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The field and curve have to admit a primitive root of unity in order to make the efficient endomorphism work, so that's going to be part of the selection criteria for any of the K curves.

primitive root ?

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Now I understand. It is slightly more complicated than that.
Private keys are not multiple of 18051648. Private keys are power of z mod q, where z is a primitive root mod q.

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primitive root generate vulnerable subgroups what provide way to breack 256 bit key in seconds.On github more info about it.

You're spouting nonsense, stop linking to fake 'weak key' bullshit. These are posts of scammers tricking people into running malware.

Secp256k1 is prime ordered, there are no subgroups and all keys are equivalent.

Is that so? I thought there was a one-to-one mapping for certain range.. with N+/- some Z. While many discuss the use of cube roots, no one explains why we specifically use them. Why not use square roots, fourth roots, or seventh roots instead?