Do you recall the remarkable paper by Zhang proving that there are infinitely many pairs of primes that differ by at most 70 million? Well, thanks to work by Terence Tao and others, that bound of 70 million has been pushed down to just 12012. This website tracks the progress on that upper bound: http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_pri...