Hey, check this out, the newest prime number found today! http://story.news.yahoo.com/news?tm.../ap/20031211/ap_on_hi_te/biggest_prime_number
Cool! Just like most other very large prime numbers, this is also a Mersenne-prime: [tex]2^p-1[/tex] with [tex]p[/tex] itself prime. In this case [tex]2^{20996011}-1[/tex] was proven to be prime. Zero practical application, but very cool.
Very interesting indeed. I learned about Mersenne primes in a discrete math class this semester. It's amazing how hundreds of people worldwide are joined into finding out bigger and bigger prime numbers for well no reason at all except the fact of self enjoyment. Very cool stuff.