# Illegal prime

An **illegal prime** is a that represents information whose possession or distribution is forbidden in some . One of the first illegal primes was found in 2001. When interpreted in a particular way, it describes a that bypasses the scheme used on . Distribution of such a program in the is illegal under the . An illegal prime is a kind of .

## Contents

## Background

One of the earliest illegal prime numbers was generated in March 2001 by . Its representation corresponds to a version of the of a implementing the decryption algorithm, which can be used by a computer to circumvent a DVD’s .

Protests against the indictment of DeCSS author 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 (one method was to print it on a T-shirt). The of a number is a fundamental property of and is therefore not dependent on legal definitions of any particular jurisdiction.

The large prime database of The website records the top 20 primes of various special forms; one of them is proof of primality using the (ECPP) algorithm. Thus, if the number were large enough and proved prime using ECPP, it would be published.

## Discovery

Specifically, Carmody applied to several prime candidates of the form *k*·256<sup>*n*</sup> + *b*, where *k* was the representation of the original compressed file. Multiplying by a power of 256 adds as many trailing to the file as indicated in the which would still result in the DeCSS C code when unzipped.

Of those prime candidates, several were identified as using the open source program OpenPFGW, and one of them was proved prime using the ECPP algorithm implemented by the Titanix software. Even at the time of discovery in 2001, this 1401-digit number, of the form *k*·256<sup>2</sup> + 2083, was too small to be mentioned, so Carmody created a 1905-digit prime, of the form *k*·256<sup>211</sup> + 99, that was the tenth largest prime found using ECPP, a remarkable achievement by itself and worthy of being published on the lists of the highest prime numbers.<ref name=gloss/> In a way, by having this number independently published for a completely unrelated reason to the DeCSS code, he had been able to evade legal responsibility for the original software.

Following this, Carmody also discovered another prime, this one being directly machine language for Linux , implementing the same functionality.