Twin Primes: Case closed?

It seems the conjecture that there are an infinite number of twin primes (twin primes are two prime numbers separated by 2, like 3 and 5) has been proved. While the proof is not published yet, the reviewers feel that the authors got it right this time. They had thought they had it right a few years ago, but made a mistake. Now, it seems, the conjecture is proved.

This is quite fascinating if for no other reason that there you can make arbitrarily long sequences of numbers where none are prime. Yet, there are infinitely many prime pairs. Pretty cool, eh?