So is there any way to derive or calculate the number representation from btc address that coresponds to its private key hex?
No there is none.Bitcoin addresses like P2PKH represent a hash and hashes are irreversible which means you can not compute the public key used to get that hash.
Even if you had the public key you still wouldn't be able to compute the private key because that is another irreversible function.
What you've seen in the program you found on the internet that uses the term "key range" is a very specific code written to solve a puzzle where the creator of the puzzle intentionally created small keys in a much much smaller range than what should be used so that it can be brute forced by enthusiast who like to waste their computing power.
Yes thats true, i was just asking even if im aware aside that it may not be possible but just wanted to check again cause internet is full of untold secrets where they often promote a boxes and they tell you its a box but they never mention its interior, i think you understand what i mean
![Wink](https://bitcointalk.org/Smileys/default/wink.gif)
And the program that calculates all info is not from the internet, i created it few months ago
![Grin](https://bitcointalk.org/Smileys/default/grin.gif)
![Grin](https://bitcointalk.org/Smileys/default/grin.gif)