Question

Are prime numbers infinite?

Answer 1

There are an infinite number of prime numbers.

Explanation:

To prove this for yourself, suppose you only know a finite number of prime numbers - call them `p_1, p_2, ..., p_n`

Consider the number `q = (p_1 xx p_2 xx ... xx p_n) + 1`

`q` is not divisible by any of the prime numbers you know, so it is either prime itself or there is some other prime `p_(n+1)` which is a factor of `q`.

In either case, your list of primes was incomplete.

So the number of primes is unbounded.