Do Corys eat shrimp?

Shrimp do tend to disappear for a while when they are molting. I've had four in a tank for over a year now and I hardly ever see more than two at a time.
 
Heck, I got a single Ghost Shrimp in my Eclipse 3 with my Betta and sometimes I can't find the little guy in there. He blends in very well.
 
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