RSA-896 solution costs $75,000
Actually, that was the cash prize that RSA offered for a factorization; this cash prize has been since withdrawn.
But where did they get this number? Does anybody in the world know the factoring?
To quote RSA:
The generation took place on a Compaq laptop PC with no network connection of any kind. The process proceeded as follows:
First, 30,000 random bytes were generated using a ComScire QNG hardware random number generator, attached to the laptop's parallel port.
The random bytes were used as the seed values for the B_GenerateKeyPair function, in version 4.0 of the RSA BSAFE library. The private portion of the generated keypair was discarded. The public portion was exported, in DER format to a disk file.
The moduli were extracted from the DER files and converted to decimal for posting on the Web page.
The laptop's hard drive was destroyed.
So, if they are to be believed (and people generally do), no one currently knows the factorizations (at least, of the values that have yet to be publicly factored).