10 Feb '14

What’s The Chance Of My New Bitcoin Address Already Being Used?

Our Frequently Asked Questions (FAQ) series explains the core concepts of Bitcoin for a less technical audience.

Anyone concerned that there are not enough Bitcoin addresses or private keys available for every man, woman, child and insect on earth really have nothing to worry about.

The question can be asked in many ways and the answer is mathematical.

What if someone guesses my private key? What if my wallet generates the same address as someone else?

PSBlake on Reddit had this perfect example to illustrate the point.

Statistically speaking, unless the protocol changes to accommodate more decimal places, only 2.1e14 addresses could contain at least one Satoshi, and that’s only if everyone only had one Satoshi. If anyone has more (and pretty much everyone who has any has more than one Satoshi), then there are fewer occupied wallets.

Within the set of 2256 private keys, they only map to 2160 unique wallet addresses. So the question is how does 2160 compare to 2.1e14? One in a million? One in a trillion?

The answer is one in 6.9595 decillion. Since “decillion” isn’t a commonly used word, I’ll save you the bother of having to look it up: it’s a one with 33 zeroes after it.

To put that 6.9595 decillion figure into perspective: The Earth has a diameter of 12,742 kilometers, giving it a surface area just shy of 50 million square kilometers. A square kilometer is 1 million square meters, and a square meter is one million square millimeters, meaning the surface area of the Earth, in millimeters, is just shy of 50 quintillion mm2.

So here’s the game we’ll play. I’ve got 140 trillion earth-sized spheres. On one of them, I have randomly selected a single square millimeter as the prize winning spot. Find it, and you’ll get to spin the prize wheel to see how much you’ve won.

The prize wheel currently has about 22 million spaces. 21 million of them contain less than a dollar. But you only get to spin the wheel if you can find the secret spot on the secret sphere.

Wanna play?