Discovery
Specifically, Carmody applied Dirichlet's theorem to several prime candidates of the form k·256n + b, where k was the decimal representation of the original compressed file. Multiplying by a power of 256 adds as many trailing null characters to the gzip file as indicated in the exponent which would still result in the DeCSS C code when unzipped.
Of those prime candidates, 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. Even at the time of discovery in 2001, this 1401-digit number, of the form k·2562 + 2083, was too small to be mentioned, so Carmody created a 1905-digit prime, of the form k·256211 + 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. 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 executable machine language for Linux i386, implementing the same functionality.
Read more about this topic: Illegal Prime
Famous quotes containing the word discovery:
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“I have known no experience more distressing than the discovery that Negroes didn’t love me. Unutterable loneliness claimed me. I felt without roots, like a man without a country ...”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 10 (1962)
“One of the laudable by-products of the Freudian quackery is the discovery that lying, in most cases, is involuntary and inevitable—that the liar can no more avoid it than he can avoid blinking his eyes when a light flashes or jumping when a bomb goes off behind him.”
—H.L. (Henry Lewis)