Probability of Generating an Active Ethereum Wallet (Do you feel lucky? You shouldn’t.)

Whenever a user makes a new Ethereum wallet, the wallet is not ‘created,’ like a new file that wasn’t there before. Rather, the information is generated from possible addresses that ‘already exist’ on the blockchain. With Ethereum rapidly closing in on 100 million active and unique addresses (currently at ~88 million and climbing), it begs the question: What are the chances of generating an already active wallet that someone else is using?

First, let’s take a look at the form of public addresses on Ethereum: they are 40 hexadecimal characters, prefaced by a ‘0x’. Hexadecimal characters cover numbers ‘0 - 9’ and letters ‘a - f’, meaning there are 16 possible character variations in any Ethereum public address.

So, if there are 16 different character types and 40 characters in total, that means there are a total of 16^40 possible public address combinations. Written out in a number, that comes out to:

1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 public addresses

Wait – what kind of insane number is that?! That can’t be real.

For reference (best estimates):
Population of people on Earth:    7,800,000,000
Grains of sand on the planet:            7,500,000,000,000,000,000
Stars in the observable universe: 1,000,000,000,000,000,000,000
Atoms in an average human body:   7,000,000,000,000,000,000,000,000,000

This means that even if you generated an address for every single atom in your body, you’d still have 1,461,501,637,330,902,918,196,684,832,716,283,019,655,932,542,976 combinations to go through...

The age of the Universe itself is only ~14,000,000,000 years old. If you generated a hundred new wallets every second since the dawn of time, you wouldn’t come close to making even the smallest dent in this massive number. The odds of running across an active address are almost literally zero. You’d have a better chance of Satoshi Nakamoto knocking on your door with a bowlful of organic fortune cookies containing all of their private keys transcribed on ancient papyrus.

The point I’m trying to drive home is that you will never come across an active Ethereum address by generating a new wallet. If you did, you’d be the luckiest organism to ever exist. It would be nothing short of a superpower, hopefully used for good. But keep in mind that even if by some astronomical chance you did come across an active wallet, it would probably be filled with airdropped shitcoins.

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About Stephen Wooldridge II

I'm Educational Project Lead at MEW, dedicated to bringing awareness and education about blockchain technology to the masses. The only way to move forward is by moving together.
  • Los Angeles, CA