I’m hardly a math genius, but isn’t this basically because he’s using polar coordinates, where nearly any trend is going to look like curves and spirals?
The primes >3 are all of the form 6k+1 or 6k-1, so they are close to 6k. As k increases, the resulting marks on the polar coordinate system form nearly complete turns because 6 is close to 2 pi. Hence, spirals. See my other comment for a clearer explanation of why primes >3 all must necessarily be one more or one less than a factor of 6k where k is an integer. That is the crucial piece that the author did not make totally clear.
Hence the video making it extremely clear pretty much right off the bat that yes, any integer plotted that way will form a spiral. The video then goes into a very interesting discussion IMO into why you see the specific patterns of spirals and rays with the primes.
