Well, doesn't it make some sense given the utility of prime numbers in cryptography, that the NSA, or anyone else interested in breaking codes for that matter, would have simply dedicated a computer or two to the long-term project of determining all of the prime numbers under x bits long? Granted this would take a while, but the NSA has the time, the computers, and the other resources necessary to do this. Having all of these prime numbers would greatly reduce the effort necessary to crack PGP/RSA-type cryptosystems which rely on prime numbers. It would reduce the number of factors a brute-force attack would have to check dramatically. Or am I completely off-base?

Mephisto

Quoting from the FAQ (Bruce Schneier's "Applied Cryptography") pp. 213: 1. If everyone needs prime numbers, won't we run out? No, Santa would never run out of prime numbers for all the good little boys and girls. In fact, there are over 10^150 primes of length 512 bits or less. (For numbers of size N, the probability that a random number is prime is one in log N.) There are only 10^84 atoms in the universe. [...] Go directly to your bookstore, do not pass GO, do not collect $200 (you only need about $50, including tax) and buy this book. -- ---------------- /\ Douglas Barnes cman@illuminati.io.com / \ Chief Wizard (512) 447-8950 (d), 447-7866 (v) / () \ Illuminati Online metaverse.io.com 7777 /______\