Prime Number Crystallography

[Ken_g6]

https://www.quantamagazine.org/a-che...tern-20180514/

But in three new papers — one by Torquato, Zhang and the computational chemist Fausto Martelli that was published in the Journal of Physics A in February, and two others co-authored with de Courcy-Ireland that have not yet been peer-reviewed — the researchers report that the primes, like crystals and unlike liquids, produce a diffraction pattern.

But that's not the really interesting part. From one of the paper abstracts:

Our analysis leads to an algorithm that enables one to predict primes with high accuracy.

So, what does that mean? I imagine it does not mean a new method of proving primes. Maybe it's an improvement on or supplement to sieving? Can somebody with both knowledge and access parse this for the rest of us?

[wombatman]

https://arxiv.org/pdf/1802.10498.pdf

That's the paper without the paywall.

[Ken_g6]

Thanks, Wombatman.

This analytical expression...enables us to reconstruct, in principle, a prime-number configuration within an arbitrary interval [M, M +L].... This leads to an algorithm to reconstruct primes in a dyadic
interval with high accuracy provided that nmax is sufficiently large and M is not too large.

Ouch. 10^6 is "not too large". But that means 10^1000000 probably is.

It might lead to a slightly faster small prime sieve, but probably not that either.