Chris Caldwell (caldwell@utm.edu) maintains a list called "The Largest Known Primes." Some of the ways to get this list are:
web: http://www.utm.edu/research/primes/largest.html
gopher: unix1.utm.edu, directory 1/user/Public_FTP/pub/math/primes
ftp: math.utm.edu, directory /pub/math/primes
Finger primes@math.utm.edu for a few record primes and the current
ways to get the lists. He would like to know of any new titanic
primes (over 1000 digits) so that he can add them to his list.