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全球最大的质数印刷在纸上是什么效果?

New World's Biggest Prime Number (PRINTED FULLY ON PAPER) - Numberphile

Matt Parker: 这有个昨天刚发布的打破世界最大记录的质数
MATT PARKER: Ok, there is a new world record largest prime number ever just announced
今天我收到个特别的快递,东东还在包裹里。
yesterday and today I had a special delivery, this arrived in the post.
包裹里装的就是那个新发现的梅森质数-二的
In here we have the newly discovered Mersenne prime. In here is 2 to the power of
7千4百20万7千2百81次方。(看下我念对没) 要是你真的
74,207,281 (make sure I get that right) and if you actually were
Brady Haran: 减1?
BRADY HARAN: Minus one?
Matt Parker: 减1,减了1还是一样大。
MATT PARKER: Minus one. Trivial at that size.
要是你真的把这个2千2百万的质数打印出来的话,
If you were actually to print this number out it’s 22 million, it’s
字数超过2千2百万位。大概是2千2百33万8千6百18位,
over 22 million digits. It’s around 22,338,618
没人会蠢到把它打印出来然后快递给别人!
digits and no one would be foolish enough to get that printed and shipped to
既然这个数字已经发布了出来,那我们就拆开来看看。
them the moment the number was announced, other than us, so let’s get in there!
(拆箱中)
[Cutting]
Matt Parker: 就是这个! 就是这个!
MATT PARKER: There it is! There it is!
这就是刷新世界最大记录的数字,看!
This is the new world record, look at that!
这是2的7千4百20万7千2百81次方减1,这些都是数字,这是第二册,第二册的第三本
That is 2 to the power of 74,207,281 minus 1. These are the digits, Volume II. Volume II of III.
还有第三册,下面还有第三本
So there’s Volume III, and so there’s another third and finally here I guess
应该从头拿起,来了,第一……册
we should start at the beginning, this is, there you are, Volume… I.
看看这个最新的质数!这是……
Look at that! This is the new prime number! This is… we
我们应该是……我们肯定是最先把它打印出来的,
suspect we are, well we’re definitely the first people to have ever printed it out. I suspect
我觉得我们应该也是最后一个去把它打印出来的人。
we’re still the only people to have ever printed it out because that is over two
因为它的位数达2百万位,每个数字都跟蚂蚁一样。我曾为了这些数字看起来比较直观,
million digits printed in tiny, tiny type. I went for a monospaced typeface to
将其排版在等距印刷字体规格里。呀!这里有错!呵呵,才没有!
make it easier to locate the digits within there, oh there’s a mistake! Ah there’s not
呃……
Right, so
我觉得没人会因为一个新的质数面世而欣喜。但是偏偏
I don’t think people get very excited when a new prime number’s found, but very rarely do you
你又会去宝贝它。所以说…所以说它是一项严肃的,
actually get to pick it up and hold it. So that’s… that is some serious, they are some
有重量的……重大意义的数学知识。你看,你看这圆周率一样的数字!
weighty… that is some weighty mathem- look at that! Look at the size of that number!
看这个,我是提倡绿色无污染的,我不想浪费纸张,正反面我都打印了。
And this, obviously I’m environmentally friendly, I wanna waste paper, so it’s front and back.
这年代啊,数学家的爱好之一就是去研究发掘一些新的质数,
Now, finding prime numbers is a common hobby for
就你所知的上千年的
mathematicians and you know for millennia,
千千万万年前的数学家,
thousands and thousands of years,
他们都迷于发掘质数和无因质数,
mathematicians have been obsessed with finding prime numbers,
所以这个年代,
numbers with no factors and now, it’s getting harder
去发掘一些比前人发现的更大的质数来打破记录是越来越难了。
and harder to break the world record of the biggest prime number ever found and
3年前的一项世界记录是距今最近的记录了,
so the previous world record was three years ago and if anyone has been
如果有人长期看我们的《数字狂》的话,你应该能想起我们聊过的一个话题。
watching Numberphile videos for that long you remember we covered it. Tony did a
Tony先前创下的那个保持了3年的世界记录,
video on the previous world record and that record stood for three years and now we
现在我们有人打破了,但是这项记录来得可要艰难多了。
have another one but they’re getting so much harder to find and so this one is
这次发现的质数比之前的位数多了将近5百万位,
almost five million digits longer than the previous one and so it’s gone from
所以这个记录是从大约1千7百万位的质数提升到大约2千2百万位。你可能觉得这数学家的工作不太……数学家的工作可牛了。
around 17 million up to around 22 million, you think thats not a… it’s a decent job, but don’t forget
但别忘了之前每一个质数的位数都是以10的倍数递增的,所以递增5百万的量,
every digit, the number is 10 times the size and so that’s another five million
那可是相当惊人的。换个说法,那可是严重超标的!
orders of magnitude bigger. I mean, that’s just off the scale. So, the
这个记录是中央密苏里州立大学的Curtis Cooper教授创下的,
record has now been taken by Professor Curtis Cooper. He’s at the University of Central Missouri
他在大学里管理及运行大量的计算机。
and he was running loads of computers there. He found this prime, he
他发掘的这个质数打破了先前自己的世界记录,
won the world record off the previous holder which was Professor Curtis Cooper
这是他第四次打破世界记录,他……呃,他把这些质数都整成一家人了。
of the University of Central Missouri so he’s won, it’s his fourth! He’s…. he’s hogging them
我……我也是搞软件的。我是真想搞个新的世界记录出来。
to be entire- I mean I… I run the software too. I really want to find a world record
我为前100个发掘出最大质数的人感到开心
I’d be happy with anything in the top 100 biggest known primes but no he’s
大概10年前他发掘了2个最大质数使他的记录稳居榜首
hogging the top spot and so he found two in a pair about a decade ago and then
当有人把他的最大记录打破之后,他在3年前又发掘出更大的把榜首位置夺了回去
someone else got the world record back and then he regained the world record
现在他发掘更大的质数打破自己先前的记录不过是在巩固自己的地位而已。
three years ago and now he’s just cemented his position. He is
他真是质数之父。如果你想尝试去发掘存在的比之前更大的质数,这有个方法:
Captain Prime. So the way this works if you wanna try and find the biggest prime
你什么都不用做,真的,尽管下载一堆软件让计算机自己运行就可以了
known to humankind is you just, you don’t have to do anything really, you download a bit of
就像我刚说的,我办公室有台正运行着很多软件的计算机
software and you run it on your computer. So, as we speak there’s a computer in my
现正尝试发掘新的数值更大的质数。一些中心服务器
office running a bit of software to try and find prime numbers and some central server
会发一些待验证是否为质数的数字给你。你的计算机只管排查即可
will send your computer a candidate number. Your computer will then check it
很多时候,验证出来的数字值是破了记录,但是可惜不是质数。
to see if it’s prime or not, and, more often than not, for the vast majority, not prime!
到时你就会反馈给中央服务器只能遗憾地说一句:不好意思,这不是质数。
So you send it back and go “Sorry guys, not prime”, very occasionally you’ll
很有可能发来的数字你的电脑会在你不知情的情况下自动排查。
be sent a number your computer will check it, you won’t even know. You’ll be out and
像这种数字,排查完都要花一个月的时间。期间你可以出去做你想做的事,
about and a number like this takes about a month,
其他就交给你的计算机来处理
so your computer will sit there for a month on a number like this. At the very
最后可能会发现这个数字不是质数,如果罕见地出现了个质数,它会反馈给服务器
end… it’s not gonna be prime. But, very rarely, if it comes in prime it gets sent back
然后功劳是你的,是你发掘了新的更大的质数,是你打破了记录
and officially you found it, it’s your record. The policy is a number only
原则上是这样的:这个成为世界记录中的质数得有人见过
counts as a world record prime once it’s been seen by a human,
这个数字是明显存在的
because obviously this number’s always existed.
先于宇宙的形成,而不是我们发明的
This number predates our universe so it’s not like we’ve invented it, we’ve just
我们只不过是发掘到了它而已。计算机识别出它是质数只是第一步
spotted it and so your computer finding it is not enough. When it gets flagged up
当识别出来有人知道了它的存在后会再次验证
that it exists and human goes, “Hey, check it out!” That’s when it officially counts as a
末了才能冠以质数之名。这时你才算成功了,还会有奖品。当然这是后话了
new prime number and, so yes you can win, well there’s a prize, but that’s beside the point.
你成功之后,会被奉为发掘者并得到赞美和认可,这你懂的。诶,羡慕嫉妒恨
You can win, you know, accolades and recognition as The Finder. I’m so envious!
Brandy Haran: 这个听起来就像中彩票一样,这Curtis Cooper教授都连中四回了,他是不是有什么秘诀?
BRADY HARAN: Sounds like a lottery, winning it, and yet this one guy’s won it four times. What’s his secret?
Matt Parker: 呃,他们筛选数字这件事听起来就像是中彩票一样,对吧!
MATT PARKER: It does sound like a lottery doesn’t it, that they’re just handing out numbers err…
教授成功的秘诀就是: 他有超多计算机。他管理运行的台式计算机就有800台
Curtis’s secret is he has a lot of computers. So he’s running it on 800 desktop
所以有次他在中央密苏里州立大学的时候跟人说:
computers. So he had a chat with the people at the University of Central Missouri and said
“瞧瞧你们的计算机,在实验室昼夜不分地运行”
“Look, all your computers, you’ve got them running in the labs around the night,
“像是一天24小时不用停那样。”明显这样效率更高
like they’re on 24 hours,” because apparently it’s easier to push updates
所以他们根本不会让计算机停下来
and things to the computers and so they deliberately keep them on.
还说:“我们要把计算机的功能都用上。”
And he goes, “We don’t waste all that computing power.”
所以他们同意教授
And so they agreed to let him put the
把”互联网梅森质数大搜索”或者是简称”G.I.M.P.S”写进学校的电脑
Great Internet Mersenne Prime Search or G.I.M.P.S. for shorthand, terrible,
呃,如果你想网上搜的话,不用谷歌……直接打全称”互联网梅森质数大搜索”就可以了
Ah, if you’re gonna look it up online, don’t Google… type out all of “Great Internet Mersenne
教授都把它写进计算机去了。那800台在校的计算机
Prime Search” and he put it on all the computers. And so for the 800 computers at the
不管多久没被人点击使用过
university there, whenever they’re not being used they kick in and start doing
有些电脑就一整个月搁在那,白天供人学习使用
this. So some computer sat there for a month, during the day it was helping people learn,
有人用来做作业和一些学习上的事情
people were coming in using it for assignments and university work and at night when everyone
到了晚上,使用者离开关机后,它就会自动启动去跟数字奋斗
turned the lights out, it would fire back up again, it would reopen this number
找到它上次暂停的位置然后继续排查
and go “Right where am I up to?” right and then it would carry on and it would check if it is
如果找到质数,它就会突然发出“叮”一声
prime or not, and for one of them it suddenly… ding! At the end result, it
之后会把这个结果反馈到服务器里。简直是太神了!
was prime and got sent off to the server. Absolutely incredible!
在Lucas-Lehmer序列里的第12个平方,我们只能看到8191这个结果
MATT PARKER: The 12th term in the Lucas-Lehmer sequence, but we only have to find it mod 8191.
再来的话也跟之前一样,4个平方得到14再平方……
So to start with it’s the same, you have 4 you’d square that, you would get 14 you’ll square that…

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