If $p$ is a prime of size 5 or greater then it is not good. We can pick a prime $q$ such that $q$ is greater than $p$ and less than $2p-1$. If $p$ is greater than 24 we can find such a number by using a result from this paper: Jitsuro Nagura (1952). "On the interval containing at least one prime number". Proc. Japan Acad. 28: 177–181. The result is that for any number greater than 24 there is always a prime between $n$ and $(1 + 1 / 5)n$. I found this result [here][1].For 5 we have value 7, for 7, 11, for 11, 17, for 13, 17, for 17, 29 and for 23 29. Thus for $n$ equal to 5 or greater we can always find such a value.  $q/p^{2}$ has to be represented by a parallel circuit of size two with two parallel elements of the form $a/p$ and $b/p$ with $a$ and $b$ less than $p$ hence it must be of the form $1-ab/p^{2}$ with $a$ and $b$ less than $p$ but $ab$ must be less than $(p-1)(p-1)$ but then smallest value that can be so expressed is $2p-1/p^{2}$ and we have a contradiction. 

2 is good. We can get any odd number in the range 1 to $2^{k+1}$ from an odd number in the range 1 to $2^{k}$ by either taking it in series with the element 1/2 for those numbers less than $2^{k}$ or in parallel for those numbers greater than $2^{k}$. If 2 is good then $2^{m}$ will be good because any fraction with its denominator a power of $2^{m}$ will have a denominator a power of 2.


  [1]: http://en.wikipedia.org/wiki/Bertrand%27s_postulate