
New record prime: 2^{74,207,281}1 with 22,338,618 digits by Cooper, Woltman, Kurowski, Blosser & GIMPS (7 Jan 2016). 

When designing algorithms, sometimes we need a list of the primes just less than a power of two. For example, we might need the largest 64 bit prime for a random number generator. Below we list links to lists of these primes. 
Another prime page by Chris K. Caldwell <caldwell@utm.edu> 