No, the words 'thirteen' and 'old' are adjectives; the words 'years' is the noun they describe.
In the form a 'thirteen year old' followed by a noun is an adjective phrase:
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Thats a interesting question. 13 years old
princedon is really 14 years old now but he is not 13 years old
His sister is 13 years old
The answer depends on your 13 year old what! And what has your 13 year old possession got to do with your age, anyway?
13