Illegal prime
en.wikipedia.org
en.wikipedia.org
Call the cops.
Context and intention matters for the law - if your message is a numerically encoded death threat and the intended recipient already knows how to decode it (e.g because you sent the key in a previous message) then it would be reasonable to call the cops.
Whether the CSS key should be illegal to share is a different discussion.
The authors are clearly targeting unsophisticated audience with that article; feels like the "sovereign citizen" grade of legal analysis.
But if associated with other information such that this value is understood to be a social security number (if it were a valid SSN), it becomes illegal to share it, or even have it, in some circumstances.
It doesn’t make sense to think of SSNs as stolen identities unless the thief knows the names associated with them.
The article links to "illegal numbers", which weasely states "if communicating a specific set of information is illegal in some way, then the number may be illegal as well". Note the "may", and the only references seem to be pure speculation.
Some people argue any kind of copyright and IP rights should be abolished, but who would argue it should be completely legal to phone in a bomb threat because "it is really just a number represented as sound"?
Well yes, the notion of illegal numbers is a construct of the silly argument presented. You can decompose anything proscribed into the elements that make it up and then try to claim the elements are ipso facto proscribed.
Mens rea, for example, is really referring to sequences of electrical impulses in your brain, so again by the line of argument there is a physical phenomenon that is criminial.
I think its asininity (or whatever) is the point. The idea that information can be illegal leads, I think ineluctably, to the 'illegal primes'; so I think that this is meant as a slightly snarky argument against the idea that information can be illegal.
If I were to shorten it to one sentence, it would be this: the law doesn't deal with static, mathematical reality. It considers provenance.
Bits have no color. But human beings do different things in order to develop different bit sequences. Take the bit sequence corresponding to a movie. The bits have no color. But that’s irrelevant. What matters is what you did to get that information. If you can prove that the bits came from an RNG that’s not copyright infringement. Likewise, if you recompress a file you copied and totally change the bit sequence, it’s still infringement. The law doesn’t care about the bits; they are tangential to human actions.
Saying that “certain bit sequences are illegal” is reductio ad absurdum like saying that laws against battery amount to making certain sequences of muscle fiber contractions illegal. The law doesn’t care about the muscle fibers that contracted; that is entirely incidential to the fact that you punched someone.
The article isn't great in how it explains, and it's unfriendly toward the legal profession, but it makes the same claims you do.
rayiner: > If you can prove that the bits came from an RNG that’s not copyright infringement.
article: > It doesn't matter that it looks like, or maybe even is bit-for-bit identical with, some other file that you could get from a random number generator. It happens that you didn't get it from a random number generator.
The law regulates human conduct; crimes require a human action combined with a human state of mind. Things (bits, guns, etc.) are relevant to the extent that people take actions with them. To address the RNG example: the law doesn't care about whether the bits came from an RNG or an original copy per se. The law cares about those things only to the extent that they imply that someone generated the bits randomly versus copying them from the original. (Note the focus on verbs.)
In the RNG example the distinction does not matter, but consider something like insider information about an upcoming merger. The provenance is a leak from someone inside the company. Whether it is legal or illegal depends on what you do with it (trade on it versus publish it), and what you were thinking when you did it (even if you trade on it, if you didn't know it was insider information then there is no crime).
We can try applying your narrative to the number 3.14, supposing laws had made finding the circumference of a circle illegal. Sure, "3.14" isn't illegal on its own (and sometimes it even shows up in the amount of change you're owed). But referencing the number is basically referencing a specific use. And so we can infer that the people broadcasting the number are doing so to highlight how easy finding the circumference of a circle is, and thus induce people to do so.
The informational content of 3.14 is say 12 bits and the original AACS key is 128 bits. Whereas a movie is roughly 10,000,000,000 bits, and even a song is around 32,000,000 bits. These "illegal primes" are very close, if not in, the domain of bona fide facts. And the law generally doesn't criminalize facts (like 3.14), although not for lack of trying!
> The informational content of 3.14 is say 12 bits and the original AACS key is 128 bits.
3.14 is irrelevant for finding the circumference of a circle (from its radius, I guess you meant); it is π that is relevant for finding the circumference, and (conjecturally) the informational content of π is infinite.
The comment may have been predictable, but it doesn't seem to me to be invalid. The error resulting from representing π as 3.14 is relatively small numerically, but, in terms of information loss, it is (conjecturally) infinite. (The information encoded in the 1000th decimal place is, information-theoretically though not numerically, just as significant as that encoded in the 1st decimal place.) It therefore seems to me to be false that it is much less than the (finite) error resulting from representing a common movie using 10 Gb.
You can make a similar argument about digitizing film via sampling, rather than digitally recording the state of every atom - you're throwing away a huge amount of information. Not infinite of course, but dwarfing what it takes to accurately represent the movie. That's a philosophical curiosity, but not really relevant to the qualitative situation.
My point with 3.14 was that everybody recognizes it as a reference to pi, and it works well enough to calculate the circumference of a circle in an engineering context.
(FWIW I personally hate "Pi Day" as March 14th, as it reeks of numerology. It should probably be the day/time when the Earth has traveled around the sun its distance from the sun)
Yes, good point. I was using the term informally, and probably incorrectly, to mean that π (conjecturally) contains any finite string of digits (in any base)—what is formally called 'normality' (https://en.wikipedia.org/wiki/Normal_number). Apropos of your correct belief, there's a lovely so called 'spigot algorithm' due to Bailey–Borwein–Plouffe that can generate any hexadecimal digit of π that you please without having to generate intermediate digits: https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula .
Incidentally, wouldn't that be the less compelling "1 radian day"? Also, to celebrate such a day, we'd have to decide: travelled since when?, and then we're right back to arbitrariness (why choose January 1, or whatever other date/time is chosen)?
For me, while it's hardly an accurate picture of what math is or why it matters, I'm happy enough to have anything that gives people a positive impression of mathematics.
The interesting part here is the obvious contradiction that prime numbers seem innocent but in the end, they are numbers, and numbers can represent anything.
Again, the obvious question to rise here is: How is it possible that a government can forbid information?
Are you really surprised that most of them comply? What other choice do they have?
Definition weapon - a thing designed or used for inflicting bodily harm or physical damage.
But certainly information can be used for extortion, or to otherwise coerce people against their will, and maybe that's enough?
"Information" is a noun, hence it is a "thing".
Furthermore, the 'physical damage' it can inflict is the destruction or manipulation of physical memory cell states.
By itself, it is harmless, but when paired with an appropriate device, by a user with malicious intent, it can then be used to cause harm.
I think that intent and plausibility play the most important roles here.
Also, if the number of bits you need to describe an illegal prime is of the same order as the number of bits in the prime itself, then you have a weak case.
source?
As you increase length, the number of possible strings grows exponentially. There are only a few (relatively) much smaller strings you can map to.
To point to the "Nth prime" would require almost as many digits as the prime itself. Mabe it's more efficient for very large primes, but I don't think so.
Whenever this attempt at reductio-ad-absurdem comes up, I find it pretty unconvincing. It's not that they are banning a number, just like if you make certain images illegal you're not banning "light" and if you make slander illegal you're not banning "sound, which is just vibrations in the air." Describing the medium of speech is kind of silly, because the point is the information contained in the media. The fact that the law addresses abstract concepts isn't exactly groundbreaking.
By having enough capacity for organised violence to make their will stick. And if they lose that, they are no longer a government.
If they dont do this, no one cares about 'the law'.
The only major dispute between governments is which groups of minorities to target.
Yes, but that would be a silly definition; governments rarely persecute as an end goal.
A more sensible one would be: a government is what controls a state, and a state is an organisation with a monopoly of legitimate force on an area of land.
The persecution perspective raises several ideas to the surface that get buried under the monopoly of force definition. The latter is concerned with collection of power, but the former is concerned with the use of power. Further, in countries such as the US, there are numerous arms among the citizens and the government cannot be truly said to have a monopoly of force (disproving the definition at least in part).
To what end is a monopoly of force? There is always a moral judgement in the use of power and always a line in the sand concerning who should be persecuted. Sometimes that line is murderers and sometimes it is homosexuality or saying things the majority disagree with.
Further, the persecution definition is more accurate in that it places the responsibility into the correct hands. Governments are formed by the people who consent to them and have no life of themselves. Even in a place like North Korea, most people endorse a government that most of us find horrible. The position of that line of persecution isn't determined solely by government fiat -- it is a result of the people's consent and inaction.
A government would find catching murderers impossible if the general population did not (as a majority) support and help them. Slaves would not have escaped from the South in any significant number if so many people in the North had not consented. Likewise, lynchings, kangaroo courts, and Jim Crow would not happen if the majority of people had not consented.
Very importantly, this view forces home the effects of intolerance. When a large group of people silence their opposition "freedom of speech isn't freedom from repercussions" they are in fact exercising this exact type of governmental persecution power, but without the tolerance that is otherwise "agreed" upon.
This raises what is (to me) the most interesting argument of all. Speaking of the US. We agree that the government cannot punish people for controversial, but non-inciteful speech. We are the government ("by the people"). We simultaneously agree that we can do the exact opposite in our personal lives and ruin someone we disagree with. This shows our true line in the sand is very much not in sync with the one we voted for and illustrates a very complex, but dangerous cognitive dissonance.
I could go on, but this lens is the most useful one I've seen for looking at how society, morality, and government interact.
For instance, if you encoded the entire design of a nuclear weapon (or some other highly classified military secret) inside a prime, saying "but it's just a prime!" is a very silly excuse for exchanging that information. The question is: "what kind of information should be illegal to exchange", not "which format of information should be protected".
"11234349387298245791029384857" may or may not be an illegal number. Nobody cares and mathematicians can use it to their heart's content. That is, until I attach the metadata to it: "This number is the AES key embedded in every YthnVideo Disc Player". Now it's illegal. Number = legal. Number + metadata = illegal.
At least, that's how it should be.
If from a completely different domain, someone who has no relationship whatsoever to the maintainer of that first site creates a page explaining how DVD players contain AES keys and then links to one of the pages on the first page, from the perspective of a web user, that's number + metadata = illegal, right? And yet the number itself is legal. And the text by itself is legal. The combination is illegal, but the combination doesn't really exist.
Of course, the answer is probably that the text is illegal in the US, because the DMCA overrides the first amendment. Whether the text includes the number or a link to the number, it all interferes with the ability of a company to make money, so it's illegal.
The link is the illegal metadata. It's fine to explain that DVD players use cryptographic keys. It's fine to explain how said keys work. It's fine to have a list of prime numbers on your website for fun. It's not okay to link the two together. The link itself is exactly the type of illegal metadata I'm talking about.
Any type of pointing, eyebrow wiggling, coughing, etc. providing people with metadata on why certain numbers have cryptographic significance for a particular product is not okay (in my opinion).
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.
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"
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.
I sometimes make the joke that unicode sequences make people extremely angry. It's a gentle reminder not to take everything so seriously. But everyone still understands that it isn't actually the sequential placement of glyphs that make people angry.
To complete the 'illegality' you need three pieces of information used in tandem:
1) the prime number (which is innocent in its own right)
2) the decompression algorithm (also innocent in its own right)
3) the knowledge that some specific prime number, when viewed through the lens of the decompression algorithm, yields an 'illegal' interpretation. (not illegal in its own right?)
The issue only comes from all three being present. If you have #2 and #3, #1 can be the last puzzle piece needed to create the required set, but no one piece is in-and-of-itself the source of the issue.
Of course, if the compression algorithm is one that's very commonly used like gzip or jpeg, a jury will infer intent from the totality of the circumstances and your lawyer will have a really hard time talking them out of it.
Everything is information. How can murder be forbidden? It's just an arrangement of quarks?!
edit: am I the only one who thinks that this whole pifs filesystem was meant as a joke?
Whether that is true is related to the normalness [1] of the number pi, but this property has not been proven. See also: [2].
[1] https://en.wikipedia.org/wiki/Normal_number
[2] http://www.askamathematician.com/2009/11/since-pi-is-infinit...
Naw man, physics still apply, you dont get gandalf just because you went a few million light years toward Andromedia
"Googol and Googolplex - Numberphile" - https://www.youtube.com/watch?v=8GEebx72-qs
I assume jgtrosh's question is more of a probability and estimation question. E.g. the string "Hello world" takes up 11 bytes and what's the size of the index into pi? To generalize a little more, to store any 11-byte sequence, what is the estimated size to store its index? To find the exact 256^11 byte sequence in pi, there will be many cases where the sizeof(index) is greater than the data itself.
So on average, the offset for a given binary sequence will be on the order of 2^N (I’ve used some hand-waving here). You need N bits for that, you you’ve gained basically nothing.
Edited to fixed terrible spelling
That reminds me of a compression program I once wrote. It had the following properties:
1. It accepts any non-empty file other than a file consisting of a single 0 byte.
2. It is easily reversible.
3. The output is never larger than the input.
4. The output is smaller than the input for some files.
5. If a file is larger than 1 byte, iterating enough times will always eventually produce a smaller file. What is "enough times" depends on the file content.
(I wrote this partly as a joke, and partly as a counterexample to some proofs I'd seen on Usenet about the limitations of compression programs where the proofs had not been sufficiently precise in specifying the conditions necessary for them to apply).
It is actually quite simple:
1. If the file is empty or a single byte that is 0, report that the input is not acceptable and exit.
2. If the file is N bytes, treat it as if it is an 8N bit unsigned integer, I.
3. If I is 0, the output file is N-1 bytes all with value 0xFF.
4. If I is not 0, subtract 1, and output the result.
(Decompression is left as an exercise for the reader).
Another way to look at this is to imagine that we have a sorted list of all possible files. The primary sort key is file size. The secondary sort key is the numerical value of the file when treated as an 8N bit unsigned integer, where N is the file size.
My compression algorithm is simply to replace each file with the file immediately ahead of it on that file list.
Viewed that way, it is pretty obvious that all my claims are true. It accepts any non-empty file other than the first file on the list (single 0 byte). To reverse it, replace the input with the file immediately after it from the list. The list is ordered by file size, so stepping down in the list never gives a larger file, and sometimes gives a smaller file. The output file is on the list, so you can obviously iterate.
The catch, of course, is that while yes, you can take your 1 TB of arbitrary data (even true random data!) and apply my algorithm iteratively to get down to, say, a 1 byte file, and yes, you can apply the decompression algorithm iteratively to recover your 1 TB from, to do that you have to know how many times to iterate on the decompression end.
The number of iterations required for an uncompressed file of N bytes to compress down to a byte is on the order of 2^(8N), so you will need about N bytes to store the iteration count.
So net result is that it can replace an N byte file with a 1 byte file...but it is going to drop N bytes of metadata on you that you'll need to store somewhere.
pi = N/(1-b^k) which is rational.
(And if you set k=0, you get that pi "contains itself" in the sense that pi from the 1st digit onward is of course pi)
Well it does, trivially.
You’re probably thinking of set theory but the file system is about storing information in a sequence and an offset. Seen that way, π can be stored with offset 0.
This is not true. Pi is probably irrational, which means we know it doesn't repeat itself. However, it is not proven to be normal, so it's a conjecture (but not fact) that it contains every finite sequence of digits at some point.
Pi is provably irrational, and probably normal!
Damn autocorrect! And it's too late to edit it, too.
Yes, that should say "provably irrational".
It is legitimate and provably effective to legally limit the demand for some items, like ivory, for example, by making it contraband, interdicting trade, and punishing possession.
So what is the outrage actually about? A lot of it is about corporations asserting property rights in publishing and enforcing those supposed rights in ways that result in bad decisions, bad designs, bad products, insecure systems, and bad uses of law enforcement related to computing.
The solution isn't to "make all numbers legal" because that's not the question. The solution is to address the problems in the real world, where they make sense. Limit copyright terms. Limit laws to publisher-scale theft for profit. And that boils down to nerfing corporate money in politics.
Whats the proof then? Last I checked, despite all laws, ivory animals are being poached into extinction. It might be more effective than doing something like paying poachers to poach even more animals, but that isn't proof it is an effective means to stopping the problem of poaching animals into extinction.
All current computer media can be represented as an integer. You're suggesting that no media is illegal?
This sort of "everything is allowed" arguments just seems like a way to avoid having to think carefully about what restrictions are reasonable, and what constitutes responsible use of information. Simply lazy irresponsibility.
Regarding responsibility: https://news.ycombinator.com/item?id=16933814
Truth is, often correlations are the only things we can go after to fight the things we don't want.
It certainly makes for an interesting discussion, however, your view is fringe here -- the laws of virtually every free democracy on the planet encapsulate the idea of some information being illegal.
HOWEVER: the gp point wasn't coming at it from your perspective there. They were saying (as I understood it) the fact that integers are "just numbers" meant that banning them was nonsensical. By extension, the illegality of distributing them would also be nonsensical.
Illegal to disseminate, not to own. There should be no punishment for being able to access or possessing information; Liability should squarely sit with the publisher, intentional or otherwise.
The law for all it's flaws is ultimately a practical discipline, not abstract logic. Unless you're against all laws in general, which is a thing for some people.
According to your assessment here you're an accessory to a crime - a willing and necessary participant. You said (hypothetically) you downloaded it, but that distribution should be illegal. Distribution and reception are linked, you can't get it without the distribution.
Demand for distribution fuels the supply.
I absolutely would maintain the illegality of ownership of some types of information (mitigations aside) - child pornography, imagery of rape or assault are obvious ones.
Freely allowing the supply and acquisition of details on making nukes is fine, because acquiring the components is difficult and can be controlled.
My quandary is that I want to be liberal to allow curiosity and educational intent to be fulfilled; but realise that there are elements who abuse the free acquisition of information that enables great harm (how to make a fertiliser bomb, how to make ricin).
And I don't believe that you wholly don't care. I'm almost certain you must have some photos, or potentially may have some situations, if you were photographed, that are embarrassing and that you wouldn't want the general public (parents, coworkers, boss) to see.
You can care, you may not want these photos to be where they are, and you may attempt to have them removed if it is possible, but you don't have the right to punish people for not caring, and you don't have the right to force people to care for the things you do.
I personally hate being on photos, so I try to avoid it to my best ability. I also asked someone to have a photo of me removed from somewhere. This is all understandable. The problem occurs when you are trying to dictate other people's lives by threatening to use violence against them for not conforming to your beliefs, etc. No need to resort to violence, come on.
I have a feeling you would attempt to beat me up for my tone alone because you perceive it to be hostile. Not cool. :P
But I think we should consider a major division between the rules of sharing information and the rules of possessing information. If I know how to make something bad, that shouldn't be wrong. If I share that for the sake of a discussion, that shouldn't be wrong. If I share it with someone who will use it to cause harm, knowingly aiding them in causing harm... well isn't that where we should say wrong has been done?
(It should be pointed out that it's not been shown that this would actually be upheld by the courts).
You might be quite right in that no information should be illegal to posses. That, however, does not make it so. There's plenty of information that is illegal to posses. The fact that you don't like it doesn't make it less so.
Consider your argument with respect to privacy and data issues - obviously possession of information can be in and of itself harmful because it can be something that other people have a right to restrict your access to.
And how does one come to possess information without creating or receiving (distributing) it?
Or maybe....we should look at who is distributing material that we have a problem with, and target it there? As a society we should never be putting people in jail for just owning a certain piece of information, would you not agree?
Let me put it this way - you can go on google right now, type in "two teenagers kill man with screwdriver", and very quickly(on dailymotion) find an EXTREMELY graphic video of two guys killing a person with a screwdriver, picking out his eyeball and playing with it, while he's still alive etc etc. It's absolutely sickening and it shows a horrendous crime being committed. Yet watching and/or downloading such a video is not a crime in itself. If police ever found such a video on your drive they would probably go "wtf dude" but nothing would happen to you. How is that different from the video you described? Because someone might wank to it? What if someone gets off on the one I described? Is it a crime before or after you get aroused?
Instead, like I said - simply having a video/picture/text/drawing of literally anything shouldn't be a crime in itself.
Consider this - how many people do you think make YouTube style vlogs then DON'T upload them to YouTube? Not many right - the audience is part of the inventive for making the video. Among paedophile communities first generation IIOC are highly prized.
Source: I am a criminal investigator who works exclusively on CSE
EDIT: Actually, I'm trying to come up with reasons that apply to child pornography but without any success. Not saying that they are not going to offer you a "reasonable" insight, but at this moment I can't think of anything. Perhaps something anatomy related? Medical value/curiosity?
On another note: yeah, people do crazy shit for the likes and subscribers, it's pathetic and sickening. All those challenges, etc. Ugh. I try to avoid that side of the Internet. Is it just me or is there really a decline? Yesterday I read how in UK schools they had to remove analog clocks because kids couldn't tell the time off it.
I don't know, I know so many parents who are doing a great job. Their kids don't care much about social media, they are not interested in getting likes, not interested in being YouTubers, know the potential dangers of the Internet, and so on.
[1] Albeit I don't download them, but at the same time you can probably do the same with child pornography, though from a technical point of view you probably have them cached which could be considered possession I guess.
Incidentally there isn’t a single country (as far as I could find) where owning Mein Kampf is or was illegal. There’s a common misconception that its possession is or was illegal in Germany. However, this was never the case. Until 2016 the state of Bavaria owned the exclusive copyright and prohibited its publication. But that’s it.
There is a lot of content out there which is illegal to possess, not just DMCA circumvention, and thanks to the wonderful power of mathematics that content can always be expressed as a number.
Extending your analogy, you could have a random bit sequence, XOR it with the content and distribute only the random sequence and the XORed sequence, making it a nonce-sense.
You might even decline to mention which well-defined bit sequence you used, and just leave it as an exercise for the reader to try XORing with pi, e, phi, sqrt(2), etcetera on their own.
There are no illegal numbers. But if you provide context, they can become illegal data. Let's take child pornography for an example, because that's universally accepted as illegal. I could come up with a formula which translates a huge number into a bitmap. I could post the number (i.e. the input for the formula) online, because it is absolutely meaningless to anyone else. But when I publish my formula, it is no longer a number. It's data which can be interpreted as something meaningful, an image.
Everything is just a number without context.
You can literally arbitrarily associate any number to anything and ban it based on that, which they did:
> In 2012, it was reported that the numbers 89, 6, and 4 each became banned search terms on search engines in China, because of the date (1989-06-04) of the June Fourth Massacre in Tiananmen Square.
> Due to the association with gangs, in 2012 a school district in Colorado banned the wearing of jerseys that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31).
> In 2017, far-right Slovak politician Marian Kotleba was criminally charged for donating 1,488 euro to a charity.
It's closely related to hate speech laws where the only requirement is perceived threat. Fun times. :D
Banning specific representations of an idea is a game of whack-a-mole. As soon as you ban one symbolic representation, a new one will be created.
https://en.wikipedia.org/wiki/Chilling_effect
The website dedicated to the topic of the OP article is even called... http://chillingeffects.org/ (since renamed to https://lumendatabase.org/ )
> An illegal number is a number that represents information which is illegal to possess, utter, propagate, or otherwise transmit in some legal jurisdiction. Any piece of digital information is representable as a number; consequently, if communicating a specific set of information is illegal in some way, then the number may be illegal as well.
A perfectly equivalent statement is that there are certain "strings that are illegal", but this is both trivially true and a clearly exposes the fallacy at play here.
A written death threat is still a death treat no matter the string encoding you use, so while yes it is an "illegal string", this is just incidental: its the threat that the string encodes that is really breaking the law.
A "written death threat" is not "illegal". I've seen plenty of such threats written on the boundaries of military sites or even electricity substations. Delivering death threats to a person may constitute illegal harassment, but so might delivering love letters. It all depends on the circumstances.
https://www.popehat.com/2012/09/19/three-generations-of-a-ha...
Please use different phrasing to discuss lawful and unlawful speech in the future.
> And it would be pretty hard to convince a judge that you didn't intent to use it as DeCSS.
so "merely distributing this prime number is not illegal" is de facto illegal.
> A large prime is notable and hence is included in public databases.
It is verifiably true that these public databases exist (bigprimes.net)
I'm not sure what you're arguing here.
The example site you gave bigprimes.net has one main database, that includes the first 1.4 billion primes. These are all much smaller than the illegal primes mentioned on the wikipedia page (they have at most 11 digits, whereas the ones mentioned on wikipedia have 1000s of digits). It also has a list of the Mersenne primes, which are the largest known primes. The largest has 23249425 digits.
So primes with 11 digits or fewer are notable (because they are small), and primes with 23249425 digits or more are notable (because they are large), but primes with around 2000 digits are not notable.
> Carmody created a 1905-digit prime, of the form k·256211 + 99, that was the tenth largest prime found using ECPP, a remarkable achievement by itself and worthy of being published on the lists of the highest prime numbers.
There should be a whole industry about it.
Doesn’t change the legal situation, of course.
Cryptography is about exchanging secrets on an insecure network.
This is about legally publishing information you're not allowed to make public.
It does change the legal situation because, from the article, it's about
> ... the representation of the illegal code in a form that had an intrinsically archivable quality. (...) The primality of a number is a fundamental property of number theory and is therefore not dependent on legal definitions of any particular jurisdiction.