Pattern to the Seemingly Random Distribution of Prime Numbers
September 21, 2018 5:30 PM Subscribe
Researchers discover a pattern to the seemingly random distribution of prime numbers.
A link to the paper.
There is talk of fractal patterns.
Should we abandon cryptography now?
posted by ChurchHatesTucker at 5:57 PM on September 21, 2018 [4 favorites]
posted by ChurchHatesTucker at 5:57 PM on September 21, 2018 [4 favorites]
“New findings about prime number distribution almost certainly irrelevant to cryptography”, according to Bruce Schneier today.
posted by traveler_ at 6:10 PM on September 21, 2018 [8 favorites]
posted by traveler_ at 6:10 PM on September 21, 2018 [8 favorites]
Asked and answered.
posted by ChurchHatesTucker at 6:14 PM on September 21, 2018 [5 favorites]
posted by ChurchHatesTucker at 6:14 PM on September 21, 2018 [5 favorites]
While we are talking about primes...there’s also this.
posted by nat at 6:18 PM on September 21, 2018 [1 favorite]
posted by nat at 6:18 PM on September 21, 2018 [1 favorite]
well, Cube 4 will be interesting, I guess.
posted by Scattercat at 6:29 PM on September 21, 2018 [3 favorites]
posted by Scattercat at 6:29 PM on September 21, 2018 [3 favorites]
It drives me crazy when papers don't define their most important terms. What is a structure factor? Who knows! *These* people aren't telling!
posted by dbx at 8:30 PM on September 21, 2018 [1 favorite]
posted by dbx at 8:30 PM on September 21, 2018 [1 favorite]
> While we are talking about primes...there’s also this.
In regard to Sir Michael Atiyah's claim that he's found a proof of the Riemann hypothesis, John Baez writes: "I predict it's not going to hold up. Atiyah's recent big claims, like his supposed proof that the 6-sphere admits no complex structures, have not been holding up. Everyone who knows him well has been too embarrassed to publicly discuss the reasons."
It gives me a very heavy heart to see such a great intellect falter, but... I would urge caution.
(ETA: caution about Atiyah's Riemann hypothesis proof, not the structure-factor-of-primes topic of this FPP.)
posted by Westringia F. at 8:57 PM on September 21, 2018
In regard to Sir Michael Atiyah's claim that he's found a proof of the Riemann hypothesis, John Baez writes: "I predict it's not going to hold up. Atiyah's recent big claims, like his supposed proof that the 6-sphere admits no complex structures, have not been holding up. Everyone who knows him well has been too embarrassed to publicly discuss the reasons."
It gives me a very heavy heart to see such a great intellect falter, but... I would urge caution.
(ETA: caution about Atiyah's Riemann hypothesis proof, not the structure-factor-of-primes topic of this FPP.)
posted by Westringia F. at 8:57 PM on September 21, 2018
I’m not a mathematician, but are prime numbers really thought to be randomly distributed? If so, why would a simple algorithm such as the Sieve of Eratosthenes and similar techniques work so well? Of course, they become unwieldy as the numbers get larger, but this is true of a lot of math. Perhaps this is a more efficient way to find very large primes?
posted by TedW at 9:42 PM on September 21, 2018 [2 favorites]
posted by TedW at 9:42 PM on September 21, 2018 [2 favorites]
While we are talking about primes...there’s also this.
I can’t help but see a custodian off to the left in that picture, erasing the blackboard. (Explanation for non US mefites.)
posted by TedW at 9:58 PM on September 21, 2018
I can’t help but see a custodian off to the left in that picture, erasing the blackboard. (Explanation for non US mefites.)
posted by TedW at 9:58 PM on September 21, 2018
I don't think anyone thought primes were truly randomly distributed for a very long time, just that they were unpredictable in their occurance along the number line. People have been looking for a pattern for a long time.
And now someone found one and I won a bet and also it'll be interesting to see how this affects cryptocurrency.
posted by fshgrl at 10:25 PM on September 21, 2018
And now someone found one and I won a bet and also it'll be interesting to see how this affects cryptocurrency.
posted by fshgrl at 10:25 PM on September 21, 2018
If so, why would a simple algorithm such as the Sieve of Eratosthenes and similar techniques work so well?
I think it would work no matter how they were distributed?
posted by thelonius at 12:34 AM on September 22, 2018 [5 favorites]
I think it would work no matter how they were distributed?
posted by thelonius at 12:34 AM on September 22, 2018 [5 favorites]
If so, why would a simple algorithm such as the Sieve of Eratosthenes and similar techniques work so well?I think it would work no matter how they were distributed?
Yes. I was going to say it's a consequence of unique factorization, but you're also using the ordering of the integers. (If everything is a prime or a product of primes and you cross out all the products of primes, what's left?) I don't readily see how to adapt it to an arbitrary unique factorization domain, nor does a quick google help.
posted by hoyland at 4:58 AM on September 22, 2018 [2 favorites]
In which I learn there is a known pattern for the large-scale structure of the universe and it's the same pattern as in prime numbers, and as found in the arrangement of color-detecting cone cells in bird’s eyes.
posted by aniola at 8:01 AM on September 22, 2018 [7 favorites]
posted by aniola at 8:01 AM on September 22, 2018 [7 favorites]
"it'll be interesting to see how this affects cryptocurrency."
Please don't use that word.
posted by el io at 10:12 PM on September 22, 2018 [1 favorite]
Please don't use that word.
posted by el io at 10:12 PM on September 22, 2018 [1 favorite]
What, "interesting"?
posted by Quasirandom at 9:01 AM on September 24, 2018
posted by Quasirandom at 9:01 AM on September 24, 2018
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posted by hoyland at 5:55 PM on September 21, 2018 [2 favorites]