Ben Green, of the Pacific Institute for Mathematical Sciences, and Terrance
Tao of UCLA, have established a remarkable result on the prime numbers, that
they contain arbitrairly long arithmetic progressions, and indeed, every
subset of the primes of postivie density also contain such progressions.
The paper is at the arXiv.
Ivars Peterson has a nice write up of it at Science News.
And also see Terrance Tao's What's New page for more background on how this
remarkable proof was found.