Make sure this is not Cloud version as they do not use serial numbers.
Welcome to the forum.
Is that the S/N that was either printed on your installation media envelope, or one sent to you via e-mail, from Adobe?
If you have any questions on your product S/N, and either bought from Adobe (Adobe Store), or Registered that product previously, you can go to Adobe.com, log-in with your Adobe ID, then go to your Adobe products page, where you will see your S/N. If you look in most other places, you will only see a truncated S/N, for security reasons.
In a worst-case, contact Adobe Customer Support (not Technical Support), and have your paperwork handy. They should be able to get the S/N issue sorted out.