RSA numbers - AbsoluteAstronomy.com

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factor

Prime factor

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's...

s) that are part of the RSA Factoring Challenge

RSA Factoring Challenge

The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography...

. The challenge was to find the prime factors but it was declared inactive in 2007. It was created by RSA Laboratories

RSA Security

RSA, the security division of EMC Corporation, is headquartered in Bedford, Massachusetts, United States, and maintains offices in Australia, Ireland, Israel, the United Kingdom, Singapore, India, China, Hong Kong and Japan....

in March 1991 to encourage research into computational number theory

Computational number theory

In mathematics, computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations...

and the practical difficulty of factoring

Integer factorization

In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....

large integer

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

s.

RSA Laboratories published a number of semiprimes with 100 to 617 decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

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. , 16 of the 54 listed numbers have been factored: The 15 smallest from RSA-100 to RSA-200, plus RSA-768.

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." 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

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

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

RSA-100

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

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

. Reportedly, the factorization took a few days using the multiple-polynomial quadratic sieve algorithm

Quadratic sieve

The quadratic sieve algorithm is a modern integer factorization algorithm and, in practice, the second fastest method known . It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve...

on a MasPar

MasPar

MasPar Computer Corporation was a minisupercomputer vendor that was founded in 1987 by Jeff Kalb. The company was based in Sunnyvale, California....

parallel computer.

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

RSA-100 = 15226050279225333605356183781326374297180681149613
80688657908494580122963258952897654000350692006139

RSA-100 = 37975227936943673922808872755445627854565536638199
× 40094690950920881030683735292761468389214899724061

It takes four hours to repeat this factorization using the program Msieve on a 2200 MHz Athlon 64

Athlon 64

The Athlon 64 is an eighth-generation, AMD64-architecture microprocessor produced by AMD, released on September 23, 2003. It is the third processor to bear the name Athlon, and the immediate successor to the Athlon XP...

processor.

RSA-110

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

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

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

The value and factorization is as follows:

RSA-120 = 227010481295437363334259960947493668895875336466084780038173
258247009162675779735389791151574049166747880487470296548479

RSA-120 = 327414555693498015751146303749141488063642403240171463406883
× 693342667110830181197325401899700641361965863127336680673013

RSA-129

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

Martin Gardner

Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...

's column in the August 1977 issue of Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

.

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

Derek Atkins

Derek A Atkins is a computer scientist specializing in Computer Security. He studied Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, and currently works at PGP Corporation....

, Michael Graff

Michael Graff

Michael Graff graduated from with a degree in Computer Engineering. Currently working at , a non-profit corporation. Michael is a co-author and one of several architects of BIND 9.In April 1984, Michael co-authored The Magic Words are Squeamish Ossifrage....

, Arjen K. Lenstra

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

and Paul Leyland

Paul Leyland

Paul Leyland is a British number theorist who has studied integer factorization and primality testing.He has contributed to the factorization of RSA-129, RSA-140, and RSA-155, as well as potential factorial primes as large as 400! + 1. He has also studied Cunningham numbers, Cullen numbers, Woodall...

, using approximately 1600 computers from around 600 volunteers connected over the Internet

Internet

The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

. A US$

United States dollar

The United States dollar , also referred to as the American dollar, is the official currency of the United States of America. It is divided into 100 smaller units called cents or pennies....

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

Free Software Foundation

The Free Software Foundation is a non-profit corporation founded by Richard Stallman on 4 October 1985 to support the free software movement, a copyleft-based movement which aims to promote the universal freedom to create, distribute and modify computer software...

.

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

The Magic Words are Squeamish Ossifrage

The text "The Magic Words are Squeamish Ossifrage" was the solution to a challenge ciphertext posed by the inventors of the RSA cipher in 1977. The problem appeared in Martin Gardner's Mathematical Games column in Scientific American. It was solved in 1993–1994 by a large joint computer...

RSA-130

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

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

and composed of Jim Cowie, Marije Elkenbracht-Huizing, Wojtek Furmanski, Peter L. Montgomery, Damian Weber and Joerg Zayer.

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

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

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

which has a root of 12574411168418005980468 modulo RSA-130.

RSA-140

RSA-140 has 140 decimal digits (463 bits), and was factored on February 2, 1999 by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

, Paul Leyland, Walter Lioen, Peter L. Montgomery, Brian Murphy and Paul Zimmermann

Paul Zimmermann

Paul Zimmermann is a French computational mathematician, working at INRIA.His interests include asymptotically-fast arithmetic — he wrote a book on algorithms for computer arithmetic with Richard Brent. He has developed some of the fastest available code for manipulating polynomials over...

.

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

MIPS-year

A MIPS-year is a measurement of computational steps for computers. MIPS means million instructions per second, and a MIPS-year is equal to the number of steps processed for one year at one million instructions per second....

s of computing time.

RSA-150

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

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

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

The value and factorization is as follows:

RSA-150 = 155089812478348440509606754370011861770654545830995430655466945774312632703
463465954363335027577729025391453996787414027003501631772186840890795964683

RSA-150 = 348009867102283695483970451047593424831012817350385456889559637548278410717
× 445647744903640741533241125787086176005442536297766153493419724532460296199

RSA-155

RSA-155 has 155 decimal digits (512 bits), and was factored on August 22, 1999 by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

, 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.

The value and factorization is as follows:

RSA-155 = 109417386415705274218097073220403576120037329454492059909138421314763499842889
34784717997257891267332497625752899781833797076537244027146743531593354333897

RSA-155 = 102639592829741105772054196573991675900716567808038066803341933521790711307779
× 106603488380168454820927220360012878679207958575989291522270608237193062808643

The factorization was found using the general number field sieve

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

algorithm and an estimated 8000 MIPS-year

MIPS-year

s of computing time.

RSA-160

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

University of Bonn

The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...

and the German

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

Federal Office for Information Security

The Bundesamt für Sicherheit in der Informationstechnik is the German government agency in charge of managing computer and communication security for the German government...

(BSI). The team contained J. Franke

Jens Franke

Jens Franke is a German mathematician. He holds a chair at the University of Bonn's Hausdorff Center for Mathematics since 1992. Franke's research has covered various problems of number theory, algebraic geometry and analysis on locally symmetric spaces.Franke attended the University of Jena,...

, F. Bahr, T. Kleinjung, M. Lochter, and M. Böhm.

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

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

algorithm.

RSA-170

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

Fachhochschule Braunschweig/Wolfenbüttel

Fachhochschule Braunschweig/Wolfenbüttel , also known as Ostfalia, is a German Fachhochschule established in 1971....

.

The value and factorization is as follows:

RSA-170 = 2606262368413984492152987926667443219708592538048640641616478519185999962854206936145
0283931914514618683512198164805919882053057222974116478065095809832377336510711545759

RSA-170 = 3586420730428501486799804587268520423291459681059978161140231860633948450858040593963
× 7267029064107019078863797763923946264136137803856996670313708936002281582249587494493

The factorization was found using the general number field sieve

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

algorithm.

RSA-576

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

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

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

algorithm.

RSA-180

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

Moscow State University

Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...

, Russia.

RSA-180 = 1911479277189866096892294666314546498129862462766673548641885036388072607034
3679905877620136513516127813425829612810920004670291298456875280033022177775
2773957404540495707851421041

RSA-180 = 400780082329750877952581339104100572526829317815807176564882178998497572771950624613470377
× 476939688738611836995535477357070857939902076027788232031989775824606225595773435668861833

The factorization was found using the general number field sieve

General number field sieve

In number theory, the general number field sieve is the most efficient classical algorithm known for factoring integers larger than 100 digits...

algorithm implementation running on 3 Intel Core i7 PCs.

RSA-190

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

RSA-190 = 1907556405060696491061450432646028861081179759533184460647975622318915025587
1841757540549761551215932934922604641526300932385092466032074171247261215808
58185985938946945490481721756401423481

RSA-190 = 31711952576901527094851712897404759298051473160294503277847619278327936427981256542415724309619
× 60152600204445616415876416855266761832435433594718110725997638280836157040460481625355619404899

RSA-640

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

RSA-640 = 31074182404900437213507500358885679300373460228427275457
20161948823206440518081504556346829671723286782437916272
83803341547107310850191954852900733772482278352574238645
4014691736602477652346609

RSA-640 = 16347336458092538484431338838650908598417836700330923121
81110852389333100104508151212118167511579
× 19008712816648221131268515739354139754718967899685154936
66638539088027103802104498957191261465571

The computation took 5 months on 80 2.2 GHz AMD

Advanced Micro Devices

Advanced Micro Devices, Inc. or AMD is an American multinational semiconductor company based in Sunnyvale, California, that develops computer processors and related technologies for commercial and consumer markets...

Opteron

Opteron is AMD's x86 server and workstation processor line, and was the first processor which supported the AMD64 instruction set architecture . It was released on April 22, 2003 with the SledgeHammer core and was intended to compete in the server and workstation markets, particularly in the same...

CPUs

Central processing unit

The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

.

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

RSA-200

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

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

RSA-200 = 2799783391122132787082946763872260162107044678695542853756000992932612840010
7609345671052955360856061822351910951365788637105954482006576775098580557613
579098734950144178863178946295187237869221823983

RSA-200 = 3532461934402770121272604978198464368671197400197625023649303468776121253679
423200058547956528088349
× 7925869954478333033347085841480059687737975857364219960734330341455767872818
152135381409304740185467

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

GHZ

GHZ or GHz may refer to:# Gigahertz .# Greenberger-Horne-Zeilinger state — a quantum entanglement of three particles.# Galactic Habitable Zone — the region of a galaxy that is favorable to the formation of life....

Opteron

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

RSA-210

RSA-210 has 210 decimal digits (696 bits), and has not been factored so far.

RSA-210 = 2452466449002782119765176635730880184670267876783327597434144517150616008300
3858721695220839933207154910362682719167986407977672324300560059203563124656
1218465817904100131859299619933817012149335034875870551067

RSA-704

RSA-704 has 704 bits (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 (729 bits), and has not been factored so far.

RSA-220 = 2260138526203405784941654048610197513508038915719776718321197768109445641817
9666766085931213065825772506315628866769704480700018111497118630021124879281
99487482066070131066586646083327982803560379205391980139946496955261

RSA-230

RSA-230 has 230 decimal digits (762 bits), and has not been factored so far.

RSA-230 = 1796949159794106673291612844957324615636756180801260007088891883553172646
0341490933493372247868650755230855864199929221814436684722874052065257937
4956943483892631711525225256544109808191706117425097024407180103648316382
88518852689

RSA-232

RSA-232 has 232 decimal digits (768 bits), and has not been factored so far.

RSA-232 = 1009881397871923546909564894309468582818233821955573955141120516205831021338
5285453743661097571543636649133800849170651699217015247332943892702802343809
6090980497644054071120196541074755382494867277137407501157718230539834060616
2079

RSA-768

RSA-768 has 768 bits (232 decimal digits), and was factored on December 12, 2009 by Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen K. Lenstra

Arjen Lenstra

Arjen Klaas Lenstra is a Dutch mathematician. He studied mathematics at the University of Amsterdam.He is currently a professor at the EPFL , in the Laboratory for Cryptologic Algorithms, and...

, Emmanuel Thomé, Pierrick Gaudry, Alexander Kruppa, Peter Montgomery

Peter Montgomery

Peter Lawrence Montgomery is an American mathematician who has published widely in the more mathematical end of the field of cryptography. He is currently a researcher in the cryptography group at Microsoft Research....

, Joppe W. Bos, Dag Arne Osvik, Herman te Riele, Andrey Timofeev, and Paul Zimmermann

Paul Zimmermann

.

RSA-768 = 12301866845301177551304949583849627207728535695953347921973224521517264005
07263657518745202199786469389956474942774063845925192557326303453731548268
50791702612214291346167042921431160222124047927473779408066535141959745985
6902143413

RSA-768 = 33478071698956898786044169848212690817704794983713768568912431388982883793
878002287614711652531743087737814467999489
× 36746043666799590428244633799627952632279158164343087642676032283815739666
511279233373417143396810270092798736308917

RSA-240

RSA-240 has 240 decimal digits (795 bits), and has not been factored so far.

RSA-240 = 1246203667817187840658350446081065904348203746516788057548187888832896668011
8821085503603957027250874750986476843845862105486553797025393057189121768431
8286362846948405301614416430468066875699415246993185704183030512549594371372
159029236099

RSA-250

RSA-250 has 250 decimal digits (829 bits), and has not been factored so far.

RSA-250 = 2140324650240744961264423072839333563008614715144755017797754920881418023447
1401366433455190958046796109928518724709145876873962619215573630474547705208
0511905649310668769159001975940569345745223058932597669747168173806936489469
9871578494975937497937

RSA-260

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

RSA-260 = 2211282552952966643528108525502623092761208950247001539441374831912882294140
2001986512729726569746599085900330031400051170742204560859276357953757185954
2988389587092292384910067030341246205457845664136645406842143612930176940208
46391065875914794251435144458199

RSA-270

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

RSA-270 = 2331085303444075445276376569106805241456198124803054490429486119684959182451
3578286788836931857711641821391926857265831491306067262691135402760979316634
1626693946596196427744273886601876896313468704059066746903123910748277606548
649151920812699309766587514735456594993207

RSA-896

RSA-896 has 896 bits (270 decimal digits), and 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 (928 bits), and has not been factored so far.

RSA-280 = 1790707753365795418841729699379193276395981524363782327873718589639655966058
5783742549640396449103593468573113599487089842785784500698716853446786525536
5503525160280656363736307175332772875499505341538927978510751699922197178159
7724733184279534477239566789173532366357270583106789

RSA-290

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

RSA-290 = 3050235186294003157769199519894966400298217959748768348671526618673316087694
3419156362946151249328917515864630224371171221716993844781534383325603218163
2549201100649908073932858897185243836002511996505765970769029474322210394327
60575157628357292075495937664206199565578681309135044121854119

RSA-300

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

RSA-300 = 2769315567803442139028689061647233092237608363983953254005036722809375824714
9473946190060218756255124317186573105075074546238828817121274630072161346956
4396741836389979086904304472476001839015983033451909174663464663867829125664
459895575157178816900228792711267471958357574416714366499722090015674047

RSA-309

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

RSA-309 = 1332943998825757583801437794588036586217112243226684602854588261917276276670
5425540467426933349195015527349334314071822840746357352800368666521274057591
1870128339157499072351179666739658503429931021985160714113146720277365006623
6927218079163559142755190653347914002967258537889160429597714204365647842739
10949

RSA-1024

RSA-1024 has 1,024 bits (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

Public-key cryptography

Public-key cryptography refers to a cryptographic system requiring two separate keys, one to lock or encrypt the plaintext, and one to unlock or decrypt the cyphertext. Neither key will do both functions. One of these keys is published or public and the other is kept private...

authentication algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

, 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 (1,028 bits), and has not been factored so far.

RSA-310 = 1848210397825850670380148517702559371400899745254512521925707445580334710601
4125276757082979328578439013881047668984294331264191394626965245834649837246
5163148188847336415136873623631778358751846501708714541673402642461569061162
0116380982484120857688483676576094865930188367141388795454378671343386258291
687641

RSA-320

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

RSA-320 = 2136810696410071796012087414500377295863767938372793352315068620363196552357
8837094085435000951700943373838321997220564166302488321590128061531285010636
8571638978998117122840139210685346167726847173232244364004850978371121744321
8270343654835754061017503137136489303437996367224915212044704472299799616089
2591129924218437

RSA-330

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

RSA-330 = 1218708633106058693138173980143325249157710686226055220408666600017481383238
1352456802425903555880722805261111079089882303717632638856140900933377863089
0634828167900405006112727432172179976427017137792606951424995281839383708354
6364684839261149319768449396541020909665209789862312609604983709923779304217
01862444655244698696759267

RSA-340

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

RSA-340 = 2690987062294695111996484658008361875931308730357496490239672429933215694995
2758588771223263308836649715112756731997946779608413232406934433532048898585
9176676580752231563884394807622076177586625973975236127522811136600110415063
0004691128152106812042872285697735145105026966830649540003659922618399694276
990464815739966698956947129133275233

RSA-350

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

RSA-350 = 2650719995173539473449812097373681101529786464211583162467454548229344585504
3495841191504413349124560193160478146528433707807716865391982823061751419151
6068496555750496764686447379170711424873128631468168019548127029171231892127
2886825928263239383444398948209649800021987837742009498347263667908976501360
3382322972552204068806061829535529820731640151

RSA-360

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

RSA-360 = 2186820202343172631466406372285792654649158564828384065217121866374227745448
7764963889680817334211643637752157994969516984539482486678141304751672197524
0052350576247238785129338002757406892629970748212734663781952170745916609168
9358372359962787832802257421757011302526265184263565623426823456522539874717
61591019113926725623095606566457918240614767013806590649

RSA-370

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

RSA-370 = 1888287707234383972842703127997127272470910519387718062380985523004987076701
7212819937261952549039800018961122586712624661442288502745681454363170484690
7379449525034797494321694352146271320296579623726631094822493455672541491544
2700993152879235272779266578292207161032746297546080025793864030543617862620
878802244305286292772467355603044265985905970622730682658082529621

RSA-380

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

RSA-380 = 3013500443120211600356586024101276992492167997795839203528363236610578565791
8270750937407901898070219843622821090980641477056850056514799336625349678549
2187941807116344787358312651772858878058620717489800725333606564197363165358
2237779263423501952646847579678711825720733732734169866406145425286581665755
6977260763553328252421574633011335112031733393397168350585519524478541747311

RSA-390

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

RSA-390 = 2680401941182388454501037079346656065366941749082852678729822424397709178250
4623002472848967604282562331676313645413672467684996118812899734451228212989
1630084759485063423604911639099585186833094019957687550377834977803400653628
6955344904367437281870253414058414063152368812498486005056223028285341898040
0795447435865033046248751475297412398697088084321037176392288312785544402209
1083492089

RSA-400

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

RSA-400 = 2014096878945207511726700485783442547915321782072704356103039129009966793396
1419850865094551022604032086955587930913903404388675137661234189428453016032
6191193056768564862615321256630010268346471747836597131398943140685464051631
7519403149294308737302321684840956395183222117468443578509847947119995373645
3607109795994713287610750434646825511120586422993705980787028106033008907158
74500584758146849481

RSA-410

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

RSA-410 = 1965360147993876141423945274178745707926269294439880746827971120992517421770
1079138139324539033381077755540830342989643633394137538983355218902490897764
4412968474332754608531823550599154905901691559098706892516477785203855688127
0635069372091564594333528156501293924133186705141485137856845741766150159437
6063244163040088180887087028771717321932252992567756075264441680858665410918
431223215368025334985424358839

RSA-420

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

RSA-420 = 2091366302476510731652556423163330737009653626605245054798522959941292730258
1898373570076188752609749648953525484925466394800509169219344906273145413634
2427186266197097846022969248579454916155633686388106962365337549155747268356
4666583846809964354191550136023170105917441056517493690125545320242581503730
3405952887826925813912683942756431114820292313193705352716165790132673270514
3817744164107601735413785886836578207979

RSA-430

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

RSA-430 = 3534635645620271361541209209607897224734887106182307093292005188843884213420
6950355315163258889704268733101305820000124678051064321160104990089741386777
2424190744453885127173046498565488221441242210687945185565975582458031351338
2070785777831859308900851761495284515874808406228585310317964648830289141496
3289966226854692560410075067278840383808716608668377947047236323168904650235
70092246473915442026549955865931709542468648109541

RSA-440

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

RSA-440 = 260142821195560259007078848737132055053981080459523528942350858966
339127083743102526748005924267463190079788900653375731605419428681
140656438533272294845029942332226171123926606357523257736893667452
341192247905168387893684524818030772949730495971084733797380514567
326311991648352970360740543275296663078122345977663907504414453144
081718020709040727392759304102993590060596193055907019396277252961
16299946059898442103959412221518213407370491

RSA-450

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

RSA-450 = 1984634237142836623497230721861131427789462869258862089878538009871598692569
0078791591684242367262529704652673686711493985446003494265587358393155378115
8032447061155145160770580926824366573211993981662614635734812647448360573856
3132247491715526997278115514905618953253443957435881503593414842367096046182
7643434794849824315251510662855699269624207451365738384255497823390996283918
3287667419172988072221996532403300258906083211160744508191024837057033

RSA-460

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

RSA-460 = 1786856020404004433262103789212844585886400086993882955081051578507634807524
1464078819812169681394445771476334608488687746254318292828603396149562623036
3564554675355258128655971003201417831521222464468666642766044146641933788836
8932452217321354860484353296131403821175862890998598653858373835628654351880
4806362231643082386848731052350115776715521149453708868428108303016983133390
0416365515466857004900847501644808076825638918266848964153626486460448430073
4909

RSA-1536

RSA-1536 has 1,536 bits (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 (1,559 bits), and has not been factored so far.

RSA-470 = 1705147378468118520908159923888702802518325585214915968358891836980967539803
6897711442383602526314519192366612270595815510311970886116763177669964411814
0957486602388713064698304619191359016382379244440741228665455229545368837485
5874455212895044521809620818878887632439504936237680657994105330538621759598
4047709603954312447692725276887594590658792939924609261264788572032212334726
8553025718835659126454325220771380103576695555550710440908570895393205649635
76770285413369

RSA-480

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

RSA-480 = 3026570752950908697397302503155918035891122835769398583955296326343059761445
7144169659817040125185215913853345598217234371231338324773210726853524776378
4105186549246199888070331088462855743520880671299302895546822695492968577380
7067958428022008294111984222973260208233693152589211629901686973933487362360
8129660418514569063995282978176790149760521395548532814196534676974259747930
6858645849268328985687423881853632604706175564461719396117318298679820785491
875674946700413680932103

RSA-490

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

RSA-490 = 1860239127076846517198369354026076875269515930592839150201028353837031025971
3738522164743327949206433999068225531855072554606782138800841162866037393324
6578171804201717222449954030315293547871401362961501065002486552688663415745
9758925793594165651020789220067311416926076949777767604906107061937873540601
5942747316176193775374190713071154900658503269465516496828568654377183190586
9537640698044932638893492457914750855858980849190488385315076922453755527481
1376719096144119390052199027715691

RSA-500

RSA-500 has 500 decimal digits (1,659 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 (2,048 bits) and has not been factored so far.

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

RSA-2048

RSA-2048 has 2,048 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 768 bits long (232 decimal digits), and the RSA-2048 may not be factorizable for many years to come, unless considerable advances are made in integer factorization

Integer factorization

or computational power in the near future.

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

External links

RSA Laboratories, The RSA Factoring Challenge.
Burt Kaliski
Burt Kaliski
Burton S. "Burt" Kaliski, Jr. is a cryptographer, director of the EMC Innovation Network at EMC Corporation since its 2006 acquisition of RSA Security...

(1991-03-18), RSA factoring challenge, the original challenge announcement on sci.crypt.
Steven Levy
Steven Levy
Steven Levy is an American journalist who has written several books on computers, technology, cryptography, the Internet, cybersecurity, and privacy.-Career:...

(March 1996), Wisecrackers in Wired News
Wired News
Wired News is an online technology news website, formerly known as HotWired, that split off from Wired magazine when the magazine was purchased by Condé Nast Publishing in the 1990s. Wired News was owned by Lycos not long after the split, until Condé Nast purchased Wired News on July 11, 2006...

. Has coverage on RSA-129.
Eric W. Weisstein, Mathematica package for RSA numbers.

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

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

See also

External links