happyglucky

"there's no connection between spirals and prime numbers"

You just shot yourself in the foot :( Yes, there is a connection. If you add up the total distance each line makes in a tick, its equivalent to the harmonic series, which is a special case of the zeta function. This is where the spiral comes from. Its a dirct consequence of the fact that each number has period 1/n. The spiral emerges naturally, its not programmed or forced into that shape.

A number of very elementary things. It gives a very intuitive visualization of twin primes, as they lie before and after highly composite numbers (which are also easily visualized), as well as a visual explanation for why the prime gaps tend to increase, as larger numbers are likely to collide with a factor. You can also use it to explain prime factors, least common multiples up to N (when the first N lines come into alignment), and the cyclical nature of factors in general. This is a creative pedagogical tool, not a breakthrough in number theory.

Visualizations aren't meant to highlight anything new, but rather to bring to light and visualize what is already known.

I'd just take my shoe off, throw it up in the air while spinning it, and use the wall it ends up pointing to.