At Inkling Markets, you can bet on which of the seven Millennium Problems will be solved first.
The choices include the option "none", which is defined as "All problems will resist a solution indefinitely."; I'm not sure who would bet on that, because "indefinitely" means no one will ever be able to claim the prize.
I wonder about the efficiency of prediction markets when most of the people involved don't know what they're talking about. People talk about "the wisdom of crowds". But do the crowds need to be at least somewhat informed? And are the people who will take part in this particular prediction market informed enough as to not be totally worthless? (I suspect, for example, that people will vote for the problem they've heard of; the story of Perelman's proof of the Poincare conjecture was pretty widely distributed in the media about a year ago. It was overshadowed by the Pluto-isn't-a-planet story which broke around the same time, though.)
Incidentally, I'd bet on Poincare, for the obvious reason that Perelman came up with a proof! The CMI hasn't announced that they're giving him the prize yet, because there's a certain waiting period involved in order to make sure that the proof becomes widely accepted, but clearly that's the one furthest along the pipeline.
So in this particular case, the fact that people have heard of the Poincare conjecture is probably because of its connection to these prizes and the proposed proof.
A more interesting prediction market would be for the second Millennium Prize to be claimed.