5 ms·

First proof that infinitely many prime numbers come in pairs (2013)

21 points by valera_rozuvan 11y ago

AnimalMuppet 11y ago
Note: 2013.
- valera_rozuvan 11y ago
  In 2014 they were able to further improve the results of Zhang. Polymath8 project "Bounded gaps between primes" http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes http://michaelnielsen.org/polymath1/index.php?title=Bounded_... .
nathan_f77 11y ago
Oh, this is from 2013. I was getting excited to read about a new discovery.
- valera_rozuvan 11y ago
  A post by by Terence Tao. What's new in 2015: "Gaps between primes". https://terrytao.wordpress.com/2015/07/06/gaps-between-primes/ https://terrytao.wordpress.com/2015/07/06/gaps-between-prime...
- ikeboy 11y ago
  If you didn't know about it, what's the difference to you? As long as it hasn't been disproven, and you'd have been interested hearing it then, what changes? On a related topic, I sometimes wonder why people seek out new entertainment (movies, tv shows), when it's unlikely to be better than everything already made in the past. Why would you prefer watching a new movie over an old one? The obvious answers (better CGI, closer similarity to current culture, social reasons aka "what other people are watching") don't seem to fully explain it. There seems to be some "new thingy pull" that affects many people (even myself at times), yet I can't explain it.
  - nathan_f77 11y ago
    Sorry, I meant that I have already read this article a long time ago, and the title of this post got me excited to read about some new developments. As for your second point, I think you mentioned a lot of the main reasons. But I disagree that new media is unlikely to be better than everything made in the past. In fact, I would say that it's very likely that a new movie or TV show will be far better than something made in the past, simply because they have much bigger budgets now, better technology, and even a better understanding of filmmaking and storytelling. Especially with recent TV shows such as Breaking Bad, Game of Thrones, True Detective. The bar has been raised very high.
    - ikeboy 11y ago
      It's possible that a random new movie will be better than a random movie in the past, but you're not talking about random low-budget ones, you're talking about high-budget ones. It's not like they didn't have some big budget films in the past, and I doubt a "better understanding of filmmaking and storytelling" is responsible for more enjoyment of current things. Also, I'm more referring to even movies from 5-10 years ago, which don't suffer from lack of technology in general, or most of the other reasons, and yet there doesn't seem to be as much consumption of them than the "new thing". Personally, I'm fine with consuming old media, but the world doesn't seem to share that with me, and I don't fully get why. There's also the availability of extensive ratings for past media, which means you can pick and choose the good ones, something harder to do when picking stuff still in theaters. As a counterpoint, I do enjoy sequels of things I've previously enjoyed (and understand the sequel effect), but that doesn't seem big enough to account for the general phenomenon either.
- smpetrey 11y ago
  I had the same thought. Brady Haran did a piece back in 2013 on it on his Numberphile channel. https://www.youtube.com/watch?v=vkMXdShDdtY https://www.youtube.com/watch?v=vkMXdShDdtY
daniel-levin 11y ago
No, this is absolutely not the first (correct) proof that infinitely many prime numbers come in pairs! That is the twin prime conjecture, and at the time of writing this comment, steadily remains a conjecture. I wonder why Nature, a publication held in high regard, would publish an article with such a title. This is not to say that the result is anything less than incredible. Terence Tao delivered a very good lecture on this result here [0] [0] https://www.youtube.com/watch?v=pp06oGD4m00 https://www.youtube.com/watch?v=pp06oGD4m00
- valera_rozuvan 11y ago
  More precise quote from the Nature article: "... Yitang Zhang ... finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures." I agree that there is a difference between "twin primes" and "pairs of primes".
  - valera_rozuvan 11y ago
    Twin primes are pairs of primes which differ by two.
- biot 11y ago
  In the video you linked, Terrence Tao calls this result "a completely correct proof" (at around 4:00). Pairs of primes includes but is not limited to twin primes.
adamzubi 11y ago
http://googler700.blogspot.com/ http://googler700.blogspot.com/

AnimalMuppet 11y ago

Note: 2013.

valera_rozuvan 11y ago
In 2014 they were able to further improve the results of Zhang. Polymath8 project "Bounded gaps between primes" http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes http://michaelnielsen.org/polymath1/index.php?title=Bounded_... .

nathan_f77 11y ago

Oh, this is from 2013. I was getting excited to read about a new discovery.

valera_rozuvan 11y ago
A post by by Terence Tao. What's new in 2015: "Gaps between primes". https://terrytao.wordpress.com/2015/07/06/gaps-between-primes/ https://terrytao.wordpress.com/2015/07/06/gaps-between-prime...
ikeboy 11y ago
If you didn't know about it, what's the difference to you? As long as it hasn't been disproven, and you'd have been interested hearing it then, what changes? On a related topic, I sometimes wonder why people seek out new entertainment (movies, tv shows), when it's unlikely to be better than everything already made in the past. Why would you prefer watching a new movie over an old one? The obvious answers (better CGI, closer similarity to current culture, social reasons aka "what other people are watching") don't seem to fully explain it. There seems to be some "new thingy pull" that affects many people (even myself at times), yet I can't explain it.
- nathan_f77 11y ago
  Sorry, I meant that I have already read this article a long time ago, and the title of this post got me excited to read about some new developments. As for your second point, I think you mentioned a lot of the main reasons. But I disagree that new media is unlikely to be better than everything made in the past. In fact, I would say that it's very likely that a new movie or TV show will be far better than something made in the past, simply because they have much bigger budgets now, better technology, and even a better understanding of filmmaking and storytelling. Especially with recent TV shows such as Breaking Bad, Game of Thrones, True Detective. The bar has been raised very high.
  - ikeboy 11y ago
    It's possible that a random new movie will be better than a random movie in the past, but you're not talking about random low-budget ones, you're talking about high-budget ones. It's not like they didn't have some big budget films in the past, and I doubt a "better understanding of filmmaking and storytelling" is responsible for more enjoyment of current things. Also, I'm more referring to even movies from 5-10 years ago, which don't suffer from lack of technology in general, or most of the other reasons, and yet there doesn't seem to be as much consumption of them than the "new thing". Personally, I'm fine with consuming old media, but the world doesn't seem to share that with me, and I don't fully get why. There's also the availability of extensive ratings for past media, which means you can pick and choose the good ones, something harder to do when picking stuff still in theaters. As a counterpoint, I do enjoy sequels of things I've previously enjoyed (and understand the sequel effect), but that doesn't seem big enough to account for the general phenomenon either.
smpetrey 11y ago
I had the same thought. Brady Haran did a piece back in 2013 on it on his Numberphile channel. https://www.youtube.com/watch?v=vkMXdShDdtY https://www.youtube.com/watch?v=vkMXdShDdtY

daniel-levin 11y ago

No, this is absolutely not the first (correct) proof that infinitely many prime numbers come in pairs! That is the twin prime conjecture, and at the time of writing this comment, steadily remains a conjecture. I wonder why Nature, a publication held in high regard, would publish an article with such a title. This is not to say that the result is anything less than incredible. Terence Tao delivered a very good lecture on this result here [0] [0] https://www.youtube.com/watch?v=pp06oGD4m00 https://www.youtube.com/watch?v=pp06oGD4m00

valera_rozuvan 11y ago
More precise quote from the Nature article: "... Yitang Zhang ... finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures." I agree that there is a difference between "twin primes" and "pairs of primes".
- valera_rozuvan 11y ago
  Twin primes are pairs of primes which differ by two.
biot 11y ago
In the video you linked, Terrence Tao calls this result "a completely correct proof" (at around 4:00). Pairs of primes includes but is not limited to twin primes.

adamzubi 11y ago

http://googler700.blogspot.com/ http://googler700.blogspot.com/