Lists of small primes 
(Another of the Prime Pages' resources)
 New record prime: 274,207,281-1 with 22,338,618 digits by Cooper, Woltman, Kurowski, Blosser & GIMPS (7 Jan 2016).


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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 (10-300 digits or so) to test various algorithms.
The Prime Pages
Another prime page by Chris K. Caldwell <caldwell@utm.edu>