Difficulty of breaking RSA for a given key size Is it true that breaking a 1024-bit RSA key is as difficult as breaking a 128 bit symmetric key (e.g. AES)? I know that breaking a RSA key is equivalent to factoring the modulus $N$. To factor it, you  have to see if any number between $2$ and $N/2$ divides $N$, right? But that would still be much greater than $2^{128}$ trials (which is the worst-case scenario for cracking a 128 bit AES key).
Then, how is breaking a 128-bit AES key the same as a 1024-bit RSA key?
No. Breaking a 1024 bit RSA key is not as difficult as breaking a 128 bit symmetric key. The consensus is that it is considerably less difficult, perhaps more comparable to breaking a 80-bit symmetric key, which is $2^{48}$ times less difficult than breaking a 128-bit key; that's a lot less difficult (a hundred million million times less difficult).

The reason is that breaking a 1024 bit RSA key can be attempted using an integer factorization algorithm, without exhaustively trying divisors. For the state of the art, see this article on the current factorization record.