Quindecillions: the arithmetic of Bitcoin's address space

After our vanity address posts, people asked whether the address already had coins in it: did `1LeArNBtc...` already have money in it, and how many wallets did the search find on the way? Both assume the address space is like a phone book, big but populated. It is not.

This new Rabbit Hole is a credited recreation of James D'Angelo's 2014 Blackboard lesson (the drawers and the pirate are his picture; the numbers are rebuilt from October 2026 data). It covers:

- why there are 2^160 addresses of the kind most people use (1.46 x 10^48) and about 2^96 private keys behind each one

- how many drawers hold coins (57,213,806 at the 25 October 2026 snapshot) and what that makes the odds for one random key: at most 1 in 2.6 x 10^40

- what our 1.44 trillion vanity tries actually passed: a 5.6 x 10^-29 chance that any one of them held coins

- where the real "found a wallet" stories come from: brain wallets (884 found by the 2016 Brain Drain paper, half drained within 21 minutes) and broken random number generators (Android 2013, two 32-bit seeds in 2023, a 40-bit seed in July 2026). In every case we could find, the attacker searched a small space a human or a bug had created.

- what public brute force has reached: the 2015 puzzle transaction (record by raw search: puzzle 69, 2^68 keys, April 2025) and the Large Bitcoin Collider (2^56 keys in ten years, last find November 2017). Pooled: at most about 2^69 keys, one part in 2^91 of the address space.

- why that is the reason nobody has to register a key before using it

Free, no ads, no affiliate links, no wallet recommendations:

https://www.learnbitcoin.com/rabbit-hole/quindecillions