[Tutor] Determining periodicity of rand.randint()

[Kent Johnson]

On Sat, Jan 31, 2009 at 3:39 PM, Tony Cappellini <cappy2112 at gmail.com> wrote:
>
>
> Has anyone ever measured how random (or deterministic) a given sequence of
> numbers generated by rand.randint() are?
>
> Using these arguments for rand.randint(0, 10000000 )
> if a program which calls rand.randint() runs for 10 hours (or a few days),
> will it keep generating a repeatable set of numbers at some point? I'm
> trying to understand the periodicity (or lack of) of the numbers generated
> by rand.randint()

According to the docs
http://docs.python.org/library/random.html
"Python uses the Mersenne Twister as the core generator. It produces
53-bit precision floats and has a period of 2**19937-1."
http://en.wikipedia.org/wiki/Mersenne_twister

2**29937-1 is about 10**13819 which is a pretty big number :-) You
would have to use over 10**13808 numbers per second to start repeating
in 10 hours. So I think you are safe.

Kent

PS The exact value of 2**19937-1 is
43154247973881626480552355163379198390539350432267115051652505414033306801376580911304513629318584665545269938257648835317902217334584413909528269154609168019007875343741396296801920114486480902661414318443276980300066728104984095451588176077132969843762134621790396391341285205627619600513106646376648615994236675486537480241964350295935168662363909047948347692313978301377820785712419054474332844529183172973242310888265081321626469451077707812282829444775022680488057820028764659399164766265200900561495800344054353690389862894061792872011120833614808447482913547328367277879565648307846909116945866230169702401260240187028746650033445774570315431292996025187780790119375902863171084149642473378986267503308961374905766340905289572290016038000571630875191373979555047468154333253474991046248132504516341796551470575481459200859472614836213875557116864445789750886277996487304308450484223420629266518556024339339190844368921018424844677042727664601852914925277280922697538426770257333928954401205465895610347658855386633902546289962132643282425748035786233580608154696546932563833327670769899439774888526687278527451002963059146963875715425735534475979734463100678367393327402149930968778296741391514599602374213629898720611431410402147238998090962818915890645693934483330994169632295877995848993366747014871763494805549996163051541225403465297007721146231355704081493098663065733677191172853987095748167816256084212823380168625334586431254034670806135273543270714478876861861983320777280644806691125713197262581763151313596429547763576367837019349835178462144294960757190918054625114143666384189433852576452289347652454631535740468786228945885654608562058042468987372436921445092315377698407168198376538237748614196207041548106379365123192817999006621766467167113471632715481795877005382694393400403061700457691135349187874888923429349340145170571716181125795888889277495426977149914549623916394014822985025331651511431278802009056808456506818877266609831636883884905621822262933986548645669080672191704740408891349835685662428063231198520436826329415290752972798343429446509992206368781367154091702655772727391329424277529349082600585884766523150957417077831910016168475685658673192860882070179760307269849987354836042371734660257694347235506301744118874141292438958141549100609752216882230887611431996472330842380137110927449483557815037586849644585749917772869926744218369621137675101083278543794081749094091043084096774144708436324279476892056200427227961638669149805489831121244676399931955371484012886360748706479568669048574782855217054740113945929622177502575565811067452201448981991968635965361551681273982740760138899638820318776303668762730157584640042798880691862640268612686180883874939573818125022279689930267446255773959542469831637863000171279227151406034129902181570659650532600775823677398182129087394449859182749999007223592423334567850671186568839186747704960016277540625331440619019129983789914712515365200336057993508601678807687568562377857095255541304902927192220184172502357124449911870210642694565061384919373474324503966267799038402386781686809962015879090586549423504699190743519551043722544515740967829084336025938225780730880273855261551972044075620326780624448803490998232161231687794715613405793249545509528052518010123087258778974115817048245588971438596754408081313438375502988726739523375296641615501406091607983229239827240614783252892479716519936989519187808681221191641747710902480633491091704827441228281186632445907145787138351234842261380074621914004818152386666043133344875067903582838283562688083236575482068479639546383819532174522502682372441363275765875609119783653298312066708217149316773564340379289724393986744139891855416612295739356668612658271234696438377122838998040199739078061443675415671078463404673702403777653478173367084844734702056866636158138003692253382209909466469591930161626097920508742175670306505139542860750806159835357541032147095084278461056701367739794932024202998707731017692582046210702212514120429322530431789616267047776115123597935404147084870985465426502772057300900333847905334250604119503030001704002887892941404603345869926367501355094942750552591581639980523190679610784993580896683299297681262442314008657033421868094551740506448829039207316711307695131892296593509018623094810557519560305240787163809219164433754514863301000915916985856242176563624771328981678548246297376249530251360363412768366456175077031977457534912806433176539995994343308118470147158712816149394421276614228262909950055746981053206610001560295784656616193252269412026831159508949671513845195883217147982748879261851417819979034417285598607727220866677680426090308754823803345446566305619241308374452754668143015487710877728011086004325892262259413968285283497045571062757701421761565262725153407407625405149931989494459106414660534305378576709862520049864880961144869258603473714363659194013962706366851389299692869491805172556818508298824954954815796063169517658741420159798754273428026723452481263569157307213153739781041627653715078598504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