Paper wallet related question: could I not just write down any 2^256 bit number I can think of to create a private key? If I can, why is this never done? And would I necessarily need software to hash out the public key, or could this also be done offline by hand?
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Yes, you can choose any 256-bit number as a Bitcoin private key (as long as it’s between 1 and 2^256‑1). However, coming up with a random number on your own isn’t safe because humans aren’t very good at making truly random choices and mistakes can happen easily. Plus, after picking your number, you still need to calculate the public key using complex math (elliptic curve multiplication), which isn’t practical to do by hand without software. That’s why people use wallet software or hardware wallets that generate keys securely and handle the math automatically.
Makes sense! Thanks 😃