
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). 

The Prime Pages have a variety of information related to primes. This includes (perhaps unbelievably) methods to listen to primes and prime factorizations, which I am attempting to index here. 
Another prime page by Chris K. Caldwell <caldwell@utm.edu> 