
Illegal prime - niyazpk
http://en.wikipedia.org/wiki/Illegal_prime
======
randomwalker
Y'all totally missed what's going on here.

Primepages (<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.

~~~
baddox
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
The probability of you doing that without piracy is so vanishingly small as to
be irrelevant.

------
fserb
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
"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> If that doesn't seem
related, think more; it is, it very much is.

~~~
tjic
> you're subtly begging the question.

You are the first person to correctly use the phrase "beg the question" in
something I've read in the last three weeks.

Congratulations!

------
mixmax
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>)

This is the only place I know where information like that would be considered
pretty cool :-)

Now somebody guess my birthday.

~~~
niyazpk
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

~~~
smokinn
Thanks for the list but he said 6 digits... So the format is probably dd-mm-
yy.

~~~
niyazpk
Oops! Corrected.

------
WilliamLP
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
>> 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_Ac...](http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Act#Criticisms)

That is mind-boggling.

------
wizard_2
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
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
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.

~~~
almost
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 1 _10^2+2_ 10^1+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
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?

~~~
axod
The simplest, and most common representation would be for a file to simply be
a string of binary bits representing a large number.

eg:

    
    
       big_number = 0;
    
       while(!feof(file)) {
          big_number = (big_number<<8) | file.readByte();
       }

~~~
Rod
I am pointing at the forest, and you're looking at the trees. We're not even
talking about the same thing. I am taking a very high-level, abstract view of
the problem. You're thinking of implementation.

~~~
axod
Right. You're just saying there are an infinite number of ways you could
convert a string of binary digits into a 'number'.

Well sure :/ Of course there are.

At the simplest form you could swap things around, represent a fractional part
of a number etc, at the more complex side you just have encryption.

But those are different things to your question "So, I ask again, how can an
image be a number?"

~~~
Rod
For an image to _be_ a number, I demand a one-to-one correspondence between
images and numbers. Lacking that, I merely say that an image _can be_
represented by a number, but this is trivial. Hence, I repeat: we're not even
discussing the same thing.

~~~
axod
>> "So, I ask again, how can an image be a number?

>> "Lacking that, I merely say that an image can be represented by a number,
but this is trivial"

I think you're arguing with yourself at this point.

~~~
Rod
Note that: "is" and "is represented by" are not the same on my book (which is
obvious from the previous comments). If you want to counter-argument, try
harder.

~~~
barrkel
I wonder what you mean by "is". Nothing really "is" anything but itself. The
only other "is", the one that real people actually use, is "is represented by"
or "is a representation of", or "is an instance of", etc.

For example, this --> A <\-- looks like the letter A. But it isn't the letter
A. It "is" only a representation, a bit-pattern with decimal notation 65, a
glyph drawn from a font, a set of pixel elements on a graphics surface, a
pattern of light on a display, a bunch of photons traveling through space, a
group of excited photoreceptor cells, a set of signals traveling through
neurons, etc. And it is none of these things, because none of them capture the
essence of the pattern, repeated over human experiences.

So it seems to me that if you're trying to win an argument by drawing a
distinction between "is" and "is represented by", you are not going to
convince anyone who's put much thought into it. "Ceci n'est pas une pipe"; but
a representation of a pipe is a (more or less faithful) representation of a
pipe, whether you are blind or not, and so a number is a digital image, and
vice versa.

~~~
KonaB
I think one must draw a distinction between the physical world and the
metaphysical one. For a platonist, numbers do exist outside of any physical
reality and, therefore, a number and its representation are not the same
thing.

I am not a mathematician, but to me this discussion reminds me of a vector
having different coordinates, depending on what coordinate system we choose.
Those are all different representations of the same thing. Likewise, a number
can be represented in many different ways (binary, oct, hex, etc), but they
all represent the same number. Is the vector its representation? If so, then
the vector is many things, which is a funny definition of "to be". If the
vector is itself, then it cannot be equal to any of its representations, it's
something beyond its representation.

~~~
joeyo
I don't think it's at all a given that Hylaean Theoric Worlds exist
independently the Arbran Causal Domain.

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

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

~~~
etherealG
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
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.

