"*You could go into child key derivation and how the public key of hardened child keys cannot be derived using an xpub. But I guess you are getting there.*" 

Already covered, yet not included as it was still a bit wordy, I'll include it another time.

"*My impression is that the G point might have been chosen based on it producing a high enough n before repeating the sequence when adding to itself mod p.*"

Yes. As for p and n, and don't know exactly, only that that's their denotation.

Fabs

bitcoin_beginners

[TECHNICAL] Initial draft of my [personal] summary on part #2 of HD-wallets /ECC

You could go into child key derivation and how the public key of hardened child keys cannot be derived using an xpub. But I guess you are getting there.

How are *G*, *p* and *n* chosen/discovered?
I assume *p* was the largest prime number that fit into 256 bits? My impression is that the *G* point might have been chosen based on it producing a high enough *n* before repeating the sequence when adding to itself *mod p*.