Large Prime

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.

REFERENCES:

Lifchitz, H. and Lifchitz, R. "PRP Records: Probable Primes Top 10000."

Moore, P. "Welcome to 'Five or Bust!' " Oct. 8, 2009. https://www.mersenneforum.org/showthread.php?t=10754.