RSA numbers
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2008-07-11T10:58:38Z
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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understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active."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 – very approximately – 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]]