Name: New World's Biggest Prime Number (PRINTED FULLY ON PAPER) - Numberphile
Uploaded: 2020-03-27T18:04:32.000Z
Duration: 6 min 39 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

The superlative

MATT PARKER: Ok, there is a new world record largest prime number ever just announced

Past simple

yesterday and today I had a special delivery, this arrived in the post.

In here we have the newly discovered Mersenne prime. In here is 2 to the power of

74,207,281 (make sure I get that right) and if you actually were

MATT PARKER: Minus one. Trivial at that size.

If you were actually to print this number out it's 22 million, it's

over 22 million digits. It's around 22,338,618

digits and no one would be foolish enough to get that printed and shipped to

them the moment the number was announced, other than us, so let's get in there!

This is the new world record, look at that!

That is 2 to the power of 74,207,281 minus 1. These are the digits, Volume II. Volume II of III.

So there's Volume III, and so there's another third and finally here I guess

we should start at the beginning, this is, there you are, Volume... I.

Look at that! This is the new prime number! This is... we

suspect we are, well we're definitely the first people to have ever printed it out. I suspect

we're still the only people to have ever printed it out because that is over two

million digits printed in tiny, tiny type. I went for a monospaced typeface to

make it easier to locate the digits within there, oh there's a mistake! Ah there's not

I don't think people get very excited when a new prime number's found, but very rarely do you

actually get to pick it up and hold it. So that's... that is some serious, they are some

weighty... that is some weighty mathem- look at that! Look at the size of that number!

And this, obviously I'm environmentally friendly, I wanna waste paper, so it's front and back.

Now, finding prime numbers is a common hobby for

mathematicians and you know for millennia,

mathematicians have been obsessed with finding prime numbers,

numbers with no factors and now, it's getting harder

and harder to break the world record of the biggest prime number ever found and

so the previous world record was three years ago and if anyone has been

watching Numberphile videos for that long you remember we covered it. Tony did a

video on the previous world record and that record stood for three years and now we

have another one but they're getting so much harder to find and so this one is

almost five million digits longer than the previous one and so it's gone from

around 17 million up to around 22 million, you think thats not a... it's a decent job, but don't forget

every digit, the number is 10 times the size and so that's another five million

orders of magnitude bigger. I mean, that's just off the scale. So, the

record has now been taken by Professor Curtis Cooper. He's at the University of Central Missouri

and he was running loads of computers there. He found this prime, he

won the world record off the previous holder which was Professor Curtis Cooper

of the University of Central Missouri so he's won, it's his fourth! He's.... he's hogging them

to be entire- I mean I... I run the software too. I really want to find a world record

I'd be happy with anything in the top 100 biggest known primes but no he's

hogging the top spot and so he found two in a pair about a decade ago and then

someone else got the world record back and then he regained the world record

three years ago and now he's just cemented his position. He is

Captain Prime. So the way this works if you wanna try and find the biggest prime

known to humankind is you just, you don't have to do anything really, you download a bit of

software and you run it on your computer. So, as we speak there's a computer in my

office running a bit of software to try and find prime numbers and some central server

will send your computer a candidate number. Your computer will then check it

to see if it's prime or not, and, more often than not, for the vast majority, not prime!

So you send it back and go "Sorry guys, not prime", very occasionally you'll

be sent a number your computer will check it, you won't even know. You'll be out and

about and a number like this takes about a month,

so your computer will sit there for a month on a number like this. At the very

end... it's not gonna be prime. But, very rarely, if it comes in prime it gets sent back

and officially you found it, it's your record. The policy is a number only

counts as a world record prime once it's been seen by a human,

because obviously this number's always existed.

This number predates our universe so it's not like we've invented it, we've just

spotted it and so your computer finding it is not enough. When it gets flagged up

that it exists and human goes, "Hey, check it out!" That's when it officially counts as a

new prime number and, so yes you can win, well there's a prize, but that's beside the point.

You can win, you know, accolades and recognition as The Finder. I'm so envious!

BRADY HARAN: Sounds like a lottery, winning it, and yet this one guy's won it four times. What's his secret?

MATT PARKER: It does sound like a lottery doesn't it, that they're just handing out numbers err...

Curtis's secret is he has a lot of computers. So he's running it on 800 desktop

computers. So he had a chat with the people at the University of Central Missouri and said

"Look, all your computers, you've got them running in the labs around the night,

like they're on 24 hours," because apparently it's easier to push updates

and things to the computers and so they deliberately keep them on.

And he goes, "We don't waste all that computing power."

Great Internet Mersenne Prime Search or G.I.M.P.S. for shorthand, terrible,

Ah, if you're gonna look it up online, don't Google... type out all of "Great Internet Mersenne

Prime Search" and he put it on all the computers. And so for the 800 computers at the

university there, whenever they're not being used they kick in and start doing

this. So some computer sat there for a month, during the day it was helping people learn,

people were coming in using it for assignments and university work and at night when everyone

turned the lights out, it would fire back up again, it would reopen this number

and go "Right where am I up to?" right and then it would carry on and it would check if it is

prime or not, and for one of them it suddenly... ding! At the end result, it

was prime and got sent off to the server. Absolutely incredible!

MATT PARKER: The 12th term in the Lucas-Lehmer sequence, but we only have to find it mod 8191.

So to start with it's the same, you have 4 you'd square that, you would get 14 you'll square that...