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Glossary:
Prime Pages:
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A DVD (Digital Versatile Disk) can store much more information than a CD, for this reason they are often used to store movies. To prevent playing on an "unauthorized" machine, these movies are protected by CSS (Content Scramble System) a proprietary code licensed to DVD player manufacturers.
Soon after DVD's were encrypted, code to decrypt them (called DeCSS) appeared on the internet (October 1999). This code is now available in many forms (see the Gallery linked below). The shortest versions of the code take well under 600 key strokes. The Motion Picture Association of America recently sued to stop distribution of this code under the Digital Millennium Copyright Act. There are many interesting issues involved in this case, for example, is code a protect form of free speech? The court's Memorandum Order (linked below) provides a nice summary. So what has this all to do with prime numbers? At first glance: nothing. But everything stored on a computer, including poems, pictures, spreadsheets and programs, are stored as a sequence of binary bits--so they are simply numbers. Phil Carmody decided to make a version of DeCSS which was a prime number. First Carmody took the original anonymous version of the DeCSS C-code and gzip'ed it (a standard UNIX program for making files smaller). Suppose we call the resulting number k. By Dirichlet's theorem on primes in arithmetic progression, we know that for each fixed integer b relatively prime to k, there are infinitely many primes ak+b. For technical reasons, if we choose a to be a power of 256 larger than b, the resulting number can still be unzipped to get the original file. This means there are infinitely many prime numbers which yield the same code. These include: k*2562+2083 and k*256211+99. At the time these were found they both were large enough to fit on the list of largest known primes (because of the method of proof). If distributing code is illegal, and these numbers contain the code, does that make these number illegal? Related pages (outside of this work)
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