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The Prime Page Chris K. Caldwell's page on primes, especially large ones, with lots of links to related information and software.
Links to Sites Concerned with Prime Numbers and Number Theory, by Peter Meyer. You may also be interested in his Factorizer and Prime Number Spiral software.
The Great Internet Mersenne Prime Search (GIMPS) A group dedicated to using the resources of the net to find Mersenne primes and to solve other computationally intensive problems in number theory. Mersenne Primes, Golomb rulers, RC5 hacking, etc.
Gnu Multiple Precision Arithmetic Library Documentation for a portable collection of routines for manipulating large numbers. Very fast routines for a variety of platforms.
The New RSA Factoring Challenge RSA is offering prizes for factoring large numbers suitable for encryption keys.
Note: The RSA Factoring Challenge has been re-defined (hence the "New"), and the Partition numbers challenge has been discontinued. The links below are provided only for historical interest. For information on the RSA Factoring Challenge, visit the link above.
DES Challenge Coordinated Effort page This is another group that participated in the DES challenge, but didn't win.
Some references:
- [Bre89] D.M. Bressoud. Factorization and Primality Testing. Springer-Verlag, 1989.
- [Knu81] D.E. Knuth. The Art of Computer Programming, volume 2, Seminumerical Algorithms. Addison-Wesley, 2nd edition, 1981.
- [Kob94] N. Koblitz. A Course in Number Theory and Cryptography. Springer-Verlag, 1994.
- [Len87] H.W. Lenstra Jr. Factoring integers with elliptic curves. Annuals of Mathematics., 126: 649-673, 1987.
- [LL90] A.K. Lenstra and H.W. Lenstra Jr. Algorithms in number theory. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 673-715, MIT Press/Elsevier, Amsterdam, 1990.
- [Pol74] J. Pollard. Theorems of factorization and primality testing. Proceedings of Cambridge Philosophical Society, 76: 521-528, 1974.
- [Pol75] J. Pollard. Monte Carlo method for factorization. BIT, 15: 331-334, 1975.
- [BLP94] J.P. Buhler, H.W. Lenstra, and C. Pomerance. The development of the number field sieve. Volume 1554 of Lecture Notes in Computer Science, Springer-Verlag, 1994.
- [BLZ94] J. Buchmann, J. Loho, and J. Zayer. An implementation of the general number field sieve. In Advances in Cryptology - Crypto '93, pages 159-166, Springer-Verlag, 1994.
- [Sil87] R.D. Silverman. The multiple polynomial quadratic sieve. Mathematics of Computation, 48: 329-339, 1987.
- [DL95] B. Dodson and A.K. Lenstra. NFS with four large primes: An explosive experiment. In Advances in Cryptology Crypto '95, pages 372-385, Springer-Verlag, 1995.
- [LLM93] A.K. Lenstra, H.W. Lenstra Jr., M.S. Manasse, and J.M. Pollard. The factorization of the ninth Fermat number. Mathematics of Computation, 61(203): 319-349, 1993.
- [BLS88] J. Brillhart, D.H. Lehmer, J.L. Selfridge, B. Tuckerman, and S.S. Wagstaff Jr. Factorizations of bn ± 1, b = 2,3,5,6,7,10,11,12 up to High Powers. Volume 22 of Contemporary Mathematics, American Mathematical Society, 2nd edition, 1988.
- [BBC88] P. Beauchemin, G. Brassard, C. Crepeau, C. Goutier, and C. Pomerance. The generation of random numbers that are probably prime. Journal of Cryptology, 1: 53-64, 1988.
- [Riv91a] R.L. Rivest. Finding four million random primes. In Advances in Cryptology - Crypto '90, pages 625-626, Springer-Verlag, 1991.
- [BD93b] J. Brandt and I. Damgard. On generation of probable primes by incremental search. In Advances in Cryptology - Crypto '92, pages 358-370, Springer-Verlag, 1993.