The trouble with RSA is that you end up needing to increase to pretty large key lengths to have significant increases in security after somewhere around 2048 bits. For example, a 4096 bit key is not really as great as it might first appear.
I might be wrong, but I have a vague recollection that Google went with a 16384 bit RSA key for their root key on Chrome devices. It's not a frequently used key (it's used to sign the signing key that can be updated - the signing key uses weaker and faster algorithms which can be changed in new firmware releases), but it's stored in read-only firmware that can only be updated by physically opening a machine. Given that you probably want the key to be good for somewhere between 5 and 30 years, the uncertainty which exists around quantum computers right now, and the tremendous problems which could occur if this key were to be factored, I can understand why they would choose such an obnoxiously large key length.