Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0;{supset};P_1;{supset};{cdotS};{supset};P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i);=;1;for;1;{leq};i; {leq};{lceil};{frac{b+1}{2}}{ ceil};and;O(P_i);=2;for;{lceil};frac{b+3}{2} ceil;{leq};i;leq;t,;where;b=n_v$. We also show that $n_w;=;n_v$ when w is the prime divisor associated to a simple v-ideal $Q;{supset};P$ of order 2 and that w(R) = v(R) as well.