I have always enjoyed maths and used to try to solve elementary maths problems as a school kid. I can remember with joy finally solving a simple-to-state problem after hours of thinking about it. Often the solution popped out of my head almost involuntarily after I had spent a lot of time thinking about it* and then almost abandoning the effort. I recalled some history here in an early post that aroused no interest at all.
My son William out of the blue this evening asked me 'are there fewer prime numbers than natural numbers?'. Firstly, I told him that Euclid had proved that the number of primes was infinite in 300BC (a modern proof is here). Then I told him that 'counting' elements in infinite sets was analogous to but an extension of counting elements in finite sets. I then tried to tell him the little I remembered about Cantor's theorem of countable sets which intrigued me as a kid.
I told him if you can put a set into 1 to 1 correspondence with the natural numbers - a bijection - then a set is countable. In this sense there are as many even numbers as natural numbers and, as a consequence of one of Cantor's main theorems, as many rational numbers as natural numbers. There are as many primes as there are natural numbers since the nth prime number can be put into 1:1 correspondence with the number n for n=1,2,3,...... Thus the set of primes is countable.
This I hope answered his question although, to be honest, that a 10 year old asked it was far more interesting than the answer I had to scratch around to recall.
* I think I spent more time trying to think things through then than I do today. My knowledge is greater today but my brain often switches to autopilot mode and I apply knowledge rather than think.