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Mathematicians Team Up To Close the Prime Gap
Hugh Pickens DOT Com writes "On May 13, an obscure mathematician garnered worldwide attention and accolades from the mathematics community for settling a long-standing open question about prime numbers. Yitang Zhang showed that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes separated by at most 70 million. His finding was the first time anyone had managed to put a finite bound on the gaps between prime numbers, representing a major leap toward proving the centuries-old twin primes conjecture, which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13). Now Erica Klarreich reports at Quanta Magazine that other mathematicians quickly realized that it should be possible to push this separation bound quite a bit lower. By the end of May, mathematicians had uncovered simple tweaks to Zhang's argument that brought the bound below 60 million. Then Terence Tao, a winner of the Fields Medal, mathematics' highest honor, created a 'Polymath project,' an open, online collaboration to improve the bound that attracted dozens of participants. By July 27, the team had succeeded in reducing the proven bound on prime gaps from 70 million to 4,680. Now James Maynard has upped the ante by presenting an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower. Zhang's work and, to a lesser degree, Maynard's fits the archetype of the solitary mathematical genius, working for years in the proverbial garret until he is ready to dazzle the world with a great discovery. The Polymath project couldn't be more different — fast and furious, massively collaborative, fueled by the instant gratification of setting a new world record. 'It's important to have people who are willing to work in isolation and buck the conventional wisdom,' says Tao. Polymath, by contrast, is 'entirely groupthink.' Not every math problem would lend itself to such collaboration, but this one did."
We cannot allow a prime gap!
sometimes its better to go it alone, then come back to the group with your results so that someone else may profit from them.
sometimes its better to be a part a group in order to establish your ideas and discuss, then go it alone when the group holds you back.
Oh, nevermind...
If they keep this shit up, pretty soon they will prove that every number is prime.
'It's important to have people who are willing to work in isolation and buck the conventional wisdom,' says Tao. Polymath, by contrast, is 'entirely groupthink.' Not every math problem would lend itself to such collaboration, but this one did."
History is rife with examples of the lone genius making a leap forward, thereby allowing the crowd to take it even further. See The Structure of Scientific Revolutions by Thomas Kuhn.
>> which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13)
Yawn. Call me when you find a set of primes separated by one.
Will they ever learn to factor prime numbers though? I understand it's difficult, but solving it would save a lot of embarrassment when people misstate the problem.
Er...2 and 3. What do I win?
all being confiscated, you can count #s on us but not much else
Now James Maynard has upped the ante by presenting an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, (...) to push the bound even lower.
600 ought to be enough for anyone.
Set your phasers on "funky"!
Three people are asked to prove that all of the odd numbers are prime - a physicist, a mathematician and a programmer.
The physicist goes first. "3 is a prime, 5 is a prime, 7 is a prime, 9 is a ... oops, experimental error, 11 is a prime ...".
Next the mathematician takes a crack at it: "3 is a prime, 5 is a prime, 7 is a prime, and the rest by induction".
Finally it's the programmer's turn. "3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime ...".
Was it just me or did anyone else have a hard time following that summary? At first I thought it was Yitang Zhang who settled "a long-standing open question". But the first sentence is actually talking about the eight - James Maynard.
So in summary, if a pair of primes is defined by one following the other, it was theorized that we would find an infinite number of such pairs separated by 2. Various people have proven that gap to be from 70m, 60m, 4680, and now 600. Thank you James Maynard.
phony #'s be damnned
billions of innocents (all of us unchosens) in the unbalance
They are not so sexy, after all...
Ok, I'm dense.. I don't get it. What are they saying exactly?
Are they saying we will always find a prime number within 600 of another prime number?
If that were true, you'd think we'd have figured it out with the help of computers by now?
I must be wrong in my understanding.
http://www.scmp.com/lifestyle/technology/article/1256542/zhang-yitang-proof-mathematicians-life-begins-40
Maybe a bit of a feel good article, but I think some deep questions are better answered by more seasoned (and likely more stubborn) mathematicians.
This post reminded me of the singer of the band named Tool and the song Lateralus which uses Fibonacci sequence.
http://www.youtube.com/watch?v=wS7CZIJVxFY
The result is astonishing. Does anyone happen to know what the greatest known lower bound is? (i.e. the largest known difference of two successive primes?)
The prospect that one might eventually show the exact upper bound is even more astonishing.
If N is between 2 and 10^260, then the number of primes less than N is more than N / 600. So in that range the _average_ gap between consecutive primes is less than 600. For N = 10^20 it is actually quite rare that the gap between two consecutive primes is over 600.
FTFA:
"and if we assume the Elliott-Halberstam conjecture, that liminfn(pn+1pn) is less than or equal to 12"
But the gap between 113 and 127 is 14, so either the Elliott-Halberstam conjecture is wrong or the proof is dubious.
So, if the prime numbers become increasingly rare as you get bigger, but never get further apart than 600, then that's a sort of interesting result for two reasons. The obvious one is that the distance between primes increases at a decreasing rate. The subtler one is that there is some magic number out that is the LEAST upper bound for this growth in distance (I sort of doubt 600 is the smallest such bound). Whatever that least upper bound is will have profound implications for the nature of the universe. If that number is a prime, is it some sort of super-prime that can be used to predict all the other primes? If that number is composite, what is special about its prime factors? Heck, that magic number might not even be an integer. It might be some sort of transcendental number like phi, e or pi. It would be really mind-blowing to know that while integers are the simplest kind of numbers that we know, they may not be the most fundamental. Euler's Identity [e^(i*pi)+1=0] has hinted at that for quite some time. We might have to rewrite the fundamental theorem of arithmetic.
Nice. How soon do I get my FTL flying car?
http://www.conservativeintel.com/2013/11/19/single-mom-thanked-obama-for-her-169mo-insurance-then-discovered-it-will-actually-cost-her-621mo/
"Jessica Sanford of Federal Way, Wash., a freelance court reporter. She isn’t just any enrollee. As it happens, President Obama once mentioned her by name. She was so thrilled at getting a “gold” level insurance plan for herself and her son for just $169 per month that she had written Obama to thank him. And then he read from her letter and gave her a name-check in his October 21 Rose Garden speech. ...
Unfortunately, Washington State did finally got back to Sanford about her application. That $452 subsidy we said you’d get? That was a mistake. You actually get zero. So for that gold plan, instead of paying $169 per month, you’d pay $621 per month."
Awww, poor little LIV.
Suck it drones. You served up a shit sandwich, now take a big ass bite and enjoy!
That has nothing to do with prime numbers, idiot.
If you think I voted for Trump because of this post, you're wrong. I voted for Dr. Jill Stein of the Green Party. Again.
so little of what news is dragged before me these days does much to make me hopeful of humanity's prospects on this planet. This story is the rare exception. We could be a great species. We could solve what looked for centuries to be impossible problems. We could...
/. This story was not in any of my regular channels today.
Thanks
SLASHDOT: news for people who can't concentrate on work or have no life at all and got tired of yelling back at the TV.
or have quite a number of difficult and important theorems been proven in the last couple decades? Fermat's last theorem, the Poincare conjecture, now lots of progress on this conjecture? What have mathematicians been doing right recently?
Has no wiki entry or web page indicating how good he is.
Does that mean that he's a foreigner and NOT AMERICAN?
Only mathematicians would prefer a closer thigh gap...
...oh, wait. Never mind.
You've got to find them, though...
all of these are NON-CONSTRUCTIVE proofs!
The linked abstracts are pretty vague. Are there any mathematicians here who can explain how (seemingly arbitrary) large numbers like 600 or 70 million come out of these proofs? People are saying they're all tweaks of the same basic method, so what is that basic method, exactly?
Visit the
Perhaps, he was educated as to the stupidity of his remark later.
You are being MICROattacked, from various angles, in a SOFT manner.
Note if you can find the proof of this, then you have killed multiple birds with one stone.
You get the infiinite twins problem solved.
You get the Goldback conjecture solved.
And you find that is also shows that there are infinite sets
of twin primes separated by any distance.
Which means there are infinite quad primes as I mentioned above.
You are being MICROattacked, from various angles, in a SOFT manner.
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...does this affect encryption in some way? My understanding is that a lot of encryption relies on the difficulty of finding prime numbers. I may be wrong. (It's certainly not my specialty.)
Why isn't cold fjord in here blaming Snowden for all this?
Garret? I wouldn't exactly call Oxford's maths department a garret!
What an amazing discovery! Is there a pattern to the distribution to such pairs of primes? Are they composed of compound sets or is their distribution entirely unpredictable? When people make such discoveries or proofs, we get the chance in our lifetime to pose the next round of questions, the ones that might take decades (or centuries) to answer. Great news item!