MATT PARKER: Ok, there is a new world record largest prime number ever just announced
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
BRADY HARAN: Minus one?
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!
[Cutting]
MATT PARKER: There it is! There it is!
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
Right, so
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,
thousands and thousands of years,
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."
And so they agreed to let him put the
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...