Wikipedia has as good of a definition of prominence as I've seen:
Once you understand it, you realize that the southwest slope of Frissell where Connecticut's highpoint is located has a prominence of zero since there is a higher point immediately on the other side of the Mass. border.
And how 'bout a really tough question. Which state highpoints are not the most prominent points in their states? BTW, I don't have the answer to this one but can think of several likely candidates.