Uncovering multiscale order in the prime numbers via scattering

iopscience.iop.org

36 points·skor··12 comments

Very suspicious of the whole line of this work. Suspect that the “Bragg peaks” are trivial. For instance all primes > 3 are in the form 6n + 1 or 6n + 5.

> For instance all primes > 3 are in the form 6n + 1 or 6n + 5.

Really? This should have implications for the 3n+1 problem -- the Collatz Conjecture.

6n+1 or 6n-1, easier to remember.

6n±1, even easier. ;)

You can access the paper on arxiv: https://arxiv.org/abs/1802.10498

I believe there was a popular exposition of this:

https://www.quantamagazine.org/a-chemist-shines-light-on-a-s...

It was posted here: https://news.ycombinator.com/item?id=17067821

I did not really study the article, but from the abstract: is is not to be expected to find semi-regular subseries in an infinite series of prime numbers?

The sequence of primes contains arithmetic progressions of any length

https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem

From the abstract: "Our analysis leads to an algorithm that enables one to predict primes with high accuracy."

From my very, very basic understanding of/curiosity with primes, predicting primes with any sort of accuracy has been elusive. If this does, in fact, help to predict primes, it opens up all sorts of possibilities. That's my guess as to the importance of this article.

I dont have access to the article, but I imagine 'high' is a relative term. In general, the density of primes arround n is roughly 1/log n; if you could do significantly better than that say 1/sqrt(log n) you could call that high accuracy.

Meanwhile, the actual probability of predicting a prime would still be very low. Note that I am only speculating here.

This is just re-inventing sieve theory with physics jargon.

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