Take 17 minutes out of your day and watch Adam Spencer talk about the largest known prime (found in January of 2013). Amazingly engaging.

http://www.ted.com/talks/adam_spencer_why_i_fell_in_love_with_monster_prime_numbers.html

They’re millions of digits long, and it takes an army of mathematicians and machines to hunt them down — what’s not to love about monster primes? Adam Spencer, comedian and lifelong math geek, shares his passion for these odd numbers, and for the mysterious magic of math.