Odds of cracking bitcoin wallet

If you generate 1 million private keys per second, the estimate for hitting a Bitcoin wallet with funds would be as follows:

Assuming: * Total possible private keys in Bitcoin: 2²⁵⁶ (approximately 1.16 x 10⁷⁷⁾ * Estimated number of wallets with funds: 500,000,000 * You have a computing power to generate random private key at rate: 1,000,000 keys per second

Probability of hitting a wallet with funds:

Probability = Number of wallets with funds / Total possible private keys = 500,000,000 / (1.16 x 10⁷⁷⁾ ≈ 4.31 x 10^-72

Expected time to hit a wallet with funds:

Expected time = 1 / (Probability x Rate of generation) = 1 / (4.31 x 10^-72 x 1,000,000) ≈ 2.32 x 10⁶³ seconds

Converting this time to more practical units: * Years: 2.32 x 10⁶³ / (60 x 60 x 24 x 365) ≈ 7.35 x 10⁵⁵ years * Age of the universe: 7.35 x 10⁵⁵ / 13,800,000,000 ≈ 5.33 x 10⁴⁵ times the age of the universe

With a generation rate of 1 million private keys per second, the expected time to hit a wallet with funds is approximately 7.35 x 10⁵⁵ years, which is still an extraordinarily large number

Now, let's calculate how many times you would need to win the Powerball lottery jackpot in a row.

Assuming: - Odds of randomly hitting a Bitcoin wallet with funds (assuming 500,000,000 wallets with funds and 2²⁵⁶ total possible private keys) = 1 in 2.32 x 10⁷¹ - Odds of winning the Powerball lottery jackpot once = 1 in 292,201,338

To find the number of times (n) you would need to win the Powerball jackpot in a row to have odds equal to randomly hitting a Bitcoin wallet, we can set up the following equation:

(1 in 292,201,338)ⁿ = 1 in 2.32 x 10⁷¹

Taking log of both sides and solving for n:

n = log(2.32 x 10⁷¹⁾ / log(292,201,338) n ≈ 166

Sanity check:

292,201,338¹⁶⁶ ≈ 3.5 x 10^71, which is slightly higher than 2.32 x 10⁷¹

Therefore, to have odds equal to randomly hitting a Bitcoin wallet with funds, you would need to win the Powerball lottery jackpot approximately 166 times in a row.

To summarize: - To randomly hit a Bitcoin wallet with funds, it would take 5.33 x 10⁴⁵ times the age of the universe. - This is approximately the same odds as winning the Powerball jackpot 166 times in a row. - The event that is so incredibly unlikely and improbable that it can be considered effectively impossible to occur.

This calculation further emphasizes how astronomically unlikely and practically impossible it is to randomly generate a private key that hits an existing Bitcoin wallet with funds.

These incredible odds stem from the vast size of the private key space in Bitcoin (2²⁵⁶ possible keys) and the cryptographic strength of the system, making it infeasible to access funds through random guessing or brute-force methods.

Edit: Revised the math. Thanks for pointing me the error. Edit2: formatting and summarizing results