Assuming you can say two digits a second and have evolved beyond the need for food, sleep or a social life, the largest prime number ever discovered would take you more than four months to even say. So you'll forgive the Great Internet Merseene Prime Search project, the impressive minds behind the discovery, if they keep it short. Let's call it M74207281.
GIMPS discovered the prime number by multiplying 2 by itself 74,207,281 times and then subtracting 1. This obscenely large number, which you can peruse here (though it is a 44MB text document full of numbers) does little for the maths community other than continuing the never-ending exploration of every possible prime number out there. Curiously, the number was discovered using nothing more than an Intel Core i7 processor. It's the 49th prime number discovered since the search began in about 500 BCE.
The GIMPS project, located at the University of Central Missouri, beat out the previous record holder, discovered in 2013, by a cool 5 million digits. A video posted by YouTube user standupmaths breaks down the discovery and includes lengthy interview with the team's lead prof, Curtis Cooper.
Interestingly, the new prime number was actually discovered by the GIMPS machine on 17 September 2015, but it took almost four months for a flesh-and-blood researcher to notice they actually had something. Luckily, not even enough time passed between the mechanical discovery and the real one to say the 22 million prime number in its entirety.