Prime Number Crystallography
 

[url]https://www.quantamagazine.org/a-chemist-shines-light-on-a-surprising-prime-number-pattern-20180514/[/url]

[quote]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that was published in the Journal of Physics A in February, and two others co-authored with de Courcy-Ireland that have not yet been peer-reviewed — the researchers report that the primes, like crystals and unlike liquids, produce a diffraction pattern.[/quote]

But that's not the really interesting part. From [URL="http://iopscience.iop.org/article/10.1088/1742-5468/aad6be/meta"]one of the paper abstracts[/URL]:

[quote]Our analysis leads to an algorithm that enables one to predict primes with high accuracy.[/quote]

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?

[url]https://arxiv.org/pdf/1802.10498.pdf[/url]

That's the paper without the paywall.

Thanks, Wombatman. :smile:

[quote]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.[/quote]

Ouch. 10^6 is "not too large". But that means 10^1000000 probably is. :no:

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