Some Number Theory Links

[the following was added May 2001]
RSA Security, has revamped its Factoring Challenges.

Prizes now start at US$10,000 (factorization of a 576 bit modulus) to US$200,000 (factorization of a 2048 modulus).

RSA and its predecessor companies have been sponsoring factorization challenges for many years, but until now the prize money has been nominal. It is hoped that the increased bounties will draw more people to the field, and spur new research.

For details, including the challenge numbers, see:

Peter Trei, Cryptoengineer, RSA Security Inc.,

Breaking News (in November of 2000):  233-digit SNFS factorization

The Cabal announces the completion, on November 14, 2000, of the factorization with the Special Number Field Sieve(SNFS) of the 233-digit Cunningham number  2^773 + 1 into the product the numbers 3 and 533371 and three primes of  55, 71, and 102 digits, respectively. This establishes a new record for the Special Number Field Sieve.  [Note that this is somewhat easier to factor than a number of this size which is the product of only two primes of approximate equal size.  In this case the 3 and 533371 factors were easy to find.  And the remaining factor has the small 55-digit and 71-digit primes.]

The sieving was done on about 150 SGI workstations and Sun workstations and servers running at 180-450 MHz, and on about 100 PCs running at 266-600 MHz. The sieving took about five calendar months. It was started mid-April, 2000, and finished on September 15, 2000. Total sieving time was 57.4 CPU years.

The previous SNFS record was the 211-digit repunit number 10,211- = (10^211 - 1)/9, factored on April 8, 1999, also by the Cabal.

Factorization details are available from:

Maple Worksheets: Students may download the following Maple worksheets. To do so hold down the right mouse button (on a Mac just hold down the single mouse button) the select Download file to disk or Save file to Disk. Then you should be able to open the file with Maple. You might open Maple first and then while in Maple choose Open from the File menu item.

RSA Examples with Maple
Maple Introduction for Number Theory