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That’s 28 bits. Loop through 256 million of these strings, and you’re bound to find a hit.

Bitcoin difficulty is at around 50 bits (https://ycharts.com/indicators/bitcoin_average_difficulty#:~....)

It also uses SHA256.

So, if my logic is right (is it? That seems awfully cheap to me), this is about 2^22 times as easy as mining a bitcoin. Bitcoin is at about $25k, so there are people who can find hits like this one for way less than a cent.

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> Bitcoin difficulty is at around 50 bits

The minimum bitcoin difficulty of 1 corresponds to 2^32 double SHA256, so finding a block at difficulty 2^50 takes an insane 2^83 hashes...

Bitcoin difficulty is not measured in bits but its own unit (some hashrate was defined as difficulty 1, and difficulty 10 means the hash rate is 10x that). The number you see on that website is also in trillions, so the current difficulty is about 50 trillion. Also, you get more than one Bitcoin per hash (currently 6.25, halving every few years).

To mine six BTC, you currently need almost 80 bits of zeroes, so 28 bits is basically trivial.

By the pigeonhole principle, there is a sentence that writes out its entire SHA256 representation this way. Alternatively, the map from these kinds of sentences with 256 terms to 2^256 given by SHA256 admits a fixed point.

I don't believe this is necessarily true. Unless I'm misunderstand you, each of the possible variants of spelling out 32 hexadecimal characters could theoretically SHA-256 into the spelled-out hash + 1 (looping around at ff…ff).

I don't see how pigeonhole principle applies to that situation. It could well be that "zero" hashes to 1, "one" hashes to 2... and "f" hashes to 0, extended out to the hash's length.

The pigeonhole principle does not say that. It can be used to show that there are two different sentences with the same hash as each other (among any collection of 2^256 + 1 sentences), but it tells you nothing about hashes that agree with the content of the sentence. The probability that a random hash function on a collection of 2^256 sentences has a fixed point is about 1 - 1/e, and it approaches 1 as you add more variations to grow the collection infinitely. But SHA-256 isn’t actually random, so the only way to know this for sure would be to find an example.

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