Prime number “illegal”

The expression prime number “illegal” indicates a Prime number which contains information which it is interdict to hold or to distribute by the law (generally with the the United States and in France with the adoption of the law DADVSI).

A prime number “illegal” describes a Computer program which exceeds protection measures on the royalties of some DVD. Because this program was declared illegal by a court of justice of the United States of America, one could put forth the assumption that it is this number as such which could be struck of illegality.

The question subjected forever to the judgment of a court, and it is possible , although improbable insofar as the criminal law implies that is characterized an intentional element, that the number as such and its possession are declared legal, but not a certain interpretation of this one (at least in the United States).

The first prime number “illegal” was generated in March 2001 by Phil Carmody. Its binary representation corresponds to the compressed data of the Source code in language C of a computer program implementing the algorithm deciphering DeCSS. It is interdict to hold or distribute such programs (at least in the United States) according to the Digital Millennium Copyright Act.

The expression does not have any direction in mathematics, it is voluntarily ridiculous to criticize the laws which return the detention of certain programs illegal.

History

The protest against the judgment of the author of DeCSS, Jon Lech Johansen (alias DVD Jon ) and the legislation prohibiting the publication of the code of DeCSS took several forms. One of them consists in representing the illegal code in a form which is of a sufficient quality to be “intrinsically archivable”. As the bits which constitute a computer program can be represented under another digital form (basic change for example), a possibility is to find properties special which allow storage and the publication. The primality of a number is a fundamental property which exceeds the framework of the law.

Databases containing the greatest prime numbers known to date exist. Various tests is used to know if a number is first or not. Among the most effective algorithms a method based on the elliptic curved appears (algorithm ECPP for Elliptic Curve Primality Proving ).

Invention

By using the fact that the program of compression Gzip is unaware of the bytes after a Null byte finishing a compressed file normally, a panel of possible prime numbers was generated, each one of them allowing to find the code C of once dézippé DeCSS. Among those, several were identified like probable prime numbers thanks to the use of the program Open source OpenPFGW, and one among proved to be first by using the algorithm ECPP implemented by the software Titanix . At the time of the discovery, this number of 1401 digits was the tenth greater prime number found by using algorithm ECPP.

Thereafter, Carmody also created another prime number, this time implementing directly the functionality in achievable Machine language. According to a fine reading of the Digital Millennium Copyright Act , this number appears illegal in the United States.

The first prime number “illegal” was published by The Register under the title of illegal The possibly number (the potentially illegal number).

See too

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