I would give anything to have the ability to run my fingers through secp256k1 (personally) and verify how free it is of any air bubbles
What prevents you? It is all public knowledge.
There is even a challenge, where you can win hundreds of thousands of dollars if you can break their crypto
https://www.certicom.com/content/dam/certicom/images/pdfs/challenge-2009.pdf
Good luck!