Has there been any progress on the [Bouniakowsky conjecture](http://mathworld.wolfram.com/BouniakowskyConjecture.html)? In particular, has anyone been able to prove something for a particular polynomial - or for a class of them?


(I can't seem to find anything, but that could be due to the fact that there seem to be many ways of spelling Bouniakowsky.)



Progress on Bouniakowsky's Conjecture
It now goes by the name "Schinzel's Hypothesis H", which has a [Wikipedia entry](http://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H). A quantitative form is known as the "Bateman-Horn Conjecture", which also has a [Wikipedia entry](http://en.wikipedia.org/wiki/Bateman-Horn_conjecture).


Short answer: no progress, but better conjectures!


