How can you write a number as a sum of smaller numbers?
You can always end up with 1 + 1 + 1 ...
But with multiplication you get stuck.
With prime numbers.
So these are the building blocks of numbers.
How can you find them? (perhaps Sieve of Eratosthenes)
Find the first few prime numbers.
You can use this to show how one can compute GCD and LCM easily (but who cares about gcd and lcm?)
How many are there:
First ask how many numbers are there? Infinity, because for any n there is n+1
Then ask how many even numbers are there? How many non-prime numbers are there?
Then ask how many primes are there. We need to find a way to generate a larger prime from whichever primes we had...