RSA数

数学里，RSA数是大半素数（两个素数因子的乘积）的集合，属于RSA分解挑战（英语：RSA Factoring Challenge）的一部分。这项挑战由 RSA实验室在1991年3月启动，旨在鼓励对计算数论和大整数分解实际难度的研究。这个研究和RSA加密算法息息相关，因为RSA加密算法的安全性很大程度取决于半素数的分解难度。挑战在2007年中止，一部分RSA数未能被分解。^[1]

RSA实验室（RSA是该技术的创立者Rivest、Shamir和Adleman的首字母缩略词）发布了从100到617个十进制数码的大整数。奖金根据分解难度不同，最高可达US$200,000（实际发出的最高奖金为$20,000）。最小的RSA数在几天内就被分解了。大多数其他的RSA数在之后一直没能被分解。截至2020年2月 (2020-02)^[update]，表中54个大整数中，前23个已经被分解。

RSA挑战在2007年终止。RSA实验室称：“现在业界对常见对称密钥和公钥算法的密码分析强度有了相当深入的了解，这些挑战不再有效。”^[2]当时已经颁发了一些较小的奖项，而其余的奖金被收回。但人们在此后仍一直在尝试分解这些未被分解的RSA数，只不过即使成功分解也得不到这些奖金了。

第一批RSA数（从RSA-100到RSA-500）是根据十进制位数命名的。之后从RSA-576开始，改为用二进制数码。RSA-617是个例外，因为这个名字在命名方案更改前就已经有了。下面以增序列出RSA数。

RSA-100有100个十进制位（330位）。1991年4月1日，Arjen K. Lenstra宣布将其分解成功。^[3]^[4] 据称，他在MasPar平行电脑上耗时几天时间使用二次筛选法完成。^[5]

RSA-100可分解为：

RSA-100 = 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

RSA-100 = 37975227936943673922808872755445627854565536638199
        × 40094690950920881030683735292761468389214899724061

在一台2200 MHz Athlon 64处理器上，用Msieve软件可在4小时内进行分解。使用factmsieve的分布式版本Perl脚本（页面存档备份，存于互联网档案馆）运行GGNFS和Msieve （页面存档备份，存于互联网档案馆），超频到3.5 GHz Intel Core2 Quad q9300可用72分钟完成分解。^[6]

RSA-110有110个十进制数码（364位），在1992年4月由Arjen K. Lenstra和Mark S. Manasse耗时一个月完成分解。^[5] 使用factmsieve的分布式版本Perl脚本（页面存档备份，存于互联网档案馆）启动的GGNFS和Msieve （页面存档备份，存于互联网档案馆）二进制程序，在超频到3.5 GHz的Intel Core2 Quad q9300上可以在四小时内完成分解。^[6]

可分解为：

RSA-110 = 35794234179725868774991807832568455403003778024228226193532908190484670252364677411513516111204504060317568667

RSA-110 = 6122421090493547576937037317561418841225758554253106999
        × 5846418214406154678836553182979162384198610505601062333

RSA-120有120个十进制数码（397位），在1993年6月由Thomas Denny、Bruce Dodson、Arjen K. Lenstra和Mark S. Manasse分解。^[7] 计算耗时三个月。

可分解为：

RSA-120 = 227010481295437363334259960947493668895875336466084780038173258247009162675779735389791151574049166747880487470296548479

RSA-120 = 327414555693498015751146303749141488063642403240171463406883
        × 693342667110830181197325401899700641361965863127336680673013

RSA-129有129个十进制数码（426位），并非1991年RSA分解挑战的一部分，但与科学美国人1977年八月刊的马丁·加德纳的数学游戏专栏有关。^[8]

RSA-129在1994年4月由Derek Atkins、Michael Graff、Arjen K. Lenstra和Paul Leyland主导的团队分解，使用600名左右志愿者提供的通过因特网连接的约1600台电脑。^[9]^[10] RSA Security提供了100美元的奖金，团队将其捐赠给了自由软件基金会。

可分解为：

RSA-129 = 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541

RSA-129 = 3490529510847650949147849619903898133417764638493387843990820577
        × 32769132993266709549961988190834461413177642967992942539798288533

分解使用倍数多项式二次筛选法（英语：Multiple Polynomial Quadratic Sieve）算法发现。

分解挑战包含了一条使用RSA-129加密的消息：“The Magic Words are Squeamish Ossifrage”。

RSA-130有130个十进制位（430位），于1996年4月10日由Arjen K. Lenstra主导，Jim Cowie、Marije Elkenbracht-Huizing、Wojtek Furmanski、Peter L. Montgomery、Damian Weber 和Joerg Zayer组成的团队分解成功。^[11]

可分解为：

RSA-130 = 1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

RSA-130 = 39685999459597454290161126162883786067576449112810064832555157243
        × 45534498646735972188403686897274408864356301263205069600999044599

分解使用数域筛选法算法和如下多项式：

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

该多项式有一个根12574411168418005980468 mod RSA-130。

RSA-140有140个十进制位（463位），于1999年2月2日由一个Herman te Riele主导，Stefania Cavallar、Bruce Dodson、Arjen K. Lenstra、Paul Leyland、Walter Lioen、Peter L. Montgomery、Brian Murphy和Paul Zimmermann组成的团队分解成功。^[12]^[13]

可分解为：

RSA-140 = 21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471

RSA-140 = 3398717423028438554530123627613875835633986495969597423490929302771479
        × 6264200187401285096151654948264442219302037178623509019111660653946049

分解使用数域筛选法完成，估计耗费个2000 MIPS-年的计算时间。

RSA-150有150个十进制位（496位），但是之后从RSA实验室的挑战中撤出。RSA-150最终被Aoki等人于2004年使用普通数域筛选法 (GNFS)分解为两个75位的素数。

可分解为：

RSA-150 = 155089812478348440509606754370011861770654545830995430655466945774312632703463465954363335027577729025391453996787414027003501631772186840890795964683

RSA-150 = 348009867102283695483970451047593424831012817350385456889559637548278410717
        × 445647744903640741533241125787086176005442536297766153493419724532460296199

RSA-155有155个十进制位（512位），于1999年8月22日被Herman te Riele主导，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和 Paul Zimmermann组成的团队分解，耗时六个月。^[14]^[15]

可分解为：

RSA-155 = 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897

RSA-155 = 1026395928297411057720541965739916759007165678080380668033419335217907113077
          79
        × 1066034883801684548209272203600128786792079585759892915222706082371930628086
          43

分解使用普通数域筛选法完成，估计耗费个8000 MIPS-年的计算时间。

RSA-160有160个十进制位（530位），于2003年4月1日被,波恩大学和德国联邦资讯安全办公室(BSI)的团队分解。该团队包含J. Franke、F. Bahr、T. Kleinjung、M. Lochter和M. Böhm。^[16]^[17]

可分解为：

RSA-160 = 2152741102718889701896015201312825429257773588845675980170497676778133145218859135673011059773491059602497907111585214302079314665202840140619946994927570407753

RSA-160 = 4542789285848139407168619064973883165613714577846979325095998470925000415733
          5359
        × 4738809060383201619663383230378895197326892292104095794474135464881202849390
          9367

分解使用普通数域筛选法完成。

RSA-170有170个十进制数码（563位），在2009年12月29日由Fachhochschule Braunschweig/Wolfenbüttel的D. Bonenberger 和 M. Krone分解。^[18] 两天后，S. A. Danilov和I. A. Popovyan也宣布独立地完成了分解。^[19]

可分解为：

RSA-170 = 26062623684139844921529879266674432197085925380486406416164785191859999628542069361450283931914514618683512198164805919882053057222974116478065095809832377336510711545759

RSA-170 = 3586420730428501486799804587268520423291459681059978161140231860633948450858
          040593963
        × 7267029064107019078863797763923946264136137803856996670313708936002281582249
          587494493

分解使用普通数域筛选法完成。

RSA-576有174个十进制数码（576位），在2003年12月3日由波恩大学J. Franke 和 T. Kleinjung 分解。^[20]^[21]^[22] RSA Security提供了$10,000的分解奖金。

可分解为：

RSA-576 = 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059

RSA-576 = 3980750864240649373971255005503864911990643623425267084063851895759463889572
          61768583317
        × 4727721461074353025362230719730482246329146953020971164598521711305207112563
          63590397527

分解使用普通数域筛选法完成。

RSA-180有180个十进制数码（596位），于2010年5月8日由莫斯科国立大学的S. A. Danilov和I. A. Popovyan分解。^[23]

RSA-180 = 1911479277189866096892294666314546498129862462766673548641885036388072607034
          3679905877620136513516127813425829612810920004670291298456875280033022177775
          2773957404540495707851421041

RSA-180 = 4007800823297508779525813391041005725268293178158071765648821789984975727719
          50624613470377
        × 4769396887386118369955354773570708579399020760277882320319897758246062255957
          73435668861833

分解在三台Intel Core i7 CPU电脑上使用普通数域筛选法完成。

RSA-190有190个十进制数码（629位），在2010年11月由莫斯科国立大学的I. A. Popovyan和荷兰数学和电脑科学研究学会的A. Timofeev分解。^[24]

RSA-190 = 1907556405060696491061450432646028861081179759533184460647975622318915025587
          1841757540549761551215932934922604641526300932385092466032074171247261215808
          58185985938946945490481721756401423481

RSA-190 = 3171195257690152709485171289740475929805147316029450327784761927832793642798
          1256542415724309619
        × 6015260020444561641587641685526676183243543359471811072599763828083615704046
          0481625355619404899

RSA-640有193个十进制数码（640位）。RSA Security提供了US$20,000的分解奖金。在2005年11月，德国联邦资讯安全办公室的F. Bahr、M. Boehm、 J. Franke和T. Kleinjung 宣布他们使用GNFS完成了分解：^[25]^[26]^[27]

RSA-640 = 3107418240490043721350750035888567930037346022842727545720161948823206440518
          0815045563468296717232867824379162728380334154710731085019195485290073377248
          22783525742386454014691736602477652346609

RSA-640 = 1634733645809253848443133883865090859841783670033092312181110852389333100104
          508151212118167511579
        × 1900871281664822113126851573935413975471896789968515493666638539088027103802
          104498957191261465571

分解耗时五个月，在80个2.2 GHz AMD Opteron CPU上完成。

稍大些的RSA-200在2005年5月由同一团队分解。

RSA-200有200个十进制数码（663位）。2005年5月9日, F. Bahr、M. Boehm、J. Franke和 T. Kleinjung宣布^[28]^[29] 他们使用GNFS将其成功分解为：

RSA-200 = 2799783391122132787082946763872260162107044678695542853756000992932612840010
          7609345671052955360856061822351910951365788637105954482006576775098580557613
          579098734950144178863178946295187237869221823983

RSA-200 = 3532461934402770121272604978198464368671197400197625023649303468776121253679
          423200058547956528088349
        × 7925869954478333033347085841480059687737975857364219960734330341455767872818
          152135381409304740185467

多台电脑并行计算所用的CPU时间之和– 非常接近于 – 2.2 GHz Opteron 上的75年。^[28] 尽管这个估计能展示大致的工作量，但忽略了很多复杂的其他因素，具体情况在发布内容中得到了详细说明。

RSA-210有210个十进制数码（696位），于2013年9月由Ryan Propper分解：^[30]

RSA-210 = 2452466449002782119765176635730880184670267876783327597434144517150616008300
          3858721695220839933207154910362682719167986407977672324300560059203563124656
          1218465817904100131859299619933817012149335034875870551067

RSA-210 = 4359585683259407917999519653872144063854709102652201963187054821445240853452
          75999740244625255428455944579 
        × 5625457617268841037562770073044474817438769440075105451049468510945483965774
          79473472146228550799322939273

RSA-704有212个十进制数码（704位），由Shi Bai、Emmanuel Thomé 和 Paul Zimmermann分解成功。^[31] 分解结果于2012年7月2日公布。^[32] 他们获得了US$30,000现金奖励。^{[来源请求]}^[可疑]

RSA-704 = 7403756347956171282804679609742957314259318888923128908493623263897276503402
          8266276891996419625117843995894330502127585370118968098286733173273108930900
          552505116877063299072396380786710086096962537934650563796359

RSA-704 = 9091213529597818878440658302600437485892608310328358720428512168960411528640
          933367824950788367956756806141
        × 8143859259110045265727809126284429335877899002167627883200914172429324360133
          004116702003240828777970252499

RSA-220有220个十进制数码（729位），由S. Bai, P. Gaudry、A. Kruppa、 E. Thomé和P. Zimmermann分解。2016年5月13日宣布分解成功。^[33]

RSA-220 = 2260138526203405784941654048610197513508038915719776718321197768109445641817
          9666766085931213065825772506315628866769704480700018111497118630021124879281
          99487482066070131066586646083327982803560379205391980139946496955261

RSA-220 = 6863656412267566274382371499288437800130842239979164844621244993321541061441
          4642667938213644208420192054999687
        × 3292907439486349812049301549212935291916455196536233952462686051169290349309
          4652463337824866390738191765712603

RSA-230有230个十进制数码（762位），由Samuel S. Gross在 2018年8月15日分解。^[34]

RSA-230 = 1796949159794106673291612844957324615636756180801260007088891883553172646034
          1490933493372247868650755230855864199929221814436684722874052065257937495694
          3483892631711525225256544109808191706117425097024407180103648316382885188526
          89

RSA-230 = 4528450358010492026612439739120166758911246047493700040073956759261590397250
          033699357694507193523000343088601688589
        × 3968132623150957588532394439049887341769533966621957829426966084093049516953
          598120833228447171744337427374763106901

RSA-232有232个十进制数码（768位），在2020年2月17日由N. L. Zamarashkin, D. A. Zheltkov 和 S. A. Matveev分解。^[35]

RSA-232 = 1009881397871923546909564894309468582818233821955573955141120516205831021338
          5285453743661097571543636649133800849170651699217015247332943892702802343809
          6090980497644054071120196541074755382494867277137407501157718230539834060616
          2079

RSA-232 = 2966909333208360660361779924242630634742946262521852394401857157419437019472
          3262390744910112571804274494074452751891
        × 3403816175197563438006609498491521420547121760734723172735163413276050706174
          8526506443144325148088881115083863017669

RSA-768有232个十进制数码（768位），在2009年12月12日被Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen K. Lenstra, Emmanuel Thomé, Pierrick Gaudry, Alexander Kruppa, Peter Montgomery, Joppe W. Bos, Dag Arne Osvik, Herman te Riele, Andrey Timofeev和Paul Zimmermann分解，耗时两年。^[36]

RSA-768 = 1230186684530117755130494958384962720772853569595334792197322452151726400507
          2636575187452021997864693899564749427740638459251925573263034537315482685079
          1702612214291346167042921431160222124047927473779408066535141959745985690214
          3413

RSA-768 = 3347807169895689878604416984821269081770479498371376856891243138898288379387
          8002287614711652531743087737814467999489
        × 3674604366679959042824463379962795263227915816434308764267603228381573966651
          1279233373417143396810270092798736308917

分解所用的CPU时间相当于单核2.2 GHz AMD Opteron的2000年。^[36]

RSA-240有240个十进制数码（795位），在2019年11月由Fabrice Boudot、Pierrick Gaudry、Aurore Guillevic、Nadia Heninger、Emmanuel Thomé和Paul Zimmermann分解。^[37]

RSA-240 = 1246203667817187840658350446081065904348203746516788057548187888832896668011
          8821085503603957027250874750986476843845862105486553797025393057189121768431
          8286362846948405301614416430468066875699415246993185704183030512549594371372
          159029236099

RSA-240 = 5094359522858399145550510235808437141326483820241114731866602965218212064697
          46700620316443478873837606252372049619334517
        × 2446242088383181505678131390240028966538020925789314014520412213365584770951
          78155258218897735030590669041302045908071447

分解所用的时间相当于2.1 GHz Intel Xeon Gold 6130 CPU上的900个核心-年。与RSA-768的分解相比，作者认为更好的算法达到了3–4 倍的加速，更好的CPU达到了1.25–1.67倍的加速效果。

RSA-250有250个十进制数码（829位），在2020年2月由Fabrice Boudot、Pierrick Gaudry、Aurore Guillevic、Nadia Heninger、Emmanuel Thomé和Paul Zimmermann分解。他们在2月28日宣布分解成功。

RSA-250 = 2140324650240744961264423072839333563008614715144755017797754920881418023447
          1401366433455190958046796109928518724709145876873962619215573630474547705208
          0511905649310668769159001975940569345745223058932597669747168173806936489469
          9871578494975937497937

RSA-250 = 6413528947707158027879019017057738908482501474294344720811685963202453234463
          0238623598752668347708737661925585694639798853367
        × 3337202759497815655622601060535511422794076034476755466678452098702384172921
          0037080257448673296881877565718986258036932062711

如果以一个2.1 GHz Intel Xeon Gold 6130 CPU作为参考，RSA-250的分解使用了大约2700个CPU 核心-年。使用开源的CADO-NFS 软件（页面存档备份，存于互联网档案馆）基于数域筛选法进行计算。

该团队以此致敬Peter Montgomery（英语：Peter Montgomery (mathematician)），他因为计算数论与密码学研究闻名，已于2020年2月18日去世。^[38]

RSA-260有260个十进制数码（862位），目前没有被分解。

RSA-260 = 2211282552952966643528108525502623092761208950247001539441374831912882294140
          2001986512729726569746599085900330031400051170742204560859276357953757185954
          2988389587092292384910067030341246205457845664136645406842143612930176940208
          46391065875914794251435144458199

RSA-270有270个十进制数码（895位），目前没有被分解。

RSA-270 = 2331085303444075445276376569106805241456198124803054490429486119684959182451
          3578286788836931857711641821391926857265831491306067262691135402760979316634
          1626693946596196427744273886601876896313468704059066746903123910748277606548
          649151920812699309766587514735456594993207

RSA-896有270个十进制数码（896位），目前没有被分解。曾提供了$75,000的奖金。

RSA-896 = 4120234369866595438555313653325759481798116998443279828454556264338764455652
          4842619809887042316184187926142024718886949256093177637503342113098239748515
          0944909106910269861031862704114880866970564902903653658867433731720813104105
          190864254793282601391257624033946373269391

RSA-280有280个十进制数码（928位），目前没有被分解。

RSA-280 = 1790707753365795418841729699379193276395981524363782327873718589639655966058
          5783742549640396449103593468573113599487089842785784500698716853446786525536
          5503525160280656363736307175332772875499505341538927978510751699922197178159
          7724733184279534477239566789173532366357270583106789

RSA-290有290个十进制数码（962位），目前没有被分解。

RSA-290 = 3050235186294003157769199519894966400298217959748768348671526618673316087694
          3419156362946151249328917515864630224371171221716993844781534383325603218163
          2549201100649908073932858897185243836002511996505765970769029474322210394327
          60575157628357292075495937664206199565578681309135044121854119

RSA-300有300个十进制数码（995位），目前没有被分解。

RSA-300 = 2769315567803442139028689061647233092237608363983953254005036722809375824714
          9473946190060218756255124317186573105075074546238828817121274630072161346956
          4396741836389979086904304472476001839015983033451909174663464663867829125664
          459895575157178816900228792711267471958357574416714366499722090015674047

RSA-309有309个十进制数码（1,024位），目前没有被分解。

RSA-309 = 1332943998825757583801437794588036586217112243226684602854588261917276276670
          5425540467426933349195015527349334314071822840746357352800368666521274057591
          1870128339157499072351179666739658503429931021985160714113146720277365006623
          6927218079163559142755190653347914002967258537889160429597714204365647842739
          10949

RSA-1024有309个十进制数码（1,024位），目前没有被分解。曾提供了$100,000的奖金

RSA-1024 = 135066410865995223349603216278805969938881475605667027524485143851526510604
           859533833940287150571909441798207282164471551373680419703964191743046496589
           274256239341020864383202110372958725762358509643110564073501508187510676594
           629205563685529475213500852879416377328533906109750544334999811150056977236
           890927563

RSA-310有310个十进制数码（1,028位），目前没有被分解。

RSA-310 = 1848210397825850670380148517702559371400899745254512521925707445580334710601
          4125276757082979328578439013881047668984294331264191394626965245834649837246
          5163148188847336415136873623631778358751846501708714541673402642461569061162
          0116380982484120857688483676576094865930188367141388795454378671343386258291
          687641

RSA-320有320个十进制数码（1,061位），目前没有被分解。

RSA-320 = 2136810696410071796012087414500377295863767938372793352315068620363196552357
          8837094085435000951700943373838321997220564166302488321590128061531285010636
          8571638978998117122840139210685346167726847173232244364004850978371121744321
          8270343654835754061017503137136489303437996367224915212044704472299799616089
          2591129924218437

RSA-330有330个十进制数码（1,094位），目前没有被分解。

RSA-330 = 1218708633106058693138173980143325249157710686226055220408666600017481383238
          1352456802425903555880722805261111079089882303717632638856140900933377863089
          0634828167900405006112727432172179976427017137792606951424995281839383708354
          6364684839261149319768449396541020909665209789862312609604983709923779304217
          01862444655244698696759267

RSA-340有340个十进制数码（1,128位），目前没有被分解。

RSA-340 = 2690987062294695111996484658008361875931308730357496490239672429933215694995
          2758588771223263308836649715112756731997946779608413232406934433532048898585
          9176676580752231563884394807622076177586625973975236127522811136600110415063
          0004691128152106812042872285697735145105026966830649540003659922618399694276
          990464815739966698956947129133275233

RSA-350有350个十进制数码（1,161位），目前没有被分解。

RSA-350 = 2650719995173539473449812097373681101529786464211583162467454548229344585504
          3495841191504413349124560193160478146528433707807716865391982823061751419151
          6068496555750496764686447379170711424873128631468168019548127029171231892127
          2886825928263239383444398948209649800021987837742009498347263667908976501360
          3382322972552204068806061829535529820731640151

RSA-360有360个十进制数码（1,194位），目前没有被分解。

RSA-360 = 2186820202343172631466406372285792654649158564828384065217121866374227745448
          7764963889680817334211643637752157994969516984539482486678141304751672197524
          0052350576247238785129338002757406892629970748212734663781952170745916609168
          9358372359962787832802257421757011302526265184263565623426823456522539874717
          61591019113926725623095606566457918240614767013806590649

RSA-370有370个十进制数码（1,227位），目前没有被分解。

RSA-370 = 1888287707234383972842703127997127272470910519387718062380985523004987076701
          7212819937261952549039800018961122586712624661442288502745681454363170484690
          7379449525034797494321694352146271320296579623726631094822493455672541491544
          2700993152879235272779266578292207161032746297546080025793864030543617862620
          878802244305286292772467355603044265985905970622730682658082529621

RSA-380有380个十进制数码（1,261位），目前没有被分解。

RSA-380 = 3013500443120211600356586024101276992492167997795839203528363236610578565791
          8270750937407901898070219843622821090980641477056850056514799336625349678549
          2187941807116344787358312651772858878058620717489800725333606564197363165358
          2237779263423501952646847579678711825720733732734169866406145425286581665755
          6977260763553328252421574633011335112031733393397168350585519524478541747311

RSA-390有390个十进制数码（1,294位），目前没有被分解。

RSA-390 = 2680401941182388454501037079346656065366941749082852678729822424397709178250
          4623002472848967604282562331676313645413672467684996118812899734451228212989
          1630084759485063423604911639099585186833094019957687550377834977803400653628
          6955344904367437281870253414058414063152368812498486005056223028285341898040
          0795447435865033046248751475297412398697088084321037176392288312785544402209
          1083492089

RSA-400有400个十进制数码（1,327位），目前没有被分解。

RSA-400 = 2014096878945207511726700485783442547915321782072704356103039129009966793396
          1419850865094551022604032086955587930913903404388675137661234189428453016032
          6191193056768564862615321256630010268346471747836597131398943140685464051631
          7519403149294308737302321684840956395183222117468443578509847947119995373645
          3607109795994713287610750434646825511120586422993705980787028106033008907158
          74500584758146849481

RSA-410有410个十进制数码（1,360位），目前没有被分解。

RSA-410 = 1965360147993876141423945274178745707926269294439880746827971120992517421770
          1079138139324539033381077755540830342989643633394137538983355218902490897764
          4412968474332754608531823550599154905901691559098706892516477785203855688127
          0635069372091564594333528156501293924133186705141485137856845741766150159437
          6063244163040088180887087028771717321932252992567756075264441680858665410918
          431223215368025334985424358839

RSA-420有420个十进制数码（1,393位），目前没有被分解。

RSA-420 = 2091366302476510731652556423163330737009653626605245054798522959941292730258
          1898373570076188752609749648953525484925466394800509169219344906273145413634
          2427186266197097846022969248579454916155633686388106962365337549155747268356
          4666583846809964354191550136023170105917441056517493690125545320242581503730
          3405952887826925813912683942756431114820292313193705352716165790132673270514
          3817744164107601735413785886836578207979

RSA-430有430个十进制数码（1,427位），目前没有被分解。

RSA-430 = 3534635645620271361541209209607897224734887106182307093292005188843884213420
          6950355315163258889704268733101305820000124678051064321160104990089741386777
          2424190744453885127173046498565488221441242210687945185565975582458031351338
          2070785777831859308900851761495284515874808406228585310317964648830289141496
          3289966226854692560410075067278840383808716608668377947047236323168904650235
          70092246473915442026549955865931709542468648109541

RSA-440有440个十进制数码（1,460位），目前没有被分解。

RSA-440 = 2601428211955602590070788487371320550539810804595235289423508589663391270837
          4310252674800592426746319007978890065337573160541942868114065643853327229484
          5029942332226171123926606357523257736893667452341192247905168387893684524818
          0307729497304959710847337973805145673263119916483529703607405432752966630781
          2234597766390750441445314408171802070904072739275930410299359006059619305590
          701939627725296116299946059898442103959412221518213407370491

RSA-450有450个十进制数码（1,493位），目前没有被分解。

RSA-450 = 1984634237142836623497230721861131427789462869258862089878538009871598692569
          0078791591684242367262529704652673686711493985446003494265587358393155378115
          8032447061155145160770580926824366573211993981662614635734812647448360573856
          3132247491715526997278115514905618953253443957435881503593414842367096046182
          7643434794849824315251510662855699269624207451365738384255497823390996283918
          3287667419172988072221996532403300258906083211160744508191024837057033

RSA-460有460个十进制数码（1,526位），目前没有被分解。

RSA-460 = 1786856020404004433262103789212844585886400086993882955081051578507634807524
          1464078819812169681394445771476334608488687746254318292828603396149562623036
          3564554675355258128655971003201417831521222464468666642766044146641933788836
          8932452217321354860484353296131403821175862890998598653858373835628654351880
          4806362231643082386848731052350115776715521149453708868428108303016983133390
          0416365515466857004900847501644808076825638918266848964153626486460448430073
          4909

RSA-1536有463个十进制数码（1,536位），目前没有被分解。曾提供了$150,000的奖金。

RSA-1536 = 184769970321174147430683562020016440301854933866341017147178577491065169671
           116124985933768430543574458561606154457179405222971773252466096064694607124
           962372044202226975675668737842756238950876467844093328515749657884341508847
           552829818672645133986336493190808467199043187438128336350279547028265329780
           293491615581188104984490831954500984839377522725705257859194499387007369575
           568843693381277961308923039256969525326162082367649031603655137144791393234
           7169566988069

RSA-470有470个十进制数码（1,559位），目前没有被分解。

RSA-470 = 1705147378468118520908159923888702802518325585214915968358891836980967539803
          6897711442383602526314519192366612270595815510311970886116763177669964411814
          0957486602388713064698304619191359016382379244440741228665455229545368837485
          5874455212895044521809620818878887632439504936237680657994105330538621759598
          4047709603954312447692725276887594590658792939924609261264788572032212334726
          8553025718835659126454325220771380103576695555550710440908570895393205649635
          76770285413369

RSA-480有480个十进制数码（1,593位），目前没有被分解。

RSA-480 = 3026570752950908697397302503155918035891122835769398583955296326343059761445
          7144169659817040125185215913853345598217234371231338324773210726853524776378
          4105186549246199888070331088462855743520880671299302895546822695492968577380
          7067958428022008294111984222973260208233693152589211629901686973933487362360
          8129660418514569063995282978176790149760521395548532814196534676974259747930
          6858645849268328985687423881853632604706175564461719396117318298679820785491
          875674946700413680932103

RSA-490有490个十进制数码（1,626位），目前没有被分解。

RSA-490 = 1860239127076846517198369354026076875269515930592839150201028353837031025971
          3738522164743327949206433999068225531855072554606782138800841162866037393324
          6578171804201717222449954030315293547871401362961501065002486552688663415745
          9758925793594165651020789220067311416926076949777767604906107061937873540601
          5942747316176193775374190713071154900658503269465516496828568654377183190586
          9537640698044932638893492457914750855858980849190488385315076922453755527481
          1376719096144119390052199027715691

RSA-500有500个十进制数码（1,659位），目前没有被分解。

RSA-500 = 1897194133748626656330534743317202527237183591953428303184581123062450458870
          7687605943212347625766427494554764419515427586743205659317254669946604982419
          7301601038125215285400688031516401611623963128370629793265939405081077581694
          4786041721411024641038040278701109808664214800025560454687625137745393418221
          5494821277335671735153472656328448001134940926442438440198910908603252678814
          7850601132077287172819942445113232019492229554237898606631074891074722425617
          39680319169243814676235712934292299974411361

RSA-617有617个十进制数码（2,048位），目前没有被分解。

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

RSA-2048有617个十进制数码（2,048位）。它是最大的RSA数，分解成功的奖金高达$200,000。RSA-2048可能在未来很多年都无法分解，除非在不久的将来整数分解或计算能力获取相当大的进步。

RSA-2048 = 2519590847565789349402718324004839857142928212620403202777713783604366202070
           7595556264018525880784406918290641249515082189298559149176184502808489120072
           8449926873928072877767359714183472702618963750149718246911650776133798590957
           0009733045974880842840179742910064245869181719511874612151517265463228221686
           9987549182422433637259085141865462043576798423387184774447920739934236584823
           8242811981638150106748104516603773060562016196762561338441436038339044149526
           3443219011465754445417842402092461651572335077870774981712577246796292638635
           6373289912154831438167899885040445364023527381951378636564391212010397122822
           120720357

整数分解记录
RSA分解挑战（英语：RSA Factoring Challenge）
RSA私钥挑战（英语：RSA Secret-Key Challenge）

[1]
RSA Laboratories. RSA Factoring Challenge. [2008-08-05]. （原始内容存档于2013-09-21）.
[2]
RSA Laboratories. The RSA Factoring Challenge FAQ. [2008-08-05]. （原始内容存档于2013-09-21）.
[3]
RSA-100 Factored. Cryptography Watch Archive for April, 1991. 1991-04-01 [2008-08-05].^{[永久失效链接]}
[4]
RSA Honor Roll. 1999-03-05 [2008-08-05]. （原始内容存档于2009-04-12）.
[5]
Brandon Dixon and Arjen K. Lenstra. Factoring Integers Using SIMD Sieves. Lecture Notes in Computer Science 765. 1994. ISBN 978-3-540-57600-6. S2CID 21157010. doi:10.1007/3-540-48285-7.
[6]
Distributed version of the FactMsieve Perl script. 2012-03-27 [2015-06-08]. （原始内容存档于2021-12-11）.
[7]
T. Denny, B. Dodson, A. K. Lenstra, M. S. Manasse (1994), "On The Factorization Of RSA-120" （页面存档备份，存于互联网档案馆） .
[8]
RSA Honor Roll. 1999-03-05 [2008-08-06]. （原始内容存档于2009-04-12）.
[9]
The Magic Words Are Squeamish Ossifrage. [2009-11-24]. （原始内容存档于2016-03-04）.
[10]
Mark Janeba (1994), Factoring Challenge Conquered （页面存档备份，存于互联网档案馆）. Retrieved on 2008-03-10.
[11]
Arjen K. Lenstra (1996-04-12), Factorization of RSA-130 （页面存档备份，存于互联网档案馆）. Retrieved on 2008-03-10.
[12]
Herman te Riele (1999-02-04), Factorization of RSA-140 互联网档案馆的存档，存档日期2004-12-08.. Retrieved on 2008-03-10.
[13]
RSA Laboratories, RSA-140 is factored! 互联网档案馆的存档，存档日期2006-12-30.. Retrieved on 2008-03-10.
[14]
Herman te Riele (1999-08-26), New factorization record 互联网档案馆的存档，存档日期2004-12-31. (announcement of factorization of RSA-155). Retrieved on 2008-03-10.
[15]
RSA Laboratories, RSA-155 is factored! 互联网档案馆的存档，存档日期2006-12-30.. Retrieved on 2008-03-10.
[16]
Jens Franke (2003-04-01), RSA-160 （页面存档备份，存于互联网档案馆） (announcement of factorization). Retrieved on 2008-03-10.
[17]
RSA Laboratories, RSA-160 is factored! 互联网档案馆的存档，存档日期2006-12-30.. Retrieved on 2008-03-10.
[18]
D. Bonenberger and M. Krone, RSA-170 互联网档案馆的存档，存档日期2011-07-19. Retrieved on 2010-03-08.
[19]
Danilov, S. A.; Popovyan, I. A. Factorization of RSA-180 (PDF). Cryptology ePrint Archive. 9 May 2010 [2022-08-30]. （原始内容存档 (PDF)于2022-07-10）.
[20]
Jens Franke (2003-12-03), RSA576 Archive.is的存档，存档日期2012-07-14 (repost of announcement of the factorization). Retrieved on 2008-03-10.
[21]
Eric W. Weisstein (2005-12-05), RSA-576 Factored （页面存档备份，存于互联网档案馆） at MathWorld. Retrieved on 2008-03-10.
[22]
RSA Laboratories, RSA-576 is factored! 互联网档案馆的存档，存档日期2006-12-24.. Retrieved on 2008-03-10.
[23]
Danilov, S. A.; Popovyan, I. A. S.A. Danilov and I.A. Popovyan Factorization of RSA-180. Cryptology ePrint Archive. 2010 [2022-08-30]. （原始内容存档于2022-08-30）.. Retrieved on 2010-05-12.
[24]
I. Popovyan, A. Timofeev. RSA-190 factored. mersenneforum.org. 2010-11-08 [2010-11-10]. （原始内容存档于2022-08-30）.
[25]
RSA Laboratories, RSA-640 is factored! 互联网档案馆的存档，存档日期2007-01-04.. Retrieved on 2008-03-10.
[26]
Jens Franke (2005-11-04), We have factored RSA640 by GNFS （页面存档备份，存于互联网档案馆）. Retrieved on 2008-03-10.
[27]
Eric W. Weisstein (2005-11-08), RSA-640 Factored （页面存档备份，存于互联网档案馆） at MathWorld. Retrieved on 2008-03-10.
[28]
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[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

RSA-100

RSA-110

RSA-120

RSA-129

RSA-130

RSA-140

RSA-150

RSA-155

RSA-160

RSA-170

RSA-576

RSA-180

RSA-190

RSA-640

RSA-200

RSA-210

RSA-704

RSA-220

RSA-230

RSA-232

RSA-768

RSA-240

RSA-250

RSA-260

RSA-270

RSA-896

RSA-280

RSA-290

RSA-300

RSA-309

RSA-1024

RSA-310

RSA-320

RSA-330

RSA-340

RSA-350

RSA-360

RSA-370

RSA-380

RSA-390

RSA-400

RSA-410

RSA-420

RSA-430

RSA-440

RSA-450

RSA-460

RSA-1536

RSA-470

RSA-480

RSA-490

RSA-500

RSA-617

RSA-2048

参见

注记

参考资料

外部链接