Illegal prime number
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.
Background
Protest against the indictment of DeCSS author Jon Johansen 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 pages records the top 20 primes of various special forms; one of them is proof of primality using the elliptic curve primality proving (ECPP) algorithm. Thus, if the number were large enough, and proved prime using ECPP, it would be published.
Discovery
By exploitation of the fact that the gzip 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 prime 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 US.
See also
