A note on the Eisenbud–Mazur conjecture

The Eisenbud–Mazur conjecture states that given an equicharacteristic zero, regular local ring (R,m)(R,m) and a prime ideal P⊂RP⊂R, we have that P(2)⊆mPP(2)⊆mP. In this paper, we computationally prove that the conjecture holds in the special case of certain prime ideals in formal power series rings.