*This page is still heavily under construction. It will have lots
of links to the very rich web of factorization sites RSN, honest!*

My most recent publications are:

*NFSNET - the first year and the next year*, EIDMA-CWI Workshop on Factoring Large Numbers, Utrecht, Dec 12 2003.
Slides and notes are available in PowerPoint format

*Factoring Estimates for a 1024-bit RSA-Modulus*, AK Lenstra, E Tromer,
A Shamir, W Kortsmit, B Dodson, J Hughes & PC Leyland, Asiacrypt 2003, **LNCS
2894 **(2003)

*MPQS with Three Large Primes*, PC Leyland, AK Lenstra, B Dodson,
A Muffett & SS Wagstaff,
Proceedings of the ANTS-V conference in Sydney 2002, LNCS2369.
The paper (which is
(c) Springer-Verlag), is available in PostScript
and PDF format. The slides shown in Sydney are available in
PowerPoint format.

Classes of numbers I've done work on include

- Cunningham numbers
- Homogeneous Cunninghams (numbers of the form
*a*±^{n}*b*)^{n} - (Generalized) Cullen and Woodall numbers
- factorials ± 1 (My tables of factors of N!+1 and N!-1 go only as far as N = 400.)
- the HP(49) problem
- Mersenne numbers, which all take the form 2
^{n}-1. The Cunningham 2- table contains small Mersenne numbers. My table has prime exponents up to 10000 and mersenne.org has*lots*more information on Mersenne numbers. - Numbers of the form
*x*+^{y}*y*.^{x}

Please take a look, too, at the NFSNET site. I and three other people have restarted the distributed project to factor integers by the Number Field Sieve. By June 2004, we have about 200 contributors who have factored Woodall(668).c204 and over a dozen Cunningham Most and More Wanted Numbers by SNFS. The 239-digit Mersenne number M811, also known as 2,811-.c239 was finished in early June. This one is one of the largest SNFS factorizations yet attempted anywhere.

Paul Zimmermann is running ECMNET which is another distributed factoring project. It uses Lenstra's Elliptic Curve Method to find relatively small (up to 55 digits or so) factors of integers. Many people run the programs "by hand". For those who prefer an easier life, Tim Charron wrote a client/server harness to ECMNET so that the computation may proceed without human intervention. The master server for this project is running on 62.236.152.54:8194. It is currently loaded up with the Brent-Montgomery-te Riele tables.

To my home page