  We show that for an immersed two-sided minimal surface in $R^3$, there is a
lower bound on the index depending on the genus and number of ends. Using this,
we show the nonexistence of an embedded minimal surface in $R^3$ of index $2$,
as conjectured by Choe. Moreover, we show that the index of a immersed
two-sided minimal surface with embedded ends is bounded from above and below by
a linear function of the total curvature of the surface.
