Minimal Reduction

Minimal Reduction is a 8-stage geared reduction of 1-to-0.9999784. So the purple output turns almost as fast as the red input, but only the slightest bit slower. The reduction was designed with the following algorithm. Start with a gear with a maximum number of teeth, in this case 25 teeth. Take a gear that has one tooth fewer, in this case 24 teeth. This 25-to-24 is the first reduction stage. The rest of the algorithm is recursive. Copy the previous stage or set of stages, but reduce each gear by one tooth, and then cascade the two. The resulting gear ratio of the new set is the ratio between that of the previous set, and that of the one-tooth-fewer copy. The gearing ratio gets closer to 1-to-1 every recursive step, without ever actually becoming 1-to-1. The gear ratio of 1-to-0.9999784 is approximately 46347-to-46346. So for every 46347 turns of the red handle, the purple handle makes one turn fewer.

The mechanism raises two questions.
1) Does there exist an algorithm that creates a better minimal reduction, that is, same reduction with fewer gears and teeth?
2) What would be a useful application of a minimal reduction?

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