In the meantime, Terence Tao started a polymath blog here, where he initiated four discussion threads (1, 2, 3 and 4) on deterministic ways to find primes (I’m not quite sure how that’s proceeding — the last post was on August 28, 2009). (UPDATE: A new post (thread 5) was put up shortly after I published my blog post).
It remains to be seen whether any of these projects are able to reach successful conclusions or make substantial inroads into the problem. If there is another success for a polymath project, then that would be a major booster to the idea of polymath projects. Otherwise, it might raise the question of whether the unexpected degree of success of the first polymath project led by Gowers (which aimed for, and got, an elementary proof of the density Hales-Jewett theorem) was an anomaly.