DR. TONY PADILLA: The GIMPS have been at it again.
They've found a new prime number, the largest prime
number that's been found to date.
The GIMPS, of course, are the Great Internet Mersenne Prime
Search team, a network of computers and people that work
on these computers that look for large Mersenne primes.
It's a pretty big number, 2 to the power-- now, I've got to
remember this, now--
57,885,161 minus 1.
So the 57,885,161 is a prime number.
But this bad boy, the whole thing, is also a
prime number, of course.
It's a much bigger one.
And that is the largest prime number ever
to have been found.
It's the 48th Mersenne prime ever to have
been found as well.
BRADY HARAN: Can you remind us what a Mersenne prime is?
DR. TONY PADILLA: Yes.
So essentially, the Mersenne prime-- you just take 2.
You take it to some power, P--
and this is a prime number-- minus 1.
And that's your Mersenne prime.
It's pretty interesting how they've gone about finding
this, as well.
There's various things about it.
For example, the way it's done is they
have this GIMPS network.
They're a network of shared computers.
And they use their combined computing power to basically
work out, try and find these prime numbers.
So it's quite interesting, this sort of collaboration
going on to find these things.
From my point of view, it's actually reminiscent of
something that they do at the LHC to manage the data.
They basically use a network of computers around the world
to analyze that data.
So it's not always academics that are finding these things.
Anybody can get involved in the project.
And there's money on the table, as well, when it comes
to finding these things.
Curtis Cooper will win--
it looks like $3,000 for finding this number.
It's a bit of a shame for him because
this number, actually--
well, it has this many digits.
It's this many digits long.
It is 17,425,170 digits long, I think.
The reason this is a little bit annoying for Curtis Cooper
is that it's not 100 million digits long.
Because if it had been 100 million digits long, then he
would have won $150,000.
Because that's the prize on offer if he can find one
that's actually that long.
It's worth thinking about how big this number actually is.
And we've talked about big numbers in the past, Brady.
It is bigger than a googol.
It's not as big as a googolplex.
It's certainly not as big as Graham's number.
You can easily think of this number without your head
collapsing to form a black hole.
There's no problem there.
In fact, actually, it's quite easy to think of.
You could even memorize this number.
Here we have the number.
So this is the number written out in full--
quite a big file.
There you go.
It's got 17 and 1/2 million digits.
This file is about 22 meg.
Now, apparently, your brain can store about 2.5 million
gig of memory.
So technically, you could memorize this number without
having a problem.
And in fact, I'm going to be cocky here because I actually
can write this.
I'm going to write this number.
I've remembered this number.
But I've remembered it in base 2.
OK.
So let me write down it out in base 2.
I was quite impressed that I remembered this.
So the first number is 1.
The second number-- ah, it's also 1.
And the next one's also 1.
And the next one is also 1.
And I would carry on writing 1's until I got all the way to
the last number, which is also 1.
And there would be a grand total of
57,885,161 of these 1's.
And that is the number written in base 2.
So I can prove that for you if you'd like.
BRADY HARAN: Go on.
DR. TONY PADILLA: OK.
So the reason that that's what it is in base 2--
OK.
So let's look at this number.
Let's just call it P for now, rather than this 57 million.
Because we can prove this in generality.
I can actually factorize this expression.
And I can factorize this expression as follows.
It's 2 minus 1.
That's obviously 1--
multiplied by 1, plus 2, plus 2 squared, all the way up
to 2 P minus 1.
OK.
So this is obviously 1 out front.
So what I'm left with is just all the, basically, essential
units of base 2 with 1's in front.
And that's it.
So that's the proof.
So there's obviously P of these in total.
So in our case, P is 57,885,161.
And so this is how you would write it out in base 2.
BRADY HARAN: In base 10, which is what more people are
familiar with, what's the first and last digit?
DR. TONY PADILLA: So I'm going to have to look this one up.
Well, I think I know the first, actually.
actually.
It's 5, isn't it?
It's 5.
And the last one-- can I look?
BRADY HARAN: Yeah.
DR. TONY PADILLA: I've got a feeling the last one's--
well, we know it's going to be an odd number, don't we?
So we've got 1.
There we go.
Of course, we have a new perfect number from this.
And it's very easy to write down what it is.
And the perfect number that we have--
2 to the 57,885,160, multiplied by 2 to the
57,885,161 minus 1.
That's our new perfect number.
It's about 34 million digits long.
Yep.
That's our new perfect number we've got out of this.
So whew.
It's all good fun, basically.
And I think that there is an important point to come from--
these searches.
I mean, they're fun to look at.
It's nice.
It's interesting.
Oh, we found this new, big prime number.
There's a lot of technology that goes into sort of
developing the software to do these calculations.
Because basically, if you actually tried to calculate
all the divisors of this guy, you've used all the numbers
that were smaller than it and tried to see if they were
factors of that number, if you did that, just like that, sort
of blindly, you'd find that you needed more than the age
of the universe to actually do that calculation.
So there's sophisticated techniques at work here.
And all this game, and all this developing this computing
power in particular ways to multiply large numbers, really
have had sort of impact elsewhere, for example.
It's the spinoff technologies that are coming from this sort
of really mathematicians playing games.
But you should never knock mathematicians playing games.
Because the crumbs that fall off the table can be of
benefit to everybody else.
BRADY HARAN: If you'd like to see even more from this
interview, including a rather strange discussion about my
family tree, I've got an unlisted video with all the
off cuts and extra footage.
I basically didn't put it as a listed video because I didn't
want to clog up everyone's subscription boxes.
And if you want to find out more about some of these
topics and you haven't watched our back catalogue of videos,
I've also put links to our films about Mersenne primes,
perfect numbers, googols and googolplexes, Graham's number,
all that kind of stuff.
Check out the links under the video or here on the screen.