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New Largest Known Prime Number: 2^57,885,161-1
An anonymous reader writes with news from Mersenne.org, home of the Great Internet Mersenne Prime Search: "On January 25th at 23:30:26 UTC, the largest known prime number, 257,885,161-1, was discovered on GIMPS volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, GIMPS — now in its 17th year — is the longest continuously-running global 'grassroots supercomputing' project in Internet history."
111 1111 1111 == 2047 == 23 * 89
Funny how many assertions here that number disproves
Your first question: "What has it added to the study of prime numbers?", I'm not sure but...
Your second question: "What use is that? (the study of prime numbers)"
Well... Nearly all modern public key cryptography (SSL / TLS / SSH etc.) is based on the asymmetry in time between the multiplication of two prime numbers (very fast operation) and the factorization of the result back into these two primes (very very slow: the goal being to make so slow that it become impractical to do).
Actually, it's "worse" than that: the "proof" that most modern PKCS crypto works is: "It's hard to find the (prime) factors of the product of two primes".
In other words: the study of prime numbers is one of the most important area of mathematics when it comes to computer security.