Black stain in bathtub
 

We have a black stain on the bottom of a procelain bathtub. We thought
that this stain was mildew but our old tried and true solution to
mildew in the bathroom (a solution of 20% liquid laundry bleach that
will eliminate mildew stains from tile grout, tub caulk, etc.) didn't
even faze it. Scrubbing doesn't affect it. The stain doesn't cover
the entire bottom of the tub evenly, rather it's somewhat mottled in
appearance. It's a little rough to the touch. We live in Springfield,
MO and have seen a tub in another home with this same type of stain and
those folks couldn't get it off either.

Does anyone have any idea how it can be removed.