Largest prime number we can come up with?

It has been proven by Euclid that there are an infinite number of prime numbers. Thus there is no "largest prime number". However, many math professionals and hobbyists enjoy searching for large prime numbers. Since the 1950s, the largest known primes have been discovered by computer algorithms rather than by hand. As of September 2006, the largest known prime number, discovered by a collaborative effort known as GIMPS, is 232,582,657 - 1. This was confirmed to be a prime number on September 11, 2006. This number is 9,808,358 digits long and is the 44th known Mersenne prime. Its predecessor as largest known prime number, 230,402,457 - 1, was first shown to be prime on December 15, 2005 by GIMPS also.

No idea