That description can be embedded in the number. If you use ASCII it’ll be pretty obvious.
Encoding as a prime doesn’t impose any special requirements on the data. All you have to do is append a bit of junk to make the whole thing prime. The rest of it can be plain text or whatever.
> That description can be embedded in the number. If you use ASCII it’ll be pretty obvious.
In that case, the knowledge that information is encoded in that specific number and the drawing attention to that fact is the illegal metadata. In other words, numbers are just numbers - until you draw attention to specific numbers with metadata, that's when you cross the line.
If you make a website with a prominently displayed huge prime number with flashing lights and arrows, you've added illegal metadata that says "try decoding me" or "I am probably a cryptographic key to something"
That seems like a pretty loose definition of “metadata.” And the number would be illegal no matter which medium you distribute it with. The mere act of distributing it (or just possessing it) is enough.
Large numbers can mean anything depending on how you interpret them. If you provide the means (metadata) to interpret a given large number as illegal information (state secret, crypto key, etc.), why shouldn't that be illegal?
I'm not saying it shouldn't be illegal to provide the metadata needed to interpret a large number. I'm saying that lots of large numbers need no metadata to interpret them. For example, if you came across a number consisting of the raw text of this comment represented as ASCII and encoded with base 256, you'd easily be able to figure out what it said with no metadata at all. If this comment contained something illegal, then you'd easily be able to obtain that. Metadata isn't needed.
You'd still need to know that the number is a base 256 encoded string, and the chances you run across such a number in an innocent context (i.e. math publication) seems infinitesimal.
Someone who knowingly hosts a base-256 encoded secret should be held as accountable as if they had hosted the same information in picture form, morse code form, or plaintext.
Encoding as a prime doesn’t impose any special requirements on the data. All you have to do is append a bit of junk to make the whole thing prime. The rest of it can be plain text or whatever.