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The illegal prime is a prime number that, when interpreted a particular way, describes a computer program which bypasses copyright protection schemes on some DVDs. Because that program has been found illegal by American courts, this has produced debate about whether the number itself could be considered illegal.
This question has never been tested in court, and it is possible that the number itself and its possession would be found to be legal, but not a particular interpretation of it.
The number was generated on March 2001 by Phil Carmody . Its binary representation corresponds to a compressed version of the C source code of a computer program implementing the DeCSS decryption scheme. Such programs are illegal to possess or distribute under the Digital Millennium Copyright Act. The existence of infinitely many such primes is guaranteed by Dirichlet's theorem.
The DeCSS code can be used by a computer to circumvent a DVD's copy preventionCopy prevention also known as copy protection is any technical measure designed to prevent duplication of information. Copy prevention is often hotly debated, and is sometimes thought to infringe on customers's property rights: for example, the right to m. Protest against the indictment of DeCSS author Jon JohansenJon Lech Johansen (born November 18, 1983), also known as DVD Jon is a Norwegian who was involved in the release of the DeCSS software. In 2002 he was put on trial in Norway but was found not guilty of any illegal behaviour. A second trial in 2003 resulte and legislation prohibiting publication of DeCSS code took many forms. One of them was the representation of the illegal code in a form that had an intrinsically archivable quality. Since the bits making up a computer program also represent a number, the plan was for the number to have some special property that would make it archivable and publishable. The primality of a number is a fundamental property, one outside the scope of the law.
The large prime database of the prime pagesThe Prime pages is a website about prime numbers maintained by Prof. Chris Caldwell at the University of Tennessee at Martin. Hobbyist efforts to find large primes are co-ordinated at this site. The list of the "5000 largest known primes" and lists of "to records the top 20 primes of various special forms; one of them is proof of primality using the elliptic curve primality proving (ECPP) algorithmFlowcharts were often used to represent algorithms. An algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will result in a corresponding recognisable end-state (contrast with heuristic). Algor. Thus, if the number were large enough, and proved prime using ECPP, it would be published.
By exploitation of the fact that the gzipgzip is short for GNU Zip, a GNU open-source replacement for the Unix compress program. Gzip is based on the deflate algorithm, which is a combination of LZ77 and Huffman coding. Deflate' was developed in response to patents that covered LZW and other com compression program ignores bytes after the end of a null terminated compressed file, a set of candidate primes was generated, each of which would result in the DeCSS C code when unzipped. Of these several were identified as probable primeIn number theory, a probable prime (PRP is an integer that satisfies a condition also satisfied by all prime numbers. While there are probable primes that are composite (called pseudoprimes), they are rare, depending on the test used. Fermat's test for co using the open source program OpenPFGW, and one of them was proved prime using the ECPP algorithm implemented by the Titanix software. At the time of discovery, this 1401 digit number was the tenth largest prime found using ECPP.
Following this, Carmody also created another prime, this one directly executable machine language implementing the same functionality. Presumably, it is also illegal in the USA.