本文主要是介绍无穷多的素数会成对的出现，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
上午公司培训，请了一个腾讯的大牛做数据挖掘的讲座。我本来的目的是想了解一下hadoop与hbase相关的运维与部署，或多或少能了解到点什么，没想到讲的全是数据挖掘建模方面的知识。虽然现在做的是SA&DBA的事情，还好之前今天的职位是数据分析工程师，接触过一点数据分析挖掘的知识，能听懂一点。大牛讲了很多，基本的概念包括数据分类、聚类、拟合。算法也讲了很多分段建模，logit（logistic）变换，Slope One，推荐ranking=scoring+sorting+filtering，SVD对分类准确性的提高，SVM，Deep Learning，还有关于Netflix的百万美金与神经网络科学家的Hinton的故事（restricted boltzmann machines for collaborative filtering）。系统方面讲到hadoop、hbase、hive、pig与google的三架（不知道用什么单位！！！）火车：GFS、Big Table、Map/Reduce。数据、算法、系统在数据挖掘过程中的重要程度依次递减的，好的数据也不需要复杂的算法。
听完讲座之后，决定在办公室待到下午3点多再回去，叫了份外卖。准备等小伍哥一个过来，晚上和老陆，总管一起吃个饭。四个人都是从一个实验室毕业的研究生，老陆是我的师兄（或者说是师叔，汗！），小伍哥、总管和我是同一届毕业的。其实很久没见面了，也难得都在上海工作，大部分的研究生熟人都在杭州那边。
吃完饭，无聊打开facebook上看到一篇关于素数的理论（http://www.scientificamerican.com/article.cfm?id=first-proof-that-infinite-many-prime-numbers-come-in-pairs），中国人在学术上确实厉害。好久没面对数学问题，会不会脑子生锈，虽让写程序也要动脑子，耐心的看了下来。素数在笔试或者面试的时候是经常碰到的一个问题，觉得有点意思，整理了一下自己想法和网上的一些关于的素数的东西。
素数：只能被1和自己本身整除的正整数。（a positive whole number that is divisible only by 1 and by itself）
合数：能唯一表示成素数的乘积，如15=3*5。
1：一个比较特殊的数字，不能说是素数也不能说是合数。
理论：素数以2*n-1，2*+1孪生的形式出现，如（3，5），（5，7），（11，13），（17，19），（29，31） 这样成对出现，而且无穷多个。
不存在最大的素数：
很简单，反证法，假设存在最大的数据P
那么存在一个合数M，M=2*3*5*7*......*P,即M为所有的不重复的素数的乘积。
M+1 = 2*3*5*7*......*P+1按照假设“M是最大的素数”推断，M+1是合数。
实际上(M+1）不能被2、3、5，......P中任何一个素数整除，余数均为1。
很明显M+1是一个素数，M+1>P，存在比P的素数，因为假设不成立。
因而不存在最大的素数。
下面是我个人无聊时一个简单分析，不能算作证明。如果我证明了，我也不是屌丝程序员了^.^。
假设M+1=2*3*5*......P + 1是一个素数，如果存在M+3或者M-1是一个素数，那么素数孪生出现的的结果成立。
M+3 = 2*3*5......P + 3 = 3*（2*5*7......P+1）很明显是一个合数。
M-1=2*3*5*7......P-1 可能为一个素数。
假设M-1不可能为素数：
1）p=3,M-1=5,假设不成立
M-1有可能是一个素数。
下面是英语原文
First ProofThat Infinitely Many Prime Numbers Come in Pairs
A U.S.mathematician claims a breakthrough toward solving a centuries-old problem
By Maggie McKee
Mathematician Yitang Zhang has outlined a proof of a"weak" version of the twin prime conjecture.Image: Maggie McKee
From Nature magazine
Cambridge,Massachusetts
It’s a resultonly a mathematician could love. Researchers hoping to get ‘2’ as the answerfor a long-sought proof involving pairs of prime numbers are celebrating thefact that a mathematician has wrestled the value down from infinity to 70million.
“That’s only [afactor of] 35 million away” from the target, quips Dan Goldston, an analyticnumber theorist at San Jose State University in California who was not involvedin the work. “Every step down is a step towards the ultimate answer.”
That goal is theproof to a conjecture concerning prime numbers. Those are the whole numbersthat are divisible only by one and themselves. Primes abound among smallernumbers, but they become less and less frequent as one goes towards largernumbers. In fact, the gap between each prime and the next becomes larger andlarger — on average. But exceptions exist: the ‘twin primes’, which are pairsof prime numbers that differ in value by 2. Examples of known twin primes are 3and 5, or 17 and 19, or 2,003,663,613 × 2195,000 − 1 and2,003,663,613 × 2195,000 + 1.
The twin primeconjecture says that there is an infinite number of such twin pairs. Someattribute the conjecture to the Greek mathematician Euclid of Alexandria, whichwould make it one of the oldest open problems in mathematics.
The problem haseluded all attempts to find a solution so far. A major milestone was reached in2005 when Goldston and two colleagues showed that there is an infinite numberof prime pairs that differ by no more than 16. But there was a catch. “Theywere assuming a conjecture that no one knows how to prove,” says DorianGoldfeld, a number theorist at Columbia University in New York.
The new result,from Yitang Zhang of the University of New Hampshire in Durham, finds thatthere are infinitely many pairs of primes that are less than 70 million unitsapart without relying on unproven conjectures. Although 70 million seems like avery large number, the existence of any finite bound, no matter how large,means that that the gaps between consecutive numbers don’t keep growingforever. The jump from 2 to 70 million is nothing compared with the jump from70 million to infinity. “If this is right, I’m absolutely astounded,” saysGoldfeld.
Zhang presentedhis research on 13 May to an audience of a few dozen at Harvard University inCambridge, Massachusetts, and the fact that the work seems to use standardmathematical techniques led some to question whether Zhang could really havesucceeded where others failed.
But a refereereport from the Annals of Mathematics, to whichZhang submitted his paper, suggests he has. “The main results are of the firstrank,” states the report, a copy of which Zhang provided to Nature. “The author has succeeded to prove a landmarktheorem in the distribution of prime numbers. … We are very happy to stronglyrecommend acceptance of the paper for publication in the Annals.”
Goldston, whowas sent a copy of the paper, says that he and the other researchers who haveseen it “are feeling pretty good” about it. “Nothing is obviously wrong,” hesays.
For his part,Zhang, who has been working on the paper since a key insight came to him duringa visit to a friend’s house last July, says he expects that the paper’smathematical machinery will allow for the value of 70 million to be pusheddownwards. “We may reduce it,” he says.
Goldston doesnot think the value can be reduced all the way to 2 to prove the twin primeconjecture. But he says the very fact that there is a number at all is a hugebreakthrough. “I was doubtful I would ever live to see this result,” he says.
Zhang willresubmit the paper, with a few minor tweaks, this week.
This article isreproduced with permission from the magazine Nature.The article wasfirst published on May 14, 2013.
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