Is it possible to "reserve" a private key? In other words, can someone select a private key and perform an action (such as creating a specific transaction or something else) that effectively claims or reserves that key?
Reserving a Bitcoin private key and its public address can be considered as not good practice for your privacy too. If you leave your public address publicly somewhere, you should abandon that address when you feel a need of securing your privacy and anonymity better.
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.