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Marcsine: How Many Primes Are There? - Duration: 3:01.

♪ ♪ ♪

Prime numbers are everywhere.

You're walking down the street,

minding your own business, when

BAM!

Hey, are you a

prime number-

No.

Can I see some ID?

Oh, well, uh, y-uh, y-

You see, officer, that's a-

That's a very-very complicated matter for me

'Cause I, I uh...

I-I lost it, uh...

I-I lost my ID, uh...

Um, uh-

Can you show me some of your factors, sir?

My-my factors! Uh, well, uh

That's-that's pretty easy, 'cause

I, uh...

I, uh have this, uh, this calculator

Haha...uh, so I can just

Easily verify that, uh...

Well, I mean, uh...

Obviously, I could-you could divide by one,

Haha, uh, but, uh, I mean

What would that even...

I-I'm having a bit of difficulty

finding, uh, the factors, uh...

H-hey, uh, o-o-officer.

do you- do you see something there?

He's prime.

Take him out.

Good riddance.

♪ ♪ ♪

So, maybe, at one time, you've wondered

what the largest prime number is,

or, how many prime numbers there are.

And, keep in mind,

We know that there are a lot of prime numbers,

like,

a LOT of prime numbers.

But, are there

Infinite prime numbers?

Well luckily, my boi Euclid

back in the B.C.

already figured this out.

In fact, he created one of the

simplest and most elegant proofs in mathematics

to find the answer.

So, let's dive right into the proof.

♪ ♪ ♪

Alright, so let's start with

All the prime numbers we know up to this point.

So, let's start by multiplying all these prime numbers together,

to get a number, which,

by definition,

is a multiple of all these prime numbers

Now we can add one to this number,

making it a multiple of none of the prime numbers we have,

because,

if you divide this number

by one of the primes we have,

we'll always get a remainder of one.

That means that none of these prime numbers

are a factor of this number.

So, what if we found this number's prime factors?

Well, there are

two possibilities.

Either this number itself is a new prime number,

which,

there we go,

we found a new prime number,

or it has entirely new prime factors.

Do you see what we just did?

We took an arbitrarily long list

of prime numbers

and expanded it.

We could've done this with

any list of primes and said

BUT WAIT THERE'S MORE!

So if we can keep on generating

new prime numbers indefinitely,

that must mean there are

indefinite prime numbers.

Boom!

We did it!

We proved that there are an

infinite number of primes!

Now you too are

finna woke.

As the video wraps up,

it's time for another fun fact.

Lawnmowers are loud by design

to drown out the

screams of the grass.

And as always,

Thanks for watching.

♪ ♪ ♪