So, is the required centripetal force larger for large radius or small radius?
Careful, you better not use F=mv2/r, since the tangential speed is different for nuts at different radius for this scenario. So it is not clear whether smaller r (and smaller v) requires larger (or smaller) F.
Use F=mrω2 instead, since in this scenario, all the nuts have the same angular velocity ω. Then it becomes clear that at the same ω, the outer nuts doing circular motion with a larger r require a larger centripetal force compared to the inner nuts. Outer nuts skid first.
In fact, if one is situated right at the middle, no centripetal force is required at all. This explains why the bean at the middle had the last laugh.