Does galactic evolution approximate the distribution of the prime numbers?

So, this question occurred to me after watching these two videos in quick succession and then doing some additional lit search, I apologize if my terminology is imprecise/inaccurate since this isn't my field but hopefully I can communicate my meaning here:

https://www.youtube.com/watch?v=Jm7omDy5_38

https://www.youtube.com/watch?v=EK32jo7i5LQ

We just learned that our models of galactic evolution were incorrect due to data from the JWST, and we currently don't know why galaxies form into spirals. What if galaxies actually just tend towards this shape over time because they are actually approaching exactly this distribution of the prime numbers when mapped onto polar coordinates? It even makes sense; every star has a gravitational influence on every other star in the galaxy, you would expect that their orbits would be influenced by resonance, they would naturally distribute based on approximating the distribution of the prime numbers which is necessarily the most chaotic pattern/the orientation with the highest entropy. Perhaps galaxies form spirals simply because they are following the 2nd law of thermodynamics, and the fact that you see four-armed spiral galaxies is exactly because of PNT sorting all the stars into four arms. In which case "dark matter" has actually always just been the 2nd Law. There may even be some relationship to the different spiral and elliptical galaxies we see and the shape of this plot of the prime numbers at different scales: at more "zoomed out" approximations you see a more elliptical shape and at more "zoomed in" approximations you see spirals with arms of different densities.