The largest known prime numbers are Mersenne primes, the largest of these known as of September 2013 bing 
, which has a whopping 
decimal digits.
As of Sep. 2013, the largest known probable primes are the Wagstaff primes 
and 
, both found by R. Propper in Sep. 2013
and which have 
and 
decimal digits, respectively.
Other large known probable primes are the "dual Sierpinski numbers" 
(Moore 2009) given by 
and 
, which have 
and 
decimal digits, respectively.
A prime with at least 1000 decimal digits is (or used to be) known as a titanic prime.
