2. Ask her why we know prime ministers are there? Because somebody was playing with math and noticed that some numbers don't have non-trivial divisors. So with a some effort we saw a pattern that we could not see before. That was fun.
3. Maybe there are other patterns that are out there, or other things to know about primes. Clearly, it takes effort. So we keep exploring, hoping for the next dopamine hit. That's all. We are just math druggies.
> > No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years. [1]
> Since then number theory was used to crack German enigma codes and much later, figure prominently in public-key cryptography. https://en.m.wikipedia.org/wiki/A_Mathematician's_Apology
[1] Hardy's "A Mathematician's Apology" http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20... [pdf]
We pay people to play sports because we enjoy watching them do so, but that argument does not hold for maths - so your rhetorical question does not answer the implied question, I think.