I posted further down in this thread about my puzzle http://www.loyalty.org/~schoen/rsa/ http://www.loyalty.org/~schoen/rsa/ which is nominally about a partic

I posted further down in this thread about my puzzle http://www.loyalty.org/~schoen/rsa/ http://www.loyalty.org/~schoen/rsa/ which is nominally about a particular vulnerability (common factor attacks), but actually if you're interested in this topic, I suggest that you read this piece and try to solve the puzzle, because you will really get a sense of the size of the numbers involved, and what particular kinds of arithmetic operations you have to do when using RSA. I even have a section about estimating the number of prime numbers of a particular size (e.g. 512-bit primes, which are the secrets associated with 1024-bit RSA public keys). As other people have said, the size of the numbers involved will make it impractical to list all of them or crack keys by brute force. My puzzle and the associated discussion might make that a little more concrete for you! (Although tptacek might also want you to know that RSA is obsolescent, and more modern cryptography does not actually use prime factorization, but rather other kinds of arithmetic problems.)