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19 random digits is not enough to uniquely identify all human beings
Suppose that you assigned everyone a 19-digit number. What is the probability that two human beings would have the same number? It is an instance of the Birthday’s paradox.
Assuming that there are 8 billion people, the probability that at least two of them end up with the same number is given by the following table:
| digits | probability |
|---|---|
| 18 | 99.9% |
| 19 | 96% |
| 20 | 27% |
| 21 | 3% |
| 22 | 0.3% |
| 23 | 0.03% |
| 24 | 0.003% |
| 25 | 0.0003% |
If you want the probability to be effectively zero, you should use 30 digits or so.