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.

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:

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RSA-150	150	496		withdrawn but factored in 2004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		open
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

External links

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