Illegal Prime Numbers
01/05/2006 . Source: Mark R. Leeper 
It has come to Mark's attention that there is such a thing as an illegal prime number. Well, there are all sorts of prime numbers. There are Mersenne primes and Fermat primes for example, but this was the first he had ever heard anyone refer to there being an "illegal" prime. A word of explanation before I begin: in the following article I am going to mention prime numbers. Now it is customary in American writing that when an author mentions prime numbers, he should also define for the reader what a prime numbers is. In fact if they use the terms as simple as "even number" they explain that "An even number is a number that can be divided by two. Even numbers are those whole numbers that end in 0, 2, 4, 6, and 8. Even numbers the reader might be familiar with include 16 and 22, but not 5, 13, or 19."
Then in the next article they will say something like, "he punted with a three-quarter touchback to the end zone in double-overtime scrimmage." There will be not a single word of explanation as to what all that verbal granola means. It will just be assumed that OF COURSE you know what that all means, because it is after all sports terms. Everybody knows sports terms. I will just say for the benefit of those readers who are unaware of what a prime number is, you guys are really thick and need to get with the program.
It has come to my attention that there is such a thing as an illegal prime number. Well, there are all sorts of prime numbers. There are Mersenne primes and Fermat primes for example, but this was the first I had ever heard anyone refer to there being an "illegal" prime. What could that mean? Now it was immediately obvious that we did not mean illegal in the criminal sense. They cannot mean it in the sense of use-this- prime-you-might-go-to-jail. I mean prime numbers belong to everyone. No, surely there was some axiom or something that they break. There has to be some technical reason why something would be called an "illegal prime." What I discovered they mean is that these primes are numbers that are illegal in the sense that their use is prohibited by law and if you use-these-primes-you- might-go-to-jail.
How and why should a prime number become illegal? Well let us start out with whether any information can be illegal to have and to pass on to other people. Well, certainly it can. Credit card information is illegal for you to possess. And certainly you cannot make it available to other people. Some moonbat might make a case that the privacy of no information should protected by law, but few people would support such a case. I think nearly all of us believe that some information is private and should be kept from the prying eyes of other members of the public and very probably from the prying eyes of the United States Government. We all have a right to the privacy of some information, even if the current government is trying to redefine those boundaries of that information. So let us assume there is some information that it is illegal to have and to pass to other people.
That information probably can be stored on a computer. Well, any piece of information stored in a computer is stored as a string of ones and zeroes. So if possessing and sharing the information can be made illegal, possessing and sharing some strings of ones and zeroes can be illegal. Well, that seems pretty obvious also. Your Social Security number is not something that I am allowed to have and certainly making it available to other people. But it is subtler than that.
When THE DA VINCI CODE was on Dan Brown's computer, as I am guessing it once was, it was stored there as a string of ones and zeroes. If I could take that string and find the decimal equivalent of that giant binary number, I would have the entire contents of that novel encoded in a single number. If I gave that number to you, it would not be too difficult for you to write a computer program to take that giant number and reconstitute Dan Brown's whole novel. So far sharing that huge number is probably not illegal, but if you and I actually did what I describe here the courts would probably soon rule it so.
Now as to illegal primes: given an arbitrary binary string, would it be possible to find a prime number that ends in that binary string? I did not know if that was possible or not, but apparently it is by Dirichlet's "Theorem On Primes in Arithmetic Progression". This means that if there really is information that is illegal to possess and share, the courts could potentially rule that prime numbers that make that information obtainable are illegal to have and hand out.
Well, the courts have in fact ruled that a particular prime number is restricted because of information it contains. What information? Apparently someone named Jon Lech Johansen wrote a program that allowed PCs to circumvent copyright protecting software on DVDs. The program was ruled illegal as much as some hackers wanted to have it. So a mathematician named Phil Carmody compressed the program and gzipped it. (If you don't know what all that means, it just is a way to encode a program as a somewhat smaller binary number. That I was willing to explain, even if I won't explain primes.) He then found a prime number that in binary ended in that string. Supposedly it was the tenth largest prime number ever found. Whether he was open about it or not, I do not know, but word got out that this prime number has this really nice, useful, and totally illegal program embedded inside it in a way that is not too difficult to decrypt. It became a popular prime number.
The courts now had a choice. Nobody had ever thought that a prime number should or could be made illegal, but now it appeared that if all prime numbers were legal to have and to share, there would no longer be any real privacy for any information. People could take any information and find a prime number that has that information encrypted in it. Anyone with sufficient computing power could encode any information they wanted to into a prime number and publish that number to the world.
Their backs against the wall, the courts set a weird precedent and ruled that the possession and sharing of this particular prime number was also a crime. I suppose the courts did not have much choice. They probably did not have much fervour for the principle that everybody should own new discoveries in mathematics. Some mathematical knowledge, in fact, could be dangerous in other ways. Ask the people who worked on the Manhattan Project. So the courts decided that this particular prime number was actually restricted information and illegal to share. That does not stop some people.
The story of the illegal prime number can be found at http://www.answers.com/main/ntquery?s=illegal+prime. It also flouts the law and prints the illegal prime number. Hence it strikes a blow for mathematical freedom. Yeah, baby, yeah! All power to primes! All primes to powers!
Mark R. Leeper
© 2006 Mark R. Leeper |
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