The Polymath4 Project is now underway, with the first formal post here.
The basic problem is very simple and appealing: it’s to find a deterministic algorithm which will quickly generate a prime of at least some given length, ideally in time polynomial in that length. There are fast algorithms which will generate such a prime with high probability – cryptography algorithms like RSA wouldn’t work if that weren’t true. But there’s no known deterministic algorithm.
I’m going to miss the first week of the project – I’ll be camping in a field in the Netherlands, surrounded by 1000+ hackers. But I’m looking forward to catching up when I come back.
On a related note, John Baez asks what mathematicians need to know about blogs.