# 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.

### Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

## 6 thoughts on “19 random digits is not enough to uniquely identify all human beings”

1. Marcin Zukowski says:

This reminds me of an old idea for hash tables, useful esp. with complex keys.

With 128-bit hash values, if the hash function is good, the probability of an actual key conflict on the same hash value is smaller than the probability of a server getting hit by a comet 🙂 So we don’t need to do the value equality check, possibly saving a lot of time.

Alas, I never trusted a hash function enough to actually apply this in a production system.

1. Jimbo says:

It would be nice if you added the calculation for this probability.

1. Marcin Zukowski says:

Admittedly, it depends a bit on your assumptions and how you compute things

There are 3 considerations:

Size of a hash domain: `2^128`
Number of distinct keys that might be used in the same environment where a collision might cause a problem – here one can argue, I think something like `2^50` is very generous.
Probability of a meteorite hitting the Earth

From 1 and 2 we can get the probability of collision of roughly 1 in `10^9`.

Assuming a civilization-destroying meteorite hits us every 1 million years, that means that a probability of it hitting on a given day is more than 1 in `10^9`.

😀

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