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A discovery about prime numbers and what it means for the future of math (2013)

32 points by akbarnama 12y ago

akbarnama 12y ago
Another article which talks about this - http://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/ http://www.simonsfoundation.org/quanta/20130519-unheralded-m...
- huhtenberg 12y ago
  That's a much better read. Thanks!
mappu 12y ago
HN discussion from 500 days ago - https://news.ycombinator.com/item?id=5703219 https://news.ycombinator.com/item?id=5703219 What has changed since then?
- chrisbennet 12y ago
  Well, Zhang announced his findings this month (Sept 2014). Yitang “Tom” Zhang, a popular math professor at the University of New Hampshire, stunned the world of pure mathematics this month when he announced that he had proven the “bounded gaps” conjecture about the distribution of prime numbers.
  - gojomo 12y ago
    That's false. His announcement was April 2013, with paper accepted in May 2013. This site, impactlab.net, has simply plagiarized an old article from Slate and put a new date on it.
ch 12y ago
So does this mean that the primes actually distribute based on some pseudo random pattern? Certainly that is trivializing things but is this what the notion of the numbers acting random, but clearly not being random implies?
- lutusp 12y ago
  > So does this mean that the primes actually distribute based on some pseudo random pattern? To prove this, we would have to identify the hypothetical pseudorandom pattern. If we successfully identified the pattern, we could locate primes deterministically. If we could locate primes deterministically, modern encryption would collapse. So ... no. No one knows how primes are distributed among composites, and there may be no pattern, as that term is generally understood. > Certainly that is trivializing things but is this what the notion of the numbers acting random, but clearly not being random implies? Yes, but with the important distinction that a pseudorandom pattern can be recreated, given the genesis of the pattern. For example, a pseudorandom number generator will produce exactly the same pseudorandom numbers for a given initializing "seed" number. As to the primes, it's possible that their placement among the composites obeys a pattern, but we don't know what that pattern is, and this is a matter of great mathematical interest.
gojomo 12y ago
Text appears to be a cut & paste of Slate's article on the topic from May 2013: http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html http://www.slate.com/articles/health_and_science/do_the_math... (They include a link to Slate at the bottom, but no hint they've cut & pasted the entire text as if it were their own with the new September 24, 2014 publication date.)
theoh 12y ago
From the article "The gaps between successive powers of 2 grow exponentially, and there are finitely many gaps of any given size; once you get past 16, for instance, you will never again see two powers of 2 separated by a gap of size 15 or less." Unless I am mistaken, the gaps between powers of two never repeat. They keep getting bigger by a factor of two each time, right?
- x1798DE 12y ago
  Gaps are 2^n-2^(n-1) = 2^(n-1)*(2-1) = 2^(n-1) So yeah, the gaps are just powers of 2.
nkurz 12y ago
This is a wonderful article, but the blog spam URL should be changed to the original: http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html http://www.slate.com/articles/health_and_science/do_the_math... "Impact Lab" has scraped the entire 5-month old article from it's original publication, and republished it verbatim with their own ads on it. While they link to original at the bottom of the full article (no mention on the teaser page), this is egregious copyright infringement. This appears to be their entire business model: http://www.impactlab.net/impact-lab-advertising-rate-sheet/ http://www.impactlab.net/impact-lab-advertising-rate-sheet/ HN should ban them. Slate (and the other infringed parties) should sue them out of existence. It should be an open-and-shut case.
- dang 12y ago
  We noticed that and banned the site last night, but didn't change the url on this post. We've changed it now—sorry for the delay.
  - manicdee 12y ago
    NB: changes to article URLs post-publication don't appear to be reflected in the RSS feed.
    - dang 12y ago
      Thanks! Adding to list to fix. Edit: Apparently they are in fact updated, so you are likely either seeing cached items or your RSS client isn't picking up the changes.
- gojomo 12y ago
  16-month old article.

32 points by akbarnama 12y ago

Another article which talks about this - http://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/ http://www.simonsfoundation.org/quanta/20130519-unheralded-m...

huhtenberg 12y ago
That's a much better read. Thanks!

mappu 12y ago

HN discussion from 500 days ago - https://news.ycombinator.com/item?id=5703219 https://news.ycombinator.com/item?id=5703219 What has changed since then?

chrisbennet 12y ago
Well, Zhang announced his findings this month (Sept 2014). Yitang “Tom” Zhang, a popular math professor at the University of New Hampshire, stunned the world of pure mathematics this month when he announced that he had proven the “bounded gaps” conjecture about the distribution of prime numbers.
- gojomo 12y ago
  That's false. His announcement was April 2013, with paper accepted in May 2013. This site, impactlab.net, has simply plagiarized an old article from Slate and put a new date on it.

ch 12y ago

So does this mean that the primes actually distribute based on some pseudo random pattern? Certainly that is trivializing things but is this what the notion of the numbers acting random, but clearly not being random implies?

lutusp 12y ago
> So does this mean that the primes actually distribute based on some pseudo random pattern? To prove this, we would have to identify the hypothetical pseudorandom pattern. If we successfully identified the pattern, we could locate primes deterministically. If we could locate primes deterministically, modern encryption would collapse. So ... no. No one knows how primes are distributed among composites, and there may be no pattern, as that term is generally understood. > Certainly that is trivializing things but is this what the notion of the numbers acting random, but clearly not being random implies? Yes, but with the important distinction that a pseudorandom pattern can be recreated, given the genesis of the pattern. For example, a pseudorandom number generator will produce exactly the same pseudorandom numbers for a given initializing "seed" number. As to the primes, it's possible that their placement among the composites obeys a pattern, but we don't know what that pattern is, and this is a matter of great mathematical interest.

gojomo 12y ago

Text appears to be a cut & paste of Slate's article on the topic from May 2013: http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html http://www.slate.com/articles/health_and_science/do_the_math... (They include a link to Slate at the bottom, but no hint they've cut & pasted the entire text as if it were their own with the new September 24, 2014 publication date.)

theoh 12y ago

From the article "The gaps between successive powers of 2 grow exponentially, and there are finitely many gaps of any given size; once you get past 16, for instance, you will never again see two powers of 2 separated by a gap of size 15 or less." Unless I am mistaken, the gaps between powers of two never repeat. They keep getting bigger by a factor of two each time, right?

x1798DE 12y ago
Gaps are 2^n-2^(n-1) = 2^(n-1)*(2-1) = 2^(n-1) So yeah, the gaps are just powers of 2.

nkurz 12y ago

This is a wonderful article, but the blog spam URL should be changed to the original: http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html http://www.slate.com/articles/health_and_science/do_the_math... "Impact Lab" has scraped the entire 5-month old article from it's original publication, and republished it verbatim with their own ads on it. While they link to original at the bottom of the full article (no mention on the teaser page), this is egregious copyright infringement. This appears to be their entire business model: http://www.impactlab.net/impact-lab-advertising-rate-sheet/ http://www.impactlab.net/impact-lab-advertising-rate-sheet/ HN should ban them. Slate (and the other infringed parties) should sue them out of existence. It should be an open-and-shut case.

dang 12y ago
We noticed that and banned the site last night, but didn't change the url on this post. We've changed it now—sorry for the delay.
- manicdee 12y ago
  NB: changes to article URLs post-publication don't appear to be reflected in the RSS feed.
  - dang 12y ago
    Thanks! Adding to list to fix. Edit: Apparently they are in fact updated, so you are likely either seeing cached items or your RSS client isn't picking up the changes.
gojomo 12y ago
16-month old article.