# Question #ca15a

##### 2 Answers

There are many ways. I'll just show you one.

#### Explanation:

Imagine that there is a finite number of primes

The number

Prove by contradiction:

Considering a finite number of primes

#### Explanation:

We well solve this via the use of contradiction, we we can let there be a finite number of prime

And we know

But we can consider

This on the other hand is prime, as if it were not prime than we could devide it by a smaller prime and yield a natural number, we can prove this by;

let

then

were we know

But

So hence

So hence

Hence for any finite set of primes we can make a new prime, hence there is not finitely many primes

Hence there can't be a finite number of primes, hence proven via contridiction