Subject: How well would educated primates do on a Turing style test?

Many primates have now been taught to use language - either sign language or 
pointing to images on a picture board (some connected to a computer). If a 
person using a remote computer corresponded with both a person and a primate 
(all using the same picture board as the primate), would the person be able to 
tell the difference between the person and the primate? 
This was originally done by Alan Turing, to examine the 'intelligence' of 
computers, hence my use of the term 'Turing test'. Does it have a different name 
when applied to Primates, and has this been done?

Thank you in advance.

Re: How well would educated primates do on a Turing style test?