i****g
发帖数: 3896 | 1 【 以下文字转载自 Mathematics 讨论区 】
发信人: endoscopy (暂时没有), 信区: Mathematics
标 题: 数学界的重大突破，据说Annals已经接受啦
关键字: 素数
发信站: BBS 未名空间站 (Tue May 14 05:58:29 2013, 美东)
没有人八卦这个吗？
今天的Nature已经刊登了新闻。
如果最终是对的话，我觉得是近50年来数学的重大结果
可能没有FLT对数学的促进大，但是不比费尔马大定里的影响小
对搞数学的来说 证明相差为70000000的素数有无穷多对和证明相差为2的素数有无穷多
对。并没有实质性的差别。意义是一样的。
http://www.nature.com/news/first-proof-that-infinitely-many-pri
First proof that infinitely many prime numbers come in pairs
Mathematician claims breakthrough towards solving centuries-old problem.
Maggie McKee 14 May 2013
Cambridge, Massachusetts
Mathematician Yitang Zhang has outlined a proof of a 'weak' version of the
conjecture on twin prime numbers, one of the longest-standing open problems
in mathematics.
Maggie McKee
Article toolsPrint
It’s a result only a mathematician could love. Researchers hoping to get ‘
2’ as the answer for a long-sought proof involving pairs of prime numbers
are celebrating the fact that a mathematician has wrestled the value down
from infinity to 70 million.
“That’s only [a factor of] 35 million away” from the target, quips Dan
Goldston, an analytic number theorist at San Jose State University in
California who was not involved in the work. “Every step down is a step
towards the ultimate answer.”
That goal is the proof to a conjecture concerning prime numbers. Those are
the whole numbers that are divisible only by one and themselves. Primes
abound among smaller numbers, but they become less and less frequent as one
goes towards larger numbers. In fact, the gap between each prime and the
next becomes larger and larger — on average. But exceptions exist: the ‘
twin primes’, which are pairs of prime numbers that differ in value by 2.
Examples of known twin primes are 3 and 5, or 17 and 19, or 2,003,663,613 ×
2195,000 − 1 and 2,003,663,613 × 2195,000 + 1.
The twin prime conjecture says that there is an infinite number of such twin
pairs. Some attribute the conjecture to the Greek mathematician Euclid of
Alexandria, which would make it one of the oldest open problems in
mathematics.
The problem has eluded all attempts to find a solution so far. A major
milestone was reached in 2005 when Goldston and two colleagues showed that
there is an infinite number of prime pairs that differ by no more than 16 (
ref. 1). But there was a catch. “They were assuming a conjecture that no
one knows how to prove,” says Dorian Goldfeld, a number theorist at
Columbia University in New York.
Related stories
Mathematician wins award for shaping algebra
Proof claimed for deep connection between primes
Mathematicians come closer to solving Goldbach's weak conjecture
More related stories
The new result, from Yitang Zhang of the University of New Hampshire in
Durham, finds that there are infinitely many pairs of primes that are less
than 70 million units apart without relying on unproven conjectures.
Although 70 million seems like a very large number, the existence of any
finite bound, no matter how large, means that that the gaps between
consecutive numbers don’t keep growing forever. The jump from 2 to 70
million is nothing compared with the jump from 70 million to infinity. “If
this is right, I’m absolutely astounded,” says Goldfeld.
Zhang presented his research on 13 May to an audience of a few dozen at
Harvard University in Cambridge, Massachusetts, and the fact that the work
seems to use standard mathematical techniques led some to question whether
Zhang could really have succeeded where others failed.
But a referee report from the Annals of Mathematics, to which Zhang
submitted his paper, suggests he has. “The main results are of the first
rank,” states the report, a copy of which Zhang provided to Nature. “The
author has succeeded to prove a landmark theorem in the distribution of
prime numbers. … We are very happy to strongly recommend acceptance of the
paper for publication in the Annals.”
Goldston, who was sent a copy of the paper, says that he and the other | p*******d
发帖数: 81 | | t****e
发帖数: 279 | | i****g
发帖数: 3896 | 4 http://pkunews.pku.edu.cn/xwzh/2013-05/15/content_272348.htm
数学科学学院校友张益唐在孪生素数研究方面取得重大突破
日期： 2013-05-15 信息来源： 数学科学学院
日前，Nature官网发布新闻：“无穷多素数成对存在的首次证明（First proof that
infinitely many prime numbers come in pairs）”，文章报道了北大数学科学学院
78级校友张益唐在孪生素数研究方面所取得的突破性进展，他证明了孪生素数猜想的一
个弱化形式。
众所周知，素数是指正因数只有1和本身的正整数。素数在整数里面是非常稀疏的。如
果我们将素数从小到大排一个次序，那么从概率上说，随着素数的增大，下一个素数离
上一个素数应该越来越远，而孪生素数猜想是说存在无穷多对素数，他们只相差2。例
如3和5，5和7，……，2,003,663,613 × 2^195,000- 1 和 2,003,663,613 × 2^195,
000+1等等。这两个素数挨的如此之近，就像宇宙里面地球遇见了太阳一样神奇，因此
我们称它们为孪生素数。有人把孪生素数猜想归因于古希腊数学家欧几里得，这使它成
为数学领域最古老的开放问题之一。
孪生素数猜想和哥德巴赫猜想一样让无数数论学者为之着迷。他们穷尽一生想要寻找一
个证明，但是一直都没有期望的重大进展，甚至不知道它的弱形式是否成立，即能不能
找到一个正数，使得有无穷多对素数之差小于这个给定正数。比方说孪生素数猜想中的
这个正数是2。之前这方面最有名的结果是Goldston和他的两个合作者做出来的。他们
找到的正数是16，但是他们的证明需要承认另外一个未被证明的猜想，因此并不能让人
满意。
张益唐在他的文章中给出了孪生素数猜想的弱形式的一个证明，并且他不依赖于任何一
个其他猜想。他找到的正数是七千万。当然七千万离孪生素数猜想给出的2还是有一段
距离，但是相比之前人们给不出来任何一个这样的正数，张益唐的结果无疑是数论发展
中的一个重要里程碑。
张益唐的文章已投到了美国著名学术期刊《数学年刊》（Annals of Mathematics）。
他的研究结果已经获得了评委的高度评价，并且推荐接受这篇文章。著名解析数论专家
Goldston也在评阅这篇文章，他说：真不敢相信我在有生之年还能看到这个证明。
张益唐校友1978年进入北大数学科学学院攻读本科，1982年读硕，现在美国新罕布什尔
大学任教。
附：Nature官网新闻链接
http://www.nature.com/news/first-proof-that-infinitely-many-pri
编辑：李娜 | p******o
发帖数: 2682 | 5 不是学数学的，相信应当非常高深。
有没有网友能够把他的证明用科普语言描述一下？
【在 i****g 的大作中提到】
: http://pkunews.pku.edu.cn/xwzh/2013-05/15/content_272348.htm
: 数学科学学院校友张益唐在孪生素数研究方面取得重大突破
: 日期： 2013-05-15 信息来源： 数学科学学院
: 日前，Nature官网发布新闻：“无穷多素数成对存在的首次证明（First proof that
: infinitely many prime numbers come in pairs）”，文章报道了北大数学科学学院
: 78级校友张益唐在孪生素数研究方面所取得的突破性进展，他证明了孪生素数猜想的一
: 个弱化形式。
: 众所周知，素数是指正因数只有1和本身的正整数。素数在整数里面是非常稀疏的。如
: 果我们将素数从小到大排一个次序，那么从概率上说，随着素数的增大，下一个素数离
: 上一个素数应该越来越远，而孪生素数猜想是说存在无穷多对素数，他们只相差2。例
| h*******g
发帖数: 80 | 6 谢谢分享，收藏学习了：
http://phdtree.org/
【在 i****g 的大作中提到】
: http://pkunews.pku.edu.cn/xwzh/2013-05/15/content_272348.htm
: 数学科学学院校友张益唐在孪生素数研究方面取得重大突破
: 日期： 2013-05-15 信息来源： 数学科学学院
: 日前，Nature官网发布新闻：“无穷多素数成对存在的首次证明（First proof that
: infinitely many prime numbers come in pairs）”，文章报道了北大数学科学学院
: 78级校友张益唐在孪生素数研究方面所取得的突破性进展，他证明了孪生素数猜想的一
: 个弱化形式。
: 众所周知，素数是指正因数只有1和本身的正整数。素数在整数里面是非常稀疏的。如
: 果我们将素数从小到大排一个次序，那么从概率上说，随着素数的增大，下一个素数离
: 上一个素数应该越来越远，而孪生素数猜想是说存在无穷多对素数，他们只相差2。例
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