But the information is out there if you know to look for it and you look hard enough. The basics are in this note on MathForge. There's an interview with Dan Goldston in his hometown paper. And you can read the technical paper on Small gaps between primes or almost primes at ArXiv.org.
So what does the theorem actually say? It isn't that hard to explain. The prime number theorem states that the average gap between two consecutive primes pn and pn+1 is about log(pn), where "log" is the natural logarithm. But that is a very rough estimate. It is suspected that the gap can be as small as possible (two) infinitely often -- a proposition known as the twin prime conjecture. This is one of the most famous (to mathematicians) unsolved problems in number theory, right up there with the Riemann Hypothesis and Goldbach's conjecture.
The result that Goldston and colleagues have sought to prove is a little weaker. Symbolically it is that
lim infn→∞ (pn+1 - pn)/log(pn) = 0
What this says is that the ratio of the difference between the n+first prime and the nth prime to the natural logarithm of the nth prime is smaller than any positive number ε for infinitely many n, no matter how small ε is. Using the same notation, one could express the twin prime conjecture as
lim infn→∞ (pn+1 - pn) = 2
Exciting stuff, no? Well, it is to number theorists, anyhow.
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