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Encyclopedia > RSA number

The RSA numbers, listed by security company RSA Security, are certain large semiprime numbers (i.e., numbers with exactly two prime factors); they form the basis of the RSA Factoring Challenge, in which factorisations for these numbers are sought. Cash prizes have been offered for successful factorisations of RSA-576 to RSA-2048. RSA Security is a NASDAQ-traded public company. ... In mathematics, a semiprime (also called biprime or 2-almost prime) is a natural number that is the product of two (not necessarily distinct) prime numbers. ... In number theory, the prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving a remainder. ... The RSA Factoring Challenge is 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. ... This article is about the mathematical concept. ...


The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits; later, however, beginning with RSA-576, binary digits are counted instead. An exception to this is RSA-617, which was created prior to the change in the numbering scheme. Decimal, or less commonly, denary, usually refers to the base 10 numeral system. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ...


The mathematics

Let n be a RSA Number. There are prime numbers p and q such that In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are one and itself. ...

n = pq.

The problem is to find these two primes, given only n.


Let s be p + q; then the values of some basic arithmetic functions are In number theory, an arithmetic function (or number-theoretic function) f(n) is a function defined for all positive integers and having values in the complex numbers. ...

d(n) = 2
φ(n) = (p − 1)(q − 1) = n + 1 − s
σ(n) = (p + 1)(q + 1) = n + 1 + s.

The prizes and records

The following table gives an overview over all RSA numbers:

RSA Number Decimal digits Binary digits Cash prize offered Factored on Factored by
RSA-100 100 330   April 1991  
RSA-110 110 364   April 1992  
RSA-120 120 397   June 1993  
RSA-129 129 426 $100 USD April 1994 Arjen K. Lenstra et al.
RSA-130 130 430   April 10, 1996 Arjen K. Lenstra et al.
RSA-140 140 463   February 2, 1999 Herman J. J. te Riele et al.
RSA-150 150 496   withdrawn but factored in 2004
RSA-155 155 512   August 22, 1999 Herman J. J. te Riele et al.
RSA-160 160 530   April 1, 2003 Jens Franke et al., University of Bonn
RSA-170 170 563   open
RSA-180 180 596   open
RSA-190 190 629   open
RSA-200 200 663   May 2005 Jens Franke et al., University of Bonn
RSA-210 210 696   open
RSA-220 220 729   open
RSA-230 230 762   open
RSA-232 232 768   open
RSA-240 240 795   open
RSA-250 250 829   open
RSA-260 260 862   open
RSA-270 270 895   open
RSA-280 280 928   open
RSA-290 290 962   open
RSA-300 300 995   open
RSA-309 309 1024   open
RSA-310 310 1028   open
RSA-320 320 1061   open
RSA-330 330 1094   open
RSA-340 340 1128   open
RSA-350 350 1161   open
RSA-360 360 1194   open
RSA-370 370 1227   open
RSA-380 380 1261   open
RSA-390 390 1294   open
RSA-400 400 1327   open
RSA-410 410 1360   open
RSA-420 420 1393   open
RSA-430 430 1427   open
RSA-440 440 1460   open
RSA-450 450 1493   open
RSA-460 460 1526   open
RSA-470 470 1559   open
RSA-480 480 1593   open
RSA-490 490 1626   open
RSA-500 500 1659   open
RSA-576 174 576 $10,000 USD December 3, 2003 Jens Franke et al., University of Bonn
RSA-617 617 2048   open
RSA-640 193 640 $20,000 USD open
RSA-704 212 704 $30,000 USD open
RSA-768 232 768 $50,000 USD open
RSA-896 270 896 $75,000 USD open
RSA-1024 309 1024 $100,000 USD open
RSA-1536 463 1536 $150,000 USD open
RSA-2048 617 2048 $200,000 USD open

In mathematics, RSA-100 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... 1991 is a common year starting on Tuesday of the Gregorian calendar. ... In mathematics, RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... 1992 is a leap year starting on Wednesday of the Gregorian calendar. ... In mathematics, RSA-120 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... 1993 is a common year starting on Friday of the Gregorian calendar and marked the Beginning of the International Decade to Combat Racism and Racial Discrimination (1993-2003) Events Media:January January 1 - Czechoslovakia divides. ... In mathematics, RSA-129 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... 1994 was a common year starting on Saturday of the Gregorian calendar, and was designated the International year of the Family. ... In mathematics, RSA-130 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... April 10 is the 100th day of the year in the Gregorian calendar (101st in leap years). ... 1996 is a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ... In mathematics, RSA-140 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... February 2 is the 33rd day of the year in the Gregorian Calendar. ... 1999 is a common year starting on Friday of the Common Era, and was designated the International Year of Older Persons by the United Nations. ... Herman J. J. te Riele is a mathematician at Centrum voor Wiskunde en Informatica in Amsterdam with a specialisation in algorithms in discrete tomography, factorization of large numbers, cryptography in number fields, amicable numbers. ... In mathematics, RSA-150 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-155 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... August 22 is the 234th day of the year in the Gregorian Calendar (235th in leap years), with 131 days remaining. ... 1999 is a common year starting on Friday of the Common Era, and was designated the International Year of Older Persons by the United Nations. ... Herman J. J. te Riele is a mathematician at Centrum voor Wiskunde en Informatica in Amsterdam with a specialisation in algorithms in discrete tomography, factorization of large numbers, cryptography in number fields, amicable numbers. ... In mathematics, RSA-160 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... April 1 is the 91st day of the year (92nd in leap years) in the Gregorian calendar, with 274 days remaining. ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January January 1 - Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... The main building, viewed from the Hofgarten. ... In mathematics, RSA-170 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-180 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-190 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-200 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... May is the fifth month of the year in the Gregorian Calendar and one of seven Gregorian months with the length of 31 days. ... 2005 is a common year starting on Saturday of the Gregorian calendar. ... The main building, viewed from the Hofgarten. ... In mathematics, RSA-210 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-220 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-230 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-232 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-240 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-250 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-260 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-270 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-280 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-290 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-300 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-309 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-310 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-320 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-330 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-340 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-350 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-360 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-370 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-380 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-390 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-400 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-410 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-420 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-430 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-440 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-450 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-460 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-470 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-480 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-490 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-500 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-576 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... December 3 is the 337th (in leap years the 338th) day of the year in the Gregorian calendar. ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January January 1 - Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... The main building, viewed from the Hofgarten. ... In mathematics, RSA-617 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... In mathematics, RSA-640 is one of the RSA numbers - large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-704 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-768 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-896 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-1024 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-1536 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ... In mathematics, RSA-2048 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... The United States dollar is the official currency of the United States. ...

External links


  Results from FactBites:
 
RSA Number -- from Wolfram MathWorld (885 words)
RSA numbers are composite numbers having exactly two prime factors (i.e., so-called semiprimes) that have been listed in the Factoring Challenge of RSA Security® and have been particularly chosen to be difficult to factor.
While RSA numbers are much smaller than the largest known primes, their factorization is significant because of the curious property of numbers that proving or disproving a number to be prime ("primality testing") seems to be much easier than actually identifying the factors of a number ("prime factorization").
RSA Laboratories sponsors the RSA Factoring Challenge to encourage research into computational number theory and the practical difficulty of factoring large integers, and because it can be helpful for users of the RSA encryption public-key cryptography algorithm for choosing suitable key lengths for an appropriate level of security.
RSA Security - The RSA Factoring Challenge FAQ (1174 words)
The RSA Factoring Challenge is an effort, sponsored by RSA Laboratories, to learn about the actual difficulty of factoring large numbers of the type used in RSA keys.
Clearly, the factoring of a challenge-number of specific length does not mean that the RSA cryptosystem is "broken." It does not even mean, necessarily, that keys of the same length as the factored challenge number must be discarded.
The RSA challenge numbers were generated using a secure process that guarantees that the factors of each number cannot be obtained by any method other than factoring the published value.
  More results at FactBites »


 
 

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