Hello!

This is a brief bonus lecture

and what I'm gonna do in this lecture

is show you that there're infinite number

of prime numbers.

In other words,

I'm gonna prove the infinitude of primes.

Now, this is really one of the gems

of the history of mathematics

and the history of science,

and using, as we'll see in a moment,

just primitive tools for the most part

we can prove that, in fact,

there're infinite number

of prime numbers.

And, as I've indicated,

this proof goes back

to someone called Euclid,

who's generally considered

the founder (one of the founders)

of geometry

and the proof dates

to at least 300 BC.

So let's begin with the definition

of what a prime number is.

A prime number

beginning with then number 2

is an integer

greater than or equal to 2

whose only whole number divisors

are 1 and itself.

So, for instance, 2 is the smallest prime.

3 is the next prime

in the sequence of primes.

5 is the next.

7, 11, 13, and so forth.