be composite
76 random numbers tested and found to be composite
77 random numbers tested and found to be composite
78 random numbers tested and found to be composite
79 random numbers tested and found to be composite
80 random numbers tested and found to be composite
81 random numbers tested and found to be composite
82 random numbers tested and found to be composite
83 random numbers tested and found to be composite
84 random numbers tested and found to be composite
85 random numbers tested and found to be composite
86 random numbers tested and found to be composite
87 random numbers tested and found to be composite
88 random numbers tested and found to be composite
89 random numbers tested and found to be composite
90 random numbers tested and found to be composite
91 random numbers tested and found to be composite
92 random numbers tested and found to be composite
93 random numbers tested and found to be composite
94 random numbers tested and found to be composite
95 random numbers tested and found to be composite
96 random numbers tested and found to be composite
97 random numbers tested and found to be composite
98 random numbers tested and found to be composite
99 random numbers tested and found to be composite
100 random numbers tested and found to be composite
101 random numbers tested and found to be composite
102 random numbers tested and found to be composite
103 random numbers tested and found to be composite
104 random numbers tested and found to be composite
105 random numbers tested and found to be composite
106 random numbers tested and found to be composite
107 random numbers tested and found to be composite
108 random numbers tested and found to be composite
109 random numbers tested and found to be composite
110 random numbers tested and found to be composite
111 random numbers tested and found to be composite
112 random numbers tested and found to be composite
113 random numbers tested and found to be composite
114 random numbers tested and found to be composite
115 random numbers tested and found to be composite
116 random numbers tested and found to be composite
117 random numbers tested and found to be composite
118 random numbers tested and found to be composite
119 random numbers tested and found to be composite
120 random numbers tested and found to be composite
121 random numbers tested and found to be composite
122 random numbers tested and found to be composite
123 random numbers tested and found to be composite
124 random numbers tested and found to be composite
125 random numbers tested and found to be composite
126 random numbers tested and found to be composite
127 random numbers tested and found to be composite
128 random numbers tested and found to be composite
129 random numbers tested and found to be composite
130 random numbers tested and found to be composite
131 random numbers tested and found to be composite
132 random numbers tested and found to be composite
133 random numbers tested and found to be composite
134 random numbers tested and found to be composite
135 random numbers tested and found to be composite
136 random numbers tested and found to be composite
137 random numbers tested and found to be composite
138 random numbers tested and found to be composite
139 random numbers tested and found to be composite
140 random numbers tested and found to be composite
141 random numbers tested and found to be composite
142 random numbers tested and found to be composite
143 random numbers tested and found to be composite
144 random numbers tested and found to be composite
145 random numbers tested and found to be composite
146 random numbers tested and found to be composite
147 random numbers tested and found to be composite
148 random numbers tested and found to be composite
149 random numbers tested and found to be composite
150 random numbers tested and found to be composite
151 random numbers tested and found to be composite
152 random numbers tested and found to be composite
153 random numbers tested and found to be composite
154 random numbers tested and found to be composite
155 random numbers tested and found to be composite
156 random numbers tested and found to be composite
157 random numbers tested and found to be composite
158 random numbers tested and found to be composite
159 random numbers tested and found to be composite
160 random numbers tested and found to be composite
161 random numbers tested and found to be composite
162 random numbers tested and found to be composite
163 random numbers tested and found to be composite
164 random numbers tested and found to be composite
165 random numbers tested and found to be composite
166 random numbers tested and found to be composite
167 random numbers tested and found to be composite
168 random numbers tested and found to be composite
169 random numbers tested and found to be composite
170 random numbers tested and found to be composite
171 random numbers tested and found to be composite
172 random numbers tested and found to be composite
173 random numbers tested and found to be composite
174 random numbers tested and found to be composite
175 random numbers tested and found to be composite
176 random numbers tested and found to be composite
177 random numbers tested and found to be composite
178 random numbers tested and found to be composite
179 random numbers tested and found to be composite
180 random numbers tested and found to be composite
181 random numbers tested and found to be composite
182 random numbers tested and found to be composite
183 random numbers tested and found to be composite
184 random numbers tested and found to be composite
185 random numbers tested and found to be composite
186 random numbers tested and found to be composite
187 random numbers tested and found to be composite
188 random numbers tested and found to be composite
189 random numbers tested and found to be composite
190 random numbers tested and found to be composite
191 random numbers tested and found to be composite
192 random numbers tested and found to be composite
193 random numbers tested and found to be composite
194 random numbers tested and found to be composite
195 random numbers tested and found to be composite
196 random numbers tested and found to be composite
197 random numbers tested and found to be composite
198 random numbers tested and found to be composite
199 random numbers tested and found to be composite
200 random numbers tested and found to be composite
201 random numbers tested and found to be composite
202 random numbers tested and found to be composite
203 random numbers tested and found to be composite
204 random numbers tested and found to be composite
205 random numbers tested and found to be composite
206 random numbers tested and found to be composite
207 random numbers tested and found to be composite
208 random numbers tested and found to be composite
209 random numbers tested and found to be composite
210 random numbers tested and found to be composite
211 random numbers tested and found to be composite
212 random numbers tested and found to be composite
213 random numbers tested and found to be composite
214 random numbers tested and found to be composite
215 random numbers tested and found to be composite
216 random numbers tested and found to be composite
217 random numbers tested and found to be composite
218 random numbers tested and found to be composite
219 random numbers tested and found to be composite
220 random numbers tested and found to be composite
221 random numbers tested and found to be composite
222 random numbers tested and found to be composite
223 random numbers tested and found to be composite
224 random numbers tested and found to be composite
225 random numbers tested and found to be composite
226 random numbers tested and found to be composite
227 random numbers tested and found to be composite
228 random numbers tested and found to be composite
229 random numbers tested and found to be composite
230 random numbers tested and found to be composite
231 random numbers tested and found to be composite
232 random numbers tested and found to be composite
233 random numbers tested and found to be composite
234 random numbers tested and found to be composite
235 random numbers tested and found to be composite
236 random numbers tested and found to be composite
237 random numbers tested and found to be composite
238 random numbers tested and found to be composite
239 random numbers tested and found to be composite
240 random numbers tested and found to be composite
241 random numbers tested and found to be composite
242 random numbers tested and found to be composite
243 random numbers tested and found to be composite
244 random numbers tested and found to be composite
245 random numbers tested and found to be composite
246 random numbers tested and found to be composite
247 random numbers tested and found to be composite
248 random numbers tested and found to be composite
249 random numbers tested and found to be composite
250 random numbers tested and found to be composite
251 random numbers tested and found to be composite
252 random numbers tested and found to be composite
253 random numbers tested and found to be composite
> n;
40422143535463254843598084406775527992248853348490480942595191793934064766124955034711678\
32229462209
> IsPrime(n);
true
> /*
> It is extremely rare for a^(n-1) to be congruent to 1 mod n,
> except when n is prime. In practice, it just never happens.
> */
> a:=Random(10^100,10^101);
> p:=NextPrime(a);
> a:=Random(10^100,10^101);
> q:=NextPrime(a);
> n:=p*q;
> n;
22815791548076041316932613464422057578049238922645103378264622081400672603298258847205860\
15539032413965719170394468802685144361256832931377502036212115661400688358256154536519191\
07562658026990570361349
> e:=65537;
> d:=InverseMod(e,(p-1)*(q-1))
> ;
> d;
80245356849284030754428298572551143197588378651291580766437209359031616263488543330957333\
50347848869318995629200287247493628782072786586048235933253629921102246839012949566124711\
243015890872593816173
> e*d mod ((p-1)*(q-1));
1
> usydmaths:=NaiveEncoding("Computer Tutorial 6,
> MATH2068/2988 (Number Theory and Cryptography),
> School of Mathematics and Statistics,
> The University of Sydney,
> NSW 2006,
> Australia.");
> usydmaths;
[ 167211209212217216201214132184217216211214205197208132154144110177165184172150148154156\
14715015715615613214017821720919820121413218420420121121422113219721020013216721422121221\
6211203214197212204221, 14114411018319920421121120813221120213217719721620420120919721620\
51992151321972102001321832161972162052152162051992151441101842042011321852102052182012142\
15205216221132211202132183221200210201221144, 
110178183187132150148148154144110165217215216214197208205197146 ]
> NaiveDecoding(usydmaths);
Computer Tutorial 6,
MATH2068/2988 (Number Theory and Cryptography),
School of Mathematics and Statistics,
The University of Sydney,
NSW 2006,
Australia.
> /*
> My "NaiveEncoding" function simply converts the text into a sequence of numbers
> in some simple way, and "NaiveDecoding" gets the text back from the
> sequence of numbers.
> Having converted the text into a numerical form like this we can encipher
> it using RSA.
> */
> ct:=[Modexp(m,e,n): m in usydmaths];
> ct;
[ 617587466440634818821915059587791695671457942862150646155845415521970710358229975078054\
94407527975824710872926379823308984536249826450363940875429067827725502484770952770763405\
154211273511160915619626, 177940798214402214312713874313301630605495596878896352893861993\
64193069952463941447183881741017546619876999943004529780525996057194474255805128817146177\
7196431541602567680073044141021289974095146107807, 
95282965300140574685844354971398076984137160284415829782311854858534793078254122176546331\
39442400991214351258640303718549912585713387220438013523094840081185113907796250006887924\
2667118598480046680572 ]
> /*
> Like the plaintext (usydmaths), the ciphertext (ct) is a sequence of numbers.
> Now let us decipher the ciphertext:
> */
> pt:=[Modexp(m,d,n): m in ct];
> pt;
[ 167211209212217216201214132184217216211214205197208132154144110177165184172150148154156\
14715015715615613214017821720919820121413218420420121121422113219721020013216721422121221\
6211203214197212204221, 14114411018319920421121120813221120213217719721620420120919721620\
51992151321972102001321832161972162052152162051992151441101842042011321852102052182012142\
15205216221132211202132183221200210201221144, 
110178183187132150148148154144110165217215216214197208205197146 ]
> /*
> You can see that pt is exactly the same as usydmaths.
> Magma will confirm it:
> */
> pt eq usydmaths;
true
> /*
> And so, to get the text form instead of the numerical form, applyt
> the NaiveDecoding function:
> */
> NaiveDecoding(pt);
Computer Tutorial 6,
MATH2068/2988 (Number Theory and Cryptography),
School of Mathematics and Statistics,
The University of Sydney,
NSW 2006,
Australia.
> n1;
25461315923422027661959597601686672720959364234845325030741933868203253638850608180520508\
43611412873051838444791866914726074231316124273605882417588401396955851937396924249602783\
05387113840951756397333392802727025098561857159395197262823172890954695212630241408018324\
122995583616837599805511637206361
> e1;
11319597741438611912490163357763029466920269136426382875589972204818448998457430297326357\
40456508803298425885333547373374936691012781230877669140116765399738961084589784442104332\
39074650102851402614876021191472849028961993860030507077143710912488285517427718493642913\
253657873607316977318829354049369
> /*
> The pair (n1, e1) form the "public key" for this instance of the RSA
> cryptosystem. Knowing the factorization of n1 we can determine the private key.
> */
> p1;
50466940611139125118588824525183361148544241201867529127971168188836316032369792201850787\
3396175889024272264286963683347187579992194268976198679699123
> q1;
50451474995498686397561106364600288187333751361489616326726359734983942776023870783392817\
7051549647660424199059275296804304735491045588517503931437507
> p1*q1;
25461315923422027661959597601686672720959364234845325030741933868203253638850608180520508\
43611412873051838444791866914726074231316124273605882417588401396955851937396924249602783\
05387113840951756397333392802727025098561857159395197262823172890954695212630241408018324\
122995583616837599805511637206361
> p1*q1 eq n1;
true
> d1:=InverseMod(e1,(p1-1)*(q1-1));
> d1;
33859272032180445228321283194049376673184000499109116481926322902973311449280733717883082\
11767624895840385979422141256097109628072104557303953600388373815903571701245118921614281\
79856303509783504925428843844380615692759012834379885703505187709759130131876738644447275\
83690737971478513392641604754281
> /*
> Our private key is (n1, d1). When we receive a message, we  can use this
> key to recover the (numerical form) of the message. 
> The enciphered message we received in this instance was called ctext1.
> */
> ctext1;
[ 149289008161921538277893179784215595269239030778643091613102378715554516258974927007317\
40973963292301905579123804870542915558912793864764415158723923907892686800536423389166974\
87059325369085125449635730540594469736815922305840206578220733332549439960454672887580457\
56183384582159391755224739270032606, 1137198626753194656552975219597685599582800350671122\
14849561722149717487228561772878568342147717915819876013773872418895918050892326992932688\
91526551259473079347222590947846710643207877003590065265012714271240174416128958497204038\
1198182207963800195147223026694822786770915298724130531500395918411920, 
33660801253741773041767496203978933128049787030902279892251162174537045176699353026240066\
12807553536134816237083360769889160762476174416413289380301046917589460505364404586529546\
22224115236496278479577890005704703029018520803943400605170952954619398439371588888142006\
29709358933002141974563182253740, 1586788389207588251908906963702872085131427143798910884\
30976495147682931969097321719987456282768890667609844865887847755616271771440869388758338\
21752112769374834576669102296020017830499260105860706469091840789389264571400704357191615\
3328664965574861004218642450245213365120500000120930323772659642479, 
69112980046822407127451477674356331893380624068274274549043116419141990394421570849649827\
44529401557697834235654763422234778337693203764520864884958852751892731351464095849105264\
62461257370253524775569165143815333796691353490754757035209806009031248372391988833308724\
37348424825085866313595164794808, 1417156255616829468126732252933362972770114291119501218\
82022298404998400969897441864981723560097845988250251353647038451893184495244398988786283\
07951735120266891279494711632897758577495936724995050789831056652949659917250810139515793\
250652894018746895374240224036595237977517549320120293481637057329, 
18327709428176662233012624774041108226137988750613617310258899130003260150851088231516358\
33648747043045375533109729079408831477830387229861397879568654430226287191871564185902871\
56323989344741990187695301207782719141007788621635023545154560808491597796231290196709173\
288485132717180414490918560253481, 764410188584990506780492257118185131918315436582529843\
45113020011505731706448969883205729161501017341865839502375765328427874147461578912561796\
76125434596017821945515071808517913960578277491084058872565879806868524721000661245449063\
2662567648505087102953069141074357135391192010300543763235726680298, 
18689409299664190541431872305318002090440109203811369468519429007056710797048189663329320\
55663164809865629302679708406592747907833212711315383516197969475196116006147990803936608\
78793663804795492847482539772006777753601503879710517151984218058948446831543952844579122\
633047315381284062402644851318704, 204171976142742515498250140532041489438346097575731555\
48297334908442642104391336095134914880016940200830307258786542118530579893062160200126227\
86895349554923806727853314502540944922411839434036440772615600006235681187166225388372820\
63526634892526254759829043239323072866386766166447575625259198015230, 
46072953846490481878823278302641404584782889497388457410254989404564947838629352513801118\
82387792083833601504231093063258695696765903714575105942381870410264378034426961283924822\
92994304578927094287193395543676022342399144446678029235207160844082323785416056116378067\
22769206372370333840588634003218, 2526682981167037744443018788029315664813183636958449283\
23664804751433880551000349716445675636206447327882522096282432431532202497858123588222327\
62344405449944983993383961708831808440956138611243787093727560892771831735561205978061667\
9854570422441430012714739947470898069774176374024285282581286283228, 
76932506072251854156742729104057397589040220487254947652917239442371854635199857838747299\
68042052476639841719930085318562564527232888755763708663561285751073066142020929619830731\
22605307211917935840577711847543569232147143355344391026679315255953582706875472419636385\
23853966156885959276523211635204, 1064388483451018538039153885932198025937520841224768326\
67246843355044064615696154488713881986039520903918731759491446464912820146635484959477814\
67863286574774867288075881271238366124313374524563500778449161859651746201024169635859047\
6644781707727431506724902993261166439373488896452983754963043246638, 
34937601850631206935373073523657685821394610757069318189355439192264600311604215651739490\
26707375163638020580052209050412890634095879213728430276520274887173060717103093707339179\
13903939716628791451513012895854583984861522005129129403805001333848071775679934599117229\
65642645210416480307989234930702 ]
> decipheredmessage:=[Modexp(m,d1,n1): m in ctext1];
> /* 
> If we were to print this out, we would find that it is a sequence of very
> large numbers. But let us decode it to get the actual text form of the message:
> */
> NaiveDecoding(decipheredmessage);
One afternoon a big wolf waited in a dark forest for a little girl to come
along carrying a basket of food to her grandmother. Finally a little girl
did come along and she was carrying a basket of food. "Are you carrying
that basket to your grandmother?" asked the wolf. The little girl said
yes, she was. So the wolf asked her where her grandmother lived and the
little girl told him and he disappeared into the wood.

When the little girl opened the door of her grandmother's house she saw
that there was somebody in bed with a nightcap and nightgown on. She had
approached no nearer than twenty-five feet from the bed when she saw that
it was not her grandmother but the wolf, for even in a nightcap a wolf
does not look any more like your grandmother than the Metro-Goldwyn lion
looks like Calvin Coolidge. So the little girl took an automatic out of
her basket and shot the wolf dead.

Moral: It is not so easy to fool little girls nowadays as it used to be.
> n2;
16941350618037412441535370462916660657494036561523482879545893931746691835787951703871227\
96697316759860110507518877392092990917655633749150096500090435570449258968849307946076273\
73099192758461047791100612456837062561092548435702629336199007925257391387607505509601833\
222026985300506305571570707493827
> p2;
65491180162159844598242828338314099651468899481048401625375453993747033966342755866346985\
2077080189613287345070039604640089759880760363672201416790403
> q2;
25868140681065260562819466601634371309770955076446857516082034470343339763949718291144109\
1829189195848916164711938292260615232107354385999736033673409
> n2 eq p2*q2;
true
> e2;
11658198433089979398887039680306478267119007876096937572300652920320831317961521692096200\
26167705137652445791861162688577128311669856969986307234492714816546740580274766333197230\
39159596339156411006096712418690432718367162620276815282563782280978858341339455879556388\
79731987177553937295100630578479
> d2:=InverseMod(e2,(p2-1)*(q2-1));
> decipheredmessage2:=[Modexp(m,d2,n2): m in ctext2];
> NaiveDecoding(decipheredmessage2);
Once upon a sunny morning a man who sat in a breakfast nook looked up
from his scrambled eggs to see a white unicorn with a golden horn
quietly cropping the roses in the garden. The man went up to the bedroom
where his wife was still asleep and woke her. "There's a unicorn in the
garden," he said. "Eating roses." She opened one unfriendly eye and
looked at him. "The unicorn is a mythical beast," she said, and turned
her back on him. The man walked slowly downstairs and out into the
garden. The unicorn was still there; he was now browsing among the
tulips. "Here, unicorn," said the man and pulled up a lily and gave it
to him. The unicorn ate it gravely. With a high heart, because there was
a unicorn in his garden, the man went upstairs and roused his wife
again. "The unicorn," he said, "ate a lily." His wife sat up in bed and
looked at him, coldly. "You are a booby," she said, "and I am going to
have you put in a booby-hatch." The man, who never liked the words
"booby" and "booby-hatch," and who liked them even less on a shining
morning when there was a unicorn in the garden, thought for a moment.
"We'll see about that," he said. He walked over to the door. "He has a
golden horn in the middle of his forehead," he told her. Then he went
back to the garden to watch the unicorn; but the unicorn had gone away.
The man sat among the roses and went to sleep.

And as soon as the husband had gone out of the house, the wife got up
and dressed as fast as she could. She was very excited and there was a
gloat in her eye. She telephoned the police and she telephoned the
psychiatrist; she told them to hurry to her house and bring a strait-jacket.
When the police and the psychiatrist arrived they sat down in chairs and
looked at her, with great interest. "My husband," she said, "saw a unicorn
this morning." The police looked at the psychiatrist and the psychiatrist
looked at the police. "He told me it ate a lily," she said. The psychiatrist
looked at the police and the police looked at the psychiatrist. "He told
me it had a golden horn in the middle of its forehead," she said. At a solemn
signal from the signal from the psychiatrist, the police leaped from
their chairs and seized the wife. They had a hard time subduing her, for
she put up a terrific struggle, but they finally subdued her. Just as
they got her into the strait-jacket, the husband came back into the
house.

"Did you tell your wife you saw a unicorn?" asked the police. "Of course
not," said the husband. "The unicorn is a mythical beast." "That's all I
wanted to know," said the psychiatrist. "Take her away. I'm sorry, sir,
but your wife is as crazy as a jay bird." So they took her away, cursing
and screaming, and shut her up in an institution. The husband lived
happily ever after.

Moral: Don't count your boobies until they are hatched.
> r:=1;
> N:=0;
> i:=1;
> /*
> At each step in the loop that I am about to perform, r will be
> the repunit that has i digits. N will be the number of repunits
> that have been found to be prime. We only have to test r for
> primality in the case that i is prime.
> */
> while N lt 5 do
while> r:=10*r+1;
while> i:=i+1;
while> if IsPrime(i) then
while|if> if IsProbablyPrime(r) then
while|if|if> N:=N+1;
while|if|if> "The repunit that has",i,"digits is prime. Here it is:";
while|if|if> r;
while|if|if> end if;
while|if> end if;
while> end while;
The repunit that has 2 digits is prime. Here it is:
11
The repunit that has 19 digits is prime. Here it is:
1111111111111111111
The repunit that has 23 digits is prime. Here it is:
11111111111111111111111
The repunit that has 317 digits is prime. Here it is:
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111
The repunit that has 1031 digits is prime. Here it is:
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\
1111111111111111111111111111111111111111111111111111
> UnsetLogFile();