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Mathematics版 - NYT: Solving a Riddle of Primes
相关主题
纽约时报的报道及科学院院士Sarnak的评价: Solving a Riddle of Primes不知名数学家证明了素数的稀有性质
这篇写的更详细:Bounded Gaps Between PrimesBounded gaps between primes! (初步点评,E. Kowalski’s blog)
老张的文章都没有公布,怎么就这么多人bbb张益唐在台北接受季理真专访
旁观者昏:为了人类心智的荣耀UNH mathematician receives Cole, Ostrowski prizes
2015 Shaw prize: Faltings and Iwaniec请看看这些类似twin prime conjecture的猜想有意义吗?
已有的猜想中那个最难证明? (转载)本期New Yorker有老张的报道
张是幸运的两个关于素数的猜想
有没有可能老张的文章被挑出错了三个月了,有人对张益堂的证明提出质疑吗?
相关话题的讨论汇总
话题: dr话题: zhang话题: prime话题: primes话题: said
1 (共1页)
d******s
发帖数: 180
1
http://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-p
Solving a Riddle of Primes
By KENNETH CHANG
Published: May 20, 2013
Three and five are prime numbers — that is, they are divisible only by 1
and by themselves. So are 5 and 7. And 11 and 13. And for each of these
pairs of prime numbers, the difference is 2.
Mathematicians have long believed that there are an infinite number of such
pairs, called twin primes, meaning that there will always be a larger pair
than the largest one found. This supposition, the so-called Twin Prime
Conjecture, is not necessarily obvious. As numbers get larger, prime numbers
become sparser among vast expanses of divisible numbers. Yet still —
occasionally, rarely — two consecutive odd numbers will both be prime, the
conjecture asserts.
The proof has been elusive.
But last month, a paper from a little-known mathematician arrived “out of
the blue” at the journal Annals of Mathematics, said Peter Sarnak, a
professor of mathematics at Princeton University and the Institute for
Advanced Study and a former editor at the journal, which plans to publish it
. The paper, by Yitang Zhang of the University of New Hampshire, does not
prove that there are an infinite number of twin primes, but it does show an
infinite number of prime pairs whose separation is less than a finite upper
limit — 70 million, for now. (Dr. Zhang used 70 million in his proof —
basically an arbitrary large number where his equations work.)
“It’s a deep insight,” Dr. Sarnak said. “It’s a deep result.”
Dr. Zhang said he had been working on the Twin Prime Conjecture for years
and, like everyone else, failed. “I tried everything,” he said.
Then, last July, “just very suddenly, an idea came to my mind,” Dr. Zhang
said. “I was confident in this way I could prove it.”
It took him another six months to fill in the details, but he appears to be
right. The paper has been accepted pending some small revisions. “It’s
remarkable the speed this paper was dealt with,” Dr. Sarnak said.
Dr. Zhang’s proof takes advantage of a 2005 paper by Daniel Goldston of San
Jose State University, Janos Pintz of the Alfred Renyi Institute of
Mathematics in Budapest and Cem Yildirim of Bogazici University in Istanbul,
which had shown there would always be pairs of primes closer than the
average distance between two primes.
Still, in mathematics, closer does not necessarily mean two numbers away,
and experts were unable to make further progress on the conjecture. “People
tried, and after a few years, it seemed this was really far away,” Dr.
Sarnak said.
Dr. Zhang also used techniques developed in the 1980s by Henryk Iwaniec of
Rutgers, Enrico Bombieri of the Institute for Advanced Study and John B.
Friedlander of the University of Toronto, adding his own ingenuity to tie
everything together in a way others had been unable to.
“He got it,” said Dr. Iwaniec, who has read Dr. Zhang’s paper. “There’s
no question about it.”
The next step is reducing that 70 million separation, and Dr. Zhang said “
that should be very simple.” But experts like Dr. Iwaniec said bringing it
all the way down to 2 — the full Twin Prime Conjecture — would probably
require more mathematical breakthroughs.
M****o
发帖数: 4860
2
re 刚看到

such

【在 d******s 的大作中提到】
: http://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-p
: Solving a Riddle of Primes
: By KENNETH CHANG
: Published: May 20, 2013
: Three and five are prime numbers — that is, they are divisible only by 1
: and by themselves. So are 5 and 7. And 11 and 13. And for each of these
: pairs of prime numbers, the difference is 2.
: Mathematicians have long believed that there are an infinite number of such
: pairs, called twin primes, meaning that there will always be a larger pair
: than the largest one found. This supposition, the so-called Twin Prime

j**********e
发帖数: 1034
3
Sarnak发话定调了,质疑张成就的都可以洗洗睡了

such

【在 d******s 的大作中提到】
: http://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-p
: Solving a Riddle of Primes
: By KENNETH CHANG
: Published: May 20, 2013
: Three and five are prime numbers — that is, they are divisible only by 1
: and by themselves. So are 5 and 7. And 11 and 13. And for each of these
: pairs of prime numbers, the difference is 2.
: Mathematicians have long believed that there are an infinite number of such
: pairs, called twin primes, meaning that there will always be a larger pair
: than the largest one found. This supposition, the so-called Twin Prime

C**o
发帖数: 10373
4
sarnak什么地位?

1
pair

【在 j**********e 的大作中提到】
: Sarnak发话定调了,质疑张成就的都可以洗洗睡了
:
: such

S*******e
发帖数: 525
5
三十寒窗无人问,一日成名天下扬。
l***o
发帖数: 7937
6
NAS member.

【在 C**o 的大作中提到】
: sarnak什么地位?
:
: 1
: pair

x********i
发帖数: 905
7
IAS Professor

【在 l***o 的大作中提到】
: NAS member.
1 (共1页)
相关主题
三个月了,有人对张益堂的证明提出质疑吗?2015 Shaw prize: Faltings and Iwaniec
莫宗坚谈张益唐:张没有找莫要推荐信 (转载)已有的猜想中那个最难证明? (转载)
张的文章已经被接受了,不再是据说。张是幸运的
数学界的重大突破,据说Annals已经接受啦有没有可能老张的文章被挑出错了
纽约时报的报道及科学院院士Sarnak的评价: Solving a Riddle of Primes不知名数学家证明了素数的稀有性质
这篇写的更详细:Bounded Gaps Between PrimesBounded gaps between primes! (初步点评,E. Kowalski’s blog)
老张的文章都没有公布,怎么就这么多人bbb张益唐在台北接受季理真专访
旁观者昏:为了人类心智的荣耀UNH mathematician receives Cole, Ostrowski prizes
相关话题的讨论汇总
话题: dr话题: zhang话题: prime话题: primes话题: said