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First of all, you're probably looking in the wrong place--my HPC product key is on the back of the CD case (and it's definitely 25 digits). I'm looking at the back of my manual and I don't see whatever it is you might be confusing with the product key... I do see a couple strings of numbers/letters with the phrase "Part No." stuck in the middle, but it's not 16 digits long.
Anyway, the 25-digit key you want should be on the back of the CD sleeve/case. That's where mine is.