RSA numbers 511379 224995046 2008-07-11T10:58:38Z VolkovBot 3035831 robot Adding: [[pl:RSA liczby]] In [[mathematics]], the '''RSA numbers''' are a set of large [[semiprimes]] (numbers with exactly two [[prime factor]]s) that are part of the [[RSA Factoring Challenge]]. The challenge was to find the prime factors but it was declared inactive in 2007.<ref>RSA Laboratories, [http://www.rsa.com/rsalabs/node.asp?id=2092 The RSA Factoring Challenge]. Retrieved on [[2008]]-[[03-10]].</ref> It was created by [[RSA Security|RSA Laboratories]] in 1991 to encourage research into [[computational number theory]] and the practical difficulty of [[Integer factorization|factoring]] large [[integer]]s. 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understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active."<ref>RSA Laboratories, [http://www.rsa.com/rsalabs/node.asp?id=2094 The RSA Factoring Challenge FAQ]. Retrieved on [[2008]]-[[03-10]].</ref> 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 numeral system|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. {| id="toc" class="toc" summary="Contents" ! {{MediaWiki:Toc}} |- | align="left" | [[#RSA-100|RSA-100]] | [[#RSA-110|RSA-110]] | [[#RSA-120|RSA-120]] | [[#RSA-129|RSA-129]] | [[#RSA-130|RSA-130]] | [[#RSA-140|RSA-140]] | [[#RSA-150|RSA-150]] | [[#RSA-155|RSA-155]] | [[#RSA-160|RSA-160]]<br /> [[#RSA-170|RSA-170]] | [[#RSA-576|RSA-576]] | [[#RSA-180|RSA-180]] | [[#RSA-190|RSA-190]] | [[#RSA-640|RSA-640]] | [[#RSA-200|RSA-200]] | [[#RSA-210|RSA-210]] | [[#RSA-704|RSA-704]] | [[#RSA-220|RSA-220]]<br /> [[#RSA-230|RSA-230]] | [[#RSA-232|RSA-232]] | [[#RSA-768|RSA-768]] | [[#RSA-240|RSA-240]] | [[#RSA-250|RSA-250]] | [[#RSA-260|RSA-260]] | [[#RSA-270|RSA-270]] | [[#RSA-896|RSA-896]] | [[#RSA-280|RSA-280]]<br /> [[#RSA-290|RSA-290]] | [[#RSA-300|RSA-300]] | [[#RSA-309|RSA-309]] | [[#RSA-1024|RSA-1024]] | [[#RSA-310|RSA-310]] | [[#RSA-320|RSA-320]] | [[#RSA-330|RSA-330]] | [[#RSA-340|RSA-340]] | [[#RSA-350|RSA-350]]<br /> [[#RSA-360|RSA-360]] | [[#RSA-370|RSA-370]] | [[#RSA-380|RSA-380]] | [[#RSA-390|RSA-390]] | [[#RSA-400|RSA-400]] | [[#RSA-410|RSA-410]] | [[#RSA-420|RSA-420]] | [[#RSA-430|RSA-430]] | [[#RSA-440|RSA-440]]<br /> [[#RSA-450|RSA-450]] | [[#RSA-460|RSA-460]] | [[#RSA-1536|RSA-1536]] | [[#RSA-470|RSA-470]] | [[#RSA-480|RSA-480]] | [[#RSA-490|RSA-490]] | [[#RSA-500|RSA-500]] | [[#RSA-617|RSA-617]] | [[#RSA-2048|RSA-2048]] [[#top|Top of page]] — [[#See also|See also]] — [[#Notes|Notes]] — [[#References|References]] — [[#External links|External links]] __NOTOC__ |} == RSA-100 == RSA-100 has 100 decimal digits. It was factored in April 1991 by [[Arjen Lenstra|Arjen K. Lenstra]] in a few days using [[quadratic sieve|the multiple-polynomial quadratic sieve algorithm]] on a [[MasPar]] parallel computer. 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.<ref>T. Denny, B. Dodson, A. K. Lenstra, M. S. Manasse (1994), [http://www.springerlink.com/content/n9tvubu089l1x58y/ "On The Factorization Of RSA-120"] .</ref> 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 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]].<ref>Mark Janeba (1994), [http://www.willamette.edu/~mjaneba/rsa129.html Factoring Challenge Conquered]. Retrieved on [[2008]]-[[03-10]].</ref> A [[United States dollar|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 Montgomery (mathematician)|Peter L. Montgomery]], [[Damian Weber]] and [[Joerg Zayer]].<ref>[[Arjen K. Lenstra]] ([[1996-04-12]]), [http://www.utm.edu/research/primes/notes/rsa130.html Factorization of RSA-130]. Retrieved on [[2008]]-[[03-10]].</ref> 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 x<sup>5</sup> + 9882261917482286102 x<sup>4</sup> - 13392499389128176685 x<sup>3</sup> + 16875252458877684989 x<sup>2</sup> + 3759900174855208738 x<sup>1</sup> - 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 J.J. te Riele|Herman te Riele]] and composed of [[Stefania Cavallar]], Bruce Dodson, Arjen K. Lenstra, Paul Leyland, [[Walter Lioen]], Peter L. Montgomery, [[Brian Murphy (mathematician)|Brian Murphy]] and [[Paul Zimmermann]].<ref>[[Herman J.J. te Riele|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]].</ref><ref>RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2099 RSA-140 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref> 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-year]]s 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. 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.<ref>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]].</ref><ref>RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2098 RSA-155 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref> 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-year]]s of computing time. == RSA-160 == RSA-160 was factored on [[April 1]] [[2003]] by a team from the [[University of Bonn]] and the [[Germany|German]] [[Federal Office for Information Security]] (BSI). The team contained [[Jens Franke|J. Franke]], F. Bahr, [[Thorsten Kleinjung|T. Kleinjung]], M. Lochter, and M. Böhm.<ref>[[Jens Franke]] ([[2003-04-01]]), [http://www.loria.fr/~zimmerma/records/rsa160 RSA-160] (announcement of factorization). Retrieved on [[2008]]-[[03-10]].</ref><ref> RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2097 RSA-160 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref> 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.<ref>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]].</ref><ref>[[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]].</ref><ref>RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2096 RSA-576 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref> 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:<ref>RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2964 RSA-640 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref><ref>Jens Franke ([[2005-11-04]]), [http://www.crypto-world.com/announcements/rsa640.txt We have factored RSA640 by GNFS]. Retrieved on [[2008]]-[[03-10]].</ref><ref>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]].</ref> RSA-640 = 31074182404900437213507500358885679300373460228427275457 20161948823206440518081504556346829671723286782437916272 83803341547107310850191954852900733772482278352574238645 4014691736602477652346609 RSA-640 = 16347336458092538484431338838650908598417836700330923121 81110852389333100104508151212118167511579 × 19008712816648221131268515739354139754718967899685154936 66638539088027103802104498957191261465571 The computation took 5 months on 80 2.2 GHz [[Advanced Micro Devices|AMD]] [[Opteron]] [[Central processing unit|CPUs]]. The slightly larger RSA-200 was factored in May 2005 by the same team. == RSA-200 == {{wikinews|Two hundred digit number factored}} RSA-200 has 200 decimal digits which corresponds to 663 [[bit]]s, and factors into the two 100-digit primes given below. On [[May 9]] [[2005]], F. Bahr, M. Boehm, J. Franke, and T. Kleinjung announced<ref name=announce>[[Thorsten Kleinjung]] ([[2005-05-09]]), [http://www.crypto-world.com/announcements/rsa200.txt We have factored RSA200 by GNFS]. Retrieved on [[2008]]-[[03-10]].</ref><ref>RSA Laboratories, [http://www.rsasecurity.com/rsalabs/node.asp?id=2879 RSA-200 is factored!]. Retrieved on [[2008]]-[[03-10]].</ref> 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 &ndash; very approximately &ndash; to the equivalent of 75<!-- Do NOT change this to 55. Two parts took respectively 55 and 80*3/12=20 years for 75 in total--> years work for a single 2.2 [[GHz]] [[Opteron]]-based computer.<ref name=announce/> 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 cryptography| 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 == {{reflist}} == 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]]. * [[Brandon Dixon]] and [[Arjen K. Lenstra]], [http://www.springerlink.com/link.asp?id=jdeqqpgku2xk3pve "Factoring Integers Using SIMD Sieves"] (discusses the method used for RSA-100 and RSA-110). * [[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. * {{MathWorld|title=RSA Number|urlname=RSANumber}} * Eric W. Weisstein, [http://mathworld.wolfram.com/packages/RSANumbers.m Mathematica package for RSA numbers]. [[Category:RSA Factoring Challenge]] [[Category:Integer factorization algorithms]] [[Category:Large numbers]] [[pl:RSA liczby]]