What would be the performance properties of a comb or shell sort where the gap sequence is the prime numbers?
Analyzing various gap sequences is very difficult, but it is easy to see that this would require at least approximately $n\cdot\pi(n)\sim n^2/\log(n)$ passes, since you are looping over the entire array once per prime. This makes it worse than some other simple gap sequences, such as $2^n\pm1$ or $(3^n-1)/2$, which are known to take only $\mathcal O(n^{3/2})$ passes. The other issue is the amount of time and space it would take to generate the gap sequence.
Generally a good gap sequence should grow exponentially. Intuitively we want to make $\mathcal O(\log(n))$ loops through the entire array, and with each loop involving as few swaps as possible overall. This would get you closer to $\mathcal O(n\log(n))$ complexity. There's more details on the linked Wikipedia concerning the complexity of shellsort and picking gap sequences.