A quantum computer would generate private keys readily. Quantum computers are well within the accepted laws of physics and there are multiple companies working on them. None is believed to exist with sufficient power to find an RSA private key quickly today, but I'll just mention that the first conventional computers were invented in secret for breaking codes.
I get the whole keeping it for later decryption bit but really, 4096 bit RSA is not going to be easily borked no matter what scale of computing power you throw at it.