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    Carmody also discovered another prime, this one being directly executable machine language for Linux i386, implementing the same functionality.

    Huh, that’s pretty interesting, a prime that encoded in binary translates in to executable machine language. Is this a monkeys-with-typewriters scenario where if you search deep enough in the space of primes this type of number would exist for any set of executable instructions?

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      The search must have gone the other direction: compile a valid ELF that includes (or ends with) an ignored block of data. Run a primality test on the binary, increment a bit in the block, repeat.

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      Link to previous Lobste.rs conversation about this https://lobste.rs/s/vhkucf/illegal_numbers

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        ha! my brain hasn’t failed me when i thought “i’ve posted that” ;)

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        So I guess that numbers can be illegal. But I have yet to form an opinion. Could someone on the Internet supply one for me, please?

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          Credit card numbers are obviously numbers. So if I buy something with your number, is it a valid defense to say “you can’t own a number”?

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            I think the answer would be to sidestep the question entirely. It’s not that the number itself is secret or owned, its that the number in the particular context in which it exists (in this case, as a credit card number) imbues it with a degree of specificity. That is, it is not reasonable to assert you own a number. It is reasonable to assert you own a credit card number (or at least have some vested interest in the protection of the knowledge of what that credit card number is, even if you don’t own it), because the credit card number has a functional utility beyond just being a number.

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              This logic can be extended to include any information which can be encoded into a number (i.e. any information at all).

              That is, it seems like whenever this comes up there is a lot of incredulity that any number should ever be illegal. But tbh, I’ve never found the arguments against “illegal numbers” to be very convincing because there is plenty of information that can be encoded as a number that is (and should be?) illegal to possess.

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                What exactly is illegal? Possessing the information or willingly acquiring it? Suppose I have the ability to remember very long number sequences, and stumble upon an “illegal number”. Am I a criminal if I don’t forget the number?

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                  as with most “pedantry in law” issues, the answer is “whatever common sense + the context assumes”.

                  Most things end up in front of a judge that doesn’t care that “theoretically I can generate a text file with all possible credit card numbers, is that illegal?”.

                  Though in seriousness, there’s a lot of details. (IANAL) For example, there have been cases where insider trading was not considered such, because the information was not explicitly sought out. So the context in which you obtain the information can affect things. Copying data for personal use has usually been legal, but handing it to other people sometimes isn’t.

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                    Read the law and find out?

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                      Ah, Google it. Always a classy answer, a worthy contribution.

                      But what if the law isn’t black and white, and it doesn’t have a clear answer to this case. Then you need to understand the spirit of the law. Or not. Maybe somebody else is needed to interpret the law. A judge perhaps? A lawyer?

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                        Actually I’m pretty sure the law on failure to forget a number is pretty clear.

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                  In this case, the focus would not be on the number, but on what you did with it. Did you have the right to use these funds? Of course, if the owner of the credit card gave you the number, it might be implied that you have the right to use it. Otherwise you probably obtained the number through illegal means.

                  A similar case would be breaking in to a place that happens to have its door lock protected a numeric code. You might know or guess the number, but that alone does not grant you the right to enter. Whether it is considered a break in is something that will be addressed without ever considering who owns the code.

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                  Devil’s advocate: they’re definitely illegal. It’s not a number; it’s contraband (in this case, a tarball). Just because you can construct a number (possibly prime) from it does not make the number notable. The number itself is not useful in any arithmetic / geometric way, and would be better thought of as an encoding for the tarball. You can’t just take STARWARS.AVI, tap it with a magic prime-generator-wand, and get away with it.

                  On the other hand, since they went to the effort to find a truly notable representation of the tarball (a distinctly large prime), they should be able to publish it for prime-number-records purposes. But not for DMCA purposes. So honestly I’d say it’s pseudo-legal for records/historical/cultural purposes, but illegal otherwise (honor policy). Like that Vietnam war photo that caused a kerfuffle at/on Facebook a while back.

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                  To the mind of a programmer, the idea that a number i.e. information, can be illegal is ridiculous. To the normal person though, it is perfectly fine, because it is a mean to an end, which is for the government to control what they perceive to be a legitimate business model of coming up with a particular set of information and then restricting its distribution.

                  And you can roll your eyes and explain your perfectly consistent logical framework all you want, it won’t change a mind.

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                    off topic: why was this downvoted? this whole discussion page feels like the impending “wave of trolls” has finally arrived at lobsters

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                      Exactly this. Rules and especially laws do not come from a framework of logic. Alice finds a pretty stone, takes it. It is hers now. Bob sees the stone on a patch of moss where Alice put it when she went to take a bath. He does not know anyone found it before him, so he just takes it.

                      Now, the stone itself did not change at all during all that, but the concept of ownership implies Bob stole the stone from Alice. At least that is what she would claim. If Bob had known it was Alice’s stone, him taking it would cement this even more. He then willfully stepped over a line in the sand of the societal framework Alice and Bob live in.

                      Law is all about which lines exist and where they lie. And because all of it is in sand, it changes all the time.