6 ms·

Uncovering multiscale order in the prime numbers via scattering

36 points by skor 8y ago

MeteorMarc 8y ago
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?
- adrianN 8y ago
  The sequence of primes contains arithmetic progressions of any length https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem
- benwills 8y ago
  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.
  - rocqua 8y ago
    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.
selimthegrim 8y ago
I believe there was a popular exposition of this: https://www.quantamagazine.org/a-chemist-shines-light-on-a-surprising-prime-number-pattern-20180514/ https://www.quantamagazine.org/a-chemist-shines-light-on-a-s...
- deleted 8y ago
  [deleted]
- dang 8y ago
  It was posted here: https://news.ycombinator.com/item?id=17067821 https://news.ycombinator.com/item?id=17067821
eternalban 8y ago
You can access the paper on arxiv: https://arxiv.org/abs/1802.10498 https://arxiv.org/abs/1802.10498
aj7 8y ago
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.
- sidcool 8y ago
  6n+1 or 6n-1, easier to remember.
  - DavidSJ 8y ago
    6n±1, even easier. ;)
- posterboy 8y ago
  > 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.
amvalo 8y ago
This is just re-inventing sieve theory with physics jargon.
- frozenport 8y ago
  "leading scientists take Fourier transform of numbers, impress unqualified reviewers with 3d renderings"

36 points by skor 8y ago

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?

adrianN 8y ago
The sequence of primes contains arithmetic progressions of any length https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem
benwills 8y ago
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.
- rocqua 8y ago
  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.

selimthegrim 8y ago

I believe there was a popular exposition of this: https://www.quantamagazine.org/a-chemist-shines-light-on-a-surprising-prime-number-pattern-20180514/ https://www.quantamagazine.org/a-chemist-shines-light-on-a-s...

deleted 8y ago
[deleted]
dang 8y ago
It was posted here: https://news.ycombinator.com/item?id=17067821 https://news.ycombinator.com/item?id=17067821

eternalban 8y ago

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

aj7 8y ago

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.

sidcool 8y ago
6n+1 or 6n-1, easier to remember.
- DavidSJ 8y ago
  6n±1, even easier. ;)
posterboy 8y ago
> 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.

amvalo 8y ago

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

frozenport 8y ago
"leading scientists take Fourier transform of numbers, impress unqualified reviewers with 3d renderings"