
New record prime (GIMPS): 2^{82,589,933}1 with 24,862,048 digits by P. Laroche, G. Woltman, A. Blosser, et al. (7 Dec 2018). 

What is small? Depends on your
context, but since this site focuses on titanic primes (those with more than
1000 digits), any prime with less than 1000 digits is small. Here we
provide lists of the first fifty million primes as well as a few hundred proven
small primes (10300 digits or so) to test various algorithms.

Another prime page by Chris K. Caldwell <caldwell@utm.edu> 