Talk:Illegal prime

NPOV? The Point?

I suspect that the attempt to be strictly NPOV has taken you a little too far. OK, I'm no mathematician, and I gave up programming when I sold my Z-80, but I have difficultly following the main thrust of the article - not the specifics, which are straightforward enough, but the implications of it. Tannin

There are no real world implications. The whole article is fanboy Mee krob, using a completely banal fact to make a political point. Greglocock 08:09, 4 February 2007 (UTC)

no prime number discovery

I do not think he discovered a prime number. He manipulated the program until it became a prime number and then wanted to use that prime number as a proof that the DCMA is ridiculous. I will not air my opinion about the DCMA, but since all information can be turned into a number, and without substantially changing its content, it can be turned into a prime number, the claim to have discovered a new prime number seems a bit ridiculous to me.

It's this verbiage that is ridiculous. The number in question is on a list of the largest known prime numbers. All such numbers are, of necessity, discovered. -- Jibal 11:47, 27 May 2006 (UTC)

There's nothing ridiculous about it. It just doesn't just "become" a prime number. So you've got this huge 1400 digit number, how the hell do you know if it's prime? The achievement is not in getting at the number, its the proof. -- Arvindn

And, if I use tea leaves and find 1500 digit prime numbers, does that mean I'm all wet? Or dowsing to continue the moisture theme? Discovery in mathematics (and science as well) is not legitimate or not depending on the methods used, but on the results obtained. My new string theory which unites quantum mechanics and general relativity would still be the best available (assuming it makes testable predictions which are experimentally found) even if I got it from my cat -- the one with the string jones. I agree with Arvindn, with reservation. ww 19:29, 14 Jul 2004 (UTC)

Prime numbers are "discovered" in the same way that stars, "new" species and anything else is discovered. It always exists, it's just that some human has now observed it in some fashion and written it down in a book. This just happens to be a special prime, one usable for more than just the curiosity factor. ~Nec

detail on illegality under US law

Here's the point: U.S. courts have ruled that it is illegal under the DCMA to distribute the DeCSS code, which can be used to decrypt DVDs. This entry notes that there is a large prime number which is equivalent to the hexadecimal representation of a gzip compressed form of the DeCSS C source code. This number, if downloaded, converted to binary, and uncompressed, would produce the DeCSS source, which could be compiled and used to decrypt DVDs. Thus it is presumably illegal to publish this number, which would amount to distributing the DeCSS code. Hence the web page which lists the twenty largest prime numbers identified by the technique used to find this prime would violate the DCMA.

I don't think the table of primes in itself would be illegal, but telling somebody "take the third prime from this table, decode it as hex and unzip, and you have DeCSS" would be illegal. AxelBoldt 01:38 Jan 4, 2003 (UTC)

Publishing 20 text strings, all but one of which is gibberish, that one being a CSS decrypter, would rather obviously be illegal even without telling someone which one is the decrypter. That's no different than publishing 20 digit strings that -- as is now well known -- yield those 20 text strings upon being gunzipped. The illegality is in publishing the means to decrypt CSS, and publishing the list of primes clearly provides the means. -- Jibal 11:35, 27 May 2006 (UTC)

It's just as easy to convert a child porn image into such a prime number. This obviously doesn't mean anyone would throw out child porn law because it's ridiculous. Anarchopedia 22:47, 4 June 2006 (UTC)

I don't know why you posted that as a response to my comment, since it isn't relevant to it. The discussion here is about what is or is not illegal under the DMCA, not what is or is not ridiculous, which is beyond the scope of WP. As for equal ease -- only for very very small images. i.e., you're mistaken, it's not "just as easy". -- Jibal 04:46, 6 June 2006 (UTC)

Did you know that for any number n, there exist a prime number greater than n? Thus prime number can be arbitarily large. It can be a million, or a billion digits long. 70.48.250.130 17:41, 12 June 2006 (UTC)

Non sequitur. That there are infinitely many primes has nothing to do with how easy it is to produce a prime of a given length. -- Jibal 12:27, 18 June 2006 (UTC)

See below pdf, deterministic prime generation can be done in polynomial time, so it's considered easy to compute problem.

http://www.math.princeton.edu/~annals/issues/2004/Sept2004/Agrawal.pdf 70.48.251.7 08:59, 25 June 2006 (UTC)

Again, the fact that testing a number for primality is easy does not mean finding a prime number with a given property is easy. --Ihope127 21:12, 15 December 2006 (UTC)

Put plainly, anonymous, it took days to prove the primality of this number, which represents less data than even a thumbnail image. It would take a huge amount of time to represent even a single image in a reasonable resolution. You might be able to break down an image into smaller components and convert these into primes that could be used for some purpose, but I'm still not sure what the practical advantage would be. If someone went through all that trouble, the image might very well be "intrinsically archivable" as a piece of digital history, though there are moral and legal implications of archiving an unpleasant part of history before it becomes ancient. Zuiram 20:52, 6 January 2007 (UTC)

derived work rubric under copyright law

I suppose it's related to the concept of "derived work" that's found in copyright law. If the number was obtained by transforming the DeCSS code, and supplied with instructions on how to convert it back to DeCSS, I suppose it would be found illegal. If the same number appeared in a list of primes which was plausibly claimed to be produced and published for some reason unrelated to DeCSS then I suppose it would be found legal. But as noted above, any digital work can be written as a number, and whether it's legal to put a given number on your website will depend on whether someone can argue that it was created as a derived work. This is just speculation, when dealing with copyright, who knows? ( 18:08, 4 Feb 2004 (UTC)

No no no, the issue has nothing to do with illegal copying of DeCSS code. It's the writing of DeCSS code in the first place that is (purportedly) illegal, because it provides the means to decrypt certain copyrighted material. -- Jibal 11:53, 27 May 2006 (UTC)

URLs and blocking due to protest

The last two URLs don't work. Edward 00:05, 16 Apr 2004 (UTC)

Hmm, they do for me. Odd. Lupin 09:54, 16 Apr 2004 (UTC)

Both of them redirect me to [1], you don't get that? Edward 16:14, 16 Apr 2004 (UTC)

Apparently he detects which IPs are from countries supporting the Iraq war and blocks them! Arvindn 16:57, 16 Apr 2004 (UTC)

Exactly. So I put the warning text back, with a notation not to remove it unless you've seen the protest before. I've set myself a monthly reminder to check it. TreyHarris 18:50, 11 May 2004 (UTC)

Image

This article so needs a photo of one of the illegal prime T-shirts - David Gerard 15:14, 14 Jul 2004 (UTC)

DG, very good idea. Anyone got one? ww 19:29, 14 Jul 2004 (UTC)

Dirichlet's theorem

The article states, "The existence of infinitely many such primes is guaranteed by Dirichlet's theorem." It would be nice to mention why it follows from Dirichlet's theorem - it is currently explained better in Prime number. Dan Gardner 12:51, 31 Jul 2004 (UTC)

I cannot quite see how it follows from Dirichlet's theorem at all. It's essential for this particular solution to keep the data before the "null byte" intact, and in any arithmetical progression, sooner or later the relevant data will start to be changed. Thus, one cannot simply start with one number representation and one offset and simply hope for Dirichlet to save the day - if there really are infinitely many (not very improbable as such...) illegal primes, then this definitely would merit further proof than just a reference to Dirichlet to hold up. Michiexile 14:33, 10 November 2005 (UTC)

How likely is it for a code file to be a prime number?? lysdexia 09:48, 28 Oct 2004 (UTC)

Unlikely. ^_~ -- Schnee 12:46, 28 Oct 2004 (UTC)

Actually more likely than one would think - probability of an N bit file being prime is about 1/N (that's the prime number theorem). Arvindn 21:20, 28 Oct 2004 (UTC)

Really? Isn't it actually about ln 2/N? Whatever... Through the article, it speaks of "the" illegal prime. Aren't there multiple illegal primes? (multiple versions of the DeCSS and other codes that are primes.) --Fermatprime 22:25, 6 Dec 2004 (UTC)

Not sure what you mean about the probability, as log 2/N is negative. As for "the" prime, one of the illegal primes is special because its the one that is archived on primepages.org. This aspect is easily missed, but the major reason for the fuss about the number is because it is archived in the large prime database and they (arguably) have perfectly reasonable response to a takedown notice. At least that's my understanding. Arvindn 04:11, 7 Dec 2004 (UTC)

Sorry, I guess you meant (log 2)/N. I'm a theory-head, so I tend to ignore constants all too often :) Arvindn 04:13, 7 Dec 2004 (UTC)

The number!

I've added the number, as listed in The Register. (They've had it up for three years, there's no reason we shouldn't.) - David Gerard 08:23, 9 Feb 2005 (UTC)

: Wait - is the 154th digit a "4" or an "8"?

There are two prime numbers mentioned in the text: the source code and an executable. Which one is 'the number'? 202.37.96.11 21:22, 22 Mar 2005 (UTC)

Reference to copyright protection is incorrect

The article describes the illegal primes as describing "a computer program which bypasses copyright protection schemes on some DVDs". There is a similar description as the caption under the DeCSS image.

This is incorrect. The CSS scheme in question does not prevent copying. The data on a DVD is a stream of bytes, which can be copied by any device or program that copies bytes. The CSS scheme prevents unauthorized playback (eg playing back Region One DVDs on Region Two players, etc). Describing CSS and DeCSS as being related to copy protection is factually incorrect, attempts by the DVD Consortium to muddy the water not withstanding. Steven (no user account). 203.173.29.99 14:02, 6 August 2005 (UTC)

More importantly, it's NOT ILLEGAL to possess a circumvention device. The article, as written, is flat wrong. See section 1201: http://straylight.law.cornell.edu/uscode/html/uscode17/usc_sec_17_00001201----000-.html -- any problem with changing this? The term "illegal" is woefully imprecise, though I understand its rhetorical value in this context. "Illegal to distribute" packs most of the same punch, and might actually be *true* (though rather debatably). Dreamword 06:28, 16 April 2006 (UTC)

Personal Publishing

Since 'The Number' is published both here and at The Register, would I be committing a crime/illegal act by also posting it on, say, a Weblog? I'm just curious.(The Swami 05:08, 25 August 2005 (UTC))

Maybe if you're in the US. As the article says, "this question has never been tested in court". — Matt Crypto 09:07, 25 August 2005 (UTC)

Hmm, good point... I've decided to put it on a weblog, without a description of what is it or how it could be used. It's simply listed as "The Illegal Prime", and then the number itself. I also put a disclaimer on it saying I don't condone its use for malicious purposes, and that I would remove it if any figure of the law or the operator of the weblog service requested that I do so. I figure this is the best way to cover all the bases; does this seem addequately safe? (The Swami 03:24, 26 August 2005 (UTC))

Sounds good to me...

Problem with Dirichlet's theorem

I have removed the line about Dirichlet's theorem guaranteeing an infinite amount of such primes, because basically it doesn't without an extensive argument backing the claim up. Using some 10^n*data as base to start looking for primes, Dirichlet will guarantee that in all arithmetic progressions beginning at that point, there will be infinitely many primes. However, only finitely many of them will take place early enough as to still have data+zero byte unchanged. There probably still are infinitely many primes, but it's not that easy to show. Michiexile 08:55, 21 November 2005 (UTC)

Executable on what?

It would be useful to state what the prime number is executable on (what microprocessor family) and in (if it requires a particular OS). Does anyone know? - grubber 16:04, 15 April 2006 (UTC)

file says "ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), statically linked, corrupted section header size" - so, Linux i386. Phlip 18:31, 22 July 2006 (UTC)

Thanks for the info! I suppose I should've guessed it was going to be Linux and Intel. - grubber 22:55, 22 July 2006 (UTC)

Fundamental doubt

...as our Indian friends would say. A compression algorithm can process ANY given piece of text to ANY compressed value. It will only work for that one piece of text, obviously. Usually people demonstrate this by using a single 'one' as the output of the compression algorithm. Therefore the fact that a a given prime number expands (via gzip) to a workable piece of code is interesting, but not really remarkable.

Feeding the digits of long prime numbers into a core, and executing them as machine code, is amusing, but is reminiscent of Core Wars, not maths. I think this article should be removed.

Greglocock 23:18, 15 April 2006 (UTC)

gzip isn't just any algorithm, it's a very common compression program. These primes are interesting because it pushes the idea of what is copyright, what is trade secret, and what is protected speech. - grubber 05:45, 16 April 2006 (UTC)

It's just as easy to convert a child porn image into such a prime number. It is easy to convert ANY information into such a prime. 70.48.250.130 22:44, 4 June 2006 (UTC)

No, it isn't, as it clearly depends upon the size of the compressed data -- otherwise, it would be "easy" to produce primes of any size. -- Jibal 04:52, 6 June 2006 (UTC)

It's easy to generate highly probable primes via probabilistic prime generation algorithm. 70.48.250.130 17:40, 12 June 2006 (UTC)

Non sequitur. It is harder to produce larger primes than smaller primes; that's why people bother to have lists of the largest primes. -- Jibal 12:29, 18 June 2006 (UTC)

lol, no, people make a list of largest prime because mathematical curiosity, no one needs a prime with million digits. It's very easy to generate extremely large primes for any practical purpose. See below pdf, deterministic prime generation can be done in polynomial time, so it's considered easy to compute problem.

http://www.math.princeton.edu/~annals/issues/2004/Sept2004/Agrawal.pdf 70.48.251.7 09:01, 25 June 2006 (UTC)

Finding large primes amounts to much more than mathematical curiosity; they have cyptographical significance (see RSA). Generating "highly probable primes" isn't the same as generating primes (see Probable prime). Talking about generating "extremely large primes" depends on what scale of magnitude you're speaking; 2^32,582,657 − 1 is currently the largest known prime, and took approximately nine years to generate; so at this point in our ability to uncover them, primes of this magnitude are obviously not an "easy to compute problem" 170.20.96.116 22:20, 10 October 2006 (UTC)

Publishing the primes on Wikipedia

Is it OK to publish the primes on Wikipedia and in the same breath say that distributing them may well be illegal according to U.S. law (and Wikipedia's main servers are in U.S.)? According to the policies, copyright infringement is not allowed because it "threatens our objective to build a truly free encyclopedia that anyone can redistribute, and could lead to legal problems." The same could be said about including the primes (especially as DMCA technically is about copyright), which are trivial recodings of data already deemed illegal by the courts. They don't really add anything to the article either, except by the visual appearance of their length (people would not notice at a glance if you changed random digits in the numbers, but would if their length changed substantially). I may be overly cautious, though.-- Coffee2theorems | Talk 07:30, 6 September 2006 (UTC)

I can't give any kind of formal legal opinion on this one, but I suspect that 1) the number, taken in conjunction with the article and the connected links may be a technical violation of the DMCA, 2) there's probably a better than even chance that it is not illegal, and 3) the risk of any kind of legal response is close to zero. If you wanted to be a bit more cautious, you could provide a link to the number. I would leave it there.

I'd go a bit further and point out that any number, can represent any program, in a certain compression algorithm. Therefore wiki should prevent the publication of all numbers. For instance, I have just encoded Microsfot Word as the number "1". I haven't written the decode module yet. This entire page is a bit of fanboy geekdom. Greglocock 06:50, 17 October 2006 (UTC)

Well, from that point of view, yes, you can have all sorts of mappings from integers to programs. However, it's very likely the case that law will treat some mappings differently to others, particularly if your mapping just takes an integer to its binary representation. This is a general problem with all copyright law in general, not just DMCA. It makes it illegal to distribute certain numbers (primality is a red herring, IMO) without permission if those numbers can readily be transformed into copyrighted works. I think Wikipedia should steer clear. — Matt Crypto 07:48, 17 October 2006 (UTC)

The thing is, I seriously doubt any court is going to rule that certain numbers are "illegal," even those that can be converted to... well, anything. I don't see any problem with the numbers being posted here, and in fact it's important that they are for the sake of completeness. Jeff Silvers 07:13, 18 October 2006 (UTC)

Well, IANAL, but by the article's own admission, the numbers "represent information forbidden by USA law to possess or distribute." We have to err on the side of caution. Plenty of numbers are "illegal" to distribute without permission: pirated films & music are usually large binary numbers. — Matt Crypto 07:32, 18 October 2006 (UTC)

In that case it would probably be safer to delete the entire article. Or re-title it nerd-boy trivia. As a matter of interest exactly whose laws are we obliged to respect? Given that Wiki is a world wide community and all. Greglocock 00:32, 24 October 2006 (UTC)

I disagree. I think the article covers a very important point: once you go into the digital realm, _everything_ is just a number. So trying to ban software is equivalent to trying to ban use of a number. Trying to copyright software or data files is equivalent to claiming that you can own a number. Looked at in those terms, the entire idea of banning or copyrighting software becomes ludicrous... most people just haven't realised this yet. Mark Grant 15:57, 2 February 2007 (UTC)

And not just software, of course. As (arguably) the most abstract form of knowledge, people view mathematics as being a universal and unownable resource. I guess the "illegal prime" argument is an attempt to confront people with the idea that information in general is not really any different from mathematics in that respect. Then, if we can "own" information, why not let people own parts of mathematics? Conversely, if people shouldn't own mathematics, why do we allow people to own information? (Hmm...I'm moving off-topic here...) — Matt Crypto 16:10, 2 February 2007 (UTC)

I think that since they were already were published on Wikipedia and are pretty easy to find in the article history that they should stay up until they are removed from the history. What is the point of removing them from one part of the site yet leaving them on another part if legal threats are feared? JerTheRipper 10:44, 20 March 2007 (UTC)

The Alphabet is public-domain, as are most punctuation marks. Why are books copyrightable? Because of the information they contain. Why are scanners and copy machines legal? Because they can be used for more than copying of copyrighted material and illegal duplication of currency. Ultimately, it's a matter of enforcement on the part of the copyright holders, and respect for copyright law on the part of the consumer of copyrighted works. Society and law agree to protect the right of intellectual-property right-holders (licensees, creators, owners, distributors, etc.) to profit from their work as they see fit, and as the market allows. My cousin is a locksmith, and one of the parts of doing his job is picking locks that have no keys / lost keys. Does owning and operating a lock-picking tool make him a thief? Is a person a software pirate if they are playing their store-bought region-1 DVD on a Linux system using DeCSS in private in a region-1 locale? By regulation, yes. By common sense, no. Are copy-machine vendors and 1200-dpi color scanner vendors considered counterfeiters by the Secret Service? No. Should the primes be published on Wikipedia? See Thermonuclear bomb and lockpicking, then consult a lawyer. --205.201.141.146 17:52, 20 April 2007 (UTC)

Should Illegal Number still redirect here?

The new HDDVD/AACS hex number strikes me as possibly existing properly under the heading of "illegal number" yet that page redirects directly to "illegal prime" which the HDDVD number definitely does not fit within. 76.172.89.201 02:53, 2 May 2007 (UTC)

So, does HD 09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0 DVD actually mean anythign?03:43, 2 May 2007 (UTC)