Eisenbud–Mazur conjecture on symbolic squares of prime ideals

Let $P\subset\mathbb C[[x_1,\ldots,x_N]]$ be a prime ideal in the ring of formal power series, and let $M=\langle x_1,\ldots,x_N\rangle$. Eisenbud–Mazur conjecture. The second symbolic power satisfies

$$P^{(2)}\subset M\cdot P.$$

This conjecture proposes a stronger containment than the usual comparison between symbolic and ordinary powers and motivates studying containments with additional powers of the maximal ideal. Its resolution status is not specified in the supplied text.