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I've been thinking about this for a few days, a SHA-256 algorithm outputs 64 characters which can either be a lowercase letter or a number from 0-9. Which should mean that there are 64^36 distinct SHA-256 results.

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(If we humans cannot analyze some patterns, doesn't mean AI can't) -What if someone like entering previously hashed data as a learning/training set into an AI system for example. In fact the AI thought just crossed my mind in this very moment.

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$\begingroup$ The human brain is exceptionally bad at imagining large numbers. And then it would be $36^$, not $64^$ - which is vastly different. Anyway: Hexadecimal output is not all lowercase letters. And that is just one way to express all $2^$ possible outputs (and crypto the actual number format is entirely irrelevant, just computers tend to use hexadecimal often). This reminds me of a question for a list of all 1024 bit prime numbers.

Now, Eddington's number purports (see Wiki for assumptions - hint - huge) to be the number of fundamental particles (protons + electrons, assuming that a neutron is made up of a proton and an electron)) in the universe. I put in the 2 for a 50% change of a clash - is my maths OK? So, you'd basically only have 2 * 136 (= 272) particles per SHA-256 hash to be available to store your data for a collision (+ overhead)? $\begingroup$ Consider that Eddington's number =136 * $2^ \approx 10^$.

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$\begingroup$ So, in 2600 universe-lifespans, we would have a chance of finding a collision, but only if we saved/recorded/stored every single hash discarded by all the bitcoin miners in the world, and, even then, it would just be two random block+nonce files with the same hash?

You would still have to find which two hashes these were. By "a given SHA-256 hash" I believe you mean Second Preimage Attack which cannot rely on birthday paradox. $\begingroup$ @JamesTheAwesomeDude During that time all the bitcoin miners would have a good chance that the two hashes that were calculated had the same hash.

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