How unique is the serialNumber of self-signed certificates on the client?

Question

JavaScript

For example: serialNumber: 'C7248095A7C42222'
We plan to generate keys for one hundred thousand clients. And you need a guarantee that the serial numbers are guaranteed not to match.

I'm still thinking about taking the name of the organization from the key in transliteration, so that the serial numbers do not exactly match as a uniqueness, or is it superfluous?

as I understand it, the probability of a serial match is 16 ^ 16
hexadecimal system plus 16 positions

Answer 1

The probability is negligible, but everything happens, what prevents you from checking the number for uniqueness?