Wouldn't it be possible to create as many as possible key pairs for the RSA encryption and then determine from a public key which the corresponding private key is ?
The answer to your question is very closely related to this post: https://math.stackexchange.com/questions/263588/how-many-all-prime-numbers-p-with-length-of-bits-of-p-1024-bits
Via. the prime number theorem we can calculate that there are approximately 1.26 * 10305 prime numbers less than 21024. That is a lot of numbers. For scale, a terabyte is 1012 bytes!
So yes, though this brute force approach is theoretically doable we don't, and won't, have the resources for a very long time!