Current status of the official MAX Prime Challenge.
Active
About 20000 digits
MAX Prime Challenge 20000 digits filter AUTO
Challenge:MPC-OFFICIAL-5-20000D-FILTERAUTO-P1
Classical expectation to beat
What would simple random generation predict?
Live comparison
Classical average first prime≈ 46,052 candidates
For random integers of about 20,000 digits.
Current progress550 / 2,000
Candidates tested so far versus the planned maximum.
Classical probability so far1.19%
Probability of already finding at least one prime within 550 random candidates.
Classical probability at full limit4.25%
Probability of at least one prime within all 2,000 planned candidates.
Current target.
The Challenge is trying to find a verified probable prime before the classical average of approximately
46,052 candidates.
No verified hit has been found yet, so no observed advantage can be calculated.
At the current point, the classical probability of already having found at least one prime is
1.19%.
Work units completed550 / 2000 (27.5%)
Contributors1
Verified hits0
Assigned work units:
553 Remaining work units:
1450 Participants who received work:
1 Package size:
1
How to read these numbers
Classical average≈ 46,052 candidates
For random integers of about 20,000 digits, the classical baseline predicts one prime on average every approximately 46,052 candidates.
Candidates tested so far550 candidates
This is the number of candidates examined so far in this Challenge.
Classical success probability at this point1.19%
Under simple random generation, this is the probability of finding at least one prime among the first 550 random integers of approximately 20,000 digits.
Classical success probability within the full limit4.25%
Before the Challenge began, this was the classical probability of finding at least one prime within the complete limit of 2,000 candidates.
What this Challenge means
The Challenge is still in progress. The current expectations are therefore probabilistic, not a final result. Under the classical random-integer baseline, the probability of at least one prime by the current point is 1.19%, while the probability within the full planned limit is 4.25%. An observed advantage can be calculated only after an officially verified hit.
Formulas and complete calculations
1. Probability for one random integerp ≈ 1 / (20,000 × ln(10)) = 0.0000217147The prime number theorem gives an approximate probability of 1 / ln(N). A number with 20,000 decimal digits has ln(N) approximately equal to 20,000 × ln(10).
2. Classical average number of candidates1 / p ≈ 46,052This is an average, not a guaranteed position. A prime may appear earlier or later.
3. Probability of at least one prime within the tested candidates1 − (1 − p)^550 = 1.19%This calculation refers specifically to random integers of approximately 20,000 digits.
4. Probability of at least one prime within the full planned limit1 − (1 − p)^2000 = 4.25%This is the success probability assigned by the classical random-integer baseline before the complete Challenge range is tested.
Important: these calculations use the simple classical baseline for unrestricted random integers of the same approximate digit length. They provide a transparent reference point for each Challenge. They do not replace complete density experiments, and a single first-hit result cannot by itself establish the long-run enrichment of the full sequence.
Every official result can be reproduced independently using the public MAX Prime client and the mathematical values published on this page.
Reproduce the same candidate on your computer
Open the public MAX Prime client from GitHub and use Local Mode.
Copy the published n_raw value as the local starting value,
keep the published CRT modulus M and remainder R,
select 1 iteration and test N.
The client must generate a probable prime with the same number of digits
and exactly the same SHA-256 shown on this page.
If the digit count and SHA-256 match, your computer has independently reconstructed
the same MAX Prime candidate using the public source code and the published mathematical data.
Candidates submitted to the official server and waiting for official verification.
No candidates are currently pending verification
New candidates will appear here immediately after submission and will remain separate from official results until verification is completed.
Latest official result
Most recent candidate that completed official verification successfully.
Officially verified N17064 digits
Large probable prime found
This Challenge stopped automatically when the first officially verified probable prime was found.
The result below compares the observed position of that first hit with the simple classical baseline
for random integers of comparable size.
Digits17,064
Candidates to first hit361
Classical average≈ 39,291
Classical probability at this point0.91%
Classical probability at full limit4.96%
Observed advantage108.84×
How to read these numbers
Classical average≈ 39,291 candidates
For random integers of about 17,064 digits, the classical baseline predicts one prime on average every approximately 39,291 candidates.
Observed result361 candidates
A verified probable prime was found after this number of tested candidates.
Observed advantage108.84×
The result arrived after 361 candidates instead of the classical average of about 39,291. In practice, this Challenge required about 108.84 times fewer candidate-testing operations than the classical average for random integers of the same size.
Classical success probability at this point0.91%
Under simple random generation, this is the probability of finding at least one prime among the first 361 random integers of approximately 17,064 digits.
Classical success probability within the full limit4.96%
Before the Challenge began, this was the classical probability of finding at least one prime within the complete limit of 2,000 candidates.
What this Challenge means
A verified probable prime of approximately 17,064 digits was found after 361 candidates. The classical average is about 39,291 candidates, so the observed result shows a 108.84× advantage in the number of candidate-testing operations. At the point of discovery, the classical cumulative probability of already having found at least one prime was 0.91%, compared with 4.96% within the full planned limit.
Formulas and complete calculations
1. Probability for one random integerp ≈ 1 / (17,064 × ln(10)) = 0.0000254509The prime number theorem gives an approximate probability of 1 / ln(N). A number with 17,064 decimal digits has ln(N) approximately equal to 17,064 × ln(10).
2. Classical average number of candidates1 / p ≈ 39,291This is an average, not a guaranteed position. A prime may appear earlier or later.
3. Probability of at least one prime within the tested candidates1 − (1 − p)^361 = 0.91%This calculation refers specifically to random integers of approximately 17,064 digits.
4. Probability of at least one prime within the full planned limit1 − (1 − p)^2000 = 4.96%This is the success probability assigned by the classical random-integer baseline before the complete Challenge range is tested.
5. Observed advantage in candidate-testing operations39,291 / 361 = 108.840200×This compares the classical average number of candidates with the number actually required to reach the first verified hit. It is not a probability and it is not, by itself, a measurement of long-run prime density.
Important: these calculations use the simple classical baseline for unrestricted random integers of the same approximate digit length. They provide a transparent reference point for each Challenge. They do not replace complete density experiments, and a single first-hit result cannot by itself establish the long-run enrichment of the full sequence.
Challenge:MPC-OFFICIAL-4-17000D-FILTERAUTO-P1 Title:
MAX Prime Challenge 17000 digits filter AUTO Work unit:MPC-OFFICIAL-4-17000D-FILTERAUTO-P1-WU-000360 SHA-256:cb16d481ff557452d17ff7676d4a3470961d50491325c92b70d33a3359c7d110 MAX ID:8d9f9fba88a84a72eec9b8ffc3e6c8f7d35488c66df4a6d8c7fe8534613b9bdc Nickname:
Hulk
Show full candidateIndependent verification data
Reproduce this candidate independently
These values are sufficient to reconstruct the published candidate without trusting
the private verifier.
n_raw = n0 + i × step n_effective = R + M × n_raw N = 31 + 6 × n_effective × (n_effective + 1)
Verify this result with the public MAX Prime client
You can reproduce this result independently using the public Rust client available on GitHub.
Open Local Mode, select the advanced/custom experiment and run exactly one iteration.
To avoid repeating all previous iterations, use the published n_raw value below
as the local starting value. Then copy the published CRT modulus M and remainder
R, keep the filter enabled, select N and set the number of iterations to
1.
Local n06975533181206982315222659119592079157245627789524231631538901697025858350381403311884711497504911394272077164436589289915069866515612926459606721726320900940510203145794750942590607244553845360225957611061661917211579739201425567670919369302235305809159261112435255039091648708355403676053183703254918556150593682914884279374269781303682929345538723727879217421407866281664642863419008093810261280079412466366984083783606347490991577441199125000347216036688009023085149836899052732016748512222022551908269569944433561826921424727107350055369889772892007948761551673045505049817588605567923857440169930421443865472826514786571705614965913152421949746749099901212211584384343509512418803669735713944568491716518884858407615476567118751221747176529473531588198178388873228306580685399291098304611372453401606359381676846124293758747040822308696028659318936073080757427944479244873637279230117124599162435786084970841512323799782294912609072886560247228388671224036380695303031167371184945975700298553353338987198576826994742808801772308183895826486867916593784232149481382830254268646610244639890678461291082020747849152159138782490610323234380245070395644301867593335166549441927532050924868205695294977449114774654471239741038373270654190104422949144765720925072237835524612225188385069213727094440528195000649556726872144184671248520081108988024160823145344499118842045819220059801429450093191404845647468245796445593664966188620272985834715743105170080671404817173024801700432731139420860674732387875000551495566701892787147854191336786805443642175814096953169647747854322320593487243333231952088340035321559618190464344718717616797243591045618897421401478282099953861572335302060276424904589782423920483282713297554978647375239063439236394125847210931948657058353955387402180772192808571177492592396034824298419769578075617545705763906707818093052993422132476969876148858524820807386660382606274796485034130876525618363391760526295274432450446971343116650230951297787723451521802324550341558092558975018434986403281137533919016286189290114335704260325997834928218952618704798838547289329695866722939055486114233422604230685689388373932856180802422373297360694504434549509785751715162261260724972895381669057754356575950637006942471086783115222924010252260822557459945666078352873780699799911717310003093533721304430306077572457913922736005457010693038082285821582250707376016015917853219996860103757735629242888643878794378655212498644777537944501210485100946557772694164719571315950038720365755389344343631687381993467031531127376927218406667031423951996882710704561639860456285459623805989170711072651574202962289859451537128757556250944607378937244837024938858519021248054299532669106099108446235198280588281239167877782365047253647851071648063459777926136583776647182141472864456555096312330312612737698976796446419378784698196928089510879023562458640922299445361109736594841782057208770334534273075894013813134257192008273944896275900888656819739991822738563274104145638611153386155487080242825060667031917604554186590229558403239863768971155770003637578163733904804474229546721889694083804778815609286006681401843783212540225653359273249864318802636111925674422450721574117322734683998171939327086013987591005387871736991930253735435717294058491156576855449372187129858992675433493909301363137474514260902420959295903498786812868803531811374837060095785899796384535731143557446795631352641222348498129431220504425795582864280608986722496631979050834058522424912857949105452515036346345021153569101806031088919590863216728162375457454053109824775984607859664847775305666124070797909349968258162823567107147798701431989777576608102760286925343023959171533014482840930695229075037524456773489971987850101835471966856648224466019428390335584544310219559606496395059602715603480341265852311298964652456798112615949023980021434472358319348592374612800431150901320454493540290652096472936209235314185721060838461708071587045823533273999295467878430879157057531495247169054175110891211947052510907555043345147431792379408187117009816027373126803842352869422918896881928813110456505528920426012286290286242519074337159621995617833136294476079063473350535486558801400962061519325828607365063474925657446564178878189942419787975263451804919298612718790549487541189395472809180202829665451285992350207057387695613992087506651123327856529121901282859936733039378277847129398750957931098622645479722021599512207025927332573257160072631865371548411736172565478676146771955455993527428374990570831436760349996189326240258024528138189631459869854373965056756157446951672643089245991659367061260742087732977994878410776822138145354541962562392275170099055274117898107270041927661860935123987701761828241598363869657977909129053357563916901593793775260239798584098695427513443385809266812924433744112202660858338501567584329728683573758203664994897182578723225104531853873271198818724122840117053427412219902212205932820580190092195430208280417653229608785035799840649634995255303327155264869364548499656811557761369282046017076611936881126863915276532820388416136063605779356689599623848224852394421193052101778215351533533922780904385364799793423997160754824278447505381516537488824797021518832086195458419949023615794891505927971001836780450779848251114591543281382280226087394191370359833411953247531275159164316791726873798392348296861150862262154223442006336852408874196855714098828987861537392654439763995984571529830540295966708878456918357439582983652675817759395550235300871720464754635136095692136927724110819764037221085462560817423691117158091231166472214349517287972163655072698118112314382924755037247880476750381291999206669798724602180919836076980032389068670095948798371159998384165953895222361716209985635906107133396423899388200719099200791131686613871832713228736613898588003027478915238921518041966237787484210941039622562725281705523301046645467987624839492867580474782145202574619466117770822915329147744696311749055648829741710605837894093903544576941911272011628998929736517739632351505987471289798419839119041969709494697260300994228148615412796470946743247222414400382226510706793531967323814627781207716420972452216637337114737756372778675791538466509992425914382023864893365632697087638269811855903669899109781750775852132220928522089488985524076361937353031962322908657742762146578192222390960665464387129185161873146924144466459882850295650560681870968741280756464697692919049471068317167085111420556539726917264140690406338802267677174179421024657435866581793375998787459808053547565101928328238971842410376397898703776201633663937750183438630098017464970484174382306181560243103185314279841329270762504914396017083523099335778638922029452044796305536414713807660183342896661221601790076347099671589659117845599131858797300743129594638221420727616818287387496038541135438082686699159524348378151675375435892179117381834321394881749533996505348615959670732609098797618208608571727287595341117496501325283184467194630543422105608082045098675359525613603001186251249417379443742714030356539379773060118203220030975691742112970824933919051368843195685002035519184300194724025865401483370968769146301563461294574679144025021406606063401675493705031399134696858113334972991806604470468559286172956839577736802549776893257159357364513567732159820426496679371931358355328859310584623029858271873171362943019148572524772552271907051290351805461325419126284224229397291641605844393565423510529748679939941252635393949053770900825141638281414237299999330415431259843535590469466599382818274547410169985382959703981079720688670995720123592234832408383773285039742360259157983560976363664252446145522663222830094027744743672674397631223913353189626428184697068222788164876669602873442642948678574291633369412186143087916042329048288788575967397506199271803703117154818706493815209408996500700169542259816738280568641362469146518682961825594042941036504445052090663906897202440048527894940358492802132325176568813951719370792180870255870650748966840175317993127993246670898704166480979214806961204699435639608729611408272044782170246519485932774706149014317766851147620052055165785712681916091965071864857945772464965599460800742160650929160549962885845977190382435579727483708891484644387100446190484715328238556366691784014529761745082454060693486107341153813564995255478087531768017706914476348345427501735955581303036645442039415308362330126982895509335095203507612332702285422853140416875999746850
Iterations1
TestN
CRT filterON — use the published M and R
In this one-iteration local check, the local iteration index will be zero, but the generated
n_raw, n_effective, candidate, digit count and SHA-256 must match the official
values published here.
If the digit count and SHA-256 match, your computer has independently reconstructed
the same MAX Prime candidate using the public source code and the published mathematical data.
This block has tested 83 of 2,000 new candidates, after 2,000 candidates were already completed in the previous contiguous range. Mathematical probabilities and any future observed advantage use the cumulative total.
Classical average≈ 31,076 candidates
For random integers of about 13,496 digits, the classical baseline predicts one prime on average every approximately 31,076 candidates.
Observed result2,083 candidates
A verified probable prime was found after this number of tested candidates.
Observed advantage14.92×
The result arrived after 2,083 candidates instead of the classical average of about 31,076. In practice, this Challenge required about 14.92 times fewer candidate-testing operations than the classical average for random integers of the same size.
Classical success probability at this point6.48%
Under simple random generation, this is the probability of finding at least one prime among the first 2,083 random integers of approximately 13,496 digits.
Classical success probability within the full limit12.08%
Before the Challenge began, this was the classical probability of finding at least one prime within the complete limit of 4,000 candidates.
What this Challenge means
A verified probable prime of approximately 13,496 digits was found after 2,083 candidates. The classical average is about 31,076 candidates, so the observed result shows a 14.92× advantage in the number of candidate-testing operations. At the point of discovery, the classical cumulative probability of already having found at least one prime was 6.48%, compared with 12.08% within the full planned limit.
Formulas and complete calculations
1. Probability for one random integerp ≈ 1 / (13,496 × ln(10)) = 0.0000321795The prime number theorem gives an approximate probability of 1 / ln(N). A number with 13,496 decimal digits has ln(N) approximately equal to 13,496 × ln(10).
2. Classical average number of candidates1 / p ≈ 31,076This is an average, not a guaranteed position. A prime may appear earlier or later.
3. Probability of at least one prime within the tested candidates1 − (1 − p)^2083 = 6.48%This calculation refers specifically to random integers of approximately 13,496 digits.
4. Probability of at least one prime within the full planned limit1 − (1 − p)^4000 = 12.08%This is the success probability assigned by the classical random-integer baseline before the complete Challenge range is tested.
5. Observed advantage in candidate-testing operations31,076 / 2,083 = 14.918717×This compares the classical average number of candidates with the number actually required to reach the first verified hit. It is not a probability and it is not, by itself, a measurement of long-run prime density.
Important: these calculations use the simple classical baseline for unrestricted random integers of the same approximate digit length. They provide a transparent reference point for each Challenge. They do not replace complete density experiments, and a single first-hit result cannot by itself establish the long-run enrichment of the full sequence.
Technical verification data
Work unitMPC-OFFICIAL-3-13500D-FILTERAUTO-CONT2000-P1-WU-000082
Candidate typeN
MAX ID8d9f9fba88a84a72eec9b8ffc3e6c8f7d35488c66df4a6d8c7fe8534613b9bdc
n_raw = n0 + i × step n_effective = R + M × n_raw N = 31 + 6 × n_effective × (n_effective + 1)
Verify this result with the public MAX Prime client
You can reproduce this result independently using the public Rust client available on GitHub.
Open Local Mode, select the advanced/custom experiment and run exactly one iteration.
To avoid repeating all previous iterations, use the published n_raw value below
as the local starting value. Then copy the published CRT modulus M and remainder
R, keep the filter enabled, select N and set the number of iterations to
1.
Local n02909604334558011829985849002885653779566654742202268537522457485749311043397542903961592860719600226978782237795799534575903420959821299803924263337229174016113336768094527330329478947336256177819954341110694447861174749817222765857770705210840722064408947610786871520934307439470411708663689230221474936175846080984532850866196046048141966060726349035910740286150907492233688909317844654602343428766643137498810272766882708205484171515589511926178634001137402421451334479333734834433059260555455296391134156409679825446398012770953102704416828547025546749109781448945891460122413396509998481096970092753497640567335073426013650734988750946213626372193652451028990288472552973357406412016765027560403571493746892149475460178157184647563165451799682101921571148549770735188744925397360260556268274663759619869789399130318809717359939243841610469458666790975972602702929656260313958810443483649404289978986500160794901853595859642724475717873285509803592224874450043952210284020331429254720963977421350730962120744339107062498067321890644684510401512276912078312783487704162079189819317932488259512605868930126475489931762347719307510518187509623268281165666186777437057616389776874320620232102375796172212564477107886211806794157492595083755119839582909993122633262029504883891459284092458905567303231606044958968342531923388066155703392194224866329766572726271870141409079699200523886131796480703891731934184092785403517120868326886026203963195900318053649746846358432647606684242942366838160793279179640074820369754507711238936240438487311972545750126241089384357775863832236530755511077551023205455031482880915721477195160812043304037109117394447064713798671506738433613544536472929338704459562862240728623782213101660563362988360311391987530029898705504311215036723579723519654160803196931261676555117589663292108139558415345566359392721224135141741457472207779985592455648975726436805405735681156091534710488634667620876559943323088733347710900639529678799735309956263679657736120191510604654212386792729296801918315013641007714968212892065284463466701723639004567376058378920138060168876101456954322386439853545793855720215591163090985742840946647430754340837931234986487609624119736246296179514685773934284566171610063903442930590327724456362131864046809945811746210138090189710199125308781453197661603439332348206036786903314010891255018829841996830939714633921902356418534621612323254555386346381583834472835662295461550638729658589301643700478718794877860476982811085113157230893525337078074176692445235954302175626868232328065173180122466876718564343448557307108540109163548393973998111090265226418465638451963029899056846810885596730765452871871295283486581644146393706459208990128550205914570988061775699034132855060362813796802351244521594934851933463961957750140626798156110311634404513725018500489008936169815110981102992307434887996751690094642301425421497781350027180211483567413272884986323450799156165854533479749763036014385420803654504790185672201706005502435163778242321833564195447999000136368792710686608797603663049734746899210490064595655917130059240254892630376964778675251631825290594011890452620377168168402669298246874174140874160810648716573050215985644692301678276819272571755557296196502366631178658092088342027600850365513920519030579366699402397845885053180043438413489007098422029962546043113821527759940782186781218591132503209037552538869155532543499959124249631776631141973835143405696520677136940417664056749545359857790778759181467395896289126833697954997886709409445284759765601887333401759529250730621934510712472540975297123152694845893204585589165293845988762181692574688553024677148637276315950793388658981674821779883505396364868513384372547083628603528429160856888065144238078609148011763810906180498818005721772546029351680820994916688976892951542872721669108794007657347799862547634627013897925866888591793313536307674818600335979632286508656379429871641633997464094408891810662385571910468236654084499716054690549518279164843219035098398262020978101618090401070671636501197327317441521554294226210537745367487071664825761356426213695716074772364649913916137810115497659834551048097616289729156999116645209306499659094098946330950726769277548798760772519522414152754935172685419746751524380808782613227222615311967376920107377964491919947354089862908367189957171093950076842367795553810980031530329197609961367125441750555959001577012241723003480607805344546326839132853186553348328358736111600139020528204231084535328553594077151620067625042473222303589759385747444707276144522378092379873963568657556328015447473010738293535892941875395583695986753893974423077895951447645850757904694650109215713001781999096950695118333988903736735875028692927623065759646704546729002372380098325757103934590434278099979593925094926194272019599921161379835537932173562876659847800428429006378410448587306804949730175656946660439719718875016787818259212818739133411922260045068047157117676129301058553024996164825590819305725093785648203055287415954559147170126689151981446438560553066981602665195730637168043993591801093297810385483312634349742334084632575775075384117082676950505335994649225770130367350422132166553664526593046759799384889534709985198436305915303952529921697636018821290441779271469806065636888150407746640091259019110585440293022593808228971205985797595831459907948092619210060199447335447524416487178033317168846266806971005210321447378950875127636354389506880856693750188127399380932258069561479840840435437139671948880106119097680523406089280289119929172235159876974155223964509300076198467401276289592779517752977007833617057782659981733257666468690402822166961592721625938317639739798801219614587342632821477544920179962372575496847106728993710506114811804845076041166685891160256296906886481525348095514016861189436019577606166436959144510203719945298293567601866179922135136115187004084941159031293709933333033973065698839893066698036477702621755757227102944373460320178143970137337504898824913960528494350611300263613660089734852103318356614070686105604242931920533460860883766401261328518675948172379457004086808668160356134867972652758501549334844811034523425943995571883909087058533740644821609757979226364186668528424146253953393042604934006015816805493503083243780372893744210300609048138755845356100412865150594044308738950247474611386808770202006633603683950913584819146344075272351268436861244265289207874010481756874812244664064289592119593384535042506819796743602170068989830909604863706239189828784237501750308575217614775314101897580129784196629424486550326032704055885800301562990522451358930143713248104526446739565047150805118390251014080223674448420528879594978878301394863615
Iterations1
TestN
CRT filterON — use the published M and R
In this one-iteration local check, the local iteration index will be zero, but the generated
n_raw, n_effective, candidate, digit count and SHA-256 must match the official
values published here.
If the digit count and SHA-256 match, your computer has independently reconstructed
the same MAX Prime candidate using the public source code and the published mathematical data.
For random integers of about 10,287 digits, the classical baseline predicts one prime on average every approximately 23,687 candidates.
Observed result1,005 candidates
A verified probable prime was found after this number of tested candidates.
Observed advantage23.57×
The result arrived after 1,005 candidates instead of the classical average of about 23,687. In practice, this Challenge required about 23.57 times fewer candidate-testing operations than the classical average for random integers of the same size.
Classical success probability at this point4.15%
Under simple random generation, this is the probability of finding at least one prime among the first 1,005 random integers of approximately 10,287 digits.
Classical success probability within the full limit8.10%
Before the Challenge began, this was the classical probability of finding at least one prime within the complete limit of 2,000 candidates.
What this Challenge means
A verified probable prime of approximately 10,287 digits was found after 1,005 candidates. The classical average is about 23,687 candidates, so the observed result shows a 23.57× advantage in the number of candidate-testing operations. At the point of discovery, the classical cumulative probability of already having found at least one prime was 4.15%, compared with 8.10% within the full planned limit.
Formulas and complete calculations
1. Probability for one random integerp ≈ 1 / (10,287 × ln(10)) = 0.0000422178The prime number theorem gives an approximate probability of 1 / ln(N). A number with 10,287 decimal digits has ln(N) approximately equal to 10,287 × ln(10).
2. Classical average number of candidates1 / p ≈ 23,687This is an average, not a guaranteed position. A prime may appear earlier or later.
3. Probability of at least one prime within the tested candidates1 − (1 − p)^1005 = 4.15%This calculation refers specifically to random integers of approximately 10,287 digits.
4. Probability of at least one prime within the full planned limit1 − (1 − p)^2000 = 8.10%This is the success probability assigned by the classical random-integer baseline before the complete Challenge range is tested.
5. Observed advantage in candidate-testing operations23,687 / 1,005 = 23.568849×This compares the classical average number of candidates with the number actually required to reach the first verified hit. It is not a probability and it is not, by itself, a measurement of long-run prime density.
Important: these calculations use the simple classical baseline for unrestricted random integers of the same approximate digit length. They provide a transparent reference point for each Challenge. They do not replace complete density experiments, and a single first-hit result cannot by itself establish the long-run enrichment of the full sequence.
Technical verification data
Work unitMPC-OFFICIAL-2-10000D-FILTERAUTO-P1-WU-001005
Candidate typeN
MAX ID57414e88790fe02a20c646b6507dd75d3b775b0b996f61c16a59b967882d0c54
n_raw = n0 + i × step n_effective = R + M × n_raw N = 31 + 6 × n_effective × (n_effective + 1)
Verify this result with the public MAX Prime client
You can reproduce this result independently using the public Rust client available on GitHub.
Open Local Mode, select the advanced/custom experiment and run exactly one iteration.
To avoid repeating all previous iterations, use the published n_raw value below
as the local starting value. Then copy the published CRT modulus M and remainder
R, keep the filter enabled, select N and set the number of iterations to
1.
Local n05336887583301919197898280320806565129304120806717583277909430903417118068368373050645830143438008986276254048974320150307478944100677146634746496663916284184080493514494982875242253283118523720399030097741108910988122835342659690878775269405340015169759345762209410801400310665233576768700059529546531558007569626439257117023444711183028581562860551802506959495749465291646975128787630023460738176020956172715072266995698362037568886487793753557073477251990175621164679990370884188446318891799969390084580590148451143562899953427834363805004622883216241803560158139811617649642139421869321904605643347947250178425288257284097753526672424292978805684685023887677110392336313722341290985320651360064075907294940341699924513857547339157020885370740729065513605095606330541206895812762117460400359389028227627359253169092638104330192559674561569664181707851630542384597855473743693997306714836857945942218617632585355577990443404509031071408710265783207301769589149816206785783864496373337290614050514526919190834791771408588821300648612155693381490828040890029246780923043668103770831688532710229104255241823052459165047389158031936141106084482364639518248199194601651985963948016774010095039729246658841445254768653135852957050103171346647644410774698585379733035803435332926749376697923854347112143315890904529536788659068583862318652135053722552356245322881653978063565705618692935829012312641453289667610151561106245846378029215929147901109297148062189220886850695042192780858547903861133747431180337136727451362751027990733489083647417937759348337528214349947472005324877713729372111377083251717470146868290781598668194720781983164856029282755591649114805355548479660583734602110607301681796194731727868066654498093458275727955508199306307952664183763623367091227871600797692066440090764629481725580917506518749193538660074263468838023468386422188543226789638754356149082611334969575627312251136731538692317716684851989878220282557120278389497485297691995835158607055543648323670468758686561940543137007724512051013833794937516050335919361502600674376846838247833719870470806803843249493238626009119741830603094297350078556418047552524062356637833638503117519655880208246357070646370901826340526858229188131638168740148700807745795609682887149691267926099631615854033882624429034814048935042759777341698592777841879470540834548773189296745589146680562451365614681798316822337225365649036231440164023634975367619282738268115366888227355049000073045051894081397602128821697856781916603704555217507349596451841875918511416196048896974299997094609117608299175134549811990031881437003177412252508909034917047721290384951208566068003496370579728366947876964888751908586719946202175672726167109361246417761947131467828339886947558952697238092723577725852896406428297155286077939386289848217534030110414476647948548232828599620991140441443058558995633364127965498399542509360798501939888039308290264614104033421947407570287772570621723989009088020073008075652668134676458833833285070442506430556263001840507828143948983062526356917571651690421260039632992911616928275094904275714907717522078660153456989046990633337757757819756877097722254750360460895056971955064971098932407676652797973708959624281363817216215915877905727590966397598792523485772781998366494335393094226613227987835802310246881854387333287204633047933722975616591114803084259383280013197181523788003818584186841501192836172672256941199906244840596113033103363383771299913537353983299398788859345293227285778073584869838363054392620328938816791478625567141191544935320362547590192433789006389286137783586854806795973716490095851898934500399729475868627756413703843759141572966492380445475710916687074999459306911173633528016634286849074137058069125178807488597935285857652732982423146247786394373872549970763951848939870875696876755243318274410200565406710957893041635761290644233448156384182105293133098845088245838111550937176171375892203371025158869029607081548008528821739325908062020412466474521474155903616159871819438901103410635026067683589437544278370084031356644281191735037897821051285354193311549582541802039667779497861614288696703095384881890122362720364602097429864949252185219288744201643261266727950289009989580303601221395713091644835522198950314619784096114817476586537473808259229449613201281795772612476262655103458136562492524241732996936195028882648840591726864314068144240386938653262105044692987762857225008696330509286251138025254095945980145546196717649071485602555008290079893966063458798141200684314162800094646377468963063798814466789512161284696808587422937820338451104114267839551190332571272389353940870307177317775833571930789092383102862697661866000702566380355989710300126770987704506325386875850818431042108630025158545588716920216958818283687999374419050737306346365088099916855058761518992914718867654817550656166343646868532802583222895978673035824271539305873751562395368799101353283890059013187385901856102385900907724476201046283637460464978901468953809771870357632429224899047232223123242565376403199683197310169447535510465550085518878228895665
Iterations1
TestN
CRT filterON — use the published M and R
In this one-iteration local check, the local iteration index will be zero, but the generated
n_raw, n_effective, candidate, digit count and SHA-256 must match the official
values published here.
If the digit count and SHA-256 match, your computer has independently reconstructed
the same MAX Prime candidate using the public source code and the published mathematical data.
For random integers of about 5,132 digits, the classical baseline predicts one prime on average every approximately 11,817 candidates.
Observed result317 candidates
A verified probable prime was found after this number of tested candidates.
Observed advantage37.28×
The result arrived after 317 candidates instead of the classical average of about 11,817. In practice, this Challenge required about 37.28 times fewer candidate-testing operations than the classical average for random integers of the same size.
Classical success probability at this point2.65%
Under simple random generation, this is the probability of finding at least one prime among the first 317 random integers of approximately 5,132 digits.
Classical success probability within the full limit15.57%
Before the Challenge began, this was the classical probability of finding at least one prime within the complete limit of 2,000 candidates.
What this Challenge means
A verified probable prime of approximately 5,132 digits was found after 317 candidates. The classical average is about 11,817 candidates, so the observed result shows a 37.28× advantage in the number of candidate-testing operations. At the point of discovery, the classical cumulative probability of already having found at least one prime was 2.65%, compared with 15.57% within the full planned limit.
Formulas and complete calculations
1. Probability for one random integerp ≈ 1 / (5,132 × ln(10)) = 0.0000846248The prime number theorem gives an approximate probability of 1 / ln(N). A number with 5,132 decimal digits has ln(N) approximately equal to 5,132 × ln(10).
2. Classical average number of candidates1 / p ≈ 11,817This is an average, not a guaranteed position. A prime may appear earlier or later.
3. Probability of at least one prime within the tested candidates1 − (1 − p)^317 = 2.65%This calculation refers specifically to random integers of approximately 5,132 digits.
4. Probability of at least one prime within the full planned limit1 − (1 − p)^2000 = 15.57%This is the success probability assigned by the classical random-integer baseline before the complete Challenge range is tested.
5. Observed advantage in candidate-testing operations11,817 / 317 = 37.277182×This compares the classical average number of candidates with the number actually required to reach the first verified hit. It is not a probability and it is not, by itself, a measurement of long-run prime density.
Important: these calculations use the simple classical baseline for unrestricted random integers of the same approximate digit length. They provide a transparent reference point for each Challenge. They do not replace complete density experiments, and a single first-hit result cannot by itself establish the long-run enrichment of the full sequence.
Technical verification data
Work unitMPC-OFFICIAL-1-5000D-FILTER30-P1-WU-000308
Candidate typeN
MAX ID8d9f9fba88a84a72eec9b8ffc3e6c8f7d35488c66df4a6d8c7fe8534613b9bdc
n_raw = n0 + i × step n_effective = R + M × n_raw N = 31 + 6 × n_effective × (n_effective + 1)
Verify this result with the public MAX Prime client
You can reproduce this result independently using the public Rust client available on GitHub.
Open Local Mode, select the advanced/custom experiment and run exactly one iteration.
To avoid repeating all previous iterations, use the published n_raw value below
as the local starting value. Then copy the published CRT modulus M and remainder
R, keep the filter enabled, select N and set the number of iterations to
1.
Local n01651729567231668128484893600539175844306482095074326613198841443559653055089393636882310397877105684569428739027833289666335636773057171003373039437785589684424650689666559691307295793699426919408656628216190738087936443293405622696291320462516848325957052120492559651649630988594468029000575398138565460252748327790469398003779344475344340167233437850067826091725591645612845869070285483174943854218180213583954297478968128599408764454602675536458062722622716854067989905177121673377091551603945766585822431544639950666780332829071328647639393848057068043176983509127245540089278833117178319475053725813253146287829394460486381039672232872591178389955490531004944908236517386768669014373879485455337231782325627401825730636814086455882564962503606150856101343046168993936361718687223917687653612553615293488452564306000246951888311185920824527712811652476207701861070369929673727811809444454163565020440601150919370200686893646409548712971366541069679170917481165648205402300731242265796780000700033438481707845475572224972422010150289062229195106148008217137552954184401663471839124909684020073379347337516578501065808933540395294635654825626643227737256014951970804581778981224776354873840153020891585266199084924374521706249093144413669607145621775508214788972808022470984256812328168298970235287826951481289644824711922158426095569733520303840096660638257893555273136453302467416950194273722017248092611124571572301833157029312583095129724857370417601773480527040416100047660676477147588225249682630959972450083293059255271256628579492661032294326430965203629611723337254738545032795393506855424558166456885417415950695124553120715775177491693015377400250479951558406623414981402008709819430060854744210925585699090430097508017440656715646648176503832880715590420794387585821330575225925675206369984332221332513591952868676964055958402694961421585453584036050708085740832211818212655871014962180716524370757193602252610460086261644993410819651525682909991290302134861890027422342988335208468728984783025363799491876571168106205819754072577493014571252232234955831635237484792110298483418497707329501754903226503658625642673628586839099204812360401616633173794785164818007374593330920827553107905224937742433384491511670934647724440123340028532946216969040524694621932029964982899405831596959076297166810274555393595788569545457450491437737233427428955265667524889032808980093503570081331530145207599347291505107925490376077001384879270532334594976443772662867752710041225607440012950920920961705
Iterations1
TestN
CRT filterON — use the published M and R
In this one-iteration local check, the local iteration index will be zero, but the generated
n_raw, n_effective, candidate, digit count and SHA-256 must match the official
values published here.
If the digit count and SHA-256 match, your computer has independently reconstructed
the same MAX Prime candidate using the public source code and the published mathematical data.
We use only essential cookies to keep this website and the MAX App demo working.
No advertising or tracking cookies are used.
By clicking Accept we will store a small technical cookie in your browser.
You can also choose Decline: the site will still work, but some interactive
features may be limited.