This is a bit of a general question, knowing already of HD wallets and the mnemonic system for creating, backing-up and using the bitcoin blockchain.
However say you have for example a cold/paper wallet, with just one Bitcoin Private Key. Wouldn't an easier way to back-up/save/remember that address be simply be figuring out where the key lies within the range of possible bitcoin keys and taking note of the exponent of said number? Or Additionally a 10 digit scientific notation number, pretty much the same as remembering a phone number...
Example using python:
from bit import Key
# The exact position of this key is 2^65 in int form: 36893488147419103232
privKey = Key.from_int(36893488147419103232)
This gives the outputs
3FC7umZDWPvTskbVwG7mn72M8RtW8yFSy7. This is so much easier to remember and technically as long as the key was generated randomly enough wouldn't it be just as secure but easier to remember as opposed to 12/24 words one has to write down somewhere, or the hex format or WIF format private key?
After considering other factors... It wouldn't be all that secure if you want to save a key in the range of all possible keys, some exponents of certain numbers produce floats, I assume eventually one would be limited to specific keys, rendering the security bit a quite useless, but I only tested with exponents of 2 my maths could be wrong.
Say the exponent output was always converted to an exponent of the keys position that gives a non-decimal integer, one could in a sense cover all possible keys in the range no? If so then I stand by my question.
I'm trying to understand why this won't work not proving it works.