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How Big Is 2256?

The number of possible keys, the number of possible addresses, and what the chance per key on the board actually measures.

16 October 2026 · 6 minute read

There are 2256 possible private keys, give or take a rounding error at the very top. Written out, that is:

115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936

About 1.16 × 1077. Physicists estimate the observable universe holds somewhere around 1080 atoms. The number of Bitcoin keys is in the same neighbourhood as the number of atoms in everything you could ever see through a telescope.

Addresses are smaller, and still enormous

Funds do not sit at keys, they sit at addresses, and an address is a 160-bit fingerprint of a key. So what a guesser really has to hit is one of 2160 possible addresses: about 1.46 × 1048.

The Earth contains roughly 1.3 × 1050 atoms. So all possible addresses, one per atom, would fill about one percent of the planet: roughly the Moon. Guessing one particular address is like being told one atom somewhere inside the Moon has been marked, and pointing at the right one first time.

  1. Keys tried this session Press Start
  2. Keys tried by every visitor so far Counting
  3. Powerball jackpot outcomes 2.9 × 1089 digits
  4. People alive 8.2 × 10910 digits
  5. Age of the universe in seconds 4.4 × 101718 digits
  6. Grains of sand on every beach about 101920 digits
  7. Possible Bitcoin addresses 1.5 × 104849 digits
  8. Atoms in the Earth 1.3 × 105051 digits
  9. Possible Bitcoin private keys 1.2 × 107778 digits
  10. Atoms in the observable universe about 108081 digits
Each bar is as long as its number has digits, so every notch to the right is ten times more. The orange bars are yours and everyone else’s, live. The guessing has to find one of a million marked numbers among the 49 digits of possible addresses.

Where "1 in 1.2 × 1042" comes from

The board does not need you to hit one particular address. Any of the million richest will do, which is a million marked atoms instead of one. And every key gets four tries, because it makes four kinds of address.

Each of those four addresses is compared only with funded addresses of its own kind: the two legacy addresses against 270,100 legacy targets each, the native SegWit address against 528,423, and the wrapped SegWit address against 201,477. That is 1,270,100 comparisons per key. Divide by the 2160 possible addresses and you get the chance on the board: about 1 in 1.2 × 1042.

Each grid has 100 squares and one right answer. Pick it. Then pick the right one of the next 100, and the next, 21 times in a row, first try every time. That is the chance of one random key opening one of the richest million addresses: about 1 in 1.2 × 1042.

Checking every funded address of those kinds, not just the richest million, would improve that by a factor of about 57, to 1 in 2 × 1040. Fifty-seven times nothing is still nothing.

Five Powerball jackpots

A Powerball jackpot is 1 in 292,201,338. To turn the chance per key into lottery terms, ask how many jackpots in a row, one ticket each, have the same odds. Each jackpot multiplies the odds by 2.9 × 108, so you count how many times that fits into 1.2 × 1042. It fits almost exactly five times.

So every key on the board is a ticket in a lottery you only win by winning the Powerball jackpot five draws running. The board buys a few hundred thousand of those tickets a second. The next article explains why that does not help: The Speed Problem.

Next: The Speed Problem