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13532385396179

13532385396179 - Numberphile

最好写下来 那么我们开始吧
Gonna write it down. So here we go.
我从不曾试着来读出这个数 因为它实在太庞大了
I’m not even gonna try and say it cause it’s a bit too big.
2385
Two three eight five
79
seven nine.
像不像你的工资条
Like your salary?
是 是有点像 额
Yeah, something like that, eh?
我要来告诉你关于这个数一个很有趣的现象 并且告诉你为什么有趣
So I’ll tell you something funny about this number, and I will say why this is interesting.
这个数字可以写成13乘以53的平方
This number happens to be 13 times 53 squared
乘以3853
times three eight five three
乘以96179 现在 有趣的是我写下来的这些数字是这个数的
times nine six one seven nine. Now the funny thing about that is what I’ve written down there is the prime
素数分解的素因子 所以这些都是因子 这些 13是因子 53也是因子
factorization of this number. So all these are the prime numbers, these – 13 is prime, 53 is prime,
3853是因子 96179也是因子
3,853 is prime, and 96,179 is prime.
所以这个算数列是这个数的素数分解式 但是一起来看下我们是怎么得到这个数的
So this is the prime factorization of this number, but look at how you could have got this number.
这是13
There’s your 13, right?
这是53
There’s your 53.
这是平方2的2
There’s your 2.
这是3853 这是96179
There’s your three eight five three, and there’s your nine six one seven nine.
这里我们得到什么结论 这不是我做出来的 是一个叫詹姆斯·戴维的哥们
What have we done here? I haven’t done this. This is a guy called James Davis.
他不是一个数学家 目前为止 我们还不知道他是何方神圣
He’s not a mathematician as far as we understand, we’re not really sure who he is,
他最近提出了一个反例
who’s actually very recently come up with a counterexample
是一个对约翰·康韦的1000美金奖励制命题的反例
to one of John Conway’s $1,000 problems that he’s posed.
约翰·康韦是一个大人物 著名的数学家 相当举足轻重的人
John Conway – big guy, big famous mathematician, you know, very important.
他提出了5个命题 如果有谁能够解决或是举出反例 这样的话
He’s come up with these five problems, the idea being if anybody can solve them or you know, find counter examples, that sort of thing,
那他们会得到…他会给他们1000美金
then they’ll – he will give them $1,000.
在数学界我们总有一些问题
And so we’re accustomed really in mathematics to have these problems
终你一生可能都得不到解决办法
that you don’t expect to see solved in your lifetime.
所以我觉得他欠詹姆斯·戴维斯1000美金 为什么呢
So I think he owes this guy James Davis $1,000 right? and here’s why,
那约翰·康韦是提出了什么命题咧
so what was the problem that that John Conway posed?
当然 是关于素因数的分解
Well, it’s the idea of climbing to a prime.
我来随便写个数 比如60
So if I take any number, so for example 60, say,
我现在写下来它的素因子
then what I do is I write down the prime factorization of this number.
所以在这个例子中 60等于2的平方
So in the case of 60, that’s 2 squared
乘以3再乘以5
times 3 times 5.
接下来我要做的是 -这是约翰·康韦提出的一个重复性问题
Now what I do is – this is the iteration that John Conway suggested is –
把所有的平方数 都拿下来
all those powers, I bring them down. Okay?
那么就会得到2235这个数
So I write this as two two three five.
现在我得到了2235
So I now get the number 2235.
现在我再来做这个数的素因子分解 那么会变成
Now I do the prime factorization again, so this happens to be
3乘以5
3 times 5
乘以149
times one four nine.
接着你按这样的方法 再重复分解 你就会得到一个新的数
So now you use this, you do the iteration again, you create a new number,
这个新的数当然就是35149 对吧
and the new number of course is going to be three five one four nine. OK.
这是一个素数 对不对?
This is a prime number, OK?
所以约翰·康韦的猜想是 在你做素因子分解的过程中
So John Conway’s conjecture was if you do this process,
你按照这个过程去分解任何数 那么你最后总是会得到一个素数
you carry out this process for any number, you’ll always end up with a prime number.
再来举个例
So just to give you another example
用25举例 它是5的平方数 所以5的平方 把2写下来变成了52
let’s take 25, say. It’s of course 5 squared. So 5 squared, I bring down the 2 so I make 52.
好 那52等于
Okay. 52 is
2的平方
2 squared
乘以13
times 13.
我再把2写下来
And so I bring down the 2,
现在就是一个新的数2213 而它是一个素数 是吧!
so that’s two two one three and that’s prime. Okay.
这个命题似乎是正确的 虽然我们只做了两个例子 几乎不算证明
So it seems to work, well it’s worked in two cases. That’s hardly a proof, right?
但是 有很多的例子都能证明这个猜想
But no, there’s many examples of this.
它没有 -还没有出现反例
It wasn’t – no counterexamples were known.
假设你用20这个数来分解 人们按照这个方法已经反复做了上百次的分解
If you take the number 20 for example, people have done over a hundred iterations of this, this procedure.
一直没办法得到一个素数 20是个很有趣的数字
Still not managed to climb to a prime yet. 20 is a bit of a funny one.
但是不管怎么样 目前已知的对此还未有任何反例
But anyway, there was no known counter example to this
直到几天前 詹姆斯·戴维斯这个小伙子发布了一篇博客
until just a few days ago, this guy James Davis responded to a post that a blogger,
一个叫做hans havermann的博主 在网络上讨论这个命题
a mathematician blogger called Hans Havermann had put on the Internet discussing this.
这篇博客是在几个月前发布的 大概7 8个月
So this is a few months – this is about 7 or 8 months old, this post.
然后某一天 詹姆斯·戴维斯说 我找到了解决办法
And then the other day James Davis posted “I’ve got a solution to this.”
这就是他的结论
And here was his solution.
他意识到如果你陷入一个循环 那么你最后将会得到最开始的那个数字
So what he realized of course was that if you get caught in a loop, you end up going back to the same number,
然后你就可以举出反例 对吧 因为你总会分解到以素数结尾
then you have a counterexample, right? Because you’re always supposed to end at a prime, right?
如果你是在一个循环里 那么你永远不会以素数结尾
So if you get caught in a loop, you’re never going to end up at a prime.
所以这是一个循环
So this is one loop later.
假设你遇到一个循环数 你以这个数开始 做它的素因子分解
Just straightaway you hit a loop, right, you start off with this number, you do the prime factorization,
然后像刚刚我演示的那样把所有的平方数写下来 结果组合起来又是这个数 是吧
and then you drop all the powers in the way that we’ve just described, and you end up back with the same number, okay?
所以这个 就是对猜想的反例
So this straightaway is a counterexample to the conjecture,
所以说这就是他值得 你知道的 他的1000美金
so this is how he’s earned his, you know, his thousand dollars.
它是一种 -我认为这是现在社会的美妙之处
And it’s kind of – I think it’s kind of nice that you know, today,
现在的社会 就如你知道的 即使人们不是专业的数学家 物理学家 或是什么家
even today that, you know, people can without being professional mathematicians, professional physicists, whatever,
他们仍然可以解出并且实际可行 这就是个非常棒的例子
that they can still come out and actually have an impact. This is a lovely example of it.
不知道 我不喜欢去思考早晚要来的死亡 即使它离我很近
I don’t know. I don’t like thinking of my impending death.
而且你知道的 我已经离开数学界很多年了 我不记得具体多少年
And, you know, I haven’t got all that many years left. I don’t quite know how many.
但是我还是很喜欢做一些和数学有关的事 一如既往
But I do still like doing mathematical things so I do.

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视频概述

数字狂|一个有趣的素数分解结果|以这个数开始素数分解最后再得到的却还是这个数

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收集自网络

翻译译者

陛下

审核员

审核团H

视频来源

https://www.youtube.com/watch?v=3IMAUm2WY70

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