Place the positive integers on the counterclockwise square spiral with 1 at (0,0), 2 at (1,0), and 3 at (1,1). Start at 1. From the current label x, move to an unvisited spiral cell y at minimum Euclidean distance among those for which x+y is composite. If several eligible cells have the same minimum distance, choose the one with the smallest label. Does the walk ever visit the cell labeled 2?