What are the largest primes that we know of?

Greatest Prime Number that ever found by Human Being :-  

                 The largest known primes are ones of the form (2^m - 1). The reason is that there exist efficient ways to test whether such numbers are prime. Primes of this type are called aMersenne primes.

As of Sept 2010, the largest known primes were 

2^43,112,609 - 1 

2^42,643,801 - 1 

2^37,156,667 - 1 

                 The largest is over 2 million digits long! These primes were all discovered in the last 3 years; the search for large primes has accelerated with the help of several hundred people across the internet in a project called GIMPS [the Great Internet Mersenne Prime Search].