Here's a computer scientist.

He likes to consider unusual ways of doing arithmetic.

And he came up with this idea.

You know that in school, Children have a lot of trouble when they learn arithmetic.

Well, this there's all this trouble with the carries.

It's very complicated.

So he said, Let's let's make it simple for the kiddies.

We're not gonna have any carries.

We're going to abolish all Carrie's.

We're going to change the rules Now when you add two digits to numbers like seven and eight, the result is not 15 and you're on the moon.

It's eight.

You pick the bigger of the two numbers.

So one plus one is one.

Sure, one plus two is too.

When you multiply, you pick the smaller.

So one times two is one, and that's it.

Those are the rules.

That's lunar arithmetic.

So three times eight is 33 times eight is 33 plus eight is eight.

You take the bigger is the two.

I hope they didn't actually use this on the moon.

Maybe they didn't.

Maybe they will.

Future.

Okay, I understand the rules.

I'm a bit worried about what's gonna happen here.

But let's do some real.

It's missing.

Let's do an addition.

For example, Suppose we wanted to add, say, 58 19.

What you do is you say eight plus nine is let me take the bigger of the two.

Ah, no, no carries plus nine years.

No one plus five is five.

You take the bigger to bigger of one and five is five.

The biggest of nine and eight is nine.

So 58 plus 19 is equal.

59.

That's lunar addition.

What about multiplication?

Supposedly one.

Multiply, say 17 by 24 Remember, digit my digit.

So four sevens are for four.

Very good.

You pick.

The smaller four ones are one and now 272 sevens are 22 ones are one and now we add them up.

11 plus two is to you pick the bigger of the two and you bring down the four.

So 17 times 24 is equal to 124 on the moon.

So now you can do a lot of arithmetic in Luna.

Respond Take and you can produce not an interesting number Sequences writer Neal, We're reading your loud and clear from pictures on the contingency sample.

35 a half minutes of P.

L s s time expended now beautiful view in that magnificent desolation.

What are the squares?

Funeral arithmetic Once one times one is 12 times tooth is equal to pick the smaller it's 23 times 33 squared is 36 square 67 square.

That 78 squared is 89 squared is nine.

What about 10?

Squared 10 times 10.

We have to do it zero times zero.

You pick the smaller zero times one 012001 times one is one.

You had them up 10 plus zero pick.

The bigger is it when we get 100 just like back on us.

But what about 11 square?

Well, we have to do it 11 times 11 We get 1111 atom up 11 plus one is 12 11 squared is 11 100 left, 12 squared two times two is is to two times one is 11 times two is 11 times one is one.

Always speak the smaller and we have them up.

11 plus one is 12 is two.

So 12 squared is 112 on so on 19 squared is 119 and so on.

So that's the sequence of lunar squares.

Steel of you is okay.

We'd like you to aim a little bit corner right over.

If you were interested in a formal details.

This is an associative community of distributive law.

So it it works.

We don't have some traction.

We don't have division.

But apart from that, we can do anything.

What I would like to tell you about next of the lunar primes.

What are the prime numbers on the moon?

You're really gonna like this.

And I need more paper.

Okay, I'm gonna change.

Lambert.

Roger, Nail one of the lunar probes.

What is a prime fist?

Will we have to decide what it means for number to be a prime?

Now, you remember back on Earth seven was a prime because you couldn't ride seven as two times three or anything except one time seven.

If the only way to fact arise, it is as one times itself.

And it's a prime number on the moon.

It's seven.

A prime on the moon.

Well, notice seven is equal to eight times seven, right, Because eight times seven you pick the smaller of the two, which is 7 to 7 or eight times seven.

So seven is not a prime because it has a factory ization.

But really, before we get down to the details of this, we have to decide what precisely it means to be a prime.

So formally another was a prime.

If the only factory ization is one times itself, what does one mean on the moon?

We have to say, What is one?

I put it in quotes moon.

Well, what is 11 has the property that if you want to play anything, buy one.

You get what you started with.

One times three is 31 times 111 is 111 on the moon.

That's not true.

One times three on the wound is not three.

It's one one times are well.

One times 111 happens to be 111 by accident.

That one one on the moon one times anything is basically all ones and zeroes.

One times 30 is 10 because you go through digit by digit and pick the smaller.

So one on the moon is not one.

What is one on the moon?

What you care to make a guess?

What's the number is that I haven't thought about it at nine.

It's not very good.

Fantastic, brilliant, because when you multiply something by nine, it just copies.

What it sees 97 to 79 times one is one just copies when it sees so on the moon nine is the one.

So on the moon, a prime number has the property that the only way you can fact arise.

It is nine times itself.

So seven is obviously not a crime because seven is equal to eight times seven.

What about eight?

A.

It is not a prime because and he does equal eight times eight.

So it's not a prime has a factory ization in which one of the fact neither factor is nine.

Any number it for it to be a prime.

The biggest digit has to be a 9 25 is not a prime because we could multiply that by five and get what we started with So we've gotta have a nine in the number.

So 19 is smooth.

We must have a nice There's no way to build 19 except what, 19 times?

Nine.

You can't factories because it's got a nine in it.

So if you know if it was 18 we could move to play 18 by eight and get 18.

We'd have affection ization, so you can always multiply value biggest digit and get what you started with, said the big biggest digit had better be nine.

These problems are gonna be rare than yes, but not all that red.

So how rare are they?

Well, let's look at the prime numbers.

So what about nine itself?

So back on Earth, we don't say one is a prime because it's we wouldn't have.

Unique factory ization to is the smallest prime.

But on the moon, Justin's one isn't a primer on Earth.

Nine isn't a crime, but apart from that way, get 19.

So the primes, The lunar primes 1929 39 49 59 69 79 89 92 is a prime 91 song.

This is a nine, and there's no obvious way to fact arise that you have to check that 90 is a prime.

We can't get 90 by multiplying two numbers.

You have to check it, but it's true.

It's easy to check.

99.

We get 100 9 Yes, that's a prime.

But 119 is not because, as we saw a moment ago, 19 times 19 is 119.

So 119 is not a crime, but roughly speaking, most members that have a nine in primes, so those of the lunar primes.

If we were to go to the O.

A.

I s and we're in the search window, we talked Luna crimes.

We used to call the dismal primes because teaching of arithmetic in schools suit It's a dismal definition.

I think we like lunar primes much better, so well, I can show you the graph photographs.

One of the 1st 200 terms.

Technically, it's called a pin plot because we draw a little pins.

You don't see the pins there because they're quite dense.

And then you get scatter plot justice plane graph of however many terms we have, and it looks like we're getting about What is it?

2500 terms.

There's one more thing I would like to show.

I'd like to prove that they're infinitely many primes.

You remember infinitely many lunar prime.

First of all, I'll present 100 9 his prime.

The proof of that is suppose it wasn't.

It would have to be the product of 22 digit numbers.

They would have to be two digit numbers because of the rules, so it would have to be a B times C D.

But we've got a get a one at the beginning.

So one of A and C remember how it works.

The table is the multiplication, the tableau.

You get one at the beginning, either A or C has to be a one and two get a nine at the end.

Both B and D have to be nine.

That's the other.

The only possibility, because when we do the multiplication nine times nine is nine nine times one.

Well, that's that's one pick the smaller of the two.

Okay, now we do.

The C C.

Times nine is well, it's see whatever, See is multiplying it by and nine doesn't change and see time's one well see copy zero.

So it's going to be one.

Now we add them up and we get 11 plus c.

I don't know what it is.

It's the bigger of one and see Well is gonna be see Could be one.

Anyway, what we get is the number one c nine.

But see can't be zero because if she was zero, we wouldn't get the one in front.

So this can't happen.

This is a contradiction.

If she was equal to zero, we wouldn't get the one in front.

We cannot fact arise 109.

It's a product of two primes.

And then likewise, 100009 is prime by the same argument.

That's one small step for man.

There are infinitely many primes.

Yeah, no matter how many you can put as many zeroes, there's many sinners as you want and you get a prime.

So nice proof.

Yeah, Yeah, Nice to Luna.

Prime's way.

You're coming down the ladder now are the ones that the mathematicians like these of the primes or numbers that are related to primes on Dhe They are.

They are elevated up off the ordinary numbers.

Zero 15 27 1941865 And so on.