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.

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.

The mathematics

Let n be a RSA Number. There are prime numbers p and q such that

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

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:

External links

• RSA Security: The new RSA factoring challenge
• MathWorld: RSA Number
• Mathematica package for RSA numbers