JAMES GRIME: I'm thrilled today.
We've got a present.
One of our viewers has sent us a present,
this mysterious box.
And check out the warning on the box. "Warning--
Contains numbers." Exciting?
I think so.
So shall we open up the box and see what this present is?
We actually got two of these, one for Brady, one for me.
We really appreciate that.
Thank you very much for sending this.
There we go.
We have got some mysterious object here.
I'm not sure what it is yet, Brady.
BRADY: That's awesome.
JAMES GRIME: Yeah, what do you think it's going to be?
We're going to have to plug it in.
Now, this one's yours, Brady.
I think you should have the first press
of the big red button.
BRADY: I have no idea what's going to happen here.
JAMES GRIME: Oh!
[CLICKING]
JAMES GRIME: Try again?
[CLICKING]
JAMES GRIME: Now, have you worked out
what it's doing yet?
These are prime numbers.
Each one is a new prime number.
It's a prime number generator.
This was made by our viewer Karl Lautman, and he makes
kinetic sculptures, these sculptures that move and do
exciting things.
And he's made a short series of these, and
he sent us a couple.
And you'll get the next prime number.
It's so satisfying, especially if you like having a big red
button to press.
And it gives you a feeling of the gaps between
the primes, as well.
You see that some are short.
[FAST CLICKING]
JAMES GRIME: Oh, that was nice.
That was satisfying, a nice, long gap.
It's really nice.
I mean, it's a bit of silly fun.
There's no practical use to it or anything.
But I love it.
[CLICKING]
JAMES GRIME: You can't reset it.
You're stuck now.
You have to go through all the primes until you reach
999,999, and it will wrap back to zero.
Now we're about 251,000 here.
Now, the prime number theorem, one of the big theorems in
mathematics, says that the average gap between the primes
should be round about the natural log of 251,000.
I know that's about 12, so the average gap
should be about 12.
Some are going to be bigger than 12, some are smaller.
Sometimes you get a twin prime.
[CLICKING]
JAMES GRIME: And sometimes you get a long gap.
But the really exciting number to wait four is 492,113,
because at 492,113 you get the longest prime gap that this
machine can generate.
It's a gap of 114, so I think that will be an exciting day,
when we can get to 492,113.
So Karl's put in a microprocessor in this.
I don't think it's doing anything clever.
I think it counts the gaps between the primes.
And he only has a few of these.
Perhaps we can put a link to his websites, and he can tell
people about his work.
That would be nice.
But when they're gone, they're gone, I'm afraid.
It was such a surprise.
I got a huge box delivered to my work, and I had no idea
what it was.
I wasn't told it was coming.
So I had this huge box, and I was digging
through all this packaging.
And then this is what comes out the other side.
I plugged it in.
It was given to me with a letter, so I did kind of know
what it was.
But it's the--
[CLICKING]
JAMES GRIME: Oh, it's the clicking noise.
I mean, I was so thrilled.
You do realize I had to pay the import tax for this.
BRADY: Really?
JAMES GRIME: Yeah.
He paid me back.
BRADY: Do you know what I really want?
A twin prime.
Give us a twin prime.
JAMES GRIME: Of course.
Of course I'll do that for you.
BRADY: Well, it won't be this.
It could be this.
[CLICKING]
BRADY: Could be--
no.
JAMES GRIME: What about a sexy prime?
[CLICKING]
[LAUGHING]
[CLICKING]
BRADY: Was that a twin prime?
JAMES GRIME: I think that might have been
a twin prime then.
BRADY: Woo!
Twin prime!
JAMES GRIME: And it actually shows you something about the
randomness of the primes.
They turn up frequently, but they're kind of
unpredictable as well.
Karl has very kindly signed it for us.
He's dated it, and he's numbered the primer.
That's what he's called it.
It's Primer Number 4.
And I just showed this to Brady, and he was very
disappointed because he hasn't got a prime number.
I got Number 3.
I got Primer Number 3.