Today I learned that the hash of an integer is the integer itself, except for -1. The hash of -1 is -2.

Hash of -1 is -2

The hash of a value is a numeric “signature” assigned to that value used in data structures like dictionaries and sets. Among other interpretations, a hash is supposed to be a quick way to check if two objects are different. So, if two objects have different hashes, they are different. But if two objects have the same hash, they can still be different. When this happens, we have what is called a “hash collision”.

A “hash function” – a function that is used to compute hashes – is good when hash collisions are not common. Hash collisions are impossible to avoid, but you want collisions to be as rare as possible, in some way.

The Python built-in hash computes hashes for Python objects and it's used under the hood with dictionaries, sets, and more. When applied to integers, it looks like the built-in hash returns the integer itself:

assert 0 == hash(0)
assert 1 == hash(1)
assert 46245234 == hash(46245234)
assert -83572 == hash(-83572)

Interestingly enough, the hash of -1 is -2, and so is the hash of -2:

print(hash(-1))  # -2
print(hash(-2))  # -2

This shows a very interesting hash collision that is “easy” to come by! For example, the integers 6909455589863252355 and 2297769571435864453 also share the same hash, for example, but this seems less surprising than the fact that -1 and -2 have the same hash.

I am also trying to find the first positive integer for which the hash does not match the integer itself, but so far Python is still looking for the answer:

from itertools import count

print(
    next(n for n in count() if n != hash(n))  # Python is still running this on my computer.
)

Become a better Python 🐍 developer 🚀

+35 chapters. +400 pages. Hundreds of examples. Over 30,000 readers!

My book “Pydon'ts” teaches you how to write elegant, expressive, and Pythonic code, to help you become a better developer. >>> Download it here 🐍🚀.