
Illegal prime - deadghost
https://en.wikipedia.org/wiki/Illegal_prime
======
calibas
485650789657397829309841894694286137707442087351357924019652073668698513401047237446968797439926117510973777701027447528049058831384037549709987909653955227011712157025974666993240226834596619606034851742497735846851885567457025712547499964821941846557100841190862597169479707991520048667099759235960613207259737979936188606316914473588300245336972781813914797955513399949394882899846917836100182597890103160196183503434489568705384520853804584241565482488933380474758711283395989685223254460840897111977127694120795862440547161321005006459820176961771809478113622002723448272249323259547234688002927776497906148129840428345720146348968547169082354737835661972186224969431622716663939055430241564732924855248991225739466548627140482117138124388217717602984125524464744505583462814488335631902725319590439283873764073916891257924055015620889787163375999107887084908159097548019285768451988596305323823490558092032999603234471140776019847163531161713078576084862236370283570104961259568184678596533310077017991614674472549272833486916000647585917462781212690073518309241530106302893295665843662000800476778967984382090797619859493646309380586336721469695975027968771205724996666980561453382074120315933770309949152746918356593762102220068126798273445760938020304479122774980917955938387121000588766689258448700470772552497060444652127130404321182610103591186476662963858495087448497373476861420880529443

Call the cops.

~~~
olavk
Plain text is already a numeric encoding of information. Any file is just a
big number in binary. If it is illegal for me to sell your credit card number
in plaintext then surely the same should apply to encoding the same
information in some other trivial way. Talking about "illegal primes" is
supposed to make it sound ridiculous, but you could just call it illegal
information exchange. Most people would agree at least _some_ forms of
information exchange should be illegal - threats, stolen passwords or stolen
private pictures for example.

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.

~~~
chias
Thank you. I've struggled to explain this concept to my friends and
acquaintances -- your wording makes the point very clear.

------
pxmpxm
This line of argument is rather asinine - any information can obviously be
encoded into a number, prime or otherwise. Given that there are infinite
primes and any amount of proscribed information (national security
information, child pornography, trade secrets etc) that can be encoded into
them, essentially all prime numbers would be deemed "illegal" under that line
of argument.

The authors are clearly targeting unsophisticated audience with that article;
feels like the "sovereign citizen" grade of legal analysis.

~~~
xvedejas
Is the article making much of an argument? It's a wikipedia article and is
therefore written in an encyclopedic tone. Do you disagree that illegal
numbers exist?

~~~
olavk
It has an "encyclopedic tone" but that does not mean it is objectively correct
or makes a sensible argument. It is not the number itself that is illegal.
What would that even mean? Humans doing certain things with certain intentions
can be illegal.

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"?

------
jameshart
seems, from the comments, like it’s time for another generation of developers
to read _What Colour Are Your Bits_ :
[http://ansuz.sooke.bc.ca/entry/23](http://ansuz.sooke.bc.ca/entry/23)

~~~
rayiner
The article is based on a false premise. The government does not make any bits
legal or illegal. It prohibits specific human actions: copying, selling,
using, etc.

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.

~~~
gowld
What is the false premise? The linked article
[http://ansuz.sooke.bc.ca/entry/23](http://ansuz.sooke.bc.ca/entry/23) is
saying the same thing you are, with an in-depth explanation.

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.

~~~
rayiner
The false premise is that the law cares about any combination of bits and/or
metadata. Even talking about "provenance" is misleading, because that puts the
focus on the data.

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).

------
ktpsns
As computer scientists and hackers at heart, we all know that text, numbers,
pictures, music, movies can be represented in each other (most likely,
everything ist represented as a list of numbers, i.e. a bytestring, i.e. a
file, nowadays).

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?

~~~
vbezhenar
Information can be used as a weapon. Government wants to control weapons and
forbid it sometimes. I think that's an obvious answer.

~~~
brador
Can information be used as a weapon?

Definition weapon - a thing designed or used for inflicting bodily harm or
physical damage.

~~~
SiempreViernes
As you've specified a weapon must be a thing, then trivially no, by
definition.

But certainly information can be used for extortion, or to otherwise coerce
people against their will, and maybe that's enough?

~~~
mojomark
> As you've specified a weapon must be a thing, then trivially no

"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.

~~~
SiempreViernes
If you want to have the argument that a "thing" can mean "information" I wish
you all the luck in getting a partner that agrees with you. Personally it's
both for me, depending on the occasion.

~~~
mojomark
There is no argument, "information" is a "thing", by definition.

------
_jomo
As pi is infinite, it also stores any imaginable information. Someone actually
went ahead and implemented a file system based on this idea:

[https://github.com/philipl/pifs](https://github.com/philipl/pifs)

~~~
hsnewman
Can pi be recursive then? Can it contain itself? I think not.

~~~
avian
No. If pi would contain itself it would be a rational number. We have a proof
that pi is irrational, hence it cannot contain itself.

~~~
gowld
Specifically, if pi contains itself, that means "pi - pi/b^k" is a terminating
fraction N in base b", where b is your choice of base (like base 10), and k is
some positive integer. So

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)

------
Zigurd
Beware of technology-generated outrage. If you can encode a message, image,
etc. as a number, some messages, like a communication of a specific threat
against a specific person, or certain types of porn, that's going to result in
"illegal numbers." When put that way, the outrage is pretty weak.

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.

~~~
PurpleBoxDragon
>It is legitimate and provably effective to legally limit the demand for some
items, like ivory, for example

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.

------
Twisell
Ultimately this is totally nonsensical because you'd have to ban an infinite
number of number because some clever boy around will definitively distribute
the number preceding the illegal one and some unrelated folk can point out
that you just have to +1 to get the illegal one. Basically none of the two
would have done anything illegal until a ruling. rince, repeat. This is utter
non-sense.

~~~
peteretep
> This is utter non-sense

All current computer media can be represented as an integer. You're suggesting
that no media is illegal?

~~~
gambiting
It shouldn't be illegal. Possession of information - be it a book, a video, a
picture, or text, should never be illegal in itself. Production and
distribution of certain kinds should be absolutely illegal, but they already
are, I don't think there's any discussion here.

~~~
SiempreViernes
I don't see the problem with banning or otherwise regulating certain
representations if that is a useful tool against the production you are trying
to stop.

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.

~~~
psyc
I have commented before about A/B testing the law to achieve statistical
outcomes, and I absolutely do see a problem with it. It tosses principles
_and_ liberties out the window. Legislating things that are correlated with
the thing you want to avoid is a utilitarian bridge too far for me.

~~~
TeMPOraL
So you'll be fine with DUI? After all, it's not the alcohol we're trying to
avoid - it's the accidents, which are correlated with alcohol (for obvious
reasons).

Truth is, often correlations are the _only_ things we can go after to fight
the things we don't want.

~~~
psyc
I think that reaching for legislation as the tool to minmax any desirable
societal metric is a bad doctrine. That does not mean I am against every
possible instance of it. DUI is very immediate. It's like putting one round in
the chamber and pointing it at a public space. But, for example, I am opposed
to restricting speech and free association as a less expensive proxy for
stopping various things.

------
qz3
I always felt that that "illegal numbers" is a misunderstanding of data.

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.

~~~
GyYZTfWBfQw
[https://en.wikipedia.org/wiki/Illegal_number](https://en.wikipedia.org/wiki/Illegal_number)
:>

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

~~~
logfromblammo
That's why the Tiananmen Square Maassacre anniversary date is commonly
referred to as "May 35th".

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.

~~~
gowld
The Chinese government isn't stupid. They do what they do because it works.
Even the _opposition_ agrees with this, hence the term

[https://en.wikipedia.org/wiki/Chilling_effect](https://en.wikipedia.org/wiki/Chilling_effect)

The website dedicated to the topic of the OP article is even called...
[http://chillingeffects.org/](http://chillingeffects.org/) (since renamed to
[https://lumendatabase.org/](https://lumendatabase.org/) )

------
GyYZTfWBfQw
Hahahahaha. Related:
[https://en.wikipedia.org/wiki/Illegal_number](https://en.wikipedia.org/wiki/Illegal_number)

> 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.

------
roystonvassey
This was an illuminating read. I was not at all aware that there are certain
numbers(!) that are illegal. Thanks for sharing

~~~
SiempreViernes
Well, I'm not sure it's fair to say the number itself is illegal: it's the
code that breaks the law, the number just happens to be one way to express it.

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.

~~~
bloak
Not really disagreeing with you, but taking it even further:

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.

~~~
TazeTSchnitzel
In much the same way that the word “fire” itself is not illegal, but shouting
it in a crowded theatre may be.

~~~
logfromblammo
No. Ken "Popehat" White wants you to read this:

[https://www.popehat.com/2012/09/19/three-generations-of-a-
ha...](https://www.popehat.com/2012/09/19/three-generations-of-a-hackneyed-
apologia-for-censorship-are-enough/)

Please use different phrasing to discuss lawful and unlawful speech in the
future.

------
IshKebab
This was clearly not written by a lawyer. I am also not a lawyer but it's
pretty clear that merely distributing this prime number is not illegal.
Distributing it _with the intent to use it to use it as DeCSS_ may be though.
And it would be pretty hard to convince a judge that you didn't intent to use
it as DeCSS.

~~~
gowld
I don't know about DeCSS in particular, but plenty of laws are strict
liability meaning intent is not required to obtain a conviction.

> 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.

------
sbhn
It’s illegal because it’s someones job to enforce it, they probably don’t get
paid much, and they have many bills to pay. And every now and then they can
impress chicks by saying they manage national security. And the department who
monitors us for usage of this number using all the latest expensive tech and
expertise, can charge it to the tax payer. Just imagine if the number got into
the hands of the enemy. ka, ching, that will be another billion dollars for my
top secret department thanks very much.

------
LinuxBender
Surely there must be a shorter number or string that I can put in my personal
information that would be illegal to copy or store. I am ok with being in
trouble for having the data, as long as everyone else with the data is in
trouble as well.

------
kazinator
So if I surreptitiously install a camera in your house and take pictures or
video, then tweak the files so that their binary images denote prime numbers,
all is cool; I'm just doing math, not invading your privacy.

------
smolsky
So, is this the right thread to mention the honorable First Prime of Apophis?
He did a few illegal things...

------
ByThyGrace
Is it of any particular relevance that such a number is a prime?

~~~
nicky0
A large prime is notable and hence is included in public databases.

~~~
OscarCunningham
That's not really true. There are loads of large primes (way more than you
could store), so they're not all notable.

~~~
paulgb
There are infinite prime numbers. What's notable is the ones we have found.

~~~
OscarCunningham
No. Even then they're not notable. For example there are 10^97.6 primes with
100 digits, of which not all have been found (not enough storage space in the
universe), but it's trivially easy to generate one at random.

~~~
paulgb
You disagreed with the statement

> 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.

~~~
OscarCunningham
I'm arguing that these numbers aren't notable just because they are large
primes. They certainly aren't included in public databases just because they
are large primes.

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.

~~~
paulgb
Ok, thanks for explaining that. It sounds like the condition for notability in
this case is the combination of size and algorithm used?

> 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.

~~~
OscarCunningham
Oh, I didn't realize the page said that. I should have read it more carefully.
You're right that it's a combination of size and method used. The Mersenne
numbers are especially easy to prove prime, so it's also interesting to keep
track of the largest primes proved by other methods. I think these days a 2000
digit prime wouldn't be notable in any case, but it sounds like it was back
when Carmody was doing this, so this was in fact a good example of an illegal
number that was independently interesting.

~~~
nicky0
Another pointless argument that could have been avoided by RTFA.

------
bambax
This could be used to circumvent other (all?) limitations of speech. Just say
"look up the nth prime and unzip it" instead of what you can't say...

There should be a whole industry about it.

~~~
klmr
This already exists, it’s called cryptography: for example, you can exchange
some prime numbers (key exchange), and then use those to apply a generic
mathematical function to the information. You then send the resulting numbers.
(In this situation it isn’t the prime numbers themselves which are illegal,
it’s the other numbers.)

Doesn’t change the legal situation, of course.

~~~
bambax
No, this is really not similar to cryptography. More like the opposite.

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._

------
mcs_
I remember the news about the example used in the post. This is a proof of a
society where 50% loves math and the rest makes money with who loves math.

