[ramshorns]

The comparison to a spiral with random points plotted doesn't seem to be enough to show that this is a pattern in the primes. It would be interesting to see, say, a spiral with everything that's not a multiple of 2 or 3 plotted. Maybe the spiral of primes just looks like it has a pattern because it's a subset of that.

[excessive]

Yes, that's very much what the video goes into. For any rational approximation of 2 pi, say 22/7, you won't get lines at multiples of 2 or multiples of 11.