A "twin prime" is a pair of prime numbers that differ by two. For example, 11 and 13, or 857 and 859. The "twin prime conjecture" states that there are an infinite number of twin primes. To this day, nobody has ever been able to prove this. It's one of the great open conjectures of number theory.
Recently, however, an unknown mathematician proved a theorem that, according to the experts, is almost the same thing. It turns out that there are an infinite number of prime pairs that differ by some number N. And what is N? We still don't know, but Yitang Zhang of the University of New Hampshire has demonstrated that it's less than 70 million.
This is why I love number theory. I mean, what's a difference of 69,999,998 between friends? Also this:
Without communicating with the field’s experts, Zhang started thinking about the problem. After three years, however, he had made no progress. “I was so tired,” he said. To take a break, Zhang visited a friend in Colorado last summer. There, on July 3, during a half-hour lull in his friend’s backyard before leaving for a concert, the solution suddenly came to him. “I immediately realized that it would work,” he said.
Isn't that just perfect?