RSA and prime-generator algorithms

Question

OK, my understanding of the mathematical workings of RSA may not be as deep as it should, so feel free to slap me over the head if this is stupid:

To generate a private

Answer 1

ive learned that you can use rsa as this :

p = prime
q = prime
n = p * q

phi(n) = phi(p) * phi(q) = p-1 * q-1

But ive heard if you do phi of an none prime its not prime -1 so it would crash at the step above (but i cant say why)