> A RSA key is the product of two primes, not any number, so you need a lot more bits to get equivalent security
This explanation doesn't seem right to me. For 1024 bit numbers, about 0.14% are prime. So that difference only loses a handful of bits. There are more than 2^2000 usable RSA-2048 keys, and simply guessing and dividing would require more than 2^1000 guesses. Those few bits lost to the prime number restriction aren't why the level of security is so low.
This explanation doesn't seem right to me. For 1024 bit numbers, about 0.14% are prime. So that difference only loses a handful of bits. There are more than 2^2000 usable RSA-2048 keys, and simply guessing and dividing would require more than 2^1000 guesses. Those few bits lost to the prime number restriction aren't why the level of security is so low.