Authenticate this Rolex datejust cal.3035, Ref. 16013, year 2001

[Ac2100]

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Its me again..

So, I found this datejust I like as well, and I need your help again to authenticate this.

Rolex datejust cal.3035, Ref. 16013, year 2001.

IF this is authentic, which whats is the best deal? the 16013 or 16233 from 1991 (I have added a picture last in this thread)
It is my first Rolex watch, and I am a newbie in this field so I really appreciate your help.

The 16013 has the box with.