The purist will tell you that it should be “couldn’t care less,” because what you are wanting to say is that you truly don’t care.  On the other hand, if you say that you “could care less,” then you are saying you still have the capacity to care even less than you currently aren’t caring.  However, by saying you “couldn’t care less,” it assumes you know your capacity for caring, that caring is something that can even be measured.  It assumes you know at exactly what point it is that you stop caring, which obviously is not now because you’re still talking about it.  How can you possibly say that somebody is not going to come along within the next minute, and by their shear, insufferable pedagogy inspire you to care even less?  Don’t deny yourself the possibilities!  You could care less.