JAMES GRIME: Yeah, we're doing sexy maths today, right?
So we're talking about sexy primes.
Well, I'm not really qualified to talk about sexiness.
I've come dressed as a salsa teacher tonight.
So hooray.
But I am qualified to talk about prime numbers.
Fortunately for me, though, in this case, sexy means another
word for six.
So it's sixy primes.
That's what we're going to do.
Let's be honest.
The reason we're doing this video is because it has a
funny name.
But let's see what a sixy prime is.
OK.
So a sixy prime--
or two primes, actually, that differ by 6.
So if I pick 5--
that's a prime number--
and 11, those are two prime numbers, and the
difference is 6.
So they called sexy primes.
We can pick another example.
Let's pick 7, and let's add on 6.
I get 13.
So a slightly bigger one, then.
Let's pick 251.
That is a prime number.
And let's add on 6, and we'll get 257.
Let's pick some sexy triplets.
Yeah, yeah.
It's getting more exciting all the time, isn't it?
This is 5, 11, and 17.
So those are three prime numbers, difference of six
between them.
These are sexy triplets.
Another one might be-- let's pick this.
I picked that one on purpose so I could use it again.
251, 257--
let's add on 6 again, and I get 263.
All right, sexy quadruplets.
Let's pick 5, 11, 17, and add on 6 again, 23.
Those are all prime numbers, and they are sexy.
Sexy quintuplet.
You're absolutely right.
5, 11, 17, 23, 29.
Those are all prime numbers, and that's a sexy quintuplet.
BRADY HARAN: That's not going to the next level,
that one, is it?
DR. JAMES GRIME: No, it isn't going to go to the next level.
You're right.
If I add on 6 again, I get 35, which is divided by 5.
It's not a prime number.
And in fact, that one is the only sexy quintuplet.
That is the only one that exists.
And I can prove to you that it's the only one that exists.
Can I?
Imagine you're going to pick a quintuplet.
We'll call the first one a, OK?
And the next one, well, you add on 6, don't you?
a plus 6.
So the next one is a plus 12.
And the next one is a plus 18.
And the next one is a plus 24.
These are my sexy quintuplets.
Now, these are all prime numbers.
Now, if you had a remainder of 0 when you divide by 5, that
means it's a multiple of 5.
Do you remember that from school?
When you divide by 5, a remainder of 0 means it's a
multiple of 5.
If you had a remainder of 5 or 10 or 15, that's another way
of saying it's a multiple of 5.
If a has a remainder of 0, then it's a multiple of 5, so
5 would work.
And we know what this is then.
If this is 5, we get 11, 17, 23, 29.
If it's a different multiple of 5, though, if it's 10 or
15, it's not a prime, right?
So we can get rid of that.
What about when you divide by 5, you get 1 left over?
By which I mean, what if it was 11, right?
You divide by 5, and you have 1 left over, a remainder of 1.
If that was true, this one over here would have a
remainder of 25.
And if it has a remainder of 25, it's a multiple of 5.
So it's not a prime.
We can keep going.
If that has a remainder 2, that has a remainder 20, and
it's a multiple of 5.
It's not prime.
If that has remainder 3, that has remainder 15.
It's a multiple of 5.
It's not prime.
If that has remainder 4, that has remainder 10.
It's a multiple of 5.
It's not prime.
It can only work if the first number had a remainder of 0,
and that only works if it's 5.
I've got something else about sexy primes.
So sexy primes, again, it's a funny name, right?
So they have a difference of 6.
There's a similar idea with other prime numbers, though.
If they differ by 2, they're called twin primes.
If they differ by 4, they're called cousin primes.
We have missed out 3's though, if they have a
difference of 3.
I don't think they have a name.
We'll call them triplet primes.
Let's call them that.
But if you think about it, if they're different by 3, one of
them has to be even if they're different by 3.
Now, there's only one even prime number.
It's 2.
So the only triplet prime will 2 and 5.
That's the only one.
But we can keep going.
If they have a difference of 5, what are we
going to call them?
Quincy primes.
Quincy--
that reminds me of Quincy solving crimes on a boat.
So if they have a difference of 5, same reason though.
They have to have one of them even.
So 2 and 7 are going to be Quincy primes.
If you keep going, we've talked about sexy primes.
So let's talk about difference of 7.
That's going to be a septic prime, which
doesn't sound very nice.
Septic prime.
One of them has to be even, so 2.
Add on 7, you get 9, which isn't prime.
There aren't any septic primes.
We've shown there's no septic primes.
If you keep going, I think the next one's
the best one, though.
Difference of 8.
What do you think that's going to be called?
Octimus Prime!
I think we can get a difference of 8, yeah.
Let's try it.
Let's have 3 and 11.
BRADY HARAN: And 19.
JAMES GRIME: There you go.
We've got an Octimus Prime triplet.
Hooray!
2 and 11 will be non, noni, noni--
nonlet.
BRADY HARAN: But surely it goes forever.
Lookit, we've got a whole industry to make here.
JAMES GRIME: I think the viewers are going to have fun
making up their own names now.
7 times 8 divide by 2.
That's 56 divided by 2.
How many--
how many arrows do you want?
So the next one, let's say we did 3--
Same thing.
--to the power of, to the power of--
oh, arrow, arrow, arrow--
Divide by 2--
--or whatever you want to call this.
--and that will give you the third perfect number for--