I'm working with Joomla and using an add-on componenet to impliment Adsense. It requires entry of the Adsense publishers number.

In the Adsense account area it lists three numbers. Each with an "ca-pub-" or something before the actual long number.

Do I have to include these prefixes to have the impressions and such recognized?

depends what you are signed up to

ca-pub is the Adsense for content.
partner-pub is for search.
ca-ref-pub is for referrals.

usually you just need pub-ref_no