Quote from: DannyHamilton on March 07, 2025, 04:14:35 PM

The odds of finding any one of those 2⁹⁶ private keys is vanishingly small. It just isn't going to happen. With nearly 2²⁵⁶ valid private keys, and only 2⁹⁶ of them being valid for a given address, you have a 0.0000000000000000000000000000000000000000000000684% chance of a collision on each attempt.

I don't understand it technically deep but I see some illustrative explanation with similar information on impossibility of finding Bitcoin private keys like finding an atom in a universe.

Bitcoin private keys.

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The size of Bitcoin’s private key space (2256) is an unfathomably large number. It is approximately 1077 in decimal. For comparison, the visible universe is estimated to contain 1080 atoms.

Private keys.

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The range of 256-bit numbers (and therefore the number of possible private keys) is unfathomably large. Just as it's impossible for the human mind to visualize the true scale of the universe, it's impossible for the human mind to comprehend the sheer size of 256-bit numbers.

Quote from: https://learnmeabitcoin.com/technical/keys/private-key/

This may seem hard to believe, but to give you some perspective, there are roughly 2256 or 1077 possible private keys, and there are roughly 1078 atoms in the universe[1]. So it's like asking two different people to randomly select an atom in the universe and for both to choose the exact same one.

To put it another way, it's like two people choosing the same grain of sand from anywhere on the earth (1018)[2]. Except each grain of sand contains another earth-worth of sand, and each grain of that sand contains another earth-worth of sand, and each grain of that sand also contains another earth worth of sand.

And even this amount of sand is still far, far less than the number of possible private keys.