No, it's not a distributed-computing thing; raw compute isn't the bottleneck. (That would only help if there were a need to check many machines that halt after a tractable-but-nontrivial number of steps; that's a narrow sweet spot, given the superexponential nature of the problem, and few machines of interest are believed to be in it.) Rather, it's a collaboration of human (mostly amateur) mathematicians chipping away at different parts of the problem.