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There are numbers for RSA Factoring Challenge. For example, RSA-896 solution costs $75,000 and the number is:

41202343698665954385553136533257594817981169984432798284545562643387644556 52484261980988704231618418792614202471888694925609317763750334211309823974 85150944909106910269861031862704114880866970564902903653658867433731720813 104105190864254793282601391257624033946373269391

But where did they get this number? Does anybody in the world know the factoring?

I know they stopped the challenge, but imagine they don't yet.

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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Actually, that was the cash prize that RSA offered for a factorization; this cash prize has been since withdrawn.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).

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    $\begingroup$ There are additionally some old posts from R. D. Silverman, who along with John Brainard allegedly generated the challenge numbers. $\endgroup$ – Samuel Neves Jul 22 '17 at 1:49

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