Let Pn(x) = 1 n! ∑( n 2i+1 ) (2i + 1). This extends to a continuous function on the 2-adic integers, the nth 2-adic partial Stirling function. We show that (−1)Pn is the only 2-adically continuous approximation to S(x, n), the Stirling number of the second kind. We present extensive information about the zeros of Pn, for which there are many interesting patterns. We prove that if e ≥ 2 and 2 + 1 ≤ n ≤ 2 + 4, then Pn has exactly 2e−1 zeros, one in each mod 2e−1 congruence. We study the relationship between the zeros of P2e+∆ and P∆, for 1 ≤ ∆ ≤ 2, and the convergence of P2e+∆(x) as e→∞.