This leads me to a question: Do mathematicians actually try to analyze primes by looking at a function that is created by combining a set of sine waves where there is one sine wave for each integer, on order to form a sieve out of the sine waves? E.g., creating a function that crosses zero only at each composite, or some such? Or is this visualization only suggestive of a broad approach?
The paper cited by the visualization is clearly attempting to do what I just described, but it appears to be the work of an amateur, and I don't read Spanish, so I can't really tell if this approach is on sound footing. I tried to Google around looking for this approach referenced in something more authoritative, but couldn't find any. I did find plenty of references to trying to analyze the function that you get from subtracting x/ln(x) from the prime staircase, using Fourier transforms and the like. But I can't see a direct connection between these approaches, other than the general inspiration of trying to break the problem down into a combination of sine waves. On the other hand, I'm well aware that a lot of identities in math are not readily obvious!