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. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100 decimal digit number called RSA-100 was factored in a few days, but many of the bigger numbers have still not been factored and are expected to remain so for quite some time. RSA Security is a NASDAQ-traded public company. ... March 18 is the 77th day of the year in the Gregorian calendar (78th in leap years). ... 1991 is a common year starting on Tuesday of the Gregorian calendar. ... In mathematics, computational number theory is a study of number theory with the aid of computer powers. ... In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. ... The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ... 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. ... In mathematics, RSA-100 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ...

This challenge is intended to track the state of the art in integer factorisation. A primary application is for choosing the key length of the RSA public-key encryption scheme. Progress in this challenge should give an insight into which key sizes are still safe and for how long. As RSA Laboratories is a provider of RSA-based products, the challenge is used by them as an incentive for the academic community to attack the core of their solutions — in order to prove its strength. In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ... In cryptography, RSA is an algorithm for public key encryption. ... PKC, see PKC (disambiguation) Public-key cryptography is a form of modern cryptography which allows users to communicate securely without previously agreeing on a shared secret key. ... In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ...

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 numeral system represents numeric values using two symbols, typically 0 and 1. ...

The mathematics

Let n be a RSA Number. There are prime numbers p and q such that In mathematics, a prime number (or prime) is a natural number greater than one whose only 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.

The challenge numbers in pink lines are numbers expressed in base 10, while the challenge numbers in orange lines are numbers expressed in base 2, and for which a cash prize is still assigned.

Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus) to... 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. ... 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 was a leap year starting on Wednesday. ... 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). ... 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 Anno Domini (or the Current 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 Anno Domini (or the Current 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. ... 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-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. ... The main building, viewed from the Hofgarten. ... 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-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. ... Wikinews has a news story related to this article: Two hundred digit number factored In mathematics, RSA-200 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... May 9 is the 129th day of the year in the Gregorian Calendar (130th in leap years). ... 2005 is a common year starting on Saturday of the Gregorian calendar and is the current year. ... 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-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-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-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-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-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-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-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-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-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-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-617 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. ... 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. ...

See also

• The Magic Words are Squeamish Ossifrage, the solution found in 1993 to another RSA challenge posed in 1977
• RSA Factoring Challenge numbers list

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. ... 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). ... 1977 was a common year starting on Saturday (the link is to a full 1977 calendar). ...

External links

• RSA Security: The new RSA factoring challenge
• MathWorld: RSA Number
• Mathematica package for RSA numbers
• The original challenge announcement on sci.crypt