Goldston-Yildrim theorem

Since there seems to be some degree of interest on this list for this
sort of thing, I will mention that my buddy Danny Goldston together
with Cem Yildirim of Turky have proven the prime gap conjecture, which
now becomes the Goldston-Yildrim theorem. This tells us that if G(p) is
the gap between the prime p and the next prime above it, then

lim inf G(p)/log(p) = 0

This is quite a ways yet from the twin primes conjecture, which Danny
and just about everyone else thinks is true, but it is a major step
forward.