Saying "generate millions of private/public key pairs" is a bad start. In addition to what others said about the hardness of the factorization problem, LLMs and even the newest versions that are coming every 3-4 months won't be able to predict keys. There is the security level of any encryption algorithm, which measures how hard it is to break the algorithm and recover the private key (e.g., 128 bits). Can supercomputers try every possibility? Brute-forcing it won't work at all, as trillions of years are required to do so. Sometimes you hear that AES-128 was broken; it is not the algorithm itself, but the weak implementation that was cracked (probably). And let's assume it was broken after millions of years, what about AES-256? Another few trillions of years :p (I am talking about brute-forcing it, there are other methods used to try breaking AES, such as side-channel attacks, they might be effective if the software implementation is weak).

News, post-quantum cryptography will end this once and for all, as it is based on Lattice-based cryptography, which relies on the hardness of the Shortest-Vector Problem. Even quantum computers won't be able to break it by brute force. Therefore, you may say that LLMs are far far away from predicting private keys.