6 ms·

Illegal prime

152 points by niyazpk 17y ago

wizard_2 17y ago
I bring this up whenever I want to point out how law lags behind technology and ends up doing silly things like making a number illegal, or making cracking cyphers like rot13 a felony. That is to say, breaking even simple encryption a felony, not rot13 specifically. People always get amused that a prime number could get them in trouble.
- k4st 17y ago
  A more relevant example, as mentioned in a linked article, is that the binary data of images such as child pornography and state secrets are also numbers and as such may be considered illegal.
  - Rod 17y ago
    How can an image be a number? This is an honest question. Isn't an image a list of numbers? These numbers could the RGB of each pixel, or the N higher Fourier coefficients, etc. From these numbers, one can compute a single number, sure. Nonetheless, the idea that an image is a number and, hence, can be made illegal, looks utterly ludicrous to me due to the fact that the image -> number mapping is certainly not injective.
    - ramanujan 17y ago
      An image is ultimately represented on disk as a binary string. Hence it is a number.
      - Rod 17y ago
        OK, Mr. "Ramanujan", let's play a game: I give you a binary string, and you tell me what image corresponds to it. Are you game? I won't tell you how the bitstring was computed from the image. I don't tell you how many pixels the image has. I don't tell you anything. I only give you the bits. Wanna play for money?
        ErrantX 17y ago
        I think his point is... the image is stored on disk in a binary form. Which can also be represented as a number (Decimal).
        Rod 17y ago
        Geees, is this HN??? Am I the one who's too stupid to explain things properly, or is everyone under the weather because it's Monday morning? An image is a 2-dimensional array. Say it's a M x N array. Suppose we use RGB so that each pixel is represented by 3 bytes. Then you have an M x N x 3 array of bytes. There are infinitely many mappings from the space of all M x N x 3 arrays of bytes into the reals. Of course you can transform the array into a number. But you can do it in many, many ways. If you know what mapping was used, and if the mapping is invertible, then you can obtain the M x N x 3 array of bytes from the number. If you don't know what mapping was used, or if the mapping is non-invertible, then you can't obtain the M x N x 3 array from the number. So, I claim that an image is NOT a number. I claim that an image is a pair (y,f), where y is a number, and f is an invertible mapping from the space of M x N x 3 arrays into the reals. You guys are looking at y, and forgetting f. That's why an image is not a number, the image is x = f^{-1} (y). In short, one must know f, and f^{-1} must exist.
        AndrewDucker 17y ago
        You're merely arguing there that a number is not necessarily an image, because it cannot be converted into one without knowing how. And you'd be right. But the image is still a number, because it's stored as a series of bits, and any series of bits is interpretable as a number.
        Rod 17y ago
        I asked: "How can an image be a number?", when I should have asked instead: "How can a number be an image?" To use the verb to be in this scenario, I demand a one-to-one correspondence between numbers and images. If a number y can represent two distinct images x1 and x2, then we can't use "is", we can only use "can be".
    - amalcon 17y ago
      A list of numbers is a number, in the same way that a string of digits is a number.
      - Rod 17y ago
        Technically, a string of digits is only a representation of a number. And such representation may not even be unique.
        deleted 17y ago
        [deleted]
    - almost 17y ago
      Nope, that's just one interpretation and it's not more valid then any other. Your argument is equivalent to saying something like this "129 isn't a single number, it's actually 110^2+210^1+9*10^0 (aka 100 + 20 + 9)". Anything that can be represented on a computer can be seen as a number, rather large numbers sometimes but still definitely numbers.
      - Rod 17y ago
        You are totally missing the point. The 3-tuple (1,2,9) may represent number 129 if you use the decimal expansion. What if you use a base-16 expansion, or a base-8 expansion? You can even choose the base so that the tuple -> number mapping is not injective (and, thus, not invertible). So, you give me a number, and I can give you infinitely many n-tuples that can be transformed into that number. Unless you know the mapping, and unless the mapping is injective, a single number is useless. It could represent infinitely many images. So, I ask again, how can an image be a number?
        jerf 17y ago
        It is more proper to talk about the number + a decoding scheme. For given triple (image, image data, encoding scheme) any one can be held constant and the other two will have an infinite number of possibilities. In particular, any image can be represented as any set of data, plus an encoding scheme for that data. Trivial (but relevant) proof: The encoding scheme can simply hard code the image in question and trigger returning that image when it sees the held-constant image data. You could choose to represent an image as image data + decoding scheme, using an agreed representation of the decoding scheme such as a computer program. Mathematically we get nowhere because we are simply moving the encoding scheme around, but in practice, since we possess concrete encoding schemes it means we can practically discuss the situation better. This is a long-winded away of agreeing with you, BTW.
        Rod 17y ago
        Thanks for wording it more precisely than I did. Most people are assuming that the mapping tuple -> number is known, while I am not. I could come up with my own invertible mapping. The cool thing would be this: - I carry a large number y with me - the police demands that I disclose y, and I do; they apply inverse mapping f^{-1} and obtain x = f^{-1}(y) which is a porn image - then I show the police that applying inverse mapping g^{-1}, one obtains a totally legit image z = g^{-1}(y) Of course, finding such a mapping g could be extremely difficult, but if the same number can be obtained from two different images, how would the police be able to accuse me of anything?
    - jsolson 17y ago
      You could view it as a list of numbers, yes. Alternatively, we all know that the file representing the image is nothing more than a collection of bytes. Bytes are nothing more than 8-element bit vectors. What if instead of treating the file as a collection of $n$ 8-element bit vectors we instead treated it as a single $n*8$-element bit vector. What we now have is a single (potentially VERY large) binary number. To make any sense out of this number we'd have to pull out individual collections of bits, but this is no more complicated than doing a bitwise AND and bit shift. Put another way: you can think of an IP-address as 4 sets of numbers between 0 and 255. For example, 192.168.1.1. You can view that same IP-address as the hexidecimal number 0xC0A80101. The hex representation is convenient, as it makes elements in the dotted quad apparent. 0xc0 = 192, 0xa8 = 168, 0x01 = 1, 0x01 = 1. Hope that helps.
      - Rod 17y ago
        That's not what I meant at all. Of course you can transform a list of bytes into a number. But can you transform a number into a list of bytes? That is the problem. If you know the "encoding" algorithm, then you can. If you do not, then you simply can't. The point I was trying to make is that a number, itself, is nothing unless there's knowledge of the encoding algorithm. A CD-reader can make sense of the bits stored on the disk because it knows the encoding algorithm. If the CD-burner and CD-reader did not "talk the same language", it would be impossible to make sense of all those bits stored on the disk. Without knowing what interleaving and channel code was used, the CD-reader can't do its job.
- Confusion 17y ago
  This has nothing to do with law lagging behind technology. Even before computers, the ability to express language in a number was well known. If someone turned a defamatory sentence into a number and spread that number together with the key to turn it into the sentence, then they would be just as guilty of defamation as when they had spread the original sentence. I surely hope you do not advocate getting rid of all laws that deal with information that could be expressed in a number, because you feel it should not count as the same incriminating information, just because it was masked with some mathematics?
WilliamLP 17y ago
This is pretty silly, isn't it? Is it that mind-boggling that data can be illegal to distribute, for example a movie or an unreleased game? The prime number is a red herring. Given the prime number theorem, the probability that an n-digit number is prime scales as 1/log n, so it's easy to pad any data with random garbage that isn't executed until you get a prime. For a gigabyte of data that might be a few billion attempts. (Proving it's a prime will be harder.)
- niyazpk 17y ago
  >> Is it that mind-boggling that data can be illegal to distribute...? The DMCA has had an impact on the worldwide cryptography research community, since an argument can be made that any cryptanalytic research violates, or might violate, the DMCA. - http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Act#Criticisms http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Ac... That is mind-boggling.
fserb 17y ago
I think the argument that "how can a number be owned or its posession be illegal" is mostly bogus. One could translate any string of text into a series of bits and back to a single number and say that a book or a picture is just a number. Then one could say that noone invented that number, and that it's just a number, so you couldn't have copyright nor protection because everything could be randomly generated, etc, etc... I think the real issue is that in the case of prime numbers made "illegal/protected", the absurd is not that they are protected, but that they are not encoding any meaningful information that a human being produced. They are a particular number (probably randomly generated) and the fact that they are used in a particular context (to encrypt data) makes them protected.
- jerf 17y ago
  "but that they are not encoding any meaningful information that a human being produced" I was sort of with you up to that point; I don't agree, but I was with you. However, now I would say you need to read the article more carefully, as the entire point is that they do indeed encode something human-produced and usable. If you use Unix, you've almost certainly got the decoder for that number sitting right on your disk right now, it doesn't get much more concrete than that. Without that, you're missing the whole point. They aren't randomly generated at all. Guess I might as well spell out the other objection I have, which is that you're subtly begging the question. You prove that the idea of owning a number is silly because the idea of owning a number is silly in your last sentence of your first paragraph. Let me give you a much better argument: flip your argument on its head, and say that of course it's perfectly sensible to own numbers. All but the smallest works translate in any reasonable encoding scheme into enormous numbers, numbers that would simply never be chosen randomly. There 0 chance that sitting here and stringing together "random numbers" will ever produce anything like a movie or picture or even coherent sentence, that doesn't already exist in the encoding scheme. (Not literally 0, depending on the circumstances, but close enough.) Therefore, the actual problem is that it does indeed make sense to own numbers; in an infinite space when we are all choosing umpteen millions or billions or trillions or well beyond that of digits, one can very plausibly stake an ownership claim on the grounds that it is clear that if somebody else ends up with the exact same number, they got it from you. Therefore, since it is sensible to own numbers, the objection that it is not collapses and then the rest of the argument against ownership does too. As I said, I don't actually agree with that line of thought. There are a lot of intricacies in the issues of encoding, and some other objections I'm leaving out, but it's still a stronger line of argument. My feeling are more related to the classic bit color essay: http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php If that doesn't seem related, think more; it is, it very much is.
oscardelben 17y ago
I still don't get how a prime number can reveal hidden information. Can someone please explain me the process?
- niyazpk 17y ago
  From the article: Its binary representation corresponds to a compressed version of the C source code of a computer program.
- etherealG 17y ago
  it doesn't reveal information except that it is a constant that is used as part of a process of encryption where without the constant cracking that encryption would be effectively impossible and with it cracking the encryption is trivial. effectively the number is the encryption, as having the number makes the encryption useless. the rest of the algorithm is pointless without the number and vice versa.
  - lt 17y ago
    That's a different number, not the one the article is about. The one in question is a compressed version of a c program that breaks encryption.
dfasfwe 17y ago
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ErrantX 17y ago
For all those commenting please read it carefully: the primes are not illegal, just number representations of apparently illegal programs.
randomwalker 17y ago
Y'all totally missed what's going on here. Primepages (http://primes.utm.edu/ http://primes.utm.edu/) lists the largest known primes of various forms. One of the categories is primes that have no special form, which are the hardest to prove prime. Chris Caldwell, the primepages maintainer, called up Phil Carmody and said, "Phil, if you can turn DeCSS into a 'general prime' that's big enough for the top 20 ever discovered, I'll be happy to host it on primepages." (Just as he would host any prime, DeCSS or not, that was big enough for the top 20.) So Phil did, cuz he's a smart guy and had a lot of computrons, and the prime went in the database. The point here is that if you're merely turning data into a number, you have no legitimate reason to distribute it other than whatever reason you had to distribute the data itself. However, primepages existed long before DeCSS became a problem, and was arguably simply doing what it always did, which is to list the top tens. I don't know if that would hold up in court -- it was never tested -- but the argument is a lot more subtle than what people are criticizing here. An aside: Phil and I worked together on some other primality records. I wrote most of that Wikipedia article back in 2002 or so, and they went and featured it.. this was all before the rules for citations/references on Wikipedia became tighter than a mouse's arsehole. So if anyone is in the mood to add some citations, that would be much appreciated.
- tshaddox 17y ago
  I don't see how "a reason to distribute it" is necessary. What if I just choose a completely random integer with 2000 digits and host it? I don't have any reason to do so, and it's certainly not illegal. Then someone comes along and generates a program that's equivalent to that number, or some digital media rights developer happens to use that number as a key for encrypting some copyrighted media. Does my original act of hosting suddenly become illegal, because I had no good reason to host the number in the first place?
  - yoden 17y ago
    The probability of you doing that without piracy is so vanishingly small as to be irrelevant.
- yoden 17y ago
mixmax 17y ago
A Danish Social security number consists of two numbers - the first one being four arbitrary digits, and the second one being the six digits of your birthday. My two numbers aren't only prime, which in and of itself would be pretty unlikely. No they're Twin primes. (http://en.wikipedia.org/wiki/Twin_prime http://en.wikipedia.org/wiki/Twin_prime) This is the only place I know where information like that would be considered pretty cool :-) Now somebody guess my birthday.
- yan 17y ago
  Now someone can guess your entire social security number :P
  - mixmax 17y ago
    Calculated risk
- pvg 17y ago
  Which two numbers? It's quite difficult for a six digit and four digit number to be twin primes. Some zany Danish date format?
- swolchok 17y ago
  Impossible? Danes write dates as dd-mm-yy according to http://en.wikipedia.org/wiki/Calendar_date http://en.wikipedia.org/wiki/Calendar_date, so your birthday can have at most one leading zero and thus is >= 10100. 9973 is the largest 4-digit prime number, and 9973 + 2 is 1) not prime and 2) not a 5-digit number.
  - mixmax 17y ago
    We're talking about two sets of twin primes, each part of the social security number being in each set. I'm sorry I didn't make it clear in the OP.
- niyazpk 17y ago
  Assuming that (1) you were born between 1950 and 1985 and (2) the danish date format is (dd-mm-yy), here are the possible DOBs: 10-01-51 30-01-51 17-03-51 14-05-51 26-05-51 27-05-51 13-06-51 16-06-51 16-07-51 18-07-51 25-07-51 25-09-51 15-10-51 21-10-51 24-10-51 21-11-51 13-12-51 17-12-51 19-12-51 28-12-51 10-01-53 17-03-53 27-05-53 16-07-53 25-07-53 21-11-53 17-12-53 24-02-57 29-06-57 25-10-57 13-02-59 24-02-59 21-03-59 29-06-59 14-07-59 17-07-59 22-08-59 15-09-59 25-10-59 26-10-59 10-11-59 24-12-59 13-02-61 10-03-61 21-03-61 31-03-61 27-04-61 23-05-61 14-07-61 17-07-61 27-07-61 22-08-61 23-08-61 26-08-61 15-09-61 12-10-61 18-10-61 21-10-61 26-10-61 10-11-61 17-11-61 24-12-61 25-12-61 10-03-63 31-03-63 27-04-63 23-05-63 27-07-63 23-08-63 26-08-63 12-10-63 18-10-63 21-10-63 17-11-63 25-12-63 13-03-67 19-03-67 11-05-67 19-06-67 15-07-67 14-08-67 20-08-67 16-09-67 25-09-67 24-10-67 17-11-67 26-11-67 29-11-67 27-02-69 13-03-69 17-03-69 19-03-69 22-04-69 11-05-69 19-06-69 29-06-69 15-07-69 28-07-69 14-08-69 20-08-69 16-09-69 25-09-69 22-10-69 24-10-69 12-11-69 15-11-69 17-11-69 26-11-69 29-11-69 11-12-69 23-12-69 27-02-71 17-03-71 22-04-71 29-04-71 29-06-71 23-07-71 28-07-71 22-10-71 12-11-71 15-11-71 22-11-71 11-12-71 23-12-71 29-04-73 23-07-73 22-11-73 15-03-77 11-04-77 19-05-77 16-08-77 22-08-77 17-10-77 25-11-77 27-12-77 18-01-79 15-03-79 11-04-79 19-05-79 11-08-79 16-08-79 22-08-79 17-10-79 14-11-79 25-11-79 10-12-79 27-12-79 18-01-81 20-03-81 16-04-81 30-05-81 14-06-81 11-08-81 15-08-81 24-08-81 14-11-81 30-11-81 10-12-81 20-03-83 16-04-83 30-05-83 14-06-83 15-08-83 24-08-83 30-11-83

152 points by niyazpk 17y ago

I bring this up whenever I want to point out how law lags behind technology and ends up doing silly things like making a number illegal, or making cracking cyphers like rot13 a felony. That is to say, breaking even simple encryption a felony, not rot13 specifically. People always get amused that a prime number could get them in trouble.

k4st 17y ago
A more relevant example, as mentioned in a linked article, is that the binary data of images such as child pornography and state secrets are also numbers and as such may be considered illegal.
- Rod 17y ago
  How can an image be a number? This is an honest question. Isn't an image a list of numbers? These numbers could the RGB of each pixel, or the N higher Fourier coefficients, etc. From these numbers, one can compute a single number, sure. Nonetheless, the idea that an image is a number and, hence, can be made illegal, looks utterly ludicrous to me due to the fact that the image -> number mapping is certainly not injective.
  - ramanujan 17y ago
    An image is ultimately represented on disk as a binary string. Hence it is a number.
    - Rod 17y ago
      OK, Mr. "Ramanujan", let's play a game: I give you a binary string, and you tell me what image corresponds to it. Are you game? I won't tell you how the bitstring was computed from the image. I don't tell you how many pixels the image has. I don't tell you anything. I only give you the bits. Wanna play for money?
      - ErrantX 17y ago
        I think his point is... the image is stored on disk in a binary form. Which can also be represented as a number (Decimal).
        Rod 17y ago
        Geees, is this HN??? Am I the one who's too stupid to explain things properly, or is everyone under the weather because it's Monday morning? An image is a 2-dimensional array. Say it's a M x N array. Suppose we use RGB so that each pixel is represented by 3 bytes. Then you have an M x N x 3 array of bytes. There are infinitely many mappings from the space of all M x N x 3 arrays of bytes into the reals. Of course you can transform the array into a number. But you can do it in many, many ways. If you know what mapping was used, and if the mapping is invertible, then you can obtain the M x N x 3 array of bytes from the number. If you don't know what mapping was used, or if the mapping is non-invertible, then you can't obtain the M x N x 3 array from the number. So, I claim that an image is NOT a number. I claim that an image is a pair (y,f), where y is a number, and f is an invertible mapping from the space of M x N x 3 arrays into the reals. You guys are looking at y, and forgetting f. That's why an image is not a number, the image is x = f^{-1} (y). In short, one must know f, and f^{-1} must exist.
        AndrewDucker 17y ago
        You're merely arguing there that a number is not necessarily an image, because it cannot be converted into one without knowing how. And you'd be right. But the image is still a number, because it's stored as a series of bits, and any series of bits is interpretable as a number.
        Rod 17y ago
        I asked: "How can an image be a number?", when I should have asked instead: "How can a number be an image?" To use the verb to be in this scenario, I demand a one-to-one correspondence between numbers and images. If a number y can represent two distinct images x1 and x2, then we can't use "is", we can only use "can be".
  - amalcon 17y ago
    A list of numbers is a number, in the same way that a string of digits is a number.
    - Rod 17y ago
      Technically, a string of digits is only a representation of a number. And such representation may not even be unique.
      - deleted 17y ago
        [deleted]
  - almost 17y ago
    Nope, that's just one interpretation and it's not more valid then any other. Your argument is equivalent to saying something like this "129 isn't a single number, it's actually 110^2+210^1+9*10^0 (aka 100 + 20 + 9)". Anything that can be represented on a computer can be seen as a number, rather large numbers sometimes but still definitely numbers.
    - Rod 17y ago
      You are totally missing the point. The 3-tuple (1,2,9) may represent number 129 if you use the decimal expansion. What if you use a base-16 expansion, or a base-8 expansion? You can even choose the base so that the tuple -> number mapping is not injective (and, thus, not invertible). So, you give me a number, and I can give you infinitely many n-tuples that can be transformed into that number. Unless you know the mapping, and unless the mapping is injective, a single number is useless. It could represent infinitely many images. So, I ask again, how can an image be a number?
      - jerf 17y ago
        It is more proper to talk about the number + a decoding scheme. For given triple (image, image data, encoding scheme) any one can be held constant and the other two will have an infinite number of possibilities. In particular, any image can be represented as any set of data, plus an encoding scheme for that data. Trivial (but relevant) proof: The encoding scheme can simply hard code the image in question and trigger returning that image when it sees the held-constant image data. You could choose to represent an image as image data + decoding scheme, using an agreed representation of the decoding scheme such as a computer program. Mathematically we get nowhere because we are simply moving the encoding scheme around, but in practice, since we possess concrete encoding schemes it means we can practically discuss the situation better. This is a long-winded away of agreeing with you, BTW.
        Rod 17y ago
        Thanks for wording it more precisely than I did. Most people are assuming that the mapping tuple -> number is known, while I am not. I could come up with my own invertible mapping. The cool thing would be this: - I carry a large number y with me - the police demands that I disclose y, and I do; they apply inverse mapping f^{-1} and obtain x = f^{-1}(y) which is a porn image - then I show the police that applying inverse mapping g^{-1}, one obtains a totally legit image z = g^{-1}(y) Of course, finding such a mapping g could be extremely difficult, but if the same number can be obtained from two different images, how would the police be able to accuse me of anything?
  - jsolson 17y ago
    You could view it as a list of numbers, yes. Alternatively, we all know that the file representing the image is nothing more than a collection of bytes. Bytes are nothing more than 8-element bit vectors. What if instead of treating the file as a collection of $n$ 8-element bit vectors we instead treated it as a single $n*8$-element bit vector. What we now have is a single (potentially VERY large) binary number. To make any sense out of this number we'd have to pull out individual collections of bits, but this is no more complicated than doing a bitwise AND and bit shift. Put another way: you can think of an IP-address as 4 sets of numbers between 0 and 255. For example, 192.168.1.1. You can view that same IP-address as the hexidecimal number 0xC0A80101. The hex representation is convenient, as it makes elements in the dotted quad apparent. 0xc0 = 192, 0xa8 = 168, 0x01 = 1, 0x01 = 1. Hope that helps.
    - Rod 17y ago
      That's not what I meant at all. Of course you can transform a list of bytes into a number. But can you transform a number into a list of bytes? That is the problem. If you know the "encoding" algorithm, then you can. If you do not, then you simply can't. The point I was trying to make is that a number, itself, is nothing unless there's knowledge of the encoding algorithm. A CD-reader can make sense of the bits stored on the disk because it knows the encoding algorithm. If the CD-burner and CD-reader did not "talk the same language", it would be impossible to make sense of all those bits stored on the disk. Without knowing what interleaving and channel code was used, the CD-reader can't do its job.
Confusion 17y ago
This has nothing to do with law lagging behind technology. Even before computers, the ability to express language in a number was well known. If someone turned a defamatory sentence into a number and spread that number together with the key to turn it into the sentence, then they would be just as guilty of defamation as when they had spread the original sentence. I surely hope you do not advocate getting rid of all laws that deal with information that could be expressed in a number, because you feel it should not count as the same incriminating information, just because it was masked with some mathematics?

WilliamLP 17y ago

This is pretty silly, isn't it? Is it that mind-boggling that data can be illegal to distribute, for example a movie or an unreleased game? The prime number is a red herring. Given the prime number theorem, the probability that an n-digit number is prime scales as 1/log n, so it's easy to pad any data with random garbage that isn't executed until you get a prime. For a gigabyte of data that might be a few billion attempts. (Proving it's a prime will be harder.)

niyazpk 17y ago
>> Is it that mind-boggling that data can be illegal to distribute...? The DMCA has had an impact on the worldwide cryptography research community, since an argument can be made that any cryptanalytic research violates, or might violate, the DMCA. - http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Act#Criticisms http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Ac... That is mind-boggling.

fserb 17y ago

I think the argument that "how can a number be owned or its posession be illegal" is mostly bogus. One could translate any string of text into a series of bits and back to a single number and say that a book or a picture is just a number. Then one could say that noone invented that number, and that it's just a number, so you couldn't have copyright nor protection because everything could be randomly generated, etc, etc... I think the real issue is that in the case of prime numbers made "illegal/protected", the absurd is not that they are protected, but that they are not encoding any meaningful information that a human being produced. They are a particular number (probably randomly generated) and the fact that they are used in a particular context (to encrypt data) makes them protected.

jerf 17y ago
"but that they are not encoding any meaningful information that a human being produced" I was sort of with you up to that point; I don't agree, but I was with you. However, now I would say you need to read the article more carefully, as the entire point is that they do indeed encode something human-produced and usable. If you use Unix, you've almost certainly got the decoder for that number sitting right on your disk right now, it doesn't get much more concrete than that. Without that, you're missing the whole point. They aren't randomly generated at all. Guess I might as well spell out the other objection I have, which is that you're subtly begging the question. You prove that the idea of owning a number is silly because the idea of owning a number is silly in your last sentence of your first paragraph. Let me give you a much better argument: flip your argument on its head, and say that of course it's perfectly sensible to own numbers. All but the smallest works translate in any reasonable encoding scheme into enormous numbers, numbers that would simply never be chosen randomly. There 0 chance that sitting here and stringing together "random numbers" will ever produce anything like a movie or picture or even coherent sentence, that doesn't already exist in the encoding scheme. (Not literally 0, depending on the circumstances, but close enough.) Therefore, the actual problem is that it does indeed make sense to own numbers; in an infinite space when we are all choosing umpteen millions or billions or trillions or well beyond that of digits, one can very plausibly stake an ownership claim on the grounds that it is clear that if somebody else ends up with the exact same number, they got it from you. Therefore, since it is sensible to own numbers, the objection that it is not collapses and then the rest of the argument against ownership does too. As I said, I don't actually agree with that line of thought. There are a lot of intricacies in the issues of encoding, and some other objections I'm leaving out, but it's still a stronger line of argument. My feeling are more related to the classic bit color essay: http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php If that doesn't seem related, think more; it is, it very much is.

oscardelben 17y ago

I still don't get how a prime number can reveal hidden information. Can someone please explain me the process?

niyazpk 17y ago
From the article: Its binary representation corresponds to a compressed version of the C source code of a computer program.
etherealG 17y ago
it doesn't reveal information except that it is a constant that is used as part of a process of encryption where without the constant cracking that encryption would be effectively impossible and with it cracking the encryption is trivial. effectively the number is the encryption, as having the number makes the encryption useless. the rest of the algorithm is pointless without the number and vice versa.
- lt 17y ago
  That's a different number, not the one the article is about. The one in question is a compressed version of a c program that breaks encryption.

dfasfwe 17y ago

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ErrantX 17y ago

For all those commenting please read it carefully: the primes are not illegal, just number representations of apparently illegal programs.

randomwalker 17y ago

Y'all totally missed what's going on here. Primepages (http://primes.utm.edu/ http://primes.utm.edu/) lists the largest known primes of various forms. One of the categories is primes that have no special form, which are the hardest to prove prime. Chris Caldwell, the primepages maintainer, called up Phil Carmody and said, "Phil, if you can turn DeCSS into a 'general prime' that's big enough for the top 20 ever discovered, I'll be happy to host it on primepages." (Just as he would host any prime, DeCSS or not, that was big enough for the top 20.) So Phil did, cuz he's a smart guy and had a lot of computrons, and the prime went in the database. The point here is that if you're merely turning data into a number, you have no legitimate reason to distribute it other than whatever reason you had to distribute the data itself. However, primepages existed long before DeCSS became a problem, and was arguably simply doing what it always did, which is to list the top tens. I don't know if that would hold up in court -- it was never tested -- but the argument is a lot more subtle than what people are criticizing here. An aside: Phil and I worked together on some other primality records. I wrote most of that Wikipedia article back in 2002 or so, and they went and featured it.. this was all before the rules for citations/references on Wikipedia became tighter than a mouse's arsehole. So if anyone is in the mood to add some citations, that would be much appreciated.

tshaddox 17y ago
I don't see how "a reason to distribute it" is necessary. What if I just choose a completely random integer with 2000 digits and host it? I don't have any reason to do so, and it's certainly not illegal. Then someone comes along and generates a program that's equivalent to that number, or some digital media rights developer happens to use that number as a key for encrypting some copyrighted media. Does my original act of hosting suddenly become illegal, because I had no good reason to host the number in the first place?
- yoden 17y ago
  The probability of you doing that without piracy is so vanishingly small as to be irrelevant.
yoden 17y ago

mixmax 17y ago

A Danish Social security number consists of two numbers - the first one being four arbitrary digits, and the second one being the six digits of your birthday. My two numbers aren't only prime, which in and of itself would be pretty unlikely. No they're Twin primes. (http://en.wikipedia.org/wiki/Twin_prime http://en.wikipedia.org/wiki/Twin_prime) This is the only place I know where information like that would be considered pretty cool :-) Now somebody guess my birthday.

yan 17y ago
Now someone can guess your entire social security number :P
- mixmax 17y ago
  Calculated risk
pvg 17y ago
Which two numbers? It's quite difficult for a six digit and four digit number to be twin primes. Some zany Danish date format?
swolchok 17y ago
Impossible? Danes write dates as dd-mm-yy according to http://en.wikipedia.org/wiki/Calendar_date http://en.wikipedia.org/wiki/Calendar_date, so your birthday can have at most one leading zero and thus is >= 10100. 9973 is the largest 4-digit prime number, and 9973 + 2 is 1) not prime and 2) not a 5-digit number.
- mixmax 17y ago
  We're talking about two sets of twin primes, each part of the social security number being in each set. I'm sorry I didn't make it clear in the OP.
niyazpk 17y ago
Assuming that (1) you were born between 1950 and 1985 and (2) the danish date format is (dd-mm-yy), here are the possible DOBs: 10-01-51 30-01-51 17-03-51 14-05-51 26-05-51 27-05-51 13-06-51 16-06-51 16-07-51 18-07-51 25-07-51 25-09-51 15-10-51 21-10-51 24-10-51 21-11-51 13-12-51 17-12-51 19-12-51 28-12-51 10-01-53 17-03-53 27-05-53 16-07-53 25-07-53 21-11-53 17-12-53 24-02-57 29-06-57 25-10-57 13-02-59 24-02-59 21-03-59 29-06-59 14-07-59 17-07-59 22-08-59 15-09-59 25-10-59 26-10-59 10-11-59 24-12-59 13-02-61 10-03-61 21-03-61 31-03-61 27-04-61 23-05-61 14-07-61 17-07-61 27-07-61 22-08-61 23-08-61 26-08-61 15-09-61 12-10-61 18-10-61 21-10-61 26-10-61 10-11-61 17-11-61 24-12-61 25-12-61 10-03-63 31-03-63 27-04-63 23-05-63 27-07-63 23-08-63 26-08-63 12-10-63 18-10-63 21-10-63 17-11-63 25-12-63 13-03-67 19-03-67 11-05-67 19-06-67 15-07-67 14-08-67 20-08-67 16-09-67 25-09-67 24-10-67 17-11-67 26-11-67 29-11-67 27-02-69 13-03-69 17-03-69 19-03-69 22-04-69 11-05-69 19-06-69 29-06-69 15-07-69 28-07-69 14-08-69 20-08-69 16-09-69 25-09-69 22-10-69 24-10-69 12-11-69 15-11-69 17-11-69 26-11-69 29-11-69 11-12-69 23-12-69 27-02-71 17-03-71 22-04-71 29-04-71 29-06-71 23-07-71 28-07-71 22-10-71 12-11-71 15-11-71 22-11-71 11-12-71 23-12-71 29-04-73 23-07-73 22-11-73 15-03-77 11-04-77 19-05-77 16-08-77 22-08-77 17-10-77 25-11-77 27-12-77 18-01-79 15-03-79 11-04-79 19-05-79 11-08-79 16-08-79 22-08-79 17-10-79 14-11-79 25-11-79 10-12-79 27-12-79 18-01-81 20-03-81 16-04-81 30-05-81 14-06-81 11-08-81 15-08-81 24-08-81 14-11-81 30-11-81 10-12-81 20-03-83 16-04-83 30-05-83 14-06-83 15-08-83 24-08-83 30-11-83