I agree that comments are likely to cause more trouble than good. In general I think arxiv should just stick to what works. One thing that should be improved is transparency. From what I’ve understood (I don’t have personal experience with this), some papers get rejected from arxiv and even some people blacklisted with no explanation. It’s important to do at least some sort of crackpot-filtering, but the mostly anonymous moderators sometimes seem to be a bit to eager in that.

]]>I plotted the Hilbert one because it does have a regular iteration algorithm, so it was not clear to me whether or not some pattern could occur.

Another line of thought (not related to space-filling curves, just to prime patterns) is to see what genetic algorithms can manage to generate. There has been one interesting attempt by James Alfred Walker and Julian Francis Miller using Cartesian Genetic Programming. There’s room for a lot of improvements and nice prime-generating algorithms there too I think.

]]>I think one of the [many] mysterious reasons that we get Ulam’s patterns for spirals is that Ulam’s and similar spirals are space feeling curves regular enough to rule out a group of non-primes (such as complete squares) on some geometric patterns in the 2D space and and thus leave other regions more likely for the prime numbers.

Then to see similar patterns we need some other space filling curves (and not Peano / Hilbert) that can capture repeatetive behavior to spot and rule out at least a subset of non-primes on a diagonal or another curve.

What are your thoughts on that?

]]>Stephen Smale.

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