Question

How many prime numbers are there? How can I prove it?

Answer 1

There are infinitely many primes and I think Euclid was the first to prove that (but someone before him may have done so).

https://primes.utm.edu/notes/proofs/infinite/euclids.html

Answer 2

But the basic idea is this: there are infinitely many numbers and because each number is factored into primes, this means you need infinitely many primes to keep up with the infinite numbers.

Answer 3

How can the prime factorization of numbers and the definition of a prime number be useful? @jim_thompson5910