Need help explainin how Euclid proved that there are an infinite number of prime numbers?

Question

I mean i know the mathmatical way but how could i put it in my own words and make it much simpler. thanks

Answer 1

Suppose there were only finitely many primes. We'll exhibit an integer that is divisible by none of them, an obvious contradiction.

In fact, take the product of all the primes. That's divisible by all the primes. Now add 1. That's divisible by none of the primes. So we're done.

If you have to be more precise, than that, it you should name the product of all the primes N, and point out that any prime that divided both N and N+1 would also have to divide their difference, which is 1. And that's a contradiction.