RSA numbers - Knowledge

346:

run by Alec Muffett (20.1% of relations, 3057 CPU days), Paul Leyland (17.5%, 2092 CPU days), Peter L. Montgomery and Stefania Cavallar (14.6%, 1819 CPU days), Bruce Dodson (13.6%, 2222 CPU days), Francois Morain and Gerard Guillerm (13.0%, 1801 CPU days), Joel Marchand (6.4%, 576 CPU days), Arjen K. Lenstra (5.0%, 737 CPU days), Paul Zimmermann (4.5%, 252 CPU days), Jeff Gilchrist (4.0%, 366 CPU days), Karen Aardal (0.65%, 62 CPU days), and Chris and Craig Putnam (0.56%, 47 CPU days)

1796:

0009733045974880842840179742910064245869181719511874612151517265463228221686 9987549182422433637259085141865462043576798423387184774447920739934236584823 8242811981638150106748104516603773060562016196762561338441436038339044149526 3443219011465754445417842402092461651572335077870774981712577246796292638635 6373289912154831438167899885040445364023527381951378636564391212010397122822 120720357

1784:

2854289188085536270740767072259373777266697344097736124333639730805176309150 6836310795312607239520365290032105848839507981452307299417185715796297454995 0235053160409198591937180233074148804462179228008317660409386563445710347785 5345712108053073639453592393265186603051504106096643731332367283153932350006 7937107541955437362433248361242525945868802353916766181532375855504886901432 221349733

1772:

4786041721411024641038040278701109808664214800025560454687625137745393418221 5494821277335671735153472656328448001134940926442438440198910908603252678814 7850601132077287172819942445113232019492229554237898606631074891074722425617 39680319169243814676235712934292299974411361

1387:

The CPU time spent on finding these factors amounted to approximately 900 core-years on a 2.1 GHz Intel Xeon Gold 6130 CPU. Compared to the factorization of RSA-768, the authors estimate that better algorithms sped their calculations by a factor of 3–4 and faster computers sped their calculation

345:

sieving: 35.7 CPU-years in total, on about one hundred and sixty 175-400 MHz SGI and Sun workstations, eight 250 MHz SGI Origin 2000 processors, one hundred and twenty 300-450 MHz Pentium II PCs, and four 500 MHz Digital/Compaq boxes; approximately equivalent to 8000 mips years;

84:

200,000 (and prizes up to $ 20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. As of February 2020, the

1046:

The polynomials were 119377138320*x^5 - 80168937284997582*y*x^4 - 66269852234118574445*y^2*x^3 + 11816848430079521880356852*y^3*x^2 + 7459661580071786443919743056*y^4*x - 40679843542362159361913708405064*y^5 and x - 39123079721168000771313449081*y (this pair has a yield of relations approximately

1201:

RSA-640 has 193 decimal digits (640 bits). A cash prize of US$ 20,000 was offered by RSA Security for a successful factorization. On November 2, 2005, F. Bahr, M. Boehm, J. Franke and T. Kleinjung of the German Federal Office for Information Security announced that they had factorized the number

1760:

9758925793594165651020789220067311416926076949777767604906107061937873540601 5942747316176193775374190713071154900658503269465516496828568654377183190586 9537640698044932638893492457914750855858980849190488385315076922453755527481 1376719096144119390052199027715691

1404:

RSA-250 = 6413528947707158027879019017057738908482501474294344720811685963202453234463 0238623598752668347708737661925585694639798853367 × 3337202759497815655622601060535511422794076034476755466678452098702384172921 0037080257448673296881877565718986258036932062711

1400:

RSA-250 = 2140324650240744961264423072839333563008614715144755017797754920881418023447 1401366433455190958046796109928518724709145876873962619215573630474547705208 0511905649310668769159001975940569345745223058932597669747168173806936489469 9871578494975937497937

88:

While the RSA challenge officially ended in 2007, people are still attempting to find the factorizations. According to RSA Laboratories, "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these

1748:

7067958428022008294111984222973260208233693152589211629901686973933487362360 8129660418514569063995282978176790149760521395548532814196534676974259747930 6858645849268328985687423881853632604706175564461719396117318298679820785491 875674946700413680932103

1383:

RSA-240 = 5094359522858399145550510235808437141326483820241114731866602965218212064697 46700620316443478873837606252372049619334517 × 2446242088383181505678131390240028966538020925789314014520412213365584770951 78155258218897735030590669041302045908071447

1379:

RSA-240 = 1246203667817187840658350446081065904348203746516788057548187888832896668011 8821085503603957027250874750986476843845862105486553797025393057189121768431 8286362846948405301614416430468066875699415246993185704183030512549594371372 159029236099

1736:

5874455212895044521809620818878887632439504936237680657994105330538621759598 4047709603954312447692725276887594590658792939924609261264788572032212334726 8553025718835659126454325220771380103576695555550710440908570895393205649635 76770285413369

1363:

RSA-768 = 3347807169895689878604416984821269081770479498371376856891243138898288379387 8002287614711652531743087737814467999489 × 3674604366679959042824463379962795263227915816434308764267603228381573966651 1279233373417143396810270092798736308917

1359:

RSA-768 = 1230186684530117755130494958384962720772853569595334792197322452151726400507 2636575187452021997864693899564749427740638459251925573263034537315482685079 1702612214291346167042921431160222124047927473779408066535141959745985690214 3413

1335:

RSA-232 = 2966909333208360660361779924242630634742946262521852394401857157419437019472 3262390744910112571804274494074452751891 × 3403816175197563438006609498491521420547121760734723172735163413276050706174 8526506443144325148088881115083863017669

1331:

RSA-232 = 1009881397871923546909564894309468582818233821955573955141120516205831021338 5285453743661097571543636649133800849170651699217015247332943892702802343809 6090980497644054071120196541074755382494867277137407501157718230539834060616 2079

1795:

RSA-2048 = 2519590847565789349402718324004839857142928212620403202777713783604366202070 7595556264018525880784406918290641249515082189298559149176184502808489120072 8449926873928072877767359714183472702618963750149718246911650776133798590957

1724:

552829818672645133986336493190808467199043187438128336350279547028265329780 293491615581188104984490831954500984839377522725705257859194499387007369575 568843693381277961308923039256969525326162082367649031603655137144791393234 7169566988069

1319:

RSA-230 = 4528450358010492026612439739120166758911246047493700040073956759261590397250 033699357694507193523000343088601688589 × 3968132623150957588532394439049887341769533966621957829426966084093049516953 598120833228447171744337427374763106901

1315:

RSA-230 = 1796949159794106673291612844957324615636756180801260007088891883553172646034 1490933493372247868650755230855864199929221814436684722874052065257937495694 3483892631711525225256544109808191706117425097024407180103648316382885188526 89

1723:

RSA-1536 = 184769970321174147430683562020016440301854933866341017147178577491065169671 116124985933768430543574458561606154457179405222971773252466096064694607124 962372044202226975675668737842756238950876467844093328515749657884341508847

1519:

RSA-1024 = 135066410865995223349603216278805969938881475605667027524485143851526510604 859533833940287150571909441798207282164471551373680419703964191743046496589 274256239341020864383202110372958725762358509643110564073501508187510676594

1783:

RSA-617 = 2270180129378501419358040512020458674106123596276658390709402187921517148311 9139894870133091111044901683400949483846818299518041763507948922590774925466 0881718792594659210265970467004498198990968620394600177430944738110569912941

1771:

RSA-500 = 1897194133748626656330534743317202527237183591953428303184581123062450458870 7687605943212347625766427494554764419515427586743205659317254669946604982419 7301601038125215285400688031516401611623963128370629793265939405081077581694

1759:

RSA-490 = 1860239127076846517198369354026076875269515930592839150201028353837031025971 3738522164743327949206433999068225531855072554606782138800841162866037393324 6578171804201717222449954030315293547871401362961501065002486552688663415745

1747:

RSA-480 = 3026570752950908697397302503155918035891122835769398583955296326343059761445 7144169659817040125185215913853345598217234371231338324773210726853524776378 4105186549246199888070331088462855743520880671299302895546822695492968577380

1735:

RSA-470 = 1705147378468118520908159923888702802518325585214915968358891836980967539803 6897711442383602526314519192366612270595815510311970886116763177669964411814 0957486602388713064698304619191359016382379244440741228665455229545368837485

1711:

RSA-460 = 1786856020404004433262103789212844585886400086993882955081051578507634807524 1464078819812169681394445771476334608488687746254318292828603396149562623036 3564554675355258128655971003201417831521222464468666642766044146641933788836

1699:

RSA-450 = 1984634237142836623497230721861131427789462869258862089878538009871598692569 0078791591684242367262529704652673686711493985446003494265587358393155378115 8032447061155145160770580926824366573211993981662614635734812647448360573856

1687:

RSA-440 = 2601428211955602590070788487371320550539810804595235289423508589663391270837 4310252674800592426746319007978890065337573160541942868114065643853327229484 5029942332226171123926606357523257736893667452341192247905168387893684524818

1675:

RSA-430 = 3534635645620271361541209209607897224734887106182307093292005188843884213420 6950355315163258889704268733101305820000124678051064321160104990089741386777 2424190744453885127173046498565488221441242210687945185565975582458031351338

1663:

RSA-420 = 2091366302476510731652556423163330737009653626605245054798522959941292730258 1898373570076188752609749648953525484925466394800509169219344906273145413634 2427186266197097846022969248579454916155633686388106962365337549155747268356

1651:

RSA-410 = 1965360147993876141423945274178745707926269294439880746827971120992517421770 1079138139324539033381077755540830342989643633394137538983355218902490897764 4412968474332754608531823550599154905901691559098706892516477785203855688127

1639:

RSA-400 = 2014096878945207511726700485783442547915321782072704356103039129009966793396 1419850865094551022604032086955587930913903404388675137661234189428453016032 6191193056768564862615321256630010268346471747836597131398943140685464051631

1627:

RSA-390 = 2680401941182388454501037079346656065366941749082852678729822424397709178250 4623002472848967604282562331676313645413672467684996118812899734451228212989 1630084759485063423604911639099585186833094019957687550377834977803400653628

1615:

RSA-380 = 3013500443120211600356586024101276992492167997795839203528363236610578565791 8270750937407901898070219843622821090980641477056850056514799336625349678549 2187941807116344787358312651772858878058620717489800725333606564197363165358

1603:

RSA-370 = 1888287707234383972842703127997127272470910519387718062380985523004987076701 7212819937261952549039800018961122586712624661442288502745681454363170484690 7379449525034797494321694352146271320296579623726631094822493455672541491544

1591:

RSA-360 = 2186820202343172631466406372285792654649158564828384065217121866374227745448 7764963889680817334211643637752157994969516984539482486678141304751672197524 0052350576247238785129338002757406892629970748212734663781952170745916609168

1579:

RSA-350 = 2650719995173539473449812097373681101529786464211583162467454548229344585504 3495841191504413349124560193160478146528433707807716865391982823061751419151 6068496555750496764686447379170711424873128631468168019548127029171231892127

1567:

RSA-340 = 2690987062294695111996484658008361875931308730357496490239672429933215694995 2758588771223263308836649715112756731997946779608413232406934433532048898585 9176676580752231563884394807622076177586625973975236127522811136600110415063

1555:

RSA-330 = 1218708633106058693138173980143325249157710686226055220408666600017481383238 1352456802425903555880722805261111079089882303717632638856140900933377863089 0634828167900405006112727432172179976427017137792606951424995281839383708354

1543:

RSA-320 = 2136810696410071796012087414500377295863767938372793352315068620363196552357 8837094085435000951700943373838321997220564166302488321590128061531285010636 8571638978998117122840139210685346167726847173232244364004850978371121744321

1531:

RSA-310 = 1848210397825850670380148517702559371400899745254512521925707445580334710601 4125276757082979328578439013881047668984294331264191394626965245834649837246 5163148188847336415136873623631778358751846501708714541673402642461569061162

1507:

RSA-309 = 1332943998825757583801437794588036586217112243226684602854588261917276276670 5425540467426933349195015527349334314071822840746357352800368666521274057591 1870128339157499072351179666739658503429931021985160714113146720277365006623

1495:

RSA-300 = 2769315567803442139028689061647233092237608363983953254005036722809375824714 9473946190060218756255124317186573105075074546238828817121274630072161346956 4396741836389979086904304472476001839015983033451909174663464663867829125664

1483:

RSA-290 = 3050235186294003157769199519894966400298217959748768348671526618673316087694 3419156362946151249328917515864630224371171221716993844781534383325603218163 2549201100649908073932858897185243836002511996505765970769029474322210394327

1471:

RSA-280 = 1790707753365795418841729699379193276395981524363782327873718589639655966058 5783742549640396449103593468573113599487089842785784500698716853446786525536 5503525160280656363736307175332772875499505341538927978510751699922197178159

1459:

RSA-896 = 4120234369866595438555313653325759481798116998443279828454556264338764455652 4842619809887042316184187926142024718886949256093177637503342113098239748515 0944909106910269861031862704114880866970564902903653658867433731720813104105

1447:

RSA-270 = 2331085303444075445276376569106805241456198124803054490429486119684959182451 3578286788836931857711641821391926857265831491306067262691135402760979316634 1626693946596196427744273886601876896313468704059066746903123910748277606548

1435:

RSA-260 = 2211282552952966643528108525502623092761208950247001539441374831912882294140 2001986512729726569746599085900330031400051170742204560859276357953757185954 2988389587092292384910067030341246205457845664136645406842143612930176940208

1712:

8932452217321354860484353296131403821175862890998598653858373835628654351880 4806362231643082386848731052350115776715521149453708868428108303016983133390 0416365515466857004900847501644808076825638918266848964153626486460448430073 4909

1303:

RSA-220 = 6863656412267566274382371499288437800130842239979164844621244993321541061441 4642667938213644208420192054999687 × 3292907439486349812049301549212935291916455196536233952462686051169290349309 4652463337824866390738191765712603

255:

sieving: estimated 500 mips years, run by Bruce Dodson (28.37%), Peter L. Montgomery and Marije Elkenbracht-Huizing (27.77%), Arjen K. Lenstra (19.11%), WWW contributors (17.17% ), Matt Fante (4.36%), Paul Leyland (1.66%), Damian Weber and Joerg Zayer (1.56%)

1287:

RSA-704 = 9091213529597818878440658302600437485892608310328358720428512168960411528640 933367824950788367956756806141 × 8143859259110045265727809126284429335877899002167627883200914172429324360133 004116702003240828777970252499

1270:

RSA-210 = 4359585683259407917999519653872144063854709102652201963187054821445240853452 75999740244625255428455944579 × 5625457617268841037562770073044474817438769440075105451049468510945483965774 79473472146228550799322939273

1299:

RSA-220 = 2260138526203405784941654048610197513508038915719776718321197768109445641817 9666766085931213065825772506315628866769704480700018111497118630021124879281 99487482066070131066586646083327982803560379205391980139946496955261

1396:

RSA-250 has 250 decimal digits (829 bits), and was factored in February 2020 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé, and Paul Zimmermann. The announcement of the factorization occurred on February 28.

349:

matrix: 224 hours on one CPU of the Cray-C916 at SARA, Amsterdam square root: four 300 MHz R12000 processors of a 24-processor SGI Origin 2000 at CWI; the successful one took 39.4 CPU-hours and the others took 38.3, 41.9, and 61.6 CPU-hours

1700:

3132247491715526997278115514905618953253443957435881503593414842367096046182 7643434794849824315251510662855699269624207451365738384255497823390996283918 3287667419172988072221996532403300258906083211160744508191024837057033

1408:

The factorisation of RSA-250 utilised approximately 2700 CPU core-years, using a 2.1 GHz Intel Xeon Gold 6130 CPU as a reference. The computation was performed with the Number Field Sieve algorithm, using the open source CADO-NFS software.

1283:

RSA-704 = 7403756347956171282804679609742957314259318888923128908493623263897276503402 8266276891996419625117843995894330502127585370118968098286733173273108930900 552505116877063299072396380786710086096962537934650563796359

1244:

RSA-200 = 3532461934402770121272604978198464368671197400197625023649303468776121253679 423200058547956528088349 × 7925869954478333033347085841480059687737975857364219960734330341455767872818 152135381409304740185467

1266:

RSA-210 = 2452466449002782119765176635730880184670267876783327597434144517150616008300 3858721695220839933207154910362682719167986407977672324300560059203563124656 1218465817904100131859299619933817012149335034875870551067

1209:

RSA-640 = 1634733645809253848443133883865090859841783670033092312181110852389333100104 508151212118167511579 × 1900871281664822113126851573935413975471896789968515493666638539088027103802 104498957191261465571

1279:

RSA-704 has 212 decimal digits (704 bits), and was factored by Shi Bai, Emmanuel Thomé and Paul Zimmermann. The factorization was announced July 2, 2012. A cash prize of US$ 30,000 was previously offered for a successful factorization.

1688:

0307729497304959710847337973805145673263119916483529703607405432752966630781 2234597766390750441445314408171802070904072739275930410299359006059619305590 701939627725296116299946059898442103959412221518213407370491

293:

sieving: 8.9 CPU-years on about 125 SGI and Sun workstations running at 175 MHZ on average, and on about 60 PCs running at 300 MHZ on average; approximately equivalent to 1500 mips years; run by Peter L. Montgomery, Stefania Cavallar,

1192:

RSA-190 = 3171195257690152709485171289740475929805147316029450327784761927832793642798 1256542415724309619 × 6015260020444561641587641685526676183243543359471811072599763828083615704046 0481625355619404899

1240:

RSA-200 = 2799783391122132787082946763872260162107044678695542853756000992932612840010 7609345671052955360856061822351910951365788637105954482006576775098580557613 579098734950144178863178946295187237869221823983

1205:

RSA-640 = 3107418240490043721350750035888567930037346022842727545720161948823206440518 0815045563468296717232867824379162728380334154710731085019195485290073377248 22783525742386454014691736602477652346609

1676:

2070785777831859308900851761495284515874808406228585310317964648830289141496 3289966226854692560410075067278840383808716608668377947047236323168904650235 70092246473915442026549955865931709542468648109541

1128:

RSA-576 has 174 decimal digits (576 bits), and was factored on December 3, 2003, by J. Franke and T. Kleinjung from the University of Bonn. A cash prize of $ 10,000 was offered by RSA Security for a successful factorization.

1165:

RSA-180 = 4007800823297508779525813391041005725268293178158071765648821789984975727719 50624613470377 × 4769396887386118369955354773570708579399020760277882320319897758246062255957 73435668861833

1188:

RSA-190 = 1907556405060696491061450432646028861081179759533184460647975622318915025587 1841757540549761551215932934922604641526300932385092466032074171247261215808 58185985938946945490481721756401423481

308:

eleven weeks (including four weeks for polynomial selection, one month for sieving, one week for data filtering and matrix construction, five days for the matrix, and 14.2 hours to find the factors using the square root)

1138:

RSA-576 = 3980750864240649373971255005503864911990643623425267084063851895759463889572 61768583317 × 4727721461074353025362230719730482246329146953020971164598521711305207112563 63590397527

1664:

4666583846809964354191550136023170105917441056517493690125545320242581503730 3405952887826925813912683942756431114820292313193705352716165790132673270514 3817744164107601735413785886836578207979

1367:

The CPU time spent on finding these factors by a collection of parallel computers amounted approximately to the equivalent of almost 2000 years of computing on a single-core 2.2 GHz AMD Opteron-based computer.

1112:

RSA-170 = 3586420730428501486799804587268520423291459681059978161140231860633948450858 040593963 × 7267029064107019078863797763923946264136137803856996670313708936002281582249 587494493

1161:

RSA-180 = 1911479277189866096892294666314546498129862462766673548641885036388072607034 3679905877620136513516127813425829612810920004670291298456875280033022177775 2773957404540495707851421041

754:

RSA-120 has 120 decimal digits (397 bits), and was factored in June 1993 by Thomas Denny, Bruce Dodson, Arjen K. Lenstra, and Mark S. Manasse. The computation took under three months of actual computer time.

1652:

0635069372091564594333528156501293924133186705141485137856845741766150159437 6063244163040088180887087028771717321932252992567756075264441680858665410918 431223215368025334985424358839

1083:

RSA-160 = 4542789285848139407168619064973883165613714577846979325095998470925000415733 5359 × 4738809060383201619663383230378895197326892292104095794474135464881202849390 9367

1047:

13.5 times that of a random polynomial selection); 124722179 relations were collected in the sieving stage; the matrix had 6699191 rows and 6711336 columns and weight 417132631 (62.27 nonzeros per row).

736:

The number can be factorized in less than four hours on overclocked to 3.5 GHz Intel Core2 Quad q9300, using GGNFS and Msieve binaries running by distributed version of the factmsieve Perl script.

1032:

RSA-155 = 1026395928297411057720541965739916759007165678080380668033419335217907113077 79 × 1066034883801684548209272203600128786792079585759892915222706082371930628086 43

304:

square root: four different dependencies were run in parallel on four 250 MHZ SGI Origin 2000 processors at CWI; three of them found the factors of RSA-140 after 14.2, 19.0 and 19.0 CPU-hours

1640:

7519403149294308737302321684840956395183222117468443578509847947119995373645 3607109795994713287610750434646825511120586422993705980787028106033008907158 74500584758146849481

721:

The number can be factorized in 72 minutes on overclocked to 3.5 GHz Intel Core2 Quad q9300, using GGNFS and Msieve binaries running by distributed version of the factmsieve Perl script.

991:

RSA-155 has 155 decimal digits (512 bits), and was factored on August 22, 1999, in a span of six months, by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson,

970:

RSA-150 has 150 decimal digits (496 bits), and was withdrawn from the challenge by RSA Security. RSA-150 was eventually factored into two 75-digit primes by Aoki et al. in 2004 using the

1628:

6955344904367437281870253414058414063152368812498486005056223028285341898040 0795447435865033046248751475297412398697088084321037176392288312785544402209 1083492089

1135:

RSA-576 = 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059

258:

matrix (67.5 hours on the Cray-C90 at SARA, Amsterdam) and square root (48 hours per dependency on an SGI Challenge processor) run by Peter L. Montgomery and Marije Elkenbracht-Huizing

354:

9 weeks for polynomial selection, plus 5.2 months for the rest (including 3.7 months for sieving, about 1 month for data filtering and matrix construction, and 10 days for the matrix)

1376:

RSA-240 has 240 decimal digits (795 bits), and was factored in November 2019 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann.

1109:

RSA-170 = 26062623684139844921529879266674432197085925380486406416164785191859999628542069361450283931914514618683512198164805919882053057222974116478065095809832377336510711545759

1255:-based computer. Note that while this approximation serves to suggest the scale of the effort, it leaves out many complicating factors; the announcement states it more precisely. 1248:

The CPU time spent on finding these factors by a collection of parallel computers amounted – very approximately – to the equivalent of 75 years work for a single 2.2

843:

In 2015, RSA-129 was factored in about one day, with the CADO-NFS open source implementation of number field sieve, using a commercial cloud computing service for about $ 30.

983:

RSA-150 = 348009867102283695483970451047593424831012817350385456889559637548278410717 × 445647744903640741533241125787086176005442536297766153493419724532460296199

96:

digits are counted instead. An exception to this is RSA-617, which was created before the change in the numbering scheme. The numbers are listed in increasing order below.

1080:

RSA-160 = 2152741102718889701896015201312825429257773588845675980170497676778133145218859135673011059773491059602497907111585214302079314665202840140619946994927570407753

1296:

RSA-220 has 220 decimal digits (729 bits), and was factored by S. Bai, P. Gaudry, A. Kruppa, E. Thomé and P. Zimmermann. The factorization was announced on May 13, 2016.

1344:

RSA-768 has 232 decimal digits (768 bits), and was factored on December 12, 2009, over the span of two years, by Thorsten Kleinjung, Kazumaro Aoki, Jens Franke,

1029:

RSA-155 = 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897

2048: 1616:

2237779263423501952646847579678711825720733732734169866406145425286581665755 6977260763553328252421574633011335112031733393397168350585519524478541747311

948:

RSA-140 = 3398717423028438554530123627613875835633986495969597423490929302771479 × 6264200187401285096151654948264442219302037178623509019111660653946049

2170: 1873: 980:

RSA-150 = 155089812478348440509606754370011861770654545830995430655466945774312632703463465954363335027577729025391453996787414027003501631772186840890795964683

325:

with line (29%) and lattice (71%) sieving, and a polynomial selection method written by Brian Murphy and Peter L. Montgomery, ported by Arjen Lenstra to use his

2940: 2914: 2891:

Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen; Thomé, Emmanuel; Bos, Joppe; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter (2010),

277:

with line (by CWI; 45%) and lattice (by Arjen K. Lenstra; 55%) sieving, and a polynomial selection method by Brian Murphy and Peter L. Montgomery; and blocked

2756: 1181:

RSA-190 has 190 decimal digits (629 bits), and was factored on November 8, 2010, by I. A. Popovyan from Moscow State University, Russia, and A. Timofeev from

1836: 1456:

RSA-896 has 270 decimal digits (896 bits), and has not been factored so far. A cash prize of $ 75,000 was previously offered for a successful factorization.

2725: 2294: 2229:; Cavallar, Stefania; Dodson, Bruce; Lenstra, Arjen; Leyland, Paul; Lioen, Walter; Montgomery, Peter; Murphy, Brian; Zimmermann, Paul (February 4, 1999) . 1100: 2230: 2195:; Cowie, Jim; Elkenbracht-Huizing, Marije; Furmanski, Wojtek; Montgomery, Peter L.; Weber, Damian; Zayer, Joerg (April 12, 1996) . Caldwell, Chris (ed.). 1604:

2700993152879235272779266578292207161032746297546080025793864030543617862620 878802244305286292772467355603044265985905970622730682658082529621

1792:

RSA-2048 has 617 decimal digits (2,048 bits). It is the largest of the RSA numbers and carried the largest cash prize for its factorization, $ 200,000.

891:

RSA-130 = 39685999459597454290161126162883786067576449112810064832555157243 × 45534498646735972188403686897274408864356301263205069600999044599

945:

RSA-140 = 21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471

826:

RSA-129 = 3490529510847650949147849619903898133417764638493387843990820577 × 32769132993266709549961988190834461413177642967992942539798288533

99:

Note: until work on this article is finished, please check both the table and the list, since they include different values and different information.

3036: 2845:

Zheltkov, Dmitry; Zamarashkin, Nikolai; Matveev, Sergey (2023), Voevodin, Vladimir; Sobolev, Sergey; Yakobovskiy, Mikhail; Shagaliev, Rashit (eds.),

2808:

Zheltkov, Dmitry; Zamarashkin, Nikolai; Matveev, Sergey (2023). Voevodin, Vladimir; Sobolev, Sergey; Yakobovskiy, Mikhail; Shagaliev, Rashit (eds.).

2987: 1944: 92:

The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits. Later, beginning with RSA-576,

1063: 837: 904:

5748302248738405200 x + 9882261917482286102 x - 13392499389128176685 x + 16875252458877684989 x + 3759900174855208738 x - 46769930553931905995

1592:

9358372359962787832802257421757011302526265184263565623426823456522539874717 61591019113926725623095606566457918240614767013806590649

2026: 1720:

RSA-1536 has 463 decimal digits (1,536 bits), and has not been factored so far. $ 150,000 was previously offered for successful factorization.

764:

RSA-120 = 327414555693498015751146303749141488063642403240171463406883 × 693342667110830181197325401899700641361965863127336680673013

192:

835 mips years run by Arjen K. Lenstra (45.503%), Bruce Dodson (30.271%), Thomas Denny (22.516%), Mark Manasse (1.658%), and Walter Lioen and

2866: 2829: 2083: 1990: 888:

RSA-130 = 1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

823:

RSA-129 = 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541

2414: 1328:

RSA-232 has 232 decimal digits (768 bits), and was factored on February 17, 2020, by N. L. Zamarashkin, D. A. Zheltkov and S. A. Matveev.

836:

The factoring challenge included a message encrypted with RSA-129. When decrypted using the factorization the message was revealed to be "

830: 1580:

2886825928263239383444398948209649800021987837742009498347263667908976501360 3382322972552204068806061829535529820731640151

1516:

RSA-1024 has 309 decimal digits (1,024 bits), and has not been factored so far. $ 100,000 was previously offered for factorization.

1237:

On May 9, 2005, F. Bahr, M. Boehm, J. Franke, and T. Kleinjung announced that they had factorized the number using GNFS as follows:

746:

RSA-110 = 6122421090493547576937037317561418841225758554253106999 × 5846418214406154678836553182979162384198610505601062333

1182: 761:

RSA-120 = 227010481295437363334259960947493668895875336466084780038173258247009162675779735389791151574049166747880487470296548479

238: 2620: 2581: 3046: 2975: 2561: 2489: 2394: 2366: 2327: 2260: 1413: 1349: 868: 338: 286: 250: 2453: 298:, and Walter M. Lioen (36.8%), Paul Leyland (28.8%), Bruce Dodson (26.6%), Paul Zimmermann (5.4%), and Arjen K. Lenstra (2.5%). 89:

challenges are no longer active." Some of the smaller prizes had been awarded at the time. The remaining prizes were retracted.

2721: 1353: 936: 343:

polynomial selection run by Brian Murphy, Peter Montgomery, Arjen Lenstra and Bruce Dodson; Dodson found the one that was used

215:

approximately 5000 mips years run by Derek Atkins, Michael Graff, Arjen K. Lenstra, Paul Leyland, and more than 600 volunteers

2070:. Lecture Notes in Computer Science. Vol. 773. Berlin, Heidelberg: Springer (published July 13, 2001). pp. 166–174. 1927: 1977:. Lecture Notes in Computer Science. Vol. 765. Berlin, Heidelberg: Springer (published July 13, 2001). pp. 28–39. 1568:

0004691128152106812042872285697735145105026966830649540003659922618399694276 990464815739966698956947129133275233

2677: 1099:

RSA-170 has 170 decimal digits (563 bits) and was first factored on December 29, 2009, by D. Bonenberger and M. Krone from

1895: 1858: 1805: 711:

RSA-100 = 37975227936943673922808872755445627854565536638199 × 40094690950920881030683735292761468389214899724061

326: 2139: 743:

RSA-110 = 35794234179725868774991807832568455403003778024228226193532908190484670252364677411513516111204504060317568667

772:

RSA-129, having 129 decimal digits (426 bits), was not part of the 1991 RSA Factoring Challenge, but rather related to

2162: 2108: 1417: 55: 2944: 2918: 1154:

RSA-180 has 180 decimal digits (596 bits), and was factored on May 8, 2010, by S. A. Danilov and I. A. Popovyan from

2764: 1170: 1143: 1117: 1088: 1036: 971: 322: 274: 230: 1556:

6364684839261149319768449396541020909665209789862312609604983709923779304217 01862444655244698696759267

932: 777: 2302: 860: 2733: 2238: 2204: 1918:

RSA Factoring Challenge Administrator (challenge-administrator@majordomo.rsasecurity.com) (January 30, 2002) .

1816: 814: 708:

RSA-100 = 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

76:

of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617

3041: 2786: 1810: 1220: 1155: 334: 282: 246: 47: 1214: 2637: 2613: 1952: 1544:

8270343654835754061017503137136489303437996367224915212044704472299799616089 2591129924218437

1312:

RSA-230 has 230 decimal digits (762 bits), and was factored by Samuel S. Gross on August 15, 2018.

1071: 93: 59: 2991: 920: 2695: 864: 1012: 1004: 810: 81: 1000: 2018: 1008: 782: 2533: 1234:

RSA-200 has 200 decimal digits (663 bits), and factors into the two 100-digit primes given below.

928: 915:

RSA-140 has 140 decimal digits (463 bits), and was factored on February 2, 1999, by a team led by

872: 144: 1996: 1520:

629205563685529475213500852879416377328533906109750544334999811150056977236 890927563

1103:. An independent factorization was completed by S. A. Danilov and I. A. Popovyan two days later. 1056: 1055:

RSA-160 has 160 decimal digits (530 bits), and was factored on April 1, 2003, by a team from the

952: 895: 876: 2809: 2357:

Bahr, F.; Franke, J.; Kleinjung, T.; Lochter, M.; Böhm, M. (April 1, 2003). Franke, Jens (ed.).

851:

RSA-130 has 130 decimal digits (430 bits), and was factored on April 10, 1996, by a team led by

690:

RSA-100 has 100 decimal digits (330 bits). Its factorization was announced on April 1, 1991, by

2411: 1040: 956: 856: 2862: 2825: 2465: 2079: 2042: 1986: 1889: 1852: 1532:

0116380982484120857688483676576094865930188367141388795454378671343386258291 687641

1263:

RSA-210 has 210 decimal digits (696 bits) and was factored in September 2013 by Ryan Propper:

974:(GNFS), years after bigger RSA numbers that were still part of the challenge had been solved. 962:

The matrix had 4671181 rows and 4704451 columns and weight 151141999 (32.36 nonzeros per row)

330: 278: 242: 2063: 1508:

6927218079163559142755190653347914002967258537889160429597714204365647842739 10949

714:

It takes four hours to repeat this factorization using the program Msieve on a 2200 MHz

2979: 2854: 2817: 2295:"New factorization record: Factorization of a 512-bits RSA key using the Number Field Sieve" 2071: 1978: 1970: 813:

100 token prize was awarded by RSA Security for the factorization, which was donated to the

69: 2681: 2624: 2585: 2565: 2493: 2418: 2398: 2290: 2226: 916: 695: 295: 234: 193: 140: 2598: 2846: 2617: 2578: 773: 291:

polynomial selection: 2000 CPU hours on four 250 MHZ SGI Origin 2000 processors at CWI

2650: 2558: 2486: 2391: 2358: 2335: 2268: 3030: 2969: 2469: 2363:

Paul Zimmermann, Laboratoire Lorrain de Recherche en Informatique et ses Applications

2192: 1345: 992: 924: 852: 798: 794: 730: 691: 148: 2000: 1421: 1020: 1016: 996: 805:, using approximately 1600 computers from around 600 volunteers connected over the 802: 790: 51: 43: 1919: 2816:. Lecture Notes in Computer Science. Cham: Springer Nature Switzerland: 114–128. 3012: 2858: 2821: 2674: 1067: 50:. The challenge was to find the prime factors of each number. It was created by 31: 1756:

RSA-490 has 490 decimal digits (1,626 bits), and has not been factored so far.

1744:

RSA-480 has 480 decimal digits (1,593 bits), and has not been factored so far.

1732:

RSA-470 has 470 decimal digits (1,559 bits), and has not been factored so far.

1708:

RSA-460 has 460 decimal digits (1,526 bits), and has not been factored so far.

1696:

RSA-450 has 450 decimal digits (1,493 bits), and has not been factored so far.

1684:

RSA-440 has 440 decimal digits (1,460 bits), and has not been factored so far.

1672:

RSA-430 has 430 decimal digits (1,427 bits), and has not been factored so far.

1660:

RSA-420 has 420 decimal digits (1,393 bits), and has not been factored so far.

1648:

RSA-410 has 410 decimal digits (1,360 bits), and has not been factored so far.

1636:

RSA-400 has 400 decimal digits (1,327 bits), and has not been factored so far.

1624:

RSA-390 has 390 decimal digits (1,294 bits), and has not been factored so far.

1612:

RSA-380 has 380 decimal digits (1,261 bits), and has not been factored so far.

1600:

RSA-370 has 370 decimal digits (1,227 bits), and has not been factored so far.

1588:

RSA-360 has 360 decimal digits (1,194 bits), and has not been factored so far.

1576:

RSA-350 has 350 decimal digits (1,161 bits), and has not been factored so far.

1564:

RSA-340 has 340 decimal digits (1,128 bits), and has not been factored so far.

1552:

RSA-330 has 330 decimal digits (1,094 bits), and has not been factored so far.

1540:

RSA-320 has 320 decimal digits (1,061 bits), and has not been factored so far.

1528:

RSA-310 has 310 decimal digits (1,028 bits), and has not been factored so far.

1504:

RSA-309 has 309 decimal digits (1,024 bits), and has not been factored so far.

3020: 2131: 1780:

RSA-617 has 617 decimal digits (2,048 bits) and has not been factored so far.

1768:

RSA-500 has 500 decimal digits (1,659 bits) and has not been factored so far.

899: 73: 39: 2075: 1492:

RSA-300 has 300 decimal digits (995 bits), and has not been factored so far.

1480:

RSA-290 has 290 decimal digits (962 bits), and has not been factored so far.

1468:

RSA-280 has 280 decimal digits (928 bits), and has not been factored so far.

1444:

RSA-270 has 270 decimal digits (895 bits), and has not been factored so far.

1432:

RSA-260 has 260 decimal digits (862 bits), and has not been factored so far.

729:

RSA-110 has 110 decimal digits (364 bits), and was factored in April 1992 by

2473: 2163:"The Magic Words are Squeamish Ossifrage - factoring RSA-129 using CADO-NFS" 1982: 715: 2330:. Other Activities: Cryptographic Challenges: The RSA Factoring Challenge. 2263:. Other Activities: Cryptographic Challenges: The RSA Factoring Challenge. 2100: 3016: 1496:

459895575157178816900228792711267471958357574416714366499722090015674047

1424:

who died on February 18, 2020, and had contributed to factoring RSA-768.

806: 2853:, vol. 14388, Cham: Springer Nature Switzerland, pp. 114–128, 2456:(repost of announcement of the factorization). Retrieved on 2008-03-10. 2432: 2203:(Mailing list). PrimePages: prime number research records and results. 1252: 1226:

The slightly larger RSA-200 was factored in May 2005 by the same team.

1217: 1060: 77: 63: 17: 2915:"[Cado-NFS-discuss] 795-bit factoring and discrete logarithms" 1352:, Joppe W. Bos, Dag Arne Osvik, Herman te Riele, Andrey Timofeev, and 699: 172: 2196: 2132:"Factoring Challenge Conquered - With a Little Help From Willamette" 2999: 2892: 2507: 2099:

Atkins, Derek; Graff, Michael; Lenstra, Arjen K.; Leyland, Paul C.

2315:

On August 22, 1999, we found that the 512-bits number RSA-155 ...

2847:"How to Make Lanczos-Montgomery Fast on Modern Supercomputers?" 2810:"How to Make Lanczos-Montgomery Fast on Modern Supercomputers?" 1484:

60575157628357292075495937664206199565578681309135044121854119

2301:(Mailing list). North Dakota University System. Archived from 2237:(Mailing list). North Dakota University System. Archived from 2062:

Denny, T.; Dodson, B.; Lenstra, A. K.; Manasse, M. S. (1994).

1249: 1930:

from the original on September 9, 2023 – via Ray Ontko.

1173:

algorithm implementation running on three Intel Core i7 PCs.

2167:

Nat McHugh: Transient Random-Noise Bursts with Announcements

907:

which has a root of 12574411168418005980468 modulo RSA-130.

1416:, an American mathematician known for his contributions to 2998:

Kazumaro Aoki, Yuji Kida, Takeshi Shimoyama, Hiroki Ueda,

2651:"mersenneforum.org - View Single Post - RSA-210 factored" 85:

smallest 23 of the 54 listed numbers have been factored.

2231:"Factorization of RSA-140 using the Number Field Sieve" 1939: 1937: 705:

The value and factorization of RSA-100 are as follows:

2299:

Number Theory List <NMBRTHRY@LISTSERV.NODAK.EDU>

2235:

Number Theory List <NMBRTHRY@LISTSERV.NODAK.EDU>

694:. Reportedly, the factorization took a few days using 301:

matrix: 100 hours on the Cray-C916 at SARA, Amsterdam

2941:"[Cado-NFS-discuss] Factorization of RSA-250" 1472:

7724733184279534477239566789173532366357270583106789

1348:, Emmanuel Thomé, Pierrick Gaudry, Alexander Kruppa, 2968:

RSA Factoring Challenge Administrator (1997-10-12),

1813:(includes table with size and status of all numbers) 1213:

The computation took five months on 80 2.2 GHz

789:

RSA-129 was factored in April 1994 by a team led by

3000:

GNFS Factoring Statistics of RSA-100, 110, ..., 150

2012: 2010: 995:, Walter Lioen, Peter L. Montgomery, Brian Murphy, 359: 3002:, Cryptology ePrint Archive, Report 2004/095, 2004 2119:– via Massachusetts Institute of Technology. 1876:. Archived from the original on September 21, 2013 1839:. Archived from the original on September 21, 2013 696:the multiple-polynomial quadratic sieve algorithm 1913: 1911: 1909: 1907: 1905: 882:The factorization was found in the third trial. 733:and Mark S. Manasse in approximately one month. 2431:Danilov, S. A.; Popovyan, I. A. (May 9, 2010). 2532:I. Popovyan, A. Timofeev (November 8, 2010). 2215:– via Notes, Proofs and other Comments. 8: 2787:"RSA-232 number has been factored – ИВМ РАН" 1132:The value and factorization are as follows: 1106:The value and factorization are as follows: 1077:The value and factorization are as follows: 1026:The value and factorization are as follows: 977:The value and factorization are as follows: 942:The value and factorization are as follows: 885:The value and factorization are as follows: 820:The value and factorization are as follows: 758:The value and factorization are as follows: 740:The value and factorization are as follows: 2609: 2607: 2047:: CS1 maint: numeric names: authors list ( 1460:190864254793282601391257624033946373269391 1448:649151920812699309766587514735456594993207 80:digits. Cash prizes of varying size, up to 1969:Dixon, Brandon; Lenstra, Arjen K. (1994). 101: 2886: 2884: 2101:"The Magic Words Are Squeamish Ossifrage" 1964: 1962: 1951:. July 9, 1993. p. 2. Archived from 54:in March 1991 to encourage research into 2982:in 2006, before the RSA challenge ended) 2726:"Factorisation of RSA-220 with CADO-NFS" 2506:Danilov, S. A.; Popovyan, I. A. (2010). 1101:Fachhochschule Braunschweig/Wolfenbüttel 1827: 1064:Federal Office for Information Security 838:The Magic Words are Squeamish Ossifrage 2894:Factorization of a 768-bit RSA modulus 2675:Factorisation of RSA-704 with CADO-NFS 2601:at MathWorld. Retrieved on 2008-03-10. 2369:from the original on September 2, 2023 2207:from the original on September 2, 2023 2173:from the original on September 2, 2023 2142:from the original on September 2, 2023 2111:from the original on September 9, 2023 2040: 1975:Advances in Cryptology — EUROCRYPT '93 1971:"Factoring Integers Using SIMD Sieves" 1887: 1850: 1412:The team dedicated the computation to 1169:The factorization was found using the 1142:The factorization was found using the 1116:The factorization was found using the 1087:The factorization was found using the 1035:The factorization was found using the 951:The factorization was found using the 894:The factorization was found using the 829:The factorization was found using the 7: 2161:McHugh, Nathaniel (March 26, 2015). 2136:Prof. Mark Janeba's Framed Home Page 2068:Advances in Cryptology — CRYPTO' 93 831:Multiple Polynomial Quadratic Sieve 677: 66:. The challenge was ended in 2007. 2988:"Challenge numbers in text format" 2169:. Sheffield, South Yorkshire, UK. 2150:– via Willamette University. 2019:"Distributed polynomial selection" 25: 2064:"On the factorization of RSA-120" 2029:from the original on July 2, 2023 1874:"The RSA Factoring Challenge FAQ" 1436:46391065875914794251435144458199 3037:Integer factorization algorithms 2597:Eric W. Weisstein (2005-11-08), 2379:We have factored RSA160 by gnfs. 2066:. In Stinson, Douglas R. (ed.). 1945:"Archive for the 'RSA' Category" 1924:challenge-rsa-honor-roll@rsa.com 1039:algorithm and an estimated 8000 955:algorithm and an estimated 2000 241:, and Saarbruecken; and blocked 58:and the practical difficulty of 2618:We have factored RSA200 by GNFS 2579:We have factored RSA640 by GNFS 673: 2757:"The Factorization of RSA-230" 2732:(Mailing list). Archived from 2334:. RSA Security. Archived from 2267:. RSA Security. Archived from 1: 2410:D. Bonenberger and M. Krone, 1806:Integer factorization records 665: 655: 625: 532: 327:multiple precision arithmetic 237:implementations by Bellcore, 2017:chris2be8 (March 27, 2012). 780:in the August 1977 issue of 650: 645: 640: 635: 630: 620: 615: 606: 601: 596: 591: 586: 581: 576: 571: 566: 557: 552: 547: 542: 537: 527: 522: 517: 508: 503: 498: 493: 488: 483: 478: 473: 468: 459: 454: 449: 444: 439: 434: 429: 424: 419: 410: 405: 400: 395: 390: 385: 380: 375: 370: 2859:10.1007/978-3-031-49432-1_9 2822:10.1007/978-3-031-49432-1_9 1973:. In Helleseth, Tor (ed.). 1418:computational number theory 1074:, M. Lochter, and M. Böhm. 168:ppmpqs by Arjen K. Lenstra 56:computational number theory 3063: 2640:. Retrieved on 2017-01-25. 2627:. Retrieved on 2008-03-10. 2588:. Retrieved on 2008-03-10. 2577:Jens Franke (2005-11-04), 2568:. Retrieved on 2008-03-10. 2508:"Factorization of RSA-180" 2496:. Retrieved on 2008-03-10. 2476:. Retrieved on 2008-03-10. 2452:Jens Franke (2003-12-03), 2433:"Factorization of RSA-180" 2401:. Retrieved on 2008-03-10. 2197:"Factorization of RSA-130" 1388:by a factor of 1.25–1.67. 1171:general number field sieve 1144:general number field sieve 1118:general number field sieve 1089:general number field sieve 1066:(BSI). The team contained 1037:general number field sieve 972:general number field sieve 861:Marije Elkenbracht-Huizing 669: 231:General Number Field Sieve 171:one month on 5/8 of a 16K 42:(numbers with exactly two 2976:The RSA Challenge Numbers 2696:"Factorization of RSA704" 2694:Bai, Shi (July 2, 2012). 2512:Cryptology ePrint Archive 2440:Cryptology ePrint Archive 2088:– via SpringerLink. 2003:– via SpringerLink. 1894:: CS1 maint: unfit URL ( 1857:: CS1 maint: unfit URL ( 1837:"RSA Factoring Challenge" 778:Mathematical Games column 663: 362: 112: 109: 106: 2421:Retrieved on 2010-03-08. 2076:10.1007/3-540-48329-2_15 1817:RSA Secret-Key Challenge 815:Free Software Foundation 329:code (LIP); and blocked 46:) that were part of the 3047:RSA Factoring Challenge 2107:(PostScript document). 1983:10.1007/3-540-48285-7_3 1811:RSA Factoring Challenge 1202:using GNFS as follows: 1156:Moscow State University 931:, Peter L. Montgomery, 48:RSA Factoring Challenge 27:Set of large semiprimes 2328:"RSA-155 is factored!" 2261:"RSA-140 is factored!" 2130:Janeba, Mark (1994) . 3023:. coverage on RSA-129 2655:www.mersenneforum.org 1023:and Paul Zimmermann. 2947:on February 28, 2020 2638:RSA-200 is factored! 2559:RSA-640 is factored! 2487:RSA-576 is factored! 2392:RSA-160 is factored! 2338:on December 30, 2006 2305:on December 31, 2004 2271:on December 30, 2006 2181:– via Blogger. 296:Herman J.J. te Riele 153:approx. 7 MIP-Years 2921:on December 3, 2019 2789:. February 17, 2020 2293:(August 26, 1999). 2241:on December 8, 2004 1955:on January 8, 2009. 1043:of computing time. 959:of computing time. 869:Peter L. Montgomery 783:Scientific American 702:parallel computer. 676: 672: 668: 339:Peter L. Montgomery 287:Peter L. Montgomery 251:Peter L. Montgomery 103: 38:are a set of large 2985:RSA Laboratories, 2974:RSA Laboratories, 2970:RSA Challenge List 2767:on August 23, 2018 2680:2012-07-02 at the 2636:RSA Laboratories, 2623:2008-03-22 at the 2614:Thorsten Kleinjung 2584:2008-06-16 at the 2564:2007-01-04 at the 2557:RSA Laboratories, 2534:"RSA-190 factored" 2492:2006-12-24 at the 2485:RSA Laboratories, 2417:2011-07-19 at the 2397:2006-12-30 at the 2390:RSA Laboratories, 1949:Cryptography Watch 1872:RSA Laboratories. 1835:RSA Laboratories. 1057:University of Bonn 953:Number Field Sieve 898:algorithm and the 896:Number Field Sieve 102: 2978:(archived by the 2868:978-3-031-49431-4 2831:978-3-031-49432-1 2538:mersenneforum.org 2466:Eric W. Weisstein 2193:Lenstra, Arjen K. 2085:978-3-540-48329-8 2023:mersenneforum.org 1992:978-3-540-48285-7 921:Stefania Cavallar 683: 682: 358: 357: 16:(Redirected from 3054: 2995: 2994:on May 21, 2013. 2990:. Archived from 2980:Internet Archive 2957: 2956: 2954: 2952: 2943:. Archived from 2937: 2931: 2930: 2928: 2926: 2917:. Archived from 2911: 2905: 2904: 2903: 2901: 2888: 2879: 2878: 2877: 2875: 2842: 2836: 2835: 2805: 2799: 2798: 2796: 2794: 2783: 2777: 2776: 2774: 2772: 2763:. Archived from 2761:cado-nfs-discuss 2752: 2746: 2745: 2743: 2741: 2736:on July 21, 2021 2730:Cado-nfs-discuss 2724:(May 13, 2016). 2722:Zimmermann, Paul 2718: 2712: 2711: 2709: 2707: 2691: 2685: 2672: 2666: 2665: 2663: 2661: 2647: 2641: 2634: 2628: 2611: 2602: 2599:RSA-640 Factored 2595: 2589: 2575: 2569: 2555: 2549: 2548: 2546: 2544: 2529: 2523: 2522: 2520: 2518: 2503: 2497: 2483: 2477: 2470:RSA-576 Factored 2463: 2457: 2450: 2444: 2443: 2437: 2428: 2422: 2408: 2402: 2388: 2382: 2381: 2376: 2374: 2354: 2348: 2347: 2345: 2343: 2332:RSA Laboratories 2324: 2318: 2317: 2312: 2310: 2291:Riele, Herman te 2287: 2281: 2280: 2278: 2276: 2265:RSA Laboratories 2257: 2251: 2250: 2248: 2246: 2227:Riele, Herman te 2223: 2217: 2216: 2214: 2212: 2189: 2183: 2182: 2180: 2178: 2158: 2152: 2151: 2149: 2147: 2127: 2121: 2120: 2118: 2116: 2096: 2090: 2089: 2059: 2053: 2052: 2046: 2038: 2036: 2034: 2014: 2005: 2004: 1966: 1957: 1956: 1941: 1932: 1931: 1926:(Mailing list). 1920:"RSA Honor Roll" 1915: 1900: 1899: 1893: 1885: 1883: 1881: 1869: 1863: 1862: 1856: 1848: 1846: 1844: 1832: 1414:Peter Montgomery 1350:Peter Montgomery 1346:Arjen K. Lenstra 1019:, Craig Putnam, 1007:, Paul Leyland, 993:Arjen K. Lenstra 927:, Paul Leyland, 925:Arjen K. Lenstra 923:, Bruce Dodson, 919:and composed of 865:Wojtek Furmanski 855:and composed of 853:Arjen K. Lenstra 799:Arjen K. Lenstra 731:Arjen K. Lenstra 692:Arjen K. Lenstra 360: 149:Arjen K. Lenstra 104: 70:RSA Laboratories 52:RSA Laboratories 21: 3062: 3061: 3057: 3056: 3055: 3053: 3052: 3051: 3027: 3026: 3009: 2986: 2965: 2960: 2950: 2948: 2939: 2938: 2934: 2924: 2922: 2913: 2912: 2908: 2899: 2897: 2890: 2889: 2882: 2873: 2871: 2869: 2844: 2843: 2839: 2832: 2807: 2806: 2802: 2792: 2790: 2785: 2784: 2780: 2770: 2768: 2755:Gross, Samuel. 2754: 2753: 2749: 2739: 2737: 2720: 2719: 2715: 2705: 2703: 2693: 2692: 2688: 2682:Wayback Machine 2673: 2669: 2659: 2657: 2649: 2648: 2644: 2635: 2631: 2625:Wayback Machine 2612: 2605: 2596: 2592: 2586:Wayback Machine 2576: 2572: 2566:Wayback Machine 2556: 2552: 2542: 2540: 2531: 2530: 2526: 2516: 2514: 2505: 2504: 2500: 2494:Wayback Machine 2484: 2480: 2464: 2460: 2451: 2447: 2435: 2430: 2429: 2425: 2419:Wayback Machine 2409: 2405: 2399:Wayback Machine 2389: 2385: 2372: 2370: 2356: 2355: 2351: 2341: 2339: 2326: 2325: 2321: 2308: 2306: 2289: 2288: 2284: 2274: 2272: 2259: 2258: 2254: 2244: 2242: 2225: 2224: 2220: 2210: 2208: 2191: 2190: 2186: 2176: 2174: 2160: 2159: 2155: 2145: 2143: 2129: 2128: 2124: 2114: 2112: 2098: 2097: 2093: 2086: 2061: 2060: 2056: 2039: 2032: 2030: 2016: 2015: 2008: 1993: 1968: 1967: 1960: 1943: 1942: 1935: 1917: 1916: 1903: 1886: 1879: 1877: 1871: 1870: 1866: 1849: 1842: 1840: 1834: 1833: 1829: 1825: 1802: 1797: 1790: 1785: 1778: 1773: 1766: 1761: 1754: 1749: 1742: 1737: 1730: 1725: 1718: 1713: 1706: 1701: 1694: 1689: 1682: 1677: 1670: 1665: 1658: 1653: 1646: 1641: 1634: 1629: 1622: 1617: 1610: 1605: 1598: 1593: 1586: 1581: 1574: 1569: 1562: 1557: 1550: 1545: 1538: 1533: 1526: 1521: 1514: 1509: 1502: 1497: 1490: 1485: 1478: 1473: 1466: 1461: 1454: 1449: 1442: 1437: 1430: 1406: 1402: 1394: 1385: 1381: 1374: 1365: 1361: 1354:Paul Zimmermann 1342: 1337: 1333: 1326: 1321: 1317: 1310: 1305: 1301: 1294: 1289: 1285: 1277: 1272: 1268: 1261: 1246: 1242: 1232: 1211: 1207: 1199: 1194: 1190: 1185:, Netherlands. 1179: 1167: 1163: 1152: 1140: 1136: 1126: 1114: 1110: 1097: 1085: 1081: 1053: 1033: 1030: 1013:François Morain 1005:Gerard Guillerm 989: 984: 981: 968: 949: 946: 937:Paul Zimmermann 917:Herman te Riele 913: 905: 892: 889: 849: 827: 824: 770: 765: 762: 752: 747: 744: 727: 712: 709: 688: 235:lattice sieving 194:Herman te Riele 28: 23: 22: 15: 12: 11: 5: 3060: 3058: 3050: 3049: 3044: 3042:Large integers 3039: 3029: 3028: 3025: 3024: 3015:(March 1996), 3008: 3007:External links 3005: 3004: 3003: 2996: 2983: 2972: 2964: 2961: 2959: 2958: 2932: 2906: 2880: 2867: 2851:Supercomputing 2837: 2830: 2814:Supercomputing 2800: 2778: 2747: 2713: 2702:(Mailing list) 2686: 2667: 2642: 2629: 2616:(2005-05-09), 2603: 2590: 2570: 2550: 2524: 2498: 2478: 2468:(2005-12-05), 2458: 2445: 2423: 2403: 2383: 2349: 2319: 2282: 2252: 2218: 2184: 2153: 2122: 2091: 2084: 2054: 2006: 1991: 1958: 1933: 1901: 1864: 1826: 1824: 1821: 1820: 1819: 1814: 1808: 1801: 1798: 1794: 1789: 1786: 1782: 1777: 1774: 1770: 1765: 1762: 1758: 1753: 1750: 1746: 1741: 1738: 1734: 1729: 1726: 1722: 1717: 1714: 1710: 1705: 1702: 1698: 1693: 1690: 1686: 1681: 1678: 1674: 1669: 1666: 1662: 1657: 1654: 1650: 1645: 1642: 1638: 1633: 1630: 1626: 1621: 1618: 1614: 1609: 1606: 1602: 1597: 1594: 1590: 1585: 1582: 1578: 1573: 1570: 1566: 1561: 1558: 1554: 1549: 1546: 1542: 1537: 1534: 1530: 1525: 1522: 1518: 1513: 1510: 1506: 1501: 1498: 1494: 1489: 1486: 1482: 1477: 1474: 1470: 1465: 1462: 1458: 1453: 1450: 1446: 1441: 1438: 1434: 1429: 1426: 1403: 1399: 1393: 1390: 1382: 1378: 1373: 1370: 1362: 1358: 1341: 1338: 1334: 1330: 1325: 1322: 1318: 1314: 1309: 1306: 1302: 1298: 1293: 1290: 1286: 1282: 1276: 1273: 1269: 1265: 1260: 1257: 1243: 1239: 1231: 1228: 1208: 1204: 1198: 1195: 1191: 1187: 1178: 1175: 1164: 1160: 1151: 1148: 1137: 1134: 1125: 1122: 1111: 1108: 1096: 1093: 1082: 1079: 1052: 1049: 1031: 1028: 1001:Jeff Gilchrist 988: 985: 982: 979: 967: 964: 947: 944: 912: 909: 903: 890: 887: 848: 845: 825: 822: 774:Martin Gardner 769: 766: 763: 760: 751: 748: 745: 742: 726: 723: 710: 707: 687: 684: 681: 680: 678:External links 661: 660: 659: 658: 653: 648: 643: 638: 633: 628: 623: 618: 611: 610: 609: 604: 599: 594: 589: 584: 579: 574: 569: 562: 561: 560: 555: 550: 545: 540: 535: 530: 525: 520: 513: 512: 511: 506: 501: 496: 491: 486: 481: 476: 471: 464: 463: 462: 457: 452: 447: 442: 437: 432: 427: 422: 415: 414: 413: 408: 403: 398: 393: 388: 383: 378: 373: 365: 364: 356: 355: 352: 341: 320: 317: 315: 311: 310: 306: 289: 272: 269: 267: 263: 262: 260: 253: 228: 225: 223: 219: 218: 216: 213: 210: 207: 204: 200: 199: 197: 190: 187: 184: 182: 178: 177: 175: 169: 166: 163: 161: 157: 156: 154: 151: 138: 135: 133: 129: 128: 127:calendar time 125: 124:compute power 122: 119: 115: 114: 111: 108: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 3059: 3048: 3045: 3043: 3040: 3038: 3035: 3034: 3032: 3022: 3018: 3014: 3011: 3010: 3006: 3001: 2997: 2993: 2989: 2984: 2981: 2977: 2973: 2971: 2967: 2966: 2962: 2946: 2942: 2936: 2933: 2920: 2916: 2910: 2907: 2896: 2895: 2887: 2885: 2881: 2870: 2864: 2860: 2856: 2852: 2848: 2841: 2838: 2833: 2827: 2823: 2819: 2815: 2811: 2804: 2801: 2788: 2782: 2779: 2766: 2762: 2758: 2751: 2748: 2735: 2731: 2727: 2723: 2717: 2714: 2701: 2697: 2690: 2687: 2683: 2679: 2676: 2671: 2668: 2656: 2652: 2646: 2643: 2639: 2633: 2630: 2626: 2622: 2619: 2615: 2610: 2608: 2604: 2600: 2594: 2591: 2587: 2583: 2580: 2574: 2571: 2567: 2563: 2560: 2554: 2551: 2539: 2535: 2528: 2525: 2513: 2509: 2502: 2499: 2495: 2491: 2488: 2482: 2479: 2475: 2471: 2467: 2462: 2459: 2455: 2449: 2446: 2441: 2434: 2427: 2424: 2420: 2416: 2413: 2407: 2404: 2400: 2396: 2393: 2387: 2384: 2380: 2368: 2364: 2360: 2353: 2350: 2337: 2333: 2329: 2323: 2320: 2316: 2304: 2300: 2296: 2292: 2286: 2283: 2270: 2266: 2262: 2256: 2253: 2240: 2236: 2232: 2228: 2222: 2219: 2206: 2202: 2198: 2194: 2188: 2185: 2172: 2168: 2164: 2157: 2154: 2141: 2137: 2133: 2126: 2123: 2110: 2106: 2102: 2095: 2092: 2087: 2081: 2077: 2073: 2069: 2065: 2058: 2055: 2050: 2044: 2028: 2024: 2020: 2013: 2011: 2007: 2002: 1998: 1994: 1988: 1984: 1980: 1976: 1972: 1965: 1963: 1959: 1954: 1950: 1946: 1940: 1938: 1934: 1929: 1925: 1921: 1914: 1912: 1910: 1908: 1906: 1902: 1897: 1891: 1875: 1868: 1865: 1860: 1854: 1838: 1831: 1828: 1822: 1818: 1815: 1812: 1809: 1807: 1804: 1803: 1799: 1793: 1787: 1781: 1775: 1769: 1763: 1757: 1751: 1745: 1739: 1733: 1727: 1721: 1715: 1709: 1703: 1697: 1691: 1685: 1679: 1673: 1667: 1661: 1655: 1649: 1643: 1637: 1631: 1625: 1619: 1613: 1607: 1601: 1595: 1589: 1583: 1577: 1571: 1565: 1559: 1553: 1547: 1541: 1535: 1529: 1523: 1517: 1511: 1505: 1499: 1493: 1487: 1481: 1475: 1469: 1463: 1457: 1451: 1445: 1439: 1433: 1427: 1425: 1423: 1419: 1415: 1410: 1398: 1391: 1389: 1377: 1371: 1369: 1357: 1355: 1351: 1347: 1339: 1329: 1323: 1313: 1307: 1297: 1291: 1281: 1274: 1264: 1258: 1256: 1254: 1251: 1238: 1235: 1229: 1227: 1224: 1222: 1219: 1216: 1203: 1196: 1186: 1184: 1176: 1174: 1172: 1159: 1157: 1149: 1147: 1145: 1133: 1130: 1123: 1121: 1119: 1107: 1104: 1102: 1094: 1092: 1090: 1078: 1075: 1073: 1069: 1065: 1062: 1058: 1050: 1048: 1044: 1042: 1038: 1027: 1024: 1022: 1018: 1014: 1010: 1009:Joel Marchand 1006: 1002: 998: 994: 986: 978: 975: 973: 965: 963: 960: 958: 954: 943: 940: 938: 934: 930: 926: 922: 918: 910: 908: 902: 901: 897: 886: 883: 880: 878: 874: 870: 866: 862: 858: 854: 846: 844: 841: 839: 834: 832: 821: 818: 816: 812: 808: 804: 800: 796: 795:Michael Graff 792: 787: 785: 784: 779: 775: 767: 759: 756: 749: 741: 738: 734: 732: 724: 722: 719: 717: 706: 703: 701: 697: 693: 685: 679: 675: 671: 667: 662: 657: 654: 652: 649: 647: 644: 642: 639: 637: 634: 632: 629: 627: 624: 622: 619: 617: 614: 613: 612: 608: 605: 603: 600: 598: 595: 593: 590: 588: 585: 583: 580: 578: 575: 573: 570: 568: 565: 564: 563: 559: 556: 554: 551: 549: 546: 544: 541: 539: 536: 534: 531: 529: 526: 524: 521: 519: 516: 515: 514: 510: 507: 505: 502: 500: 497: 495: 492: 490: 487: 485: 482: 480: 477: 475: 472: 470: 467: 466: 465: 461: 458: 456: 453: 451: 448: 446: 443: 441: 438: 436: 433: 431: 428: 426: 423: 421: 418: 417: 416: 412: 409: 407: 404: 402: 399: 397: 394: 392: 389: 387: 384: 382: 379: 377: 374: 372: 369: 368: 367: 366: 361: 353: 351: 347: 342: 340: 336: 332: 328: 324: 321: 318: 316: 313: 312: 307: 305: 302: 299: 297: 290: 288: 284: 280: 276: 273: 270: 268: 265: 264: 261: 259: 254: 252: 248: 244: 240: 236: 232: 229: 226: 224: 221: 220: 217: 214: 211: 208: 205: 202: 201: 198: 195: 191: 188: 185: 183: 180: 179: 176: 174: 170: 167: 164: 162: 159: 158: 155: 152: 150: 146: 142: 139: 136: 134: 131: 130: 126: 123: 120: 117: 116: 113:first solver 105: 100: 97: 95: 90: 86: 83: 79: 75: 72:(which is an 71: 67: 65: 61: 57: 53: 49: 45: 44:prime factors 41: 37: 33: 19: 3017:Wisecrackers 2992:the original 2951:February 28, 2949:. Retrieved 2945:the original 2935: 2923:. Retrieved 2919:the original 2909: 2900:February 10, 2898:, retrieved 2893: 2874:February 10, 2872:, retrieved 2850: 2840: 2813: 2803: 2793:February 10, 2791:. Retrieved 2781: 2769:. Retrieved 2765:the original 2760: 2750: 2738:. Retrieved 2734:the original 2729: 2716: 2704:. Retrieved 2699: 2689: 2670: 2660:February 10, 2658:. Retrieved 2654: 2645: 2632: 2593: 2573: 2553: 2543:November 10, 2541:. Retrieved 2537: 2527: 2515:. Retrieved 2511: 2501: 2481: 2461: 2448: 2439: 2426: 2406: 2386: 2378: 2371:. Retrieved 2362: 2352: 2340:. Retrieved 2336:the original 2331: 2322: 2314: 2307:. Retrieved 2303:the original 2298: 2285: 2273:. Retrieved 2269:the original 2264: 2255: 2243:. Retrieved 2239:the original 2234: 2221: 2209:. Retrieved 2200: 2187: 2175:. Retrieved 2166: 2156: 2144:. Retrieved 2135: 2125: 2115:November 24, 2113:. Retrieved 2105:Derek Atkins 2104: 2094: 2067: 2057: 2031:. Retrieved 2022: 1974: 1953:the original 1948: 1923: 1878:. Retrieved 1867: 1841:. Retrieved 1830: 1791: 1779: 1767: 1755: 1743: 1731: 1719: 1707: 1695: 1683: 1671: 1659: 1647: 1635: 1623: 1611: 1599: 1587: 1575: 1563: 1551: 1539: 1527: 1515: 1503: 1491: 1479: 1467: 1455: 1443: 1431: 1422:cryptography 1411: 1407: 1395: 1386: 1375: 1366: 1343: 1327: 1311: 1295: 1278: 1262: 1247: 1236: 1233: 1225: 1212: 1200: 1180: 1168: 1153: 1141: 1131: 1127: 1115: 1105: 1098: 1086: 1076: 1072:T. Kleinjung 1054: 1045: 1034: 1025: 1021:Chris Putnam 1017:Alec Muffett 997:Karen Aardal 990: 976: 969: 961: 950: 941: 933:Brian Murphy 929:Walter Lioen 914: 906: 893: 884: 881: 873:Damian Weber 850: 842: 835: 828: 819: 803:Paul Leyland 791:Derek Atkins 788: 781: 771: 757: 753: 739: 735: 728: 720: 713: 704: 689: 348: 344: 303: 300: 292: 257: 145:Mark Manasse 98: 91: 87: 68: 35: 29: 3013:Steven Levy 2925:December 2, 1146:algorithm. 1120:algorithm. 1091:algorithm. 1070:, F. Bahr, 877:Joerg Zayer 833:algorithm. 718:processor. 335:square root 319:1999-08-22 283:square root 271:1999-02-02 247:square root 227:1996-04-10 209:1994-04-26 186:1993-06-09 165:1992-04-14 137:1991-04-01 110:dec digits 36:RSA numbers 32:mathematics 3031:Categories 3021:Wired News 2963:References 2771:August 17, 1158:, Russia. 1041:MIPS-years 957:MIPS-years 900:polynomial 674:References 121:algorithm 74:initialism 40:semiprimes 2474:MathWorld 2373:March 10, 2359:"RSA-160" 2342:March 10, 2309:March 10, 2275:March 10, 2245:March 10, 2211:March 10, 2146:March 10, 1880:August 5, 1843:August 5, 1068:J. Franke 857:Jim Cowie 716:Athlon 64 363:Contents 196:(0.049%) 60:factoring 2700:NMBRTHRY 2678:Archived 2621:Archived 2582:Archived 2562:Archived 2490:Archived 2415:Archived 2395:Archived 2367:Archived 2205:Archived 2201:NMBRTHRY 2171:Archived 2140:Archived 2109:Archived 2043:cite web 2027:Archived 2001:21157010 1928:Archived 1890:cite web 1853:cite web 1800:See also 1788:RSA-2048 1716:RSA-1536 1512:RSA-1024 1059:and the 807:Internet 666:See also 656:RSA-2048 626:RSA-1536 533:RSA-1024 314:RSA-155 266:RSA-140 222:RSA-130 203:RSA-129 181:RSA-120 160:RSA-110 132:RSA-100 64:integers 2740:May 13, 2706:July 3, 2517:May 12, 2412:RSA-170 2177:May 25, 2033:June 8, 1776:RSA-617 1764:RSA-500 1752:RSA-490 1740:RSA-480 1728:RSA-470 1704:RSA-460 1692:RSA-450 1680:RSA-440 1668:RSA-430 1656:RSA-420 1644:RSA-410 1632:RSA-400 1620:RSA-390 1608:RSA-380 1596:RSA-370 1584:RSA-360 1572:RSA-350 1560:RSA-340 1548:RSA-330 1536:RSA-320 1524:RSA-310 1500:RSA-309 1488:RSA-300 1476:RSA-290 1464:RSA-280 1452:RSA-896 1440:RSA-270 1428:RSA-260 1392:RSA-250 1372:RSA-240 1340:RSA-768 1324:RSA-232 1308:RSA-230 1292:RSA-220 1275:RSA-704 1259:RSA-210 1253:Opteron 1230:RSA-200 1218:Opteron 1197:RSA-640 1177:RSA-190 1150:RSA-180 1124:RSA-576 1095:RSA-170 1051:RSA-160 987:RSA-155 966:RSA-150 911:RSA-140 847:RSA-130 768:RSA-129 750:RSA-120 725:RSA-110 686:RSA-100 664: 651:RSA-617 646:RSA-500 641:RSA-490 636:RSA-480 631:RSA-470 621:RSA-460 616:RSA-450 607:RSA-440 602:RSA-430 597:RSA-420 592:RSA-410 587:RSA-400 582:RSA-390 577:RSA-380 572:RSA-370 567:RSA-360 558:RSA-350 553:RSA-340 548:RSA-330 543:RSA-320 538:RSA-310 528:RSA-309 523:RSA-300 518:RSA-290 509:RSA-280 504:RSA-896 499:RSA-270 494:RSA-260 489:RSA-250 484:RSA-240 479:RSA-768 474:RSA-232 469:RSA-230 460:RSA-220 455:RSA-704 450:RSA-210 445:RSA-200 440:RSA-640 435:RSA-190 430:RSA-180 425:RSA-576 420:RSA-170 411:RSA-160 406:RSA-155 401:RSA-150 396:RSA-140 391:RSA-130 386:RSA-129 381:RSA-120 376:RSA-110 371:RSA-100 331:Lanczos 279:Lanczos 243:Lanczos 212:ppmpqs 189:ppmpqs 78:decimal 18:RSA-155 2865: 2828: 2454:RSA576 2082: 1999: 1989: 1061:German 700:MasPar 173:MasPar 141:ppmpqs 94:binary 62:large 34:, the 2436:(PDF) 1997:S2CID 1823:Notes 698:on a 670:Notes 233:with 118:date 107:name 2953:2020 2927:2019 2902:2024 2876:2024 2863:ISBN 2826:ISBN 2795:2024 2773:2018 2742:2016 2708:2012 2662:2024 2545:2010 2519:2010 2375:2008 2344:2008 2311:2008 2277:2008 2247:2008 2213:2008 2179:2016 2148:2008 2117:2009 2080:ISBN 2049:link 2035:2015 1987:ISBN 1896:link 1882:2008 1859:link 1845:2008 1420:and 1221:CPUs 935:and 875:and 811:US$ 809:. A 801:and 333:and 323:GNFS 281:and 275:GNFS 245:and 206:129 147:and 82:US$ 3019:in 2855:doi 2818:doi 2472:at 2072:doi 1979:doi 1250:GHz 1215:AMD 1183:CWI 840:". 776:'s 337:by 285:by 249:by 239:CWI 143:by 30:In 3033:: 2883:^ 2861:, 2849:, 2824:. 2812:. 2759:. 2728:. 2698:. 2653:. 2606:^ 2536:. 2510:. 2438:. 2377:. 2365:. 2361:. 2313:. 2297:. 2233:. 2199:. 2165:. 2138:. 2134:. 2103:. 2078:. 2045:}} 2041:{{ 2025:. 2021:. 2009:^ 1995:. 1985:. 1961:^ 1947:. 1936:^ 1922:. 1904:^ 1892:}} 1888:{{ 1855:}} 1851:{{ 1356:. 1223:. 1015:, 1011:, 1003:, 999:, 939:. 879:. 871:, 867:, 863:, 859:, 817:. 797:, 793:, 786:. 2955:. 2929:. 2857:: 2834:. 2820:: 2797:. 2775:. 2744:. 2710:. 2684:. 2664:. 2547:. 2521:. 2442:. 2346:. 2279:. 2249:. 2074:: 2051:) 2037:. 1981:: 1898:) 1884:. 1861:) 1847:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index