It's not the whole story. In genuine currency, serial numbers are only unique within a series. Series 2017A and series 2021 notes can (and in fact do, since they start over at A00000001A) have identical serial numbers.

In 2014, the Bureau of Engraving and Printing (BEP) accidentally assigned overlapping sets of serial numbers for replacements notes to its currency-printing facilities in both Washington, D.C. and Fort Worth, Texas. The overlap occurred from serial numbers B00000001* to B00250000* and B03200001* to B09600000*. On the lower right-side of the front of the note, the letters “FW” with the face plate number indicate it was printed in Fort Worth.

https://www.pmgnotes.com/news/article/9321/Duplicate-serial-...

Notes prior to 1996, and $1 and $2 notes, use only a 10-digit serial number so there's repeats in new series.

I can explain. But first, we have to talk about parallel universes and half-button-presses.