>One of the earliest illegal prime numbers was generated in March 2001 by Phil Carmody. Its binary representation corresponds to a compressed version of the C source code of a computer program implementing the DeCSS decryption algorithm, which can be used by a computer to circumvent a DVD's copy protection.[1][2]

https://en.wikipedia.org/wiki/Illegal_prime

> so posting the primes that make them up is sharing the encryption keys and thus against DMCA

Except it's not.

You can post the numbers alone, without including information (directly or by reference) to the application about which information is banned, all you want.

This is also my understanding, but certainly not what RIAA and folks do want because this loophole allows for much more efficient distribution of those illegal numbers. Therefore they are motivated to overblock, whether the number is accompanied with instructions or not.

If you distribute a number that represents something you're not allowed to distribute, without announcing this connection, you're not really making that secret information available to anyone. There's no loophole there.

You need to somehow include information on how to use the number, which is arguably easier to pull off, but still doesn't make it legal, just harder to find out.

How about if we first standardize a universal, generic encoding scheme which produces numbers? Then if you saw a random number somewhere, you'd know to simply try decoding it with this scheme to see whether it succeeds.

I didn't mean that a mere dissemination of numbers is illegal; rather, RIAA will try to make illegal and will penalize (not yet illegal) dissemination for any means possible exactly because of that. This has a huge implication both for who don't want get in trouble and for who want do the illegal thing.

So, if I understand correctly you could do the following:

1. Someone somewhere creates a numbered list of primes (so 1=1,2=2,3=3,4=5,5=7,6=11,7=13,8=17, etc etc) 2. You refer to "the [N]th prime" with a vastly smaller number, and people could fetch it from the list of primes. 3. They could theoretically ban the number N?

>with a vastly smaller number

Fun fact, there are a _LOT_ of prime numbers. There are about 10^22 prime numbers smaller than 10^24, so about every 100th number is prime. The ratio decreases the higher you go of course. The vastly smaller number is actually just a few bits smaller :)

If you could do that reliably, you'd obviate all compression algorithms. Unfortunately, primes don't compress like that.

Historically shared DRM keys are typically symmetric encryption keys, not asymmetric ones, and thus not primes. I am not aware of any instances of an "illegal prime" that was prime because it was the private part of an RSA-based DRM cryptosystem. As far as I know, all of them were either encoded as primes deliberately, or just coincidentally prime.

Edit: except for this one, I guess. This one wasn't about DRM, but rather just a locked down device. TI sent bogus DMCA notices for that one, but as far as I can tell there is no solid legal theory under which those primes were illegal, and nobody ever got sued, so we can file this one under "manufacturer upset they no longer control their users' devices throws a legally meaningless fit".

https://en.m.wikipedia.org/wiki/Texas_Instruments_signing_ke...

There are some encryption schemes that use raw primes as their keys.

But the first popular 'illegal prime' was a gzipped code that would defeat the DRM of DVDs. See https://en.wikipedia.org/wiki/Illegal_prime