Symbolic Powers of a Prime Ideal

Let A be a regular ring (for example, the polynominal ring in a finite number of indeterminates over a field). Let P be a prime ideal in A. In [1] Hochster raises the question whether it is possible to give conditions on A/P (for example, A/P Gorenstein) which imply that the powers of P are P-primary, (i.e. Pⁿ = P⁽ⁿ⁾ for all n).