P*****t
发帖数: 4978 | 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.
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Proof claimed for deep connection between primes
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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 |
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