Toss a Coin 256 Times: The Math Behind an Unbreakable Bitcoin Private Key

Bitcoin

Why Cracking a Bitcoin Key Is Harder Than You Can Possibly Imagine

I often see some brute-force programs constantly trying to crack Bitcoin wallet keys, claiming they’ve been lucky enough to stumble upon the keys to a few wallets and moved tens of thousands of dollars from them.

Toss a Coin 256 Times, and You Have a Bitcoin Private Key: A Cryptographic Miracle Beyond Human Computation

Cracking Bitcoin requires the power of 4 billion galaxies? Ordinary people simply cannot fathom this mathematical abyss.

If you assign 1 to heads and 0 to tails, and toss a coin 256 times in a row, then convert the resulting binary number into hexadecimal — you’ve got a Bitcoin private key. In other words, a Bitcoin private key is essentially just a 256-bit binary number. Sounds pretty basic, right? Almost like any regular computer could crack it with ease?

4 Billion Galaxies and 37 Universes: The True Scale of Bitcoin Security

2 to the power of 256 is equivalent to multiplying eight instances of 2 to the power of 32.
2^32 is approximately 4 billion.

Now do you have a sense of scale? That’s 4 billion × 4 billion × 4 billion × 4 billion × 4 billion × 4 billion × 4 billion, and then divide by 4 billion.

Let’s break it down:

The first 4 billion represents the number of hashes a modern GPU can compute per second. So that’s one high-performance computer calculating hashes at full speed.
The second 4 billion — let’s use the world’s top search engine, Google, as an example. Although Google doesn’t publicly share its server count, estimates suggest it has several million — making it one of the companies with the most servers in the world. Most of those servers aren’t even as powerful as our GPU-heavy machines. So 4 billion such computers would be roughly equivalent to 1,000 Googles in computational power.
The third 4 billion — Earth has a population of about 7.3 billion. Let’s assume more than half the people on Earth each had the computational power of 1,000 Googles.
Now the fourth 4 billion — imagine 4 billion Earths like that, essentially a galaxy of computing power. Let’s call this a galactic-scale compute power.
The fifth 4 billion — let’s bundle 4 billion of those galaxies together. Their combined compute power can process about 2^160 hashes per second.
The sixth and seventh 4 billion — let’s consider time. 4 billion seconds is approximately 126.8 years, and if you multiply that by 4 billion, you get about 507 trillion years, roughly 37 times the known age of the universe.

So what is the conclusion?

With the current level of human civilization, cracking a single Bitcoin private key would require the combined compute power of 4 billion galaxies — working nonstop for 37 times the age of the universe. And even then, the odds of success would be just 1 in (4 billion)^8.

In short, cracking a Bitcoin private key through brute force is pure fantasy — not even a network of quantum computers could come close to such a feat.

This was originally written in February 2021 — take a moment to reflect again on the brilliance of Bitcoin’s invention.

As of today, one Bitcoin is worth about $92K USD.

crypto-btc-eth-trx-2025-04-24 Toss a Coin 256 Times: The Math Behind an Unbreakable Bitcoin Private Key

Crypto Prices for BTC, ETH and TRX as of 2025-04-24

Bitcoin/BTC Wallets

Satoshi Nakamoto’s Wallet

How far would you be willing to go for $111 billion??

satoshi-nakamoto-wallet Toss a Coin 256 Times: The Math Behind an Unbreakable Bitcoin Private Key

Satoshi Nakamoto’s wallet has $111B

If someone guessed the 24 correct words to access Satoshi’s wallet they’d walk away with roughly $111 billion, making them the 15th richest person on the planet.

But how feasible is that?

A 24-word BIP39 seed represents 256 bits of entropy, about 1.16×10⁷⁷ possible combinations. Even with a hypothetical machine making 10⁵⁰ guesses per second (far beyond current capabilities) a full brute force search would still take 36,700,000,000,000,000,000 years. That’s roughly 2.7 billion times the current age of the universe (13.8 billion years).

Your funds are SAFU.

Just don’t get phished, don’t sign random transactions, and stop connecting to shady sites.

99% of losses come from users, not code.

Satoshi wouldn’t have a BIP39 seed. That standard wasn’t created until 2013. You’d be trying to guess the raw 256-bit private key from the original wallet.dat file.

I believe the US government may have already attempted that lol
They can’t be looking at $111B just chilling somewhere
They most probably may have done some brute force that was unsuccessful
Who knows, Sat may be dead. this is very true, I think a certain Korean leader would also be interested in such a prize pot.

Quantum computers will not be guessing 24 words seed phrase. They will derive the private key of the wallet from the exposed public key. With the latest announcements from Google, this will be surely possible in less than 5 years, potentially sooner.

One problem with crypto is that there is no recovery options, for example if someone have access to your wallet it’s a gameover for you nothing can help you, that’s why it’s still dangerous to keep all your savings in a single wallet.
Always create multiple wallets just for the worst case scenario.
Also any transaction will reveal your public key which is dangerous in case of quantum computing.
I hope I am wrong but maybe Satoshi is dead.

I agree, keeping funds on a hot wallet in general is asking for trouble. Multisig’s definitely help, cold wallets too but the same issue persists, if someone gets their hands on your seed phrase you’re done for. A lot of newer wallets have 2FA and other forms of security but we still have a long way to go.

Are you sure satoshis wallet is secured by Bip39 (12/24 words) not 100% sure to be fair, just going off of what most people use today. But fair point.

Rule no 1. Don’t sign random transactions
Rule no 2: Don’t connect to shady sites.

The funds are SAFU. It really is that simple, oh and stay off public WiFi.

Ah yes, Combination theory… but…

What are your thoughts on quantum computing? From what I hear we are just a few years away. People are quantum proofing assets for this cause, that’s what the likes of Min H. Kim’s tectonic and qLABS are building.

It maybe not be a threat in 10 years, but what about 15 years down the line?

Curious on what your thoughts are, just for the sake of this discussion.

Quantum computers will not be guessing 24 words seed phrase. They will derive the private key of the wallet from the exposed public key. With the latest announcements from Google, this will surely be possible in less than 5 years, potentially sooner.

So you’re saying there’s a chance? That’s good enough for my Pentium 90. It’s got Intel Inside you know.

Please stop with the guessing games. Thank-you in advance. Many Regards, Satoshi.

Here’s an idea … If everyone wants to send me the 11 words to their crypto wallet we can whittle down the combinations already in use…

I can compile a list of all of the combinations that have been used and we should have a smaller pot of ones in the “not found” list

It’s bound to be one of them that’s missing for satoshi’s Wallet

Totally legit strategy …Honest 🤣

Math

–EOF (The Ultimate Computing & Technology Blog) —

1504 words
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Toss a Coin 256 Times: The Math Behind an Unbreakable Bitcoin Private Key