RSA numbers

In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that are part of the RSA Factoring Challenge. The challenge was to find the prime factors but it was declared inactive in 2007. [RSA Laboratories, [http://www.rsa.com/rsalabs/node.asp?id=2092 The RSA Factoring Challenge] . Retrieved on 2008-03-10.] It was created by RSA Laboratories in 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers.

RSA Laboratories published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size 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 quite some time. As of March 2008, 12 of the 54 listed numbers have been factored: The 9 smallest from RSA-100 to RSA-160, plus RSA-576, RSA-640 and RSA-200.

The RSA challenge officially ended in 2007 but people can still attempt 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understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active." [RSA Laboratories, [http://www.rsa.com/rsalabs/node.asp?id=2094 The RSA Factoring Challenge FAQ] . Retrieved on 2008-03-10.] Some of the smaller prizes had been awarded at the time. The remaining prizes were retracted.

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

RSA-100

RSA-100 has 100 decimal digits. Its factorization was announced on April 1, 1991 by Arjen K. Lenstra. [cite web
url=http://cryptnet.net/people/vab/blogs/cryptowatch/1991/04/01/rsa-100-factored/
title=RSA-100 Factored
work=Cryptography Watch Archive for April, 1991
date=1991-04-01
accessdate=2008-08-05] [cite web
url=http://www.ontko.com/~rayo/primes/hr_rsa.txt
title=RSA Honor Roll
date=1999-03-05
accessdate=2008-08-05] Reportedly, the factorization took a few days using the multiple-polynomial quadratic sieve algorithm on a MasPar parallel computer.cite web |author=Brandon Dixon and Arjen K. Lenstra|url=http://www.springerlink.com/link.asp?id=jdeqqpgku2xk3pve
doi=10.1007/3-540-48285-7
title=Factoring Integers Using SIMD Sieves]

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

RSA-100 = 15226050279225333605356183781326374297180681149613 80688657908494580122963258952897654000350692006139

RSA-100 = 37975227936943673922808872755445627854565536638199 × 40094690950920881030683735292761468389214899724061

It takes eleven hours to repeat this factorization using the program [http://www.boo.net/~jasonp/qs.html Msieve] on a 2200MHz Athlon 64 processor.

RSA-110

RSA-110 was factored in April 1992 by Arjen K. Lenstra and Mark S. Manasse in approximately one month.

The value and factorization is as follows:

RSA-110 = 3579423417972586877499180783256845540300377802422822619 3532908190484670252364677411513516111204504060317568667

RSA-110 = 6122421090493547576937037317561418841225758554253106999 × 5846418214406154678836553182979162384198610505601062333

RSA-120

RSA-120 was factored in June 1993 by Thomas Denny, Bruce Dodson, Arjen K. Lenstra, and Mark S. Manasse. [T. Denny, B. Dodson, A. K. Lenstra, M. S. Manasse (1994), [http://www.springerlink.com/content/n9tvubu089l1x58y/ "On The Factorization Of RSA-120"] .] The computation took under three months of actual computer time.

The value and factorization is as follows:

RSA-120 = 227010481295437363334259960947493668895875336466084780038173 258247009162675779735389791151574049166747880487470296548479

RSA-120 = 327414555693498015751146303749141488063642403240171463406883 × 693342667110830181197325401899700641361965863127336680673013

RSA-129

RSA-129 was not part of the 1991 RSA Factoring Challenge, but rather related to Martin Gardner's column in the August 1977 issue of "Scientific American". [cite web |url=http://www.ontko.com/~rayo/primes/hr_rsa.txt |title=RSA Honor Roll |date=1999-03-05 |accessdate=2008-08-06]

RSA-129 was factored in April 1994 by a team led by Derek Atkins, Michael Graff, Arjen K. Lenstra and Paul Leyland, using about 600 computers connected over the Internet. [Mark Janeba (1994), [http://www.willamette.edu/~mjaneba/rsa129.html Factoring Challenge Conquered] . Retrieved on 2008-03-10.] A US$100 token prize was awarded by RSA Security for the factorization, which was donated to the Free Software Foundation.

The value and factorization is as follows:

RSA-129 = 11438162575788886766923577997614661201021829672124236256256184293 5706935245733897830597123563958705058989075147599290026879543541

RSA-129 = 3490529510847650949147849619903898133417764638493387843990820577 × 32769132993266709549961988190834461413177642967992942539798288533

The factorization was found using the Multiple Polynomial Quadratic Sieve algorithm.

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

RSA-130

RSA-130 was factored on April 10 1996 by a team led by Arjen K. Lenstra and composed of Jim Cowie, Marije Elkenbracht-Huizing, Wojtek Furmanski, Peter L. Montgomery, Damian Weber and Joerg Zayer. [Arjen K. Lenstra (1996-04-12), [http://www.utm.edu/research/primes/notes/rsa130.html Factorization of RSA-130] . Retrieved on 2008-03-10.]

The value and factorization is as follows:

RSA-130 = 18070820886874048059516561644059055662781025167694013491701270214 50056662540244048387341127590812303371781887966563182013214880557

RSA-130 = 39685999459597454290161126162883786067576449112810064832555157243 × 45534498646735972188403686897274408864356301263205069600999044599

The factorization was found using the Number Field Sieve algorithm and the polynomial

5748302248738405200 x⁵ + 9882261917482286102 x⁴ - 13392499389128176685 x³ + 16875252458877684989 x² + 3759900174855208738 x¹ - 46769930553931905995

which has a root of 12574411168418005980468 modulo RSA-130.

RSA-140

RSA-140 was factored on February 2 1999 by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Paul Leyland, Walter Lioen, Peter L. Montgomery, Brian Murphy and Paul Zimmermann. [Herman te Riele (1999-02-04), [http://listserv.nodak.edu/scripts/wa.exe?A2=ind9902&L=nmbrthry&P=302 Factorization of RSA-140] . Retrieved on 2008-03-10.] [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2099 RSA-140 is factored!] . Retrieved on 2008-03-10.]

The value and factorization is as follows:

RSA-140 = 2129024631825875754749788201627151749780670396327721627823338321538194 9984056495911366573853021918316783107387995317230889569230873441936471

RSA-140 = 3398717423028438554530123627613875835633986495969597423490929302771479 × 6264200187401285096151654948264442219302037178623509019111660653946049

The factorization was found using the Number Field Sieve algorithm and an estimated 2000 MIPS-years of computing time.

RSA-150

RSA-150 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 General number field sieve (GNFS), years after bigger RSA numbers that were still part of the challenge had been solved.

The value and factorization is as follows:

RSA-150 = 155089812478348440509606754370011861770654545830995430655466945774312632703 463465954363335027577729025391453996787414027003501631772186840890795964683

RSA-150 = 348009867102283695483970451047593424831012817350385456889559637548278410717 × 445647744903640741533241125787086176005442536297766153493419724532460296199

RSA-155

RSA-155 was factored on August 22 1999 by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery, Brian Murphy, Karen Aardal, Jeff Gilchrist, Gerard Guillerm, Paul Leyland, Joel Marchand, François Morain, Alec Muffett, Craig Putnam, Chris Putnam and Paul Zimmermann. [Herman te Riele (1999-08-26), [http://listserv.nodak.edu/scripts/wa.exe?A2=ind9908&L=nmbrthry&P=1905 New factorization record] (announcement of factorization of RSA-155). Retrieved on 2008-03-10.] [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2098 RSA-155 is factored!] . Retrieved on 2008-03-10.]

The value and factorization is as follows:

RSA-155 = 109417386415705274218097073220403576120037329454492059909138421314763499842889 34784717997257891267332497625752899781833797076537244027146743531593354333897

RSA-155 = 102639592829741105772054196573991675900716567808038066803341933521790711307779 × 106603488380168454820927220360012878679207958575989291522270608237193062808643

The factorization was found using the Number Field Sieve algorithm and an estimated 8000 MIPS-years of computing time.

RSA-160

RSA-160 was factored on April 1 2003 by a team from the University of Bonn and the German Federal Office for Information Security (BSI). The team contained J. Franke, F. Bahr, T. Kleinjung, M. Lochter, and M. Böhm. [Jens Franke (2003-04-01), [http://www.loria.fr/~zimmerma/records/rsa160 RSA-160] (announcement of factorization). Retrieved on 2008-03-10.] [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2097 RSA-160 is factored!] . Retrieved on 2008-03-10.]

The value and factorization is as follows:

RSA-160 = 21527411027188897018960152013128254292577735888456759801704976767781331452188591 35673011059773491059602497907111585214302079314665202840140619946994927570407753

RSA-160 = 45427892858481394071686190649738831656137145778469793250959984709250004157335359 × 47388090603832016196633832303788951973268922921040957944741354648812028493909367

The factorization was found using the General Number Field Sieve algorithm.

RSA-170

RSA-170 has a length of 170 decimal digits and has not been factored so far.

RSA-170 = 2606262368413984492152987926667443219708592538048640641616478519185999962854 2069361450283931914514618683512198164805919882053057222974116478065095809832 377336510711545759

RSA-576

RSA-576 was factored on December 3 2003 by J. Franke and T. Kleinjung from the University of Bonn. [Jens Franke (2003-12-03), [http://groups.yahoo.com/group/primenumbers/message/14113 RSA576] (repost of announcement of the factorization). Retrieved on 2008-03-10.] [Eric W. Weisstein (2005-12-05), [http://mathworld.wolfram.com/news/2003-12-05/rsa/ RSA-576 Factored] at MathWorld. Retrieved on 2008-03-10.] [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2096 RSA-576 is factored!] . Retrieved on 2008-03-10.]

The value and factorization is as follows:

RSA-576 = 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319 060606504743045317388011303396716199692321205734031879550656996221305168759307650257059

RSA-576 = 398075086424064937397125500550386491199064362342526708406385189575946388957261768583317 × 472772146107435302536223071973048224632914695302097116459852171130520711256363590397527

The factorization was found using the General Number Field Sieve algorithm.

RSA-180

RSA-180 has 180 decimal digits and has not been factored so far.

RSA-180 = 1911479277189866096892294666314546498129862462766673548641885036388072607034 3679905877620136513516127813425829612810920004670291298456875280033022177775 2773957404540495707851421041

RSA-190

RSA-190 has 190 decimal digits and has not yet been factored.

RSA-190 = 1907556405060696491061450432646028861081179759533184460647975622318915025587 1841757540549761551215932934922604641526300932385092466032074171247261215808 58185985938946945490481721756401423481

RSA-640

RSA-640 has 193 decimal digits. 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 using GNFS as follows: [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2964 RSA-640 is factored!] . Retrieved on 2008-03-10.] [Jens Franke (2005-11-04), [http://www.crypto-world.com/announcements/rsa640.txt We have factored RSA640 by GNFS] . Retrieved on 2008-03-10.] [Eric W. Weisstein (2005-11-08), [http://mathworld.wolfram.com/news/2005-11-08/rsa-640/ RSA-640 Factored] at MathWorld. Retrieved on 2008-03-10.]

RSA-640 = 31074182404900437213507500358885679300373460228427275457 20161948823206440518081504556346829671723286782437916272 83803341547107310850191954852900733772482278352574238645 4014691736602477652346609

RSA-640 = 16347336458092538484431338838650908598417836700330923121 81110852389333100104508151212118167511579 × 19008712816648221131268515739354139754718967899685154936 66638539088027103802104498957191261465571

The computation took 5 months on 80 2.2 GHz AMD Opteron CPUs.

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

RSA-200

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

On May 9 2005, F. Bahr, M. Boehm, J. Franke, and T. Kleinjung announcedThorsten Kleinjung (2005-05-09), [http://www.crypto-world.com/announcements/rsa200.txt We have factored RSA200 by GNFS] . Retrieved on 2008-03-10.] [RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2879 RSA-200 is factored!] . Retrieved on 2008-03-10.] that they had factorized the number using GNFS as follows:

RSA-200 = 2799783391122132787082946763872260162107044678695542853756000992932612840010 7609345671052955360856061822351910951365788637105954482006576775098580557613 579098734950144178863178946295187237869221823983 RSA-200 = 3532461934402770121272604978198464368671197400197625023649303468776121253679 423200058547956528088349 × 7925869954478333033347085841480059687737975857364219960734330341455767872818 152135381409304740185467

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 GHz Opteron-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.

RSA-210

RSA-210 has 210 decimal digits and has not been factored so far.

RSA-210 = 2452466449002782119765176635730880184670267876783327597434144517150616008300 3858721695220839933207154910362682719167986407977672324300560059203563124656 1218465817904100131859299619933817012149335034875870551067

RSA-704

RSA-704 has 212 decimal digits and has not been factored so far; a cash prize of US$30,000 was previously offered for a successful factorization.

RSA-704 = 74037563479561712828046796097429573142593188889231289084936232638972765034 02826627689199641962511784399589433050212758537011896809828673317327310893 0900552505116877063299072396380786710086096962537934650563796359

RSA-220

RSA-220 has 220 decimal digits and has not been factored so far.

RSA-220 = 2260138526203405784941654048610197513508038915719776718321197768109445641817 9666766085931213065825772506315628866769704480700018111497118630021124879281 99487482066070131066586646083327982803560379205391980139946496955261

RSA-230

RSA-230 has 230 decimal digits and has not been factored so far.

RSA-230 = 1796949159794106673291612844957324615636756180801260007088891883553172646 0341490933493372247868650755230855864199929221814436684722874052065257937 4956943483892631711525225256544109808191706117425097024407180103648316382 88518852689

RSA-232

RSA-232 has 232 decimal digits and has not been factored so far.

RSA-232 = 1009881397871923546909564894309468582818233821955573955141120516205831021338 5285453743661097571543636649133800849170651699217015247332943892702802343809 6090980497644054071120196541074755382494867277137407501157718230539834060616 2079

RSA-768

RSA-768 has 232 decimal digits and has not been factored so far; a cash prize of US$50,000 was previously offered for a successful factorization.

RSA-768 = 12301866845301177551304949583849627207728535695953347921973224521517264005 07263657518745202199786469389956474942774063845925192557326303453731548268 50791702612214291346167042921431160222124047927473779408066535141959745985 6902143413

RSA-240

RSA-240 has 240 decimal digits and has not been factored so far.

RSA-240 = 1246203667817187840658350446081065904348203746516788057548187888832896668011 8821085503603957027250874750986476843845862105486553797025393057189121768431 8286362846948405301614416430468066875699415246993185704183030512549594371372 159029236099

RSA-250

RSA-250 has 250 decimal digits and has not been factored so far.

RSA-250 = 2140324650240744961264423072839333563008614715144755017797754920881418023447 1401366433455190958046796109928518724709145876873962619215573630474547705208 0511905649310668769159001975940569345745223058932597669747168173806936489469 9871578494975937497937

RSA-260

RSA-260 has 260 decimal digits and has not been factored so far.

RSA-260 = 2211282552952966643528108525502623092761208950247001539441374831912882294140 2001986512729726569746599085900330031400051170742204560859276357953757185954 2988389587092292384910067030341246205457845664136645406842143612930176940208 46391065875914794251435144458199

RSA-270

RSA-270 has 270 decimal digits and has not been factored so far.

RSA-270 = 2331085303444075445276376569106805241456198124803054490429486119684959182451 3578286788836931857711641821391926857265831491306067262691135402760979316634 1626693946596196427744273886601876896313468704059066746903123910748277606548 649151920812699309766587514735456594993207

RSA-896

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

RSA-896 = 41202343698665954385553136533257594817981169984432798284545562643387644556 52484261980988704231618418792614202471888694925609317763750334211309823974 85150944909106910269861031862704114880866970564902903653658867433731720813 104105190864254793282601391257624033946373269391

RSA-280

RSA-280 has 280 decimal digits and has not been factored so far.

RSA-280 = 1790707753365795418841729699379193276395981524363782327873718589639655966058 5783742549640396449103593468573113599487089842785784500698716853446786525536 5503525160280656363736307175332772875499505341538927978510751699922197178159 7724733184279534477239566789173532366357270583106789

RSA-290

RSA-290 has 290 decimal digits and has not been factored so far.

RSA-290 = 3050235186294003157769199519894966400298217959748768348671526618673316087694 3419156362946151249328917515864630224371171221716993844781534383325603218163 2549201100649908073932858897185243836002511996505765970769029474322210394327 60575157628357292075495937664206199565578681309135044121854119

RSA-300

RSA-300 has 300 decimal digits and has not been factored so far.

RSA-300 = 2769315567803442139028689061647233092237608363983953254005036722809375824714 9473946190060218756255124317186573105075074546238828817121274630072161346956 4396741836389979086904304472476001839015983033451909174663464663867829125664 459895575157178816900228792711267471958357574416714366499722090015674047

RSA-309

RSA-309 has 309 decimal digits and has not been factored so far.

RSA-309 = 1332943998825757583801437794588036586217112243226684602854588261917276276670 5425540467426933349195015527349334314071822840746357352800368666521274057591 1870128339157499072351179666739658503429931021985160714113146720277365006623 6927218079163559142755190653347914002967258537889160429597714204365647842739 10949

RSA-1024

RSA-1024 has 309 decimal digits and has not been factored so far. US$100,000 was previously offered for factorization.

Successful factorization of RSA-1024 has important security implications for many users of the RSA public-key authentication algorithm, as the most common key length currently in use is 1024 bits.

RSA-1024 = 13506641086599522334960321627880596993888147560566702752448514385152651060 48595338339402871505719094417982072821644715513736804197039641917430464965 89274256239341020864383202110372958725762358509643110564073501508187510676 59462920556368552947521350085287941637732853390610975054433499981115005697 7236890927563

RSA-310

RSA-310 has 310 decimal digits and has not been factored so far.

RSA-310 = 1848210397825850670380148517702559371400899745254512521925707445580334710601 4125276757082979328578439013881047668984294331264191394626965245834649837246 5163148188847336415136873623631778358751846501708714541673402642461569061162 0116380982484120857688483676576094865930188367141388795454378671343386258291 687641

RSA-320

RSA-320 has 320 decimal digits and has not been factored so far.

RSA-320 = 2136810696410071796012087414500377295863767938372793352315068620363196552357 8837094085435000951700943373838321997220564166302488321590128061531285010636 8571638978998117122840139210685346167726847173232244364004850978371121744321 8270343654835754061017503137136489303437996367224915212044704472299799616089 2591129924218437

RSA-330

RSA-330 has 330 decimal digits and has not been factored so far.

RSA-330 = 1218708633106058693138173980143325249157710686226055220408666600017481383238 1352456802425903555880722805261111079089882303717632638856140900933377863089 0634828167900405006112727432172179976427017137792606951424995281839383708354 6364684839261149319768449396541020909665209789862312609604983709923779304217 01862444655244698696759267

RSA-340

RSA-340 has 340 decimal digits and has not been factored so far.

RSA-340 = 2690987062294695111996484658008361875931308730357496490239672429933215694995 2758588771223263308836649715112756731997946779608413232406934433532048898585 9176676580752231563884394807622076177586625973975236127522811136600110415063 0004691128152106812042872285697735145105026966830649540003659922618399694276 990464815739966698956947129133275233

RSA-350

RSA-350 has 350 decimal digits and has not been factored so far.

RSA-350 = 2650719995173539473449812097373681101529786464211583162467454548229344585504 3495841191504413349124560193160478146528433707807716865391982823061751419151 6068496555750496764686447379170711424873128631468168019548127029171231892127 2886825928263239383444398948209649800021987837742009498347263667908976501360 3382322972552204068806061829535529820731640151

RSA-360

RSA-360 has 360 decimal digits and has not been factored so far.

RSA-360 = 2186820202343172631466406372285792654649158564828384065217121866374227745448 7764963889680817334211643637752157994969516984539482486678141304751672197524 0052350576247238785129338002757406892629970748212734663781952170745916609168 9358372359962787832802257421757011302526265184263565623426823456522539874717 61591019113926725623095606566457918240614767013806590649

RSA-370

RSA-370 has 370 decimal digits and has not been factored so far.

RSA-370 = 1888287707234383972842703127997127272470910519387718062380985523004987076701 7212819937261952549039800018961122586712624661442288502745681454363170484690 7379449525034797494321694352146271320296579623726631094822493455672541491544 2700993152879235272779266578292207161032746297546080025793864030543617862620 878802244305286292772467355603044265985905970622730682658082529621

RSA-380

RSA-380 has 380 decimal digits and has not been factored so far.

RSA-380 = 3013500443120211600356586024101276992492167997795839203528363236610578565791 8270750937407901898070219843622821090980641477056850056514799336625349678549 2187941807116344787358312651772858878058620717489800725333606564197363165358 2237779263423501952646847579678711825720733732734169866406145425286581665755 6977260763553328252421574633011335112031733393397168350585519524478541747311

RSA-390

RSA-390 has 390 decimal digits and has not been factored so far.

RSA-390 = 2680401941182388454501037079346656065366941749082852678729822424397709178250 4623002472848967604282562331676313645413672467684996118812899734451228212989 1630084759485063423604911639099585186833094019957687550377834977803400653628 6955344904367437281870253414058414063152368812498486005056223028285341898040 0795447435865033046248751475297412398697088084321037176392288312785544402209 1083492089

RSA-400

RSA-400 has 400 decimal digits and has not been factored so far.

RSA-400 = 2014096878945207511726700485783442547915321782072704356103039129009966793396 1419850865094551022604032086955587930913903404388675137661234189428453016032 6191193056768564862615321256630010268346471747836597131398943140685464051631 7519403149294308737302321684840956395183222117468443578509847947119995373645 3607109795994713287610750434646825511120586422993705980787028106033008907158 74500584758146849481

RSA-410

RSA-410 has 410 decimal digits and has not been factored so far.

RSA-410 = 1965360147993876141423945274178745707926269294439880746827971120992517421770 1079138139324539033381077755540830342989643633394137538983355218902490897764 4412968474332754608531823550599154905901691559098706892516477785203855688127 0635069372091564594333528156501293924133186705141485137856845741766150159437 6063244163040088180887087028771717321932252992567756075264441680858665410918 431223215368025334985424358839

RSA-420

RSA-420 has 420 decimal digits and has not been factored so far.

RSA-420 = 2091366302476510731652556423163330737009653626605245054798522959941292730258 1898373570076188752609749648953525484925466394800509169219344906273145413634 2427186266197097846022969248579454916155633686388106962365337549155747268356 4666583846809964354191550136023170105917441056517493690125545320242581503730 3405952887826925813912683942756431114820292313193705352716165790132673270514 3817744164107601735413785886836578207979

RSA-430

RSA-430 has 430 decimal digits and has not been factored so far.

RSA-430 = 3534635645620271361541209209607897224734887106182307093292005188843884213420 6950355315163258889704268733101305820000124678051064321160104990089741386777 2424190744453885127173046498565488221441242210687945185565975582458031351338 2070785777831859308900851761495284515874808406228585310317964648830289141496 3289966226854692560410075067278840383808716608668377947047236323168904650235 70092246473915442026549955865931709542468648109541

RSA-440

RSA-440 has 440 decimal digits and has not been factored so far.

RSA-440 = 260142821195560259007078848737132055053981080459523528942350858966 339127083743102526748005924267463190079788900653375731605419428681 140656438533272294845029942332226171123926606357523257736893667452 341192247905168387893684524818030772949730495971084733797380514567 326311991648352970360740543275296663078122345977663907504414453144 081718020709040727392759304102993590060596193055907019396277252961 16299946059898442103959412221518213407370491

RSA-450

RSA-450 has 450 decimal digits and has not been factored so far.

RSA-450 = 1984634237142836623497230721861131427789462869258862089878538009871598692569 0078791591684242367262529704652673686711493985446003494265587358393155378115 8032447061155145160770580926824366573211993981662614635734812647448360573856 3132247491715526997278115514905618953253443957435881503593414842367096046182 7643434794849824315251510662855699269624207451365738384255497823390996283918 3287667419172988072221996532403300258906083211160744508191024837057033

RSA-460

RSA-460 has 460 decimal digits and has not been factored so far.

RSA-460 = 1786856020404004433262103789212844585886400086993882955081051578507634807524 1464078819812169681394445771476334608488687746254318292828603396149562623036 3564554675355258128655971003201417831521222464468666642766044146641933788836 8932452217321354860484353296131403821175862890998598653858373835628654351880 4806362231643082386848731052350115776715521149453708868428108303016983133390 0416365515466857004900847501644808076825638918266848964153626486460448430073 4909

RSA-1536

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

RSA-1536 = 18476997032117414743068356202001644030185493386634101714717857749106516967 11161249859337684305435744585616061544571794052229717732524660960646946071 24962372044202226975675668737842756238950876467844093328515749657884341508 84755282981867264513398633649319080846719904318743812833635027954702826532 97802934916155811881049844908319545009848393775227257052578591944993870073 69575568843693381277961308923039256969525326162082367649031603655137144791 3932347169566988069

RSA-470

RSA-470 has 470 decimal digits and has not been factored so far.

RSA-470 = 1705147378468118520908159923888702802518325585214915968358891836980967539803 6897711442383602526314519192366612270595815510311970886116763177669964411814 0957486602388713064698304619191359016382379244440751228665455229545368837485 5874455212895044521809620818878887632439504936237680657994105330538621759598 4047709603954312447692725276887594590658792939924609261264788572032212334726 8553025718835659126454325220771380103576695555550710440908570895393205649635 76770285413369

RSA-480

RSA-480 has 480 decimal digits and has not been factored so far.

RSA-480 = 3026570752950908697397302503155918035891122835769398583955296326343059761445 7144169659817040125185215913853345598217234371231338324773210726853524776378 4105186549246199888070331088462855743520880671299302895546822695492968577380 7067958428022008294111984222973260208233693152589211629901686973933487362360 8129660418514569063995282978176790149760521395548532814196534676974259747930 6858645849268328985687423881853632604706175564461719396117318298679820785491 875674946700413680932103

RSA-490

RSA-490 has 490 decimal digits and has not been factored so far.

RSA-490 = 1860239127076846517198369354026076875269515930592839150201028353837031025971 3738522164743327949206433999068225531855072554606782138800841162866037393324 6578171804201717222449954030315293547871401362961501065002486552688663415745 9758925793594165651020789220067311416926076949777767604906107061937873540601 5942747316176193775374190713071154900658503269465516496828568654377183190586 9537640698044932638893492457914750855858980849190488385315076922453755527481 1376719096144119390052199027715691

RSA-500

RSA-500 has 500 decimal digits (or 1659 bits) and has not been factored so far.

RSA-500 = 1897194133748626656330534743317202527237183591953428303184581123062450458870 7687605943212347625766427494554764419515427586743205659317254669946604982419 7301601038125215285400688031516401611623963128370629793265939405081077581694 4786041721411024641038040278701109808664214800025560454687625137745393418221 5494821277335671735153472656328448001134940926442438440198910908603252678814 7850601132077287172819942445113232019492229554237898606631074891074722425617 39680319169243814676235712934292299974411361

RSA-617

RSA-617 has 617 decimal digits (2048 bits) and has not been factored so far.

RSA-617 = 2270180129378501419358040512020458674106123596276658390709402187921517148311 9139894870133091111044901683400949483846818299518041763507948922590774925466 0881718792594659210265970467004498198990968620394600177430944738110569912941 2854289188085536270740767072259373777266697344097736124333639730805176309150 6836310795312607239520365290032105848839507981452307299417185715796297454995 0235053160409198591937180233074148804462179228008317660409386563445710347785 5345712108053073639453592393265186603051504106096643731332367283153932350006 7937107541955437362433248361242525945868802353916766181532375855504886901432 221349733

RSA-2048

RSA-2048 has a length of 2048 bits (617 decimal digits). It is the largest of the RSA numbers and carried the largest cash prize for its factorization, US$200,000. The largest factored RSA number is 663 bits long (200 decimal digits), and the RSA-2048 may not be factorizable for many years to come, unless considerable advances are made in integer factorization or computational power in the near future.

RSA-2048 = 25195908475657893494027183240048398571429282126204032027777137836043662020 70759555626401852588078440691829064124951508218929855914917618450280848912 00728449926873928072877767359714183472702618963750149718246911650776133798 59095700097330459748808428401797429100642458691817195118746121515172654632 28221686998754918242243363725908514186546204357679842338718477444792073993 42365848238242811981638150106748104516603773060562016196762561338441436038 33904414952634432190114657544454178424020924616515723350778707749817125772 46796292638635637328991215483143816789988504044536402352738195137863656439 1212010397122822120720357

See also

* RSA Factoring Challenge (includes table with size and status of all numbers)
* RSA Secret-Key Challenge
* Integer factorization records

Notes

References

* RSA Factoring Challenge Administrator (1997-10-12), [http://www.ontko.com/~rayo/primes/rsa_fact.html RSA Challenge List] .
* RSA Laboratories, [http://web.archive.org/web/20061209135708/http://www.rsasecurity.com/rsalabs/node.asp?id=2093 The RSA Challenge Numbers] (archived by the Internet Archive in 2006 before the RSA challenge ended).
* RSA Laboratories, [http://www.rsa.com/rsalabs/challenges/factoring/challengenumbers.txt Challenge numbers in text format] .
* Kazumaro Aoki, Yuji Kida, Takeshi Shimoyama, Hiroki Ueda, [http://eprint.iacr.org/2004/095/ GNFS Factoring Statistics of RSA-100, 110, ..., 150] , Cryptology ePrint Archive, Report 2004/095, 2004.

External links

* RSA Laboratories, [http://www.rsa.com/rsalabs/node.asp?id=2092 The RSA Factoring Challenge] .
* Burt Kaliski (1991-03-18), [http://www.google.com/groups?selm=BURT.91Mar18092126%40chirality.rsa.com RSA factoring challenge] , the original challenge announcement on sci.crypt.
* Steven Levy (March 1996), [http://wired.com/wired/archive/4.03/crackers.html?topic=&topic_set= Wisecrackers] in Wired News. Has coverage on RSA-129.
*
* Eric W. Weisstein, [http://mathworld.wolfram.com/packages/RSANumbers.m Mathematica package for RSA numbers] .