Advantages of using prime number as interval during a shell sort?
It is still an open question what the best gap sequence for shell sort would be; and what the performance of shell sort would be with an optimal sequence.

The "holy grail" for comparison based sorts is O(lg(n!)) ~= n*lg(n) -n performance.
No one has ever found a gap sequence for shell sort that achieves that.

Here's what we do know-
1= the last gap must always be 1 (insertion sort)
2= there should be no more than lg(n) -1 gaps
(thus the lg(n) -1 gap is always going to be 1)
3= the gaps should at least be relatively prime to each other.
4= the gaps should be between a factor of 2 or 3 of each other
5= the gaps can not be expressed by a closed form math formula if you want worst case performance better than O(n*lg^2(n)) or O(n^(3/2))  

Thus using just primes closest to (n/2)^i for the first lg(n)-2 passes can be a very good choice, but
a= we as of yet can not prove such a gap sequence would be optimal, and
b= figuring out what the gap sequence is for any given size of data set is non trivial if all of our gaps are primes.