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An illegal prime is a special prime number. Such prime numbers are called illegal, because there is a way to change them, so that they yield something illegal: a program to circumvent the Digital Millennium Copyright Act. One of the first people to find such a prime was Phil Camody. In 2001, he found a prime that contains the gzip compressed source code for a program that can circumvent the Content Scrambling System. The Content Scrambling System is used as a way to prevent DVDs from being copied. Later, other primes were found that resulted in directly runnable programs.
The United States and other countries made it illegal to publish or circulate computer programs that can circumvent copy protection. Since prime numbers are a concept from mathematics, their knowledge cannot be made illegal easily.
Any information that can be represented in binary form can be represented as a number.