In defense of Kustaanheimo’s approach it must be said that the connections between infinite and finite models are usually far more complex than one expects. A finite model is not merely a scaled-down version of an infinite model. Very often a different structure appears.  As an analogy take the (infinite set of) natural numbers. Take a finite part, say the numbers 1 up to \(L\). In the finite case it makes sense to talk about small and large numbers compared to \(L\).  This is classically not possible. So one finds additional structure.  Metaphorically speaking, by making things finite, a more detailed or “fine-grained” structure appears, that is wiped out in the presence of infinities. Perhaps the distinction between “good” and “bad” geometrical objects is such an additional feature that disappears in the classical Euclidean model.  Thus perhaps the prime numbers do have a significance. But still the question remains: is this a new sort of Pythagoreanism? More details about Kustaanheimo’s approach are to be found in the supplementary document: Finite Fields as Models for Euclidean Plane Geometry.