Frequently asked questions about primes 
(from the Prime Pages' list of frequently asked questions)
 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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Here is a list of questions and answers for many of the frequently asked questions at this site.  If you have difficulty finding what you want, you might try searching through the site.
The Prime Pages
Another prime page by Chris K. Caldwell <caldwell@utm.edu>