I have some thoughts on this. First, I want to say I am no expert on cryptography, I just know some stuff, and I took a cryptography class in University. I am very interested in this topic.
I understand that many security experts out there might get angry just by the discussion of these things, but I hope you can spare me :)
Would it be possible to break an RSA key, in for example 1 week of time, if the cracker have already spent X number of years building an index of primes by performing every permutation of existing prime keys up to 2^2048 ?
I understand this would take an immense amount of time to do, but it would only be done once.
Given the public key, you would be able to look up what the two primes are, and hence retrieve the private key instantly.
When I consider who might break such a code, I am primarily thinking about NSA and other Governments that might have spent years in research and have the resources and interest in doing so.
Breaking an 256 AES would then be easier, as AES keys are often generated using the RSA private key.
Would it be possible to build such an index ? How long would that take in permutations, and perhaps with the fastest computer in the world ?
I hope we can have a nice chat about this. We are just discussion theory here. I hope you can offer me some insight on this topic.