I think that defining prime numbers is the first step in understanding how precise Math definitions are, or even what definitions are. After discussing the definition with the students, I would also tell them one of my favourite joke (OK,OK, it is geeky), just to give them an example of Mathematical thinking:
An engineer, a physicist, and a mathematician were on a train heading north, and had just crossed the border into Scotland.
The engineer looked out of the window and said "Look! Scottish sheep are black!"
The physicist said, "No, no. Some Scottish sheep are black."
The mathematician looked irritated. "There is at least one field, containing at least one sheep, of which at least one side is black."
(This version copied from http://www-users.cs.york.ac.uk/susan/joke/3.htm)
During the first Math class this year our daughter was told by the teacher that she is wrong in thinking that 1 is not a prime number. The child tried to say that she thought she was right, but knowing the child she might have protested very quietly.
The following week, the issue arose again. This time our daughter protested again, but was made to colour 1 green as the prime numbers were to be green and composite blue. So here is the result:
Should I have had a little chat with the teacher? I was considering it, but I am not very good in confronting people and soon there were problems that would take hours to explain. So, I didn't talk to the teacher. Knowing that 1 is not a prime is just a fact and messing up facts doesn't bother me too much. What bothers me a lot is the lost opportunity to use the fact to give the students an example of Mathematical thinking, but this cannot be done if you don't have the Mathematical training and I don't think that the BC elementary school teachers have the training.
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