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# 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 NumberDecimal digitsBinary digitsCash prize offeredFactored onFactored by
RSA-100100330 April 1991
RSA-110110364 April 1992
RSA-120120397 June 1993
RSA-129129426\$100 USDApril 1994Arjen K. Lenstra et al.
RSA-130130430 April 10 1996Arjen K. Lenstra et al.
RSA-140140463 February 2 1999Herman J. J. te Riele et al.
RSA-150150496 withdrawn but factored in 2004
RSA-155155512 August 22 1999Herman J. J. te Riele et al.
RSA-160160530 April 1 2003Jens Franke et al., University of Bonn
RSA-170170563 open
RSA-180180596 open
RSA-190190629 open
RSA-200200663 open
RSA-210210696 open
RSA-220220729 open
RSA-230230762 open
RSA-232232768 open
RSA-240240795 open
RSA-250250829 open
RSA-260260862 open
RSA-270270895 open
RSA-280280928 open
RSA-290290962 open
RSA-300300995 open
RSA-3093091024 open
RSA-3103101028 open
RSA-3203201061 open
RSA-3303301094 open
RSA-3403401128 open
RSA-3503501161 open
RSA-3603601194 open
RSA-3703701227 open
RSA-3803801261 open
RSA-3903901294 open
RSA-4004001327 open
RSA-4104101360 open
RSA-4204201393 open
RSA-4304301427 open
RSA-4404401460 open
RSA-4504501493 open
RSA-4604601526 open
RSA-4704701559 open
RSA-4804801593 open
RSA-4904901626 open
RSA-5005001659 open
RSA-576174576\$10,000 USDDecember 3, 2003Jens Franke et al., University of Bonn
RSA-6176172048 open
RSA-640193640\$20,000 USDopen
RSA-704212704\$30,000 USDopen
RSA-768232768\$50,000 USDopen
RSA-896270896\$75,000 USDopen
RSA-10243091024\$100,000 USDopen
RSA-15364631536\$150,000 USDopen
RSA-20486172048\$200,000 USDopen