The Beginning: A Teenager and a DVD
In 1999, a fifteen-year-old Norwegian named Jon Lech Johansen wanted to watch DVDs on his Linux computer. There was just one problem: no Linux DVD player existed. The movie industry had locked their discs with a protection system called CSS, the Content Scramble System, and they had no intention of letting Linux users in on the fun.
So Johansen did what any resourceful teenager would do. He reverse-engineered the protection and wrote a program called DeCSS that could decrypt any DVD. He shared it with the world, and the world downloaded it eagerly.
The Motion Picture Association of America was not amused. They sued everyone they could find who was distributing the software. Courts agreed with them, ruling that under the Digital Millennium Copyright Act, even linking to DeCSS was illegal. The code itself had become contraband.
The Hackers Fight Back
The hacker community responded with a burst of creative civil disobedience. They printed the DeCSS code on t-shirts. They wrote it as poetry. They encoded it in images, in songs, in every conceivable format. The message was clear: you cannot suppress information. Code is speech, and speech wants to be free.
But one response stood out for its mathematical elegance. A programmer named Phil Carmody asked himself a simple question: what if the code were a prime number?
Every File Is a Number
To understand Carmody's insight, you need to understand something fundamental about computers. Everything stored on a computer, every file, every program, every image, is ultimately just a sequence of ones and zeros. And any sequence of ones and zeros can be interpreted as a number written in binary.
Your favorite photograph? It's a number. This essay you're reading? A number. The operating system running on your device? A very, very large number. There is no distinction between data and mathematics at the deepest level.
The DeCSS source code, compressed with gzip, was approximately 1,400 digits long when expressed in decimal notation. It was a number like any other. But was it a prime number?
Almost certainly not. Prime numbers, those divisible only by themselves and one, become increasingly rare as numbers grow larger. The odds of a random 1,400-digit number being prime are roughly one in 3,200.
The Theorem of Dirichlet
Here is where Carmody's mathematical training came into play. He knew of a theorem proven by the German mathematician Peter Gustav Lejeune Dirichlet in 1837. The theorem states that for any two positive integers that share no common factors, there are infinitely many prime numbers that leave a specific remainder when divided by one of them.
The practical implication is profound. If you have a number and you want to find a prime number that starts with those same digits, you can always find one. You just need to add the right digits to the end.
Carmody exploited a quirk of the gzip file format. Gzip files are null-terminated, meaning the decompressor ignores anything after a certain point. You can append whatever you want to the end of a gzip file and it will still decompress to the same content.
So Carmody took the gzipped DeCSS code and started adding digits to the end, searching for a combination that would make the entire number prime.
Finding the Prime
The search was not trivial. Testing whether a 1,400-digit number is prime requires sophisticated algorithms and significant computing power. Carmody used a program called OpenPFGW to identify probable primes, candidates that passed various statistical tests but weren't proven prime with mathematical certainty.
When he found a promising candidate, he used a different program called Titanix, implementing an algorithm called ECPP, the Elliptic Curve Primality Proving method. This could provide a rigorous mathematical proof that the number was indeed prime.
In March 2001, Carmody announced his discovery. He had found a 1,401-digit prime number that, when interpreted as a gzip file and decompressed, yielded the complete DeCSS source code. At the time, it was the tenth largest prime ever proven using the ECPP method.
The Illegal Prime
The implications were immediate and unsettling. If distributing DeCSS was illegal, and this prime number could be converted into DeCSS, then was the prime number itself illegal?
The question cuts to the heart of what it means to prohibit information. Prime numbers are not human inventions. They are discoveries, mathematical truths that exist independently of any legal system. The number two is prime in America and in China, under democracy and dictatorship, today and a billion years ago.
Carmody had not created anything. He had simply identified a mathematical object that happened to have an interesting property. The number existed before he found it. It would continue to exist regardless of what any court decided. Can you make a fact of mathematics illegal?
The Executable Prime
But Carmody wasn't finished. The first illegal prime required decompression to become functional code. Later that year, he discovered an even more remarkable number: an 1,811-digit prime that was directly executable.
This prime, when written in hexadecimal and saved as a file, was a valid Linux executable in the ELF format. You could run it directly, with no decompression step. The prime number itself was a working program that could decrypt DVDs.
Think about what this means. Every possible program that could ever be written already exists as a number. Every book, every song, every movie, every piece of software, every possible expression of human creativity, already exists in the infinite sequence of integers. We don't create these things; we discover them, picking them out from the vast space of mathematical possibility.
Carmody's Philosophy
Phil Carmody was careful to explain his motivations. He was not, he said, opposed to copyright or the rights of artists. He believed that ripping DVDs without intending to buy the originals was wrong and should be illegal.
"I'm a firm believer in authors' and artists' rights, the rights that are protected under copyright. However, I do not believe that the current implementation of US law is a sensible one. I believe it's logically inconsistent, and is biased towards the interests of multinational publishers and against consumers."
His illegal prime was a philosophical argument in numerical form. It demonstrated that the law as written led to absurd conclusions. You cannot criminalize mathematics. You cannot make a number illegal. And if you try, you reveal the incoherence of your position.
The Norwegian Trial
Meanwhile, in Norway, Jon Johansen faced criminal charges for creating DeCSS. The prosecution argued that he had violated laws against unauthorized access to data. But Johansen had an elegant defense: he owned the DVDs he was decrypting. He had every right to access content he had legally purchased.
In January 2003, the Oslo City Court acquitted him. The prosecution appealed, and in December 2003, the appeals court upheld the acquittal. The court found that circumventing copy protection for personal use was not a crime under Norwegian law.
The verdict was a landmark for digital rights. It established that consumers have legitimate interests in accessing content they've purchased, even if doing so requires bypassing technical protections. The law must balance the interests of copyright holders against the rights of consumers.
The Legacy
More than two decades later, the illegal primes remain a powerful symbol. They demonstrate that information cannot be contained, that attempting to prohibit knowledge leads to philosophical absurdity, that there will always be clever minds who find ways around restrictions.
The DVD copy protection system that DeCSS defeated has long since become obsolete. Streaming has replaced physical media for most consumers. But the questions raised by Carmody's discovery remain relevant.
In an age of digital rights management, of encrypted communications, of governments seeking backdoors into secure systems, we continue to grapple with the nature of information. What can be prohibited? What can be controlled? And what are the limits of law when it confronts the eternal truths of mathematics?
Somewhere in the infinite expanse of prime numbers, there are surely primes that decode to things we haven't imagined yet. Programs that don't exist. Books that haven't been written. The future, encoded in pure mathematics, waiting to be discovered.
And every single one of them is, in some sense, already there.
