I’ve been reading discussions around the idea of brute-forcing Bitcoin private keys. I understand 256-bit encryption gives us 2²⁵⁶ possible combinations, which is about 1.15 x 10⁷⁷ (115 quattuorvigintillion).

I know people often say it’s “mathematically impossible,” but I want to understand the deeper technical and statistical reasoning. Has anyone seriously tried coordinated brute-force attempts? Are there optimized methods or quantum computing paths that even slightly shift the odds?

Is it truly pointless, or are there edge cases worth considering? I'm asking from a security and theoretical standpoint — not trying to break the system, just to fully grasp its robustness.

Appreciate any insights, benchmarks, or research papers you can point me to.