So I assumed the "without I/O" clue was a hint to Base58Check encoding. Given that, if you take "BTCETHXRPPhemex" as a Base58Check string and convert it to Base10, you end up with a 27 digit number.
I took every combination of the words "BTC", "ETH", "XRP", and "Phemex" (24 combinations in total), and converted from Base58Check to Base10.
For every one of these 27-digit numbers (24 in total), I concatenated them before the prime, concatenated after the prime, and multiplied the two together.
For each of these 72 resulting numbers, I tried:
Hashing them with SHA256
Hashing them twice with SHA256 (the "Go back to step 4 again" clue makes me think we have to do something twice)
Converting them to HEX, then hashing them
I used each of the 216 results as a private key and checked the addresses. No luck.
I'm out of ideas at this point. Going to have to wait for another hint.
How do you get a 27 digit number?
If I convert it I get 26 digits
https://www.better-converter.com/Encoders-Decoders/Base58Check-to-Hexadecimal-DecoderAnd then to decimal
If I use numbers from the Base58Check wiki table, I get 30 digits

Also, shouldn't it be hexadecimal for WIF?