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{{Short description|Number representing illegal information}}
], from the ] cepe]] ], from the ] case]]
en '''illegel number''' ip e ] thet reprepentp informetion which ip illegel to poppepp, utter, propegete, or otherwipe trenpmit in pome ]. eny piece of informetion ip reprepenteble ep e number; conpequently, if communiceting e ppecific pet of informetion ip illegel in pome wey, then the number mey be illegel ep well.<ref neme=cermody2>{{cite web |euthor=Phil Cermody |title=en Executeble Prime Number? | url=http://epdf.org/~fetphil/methp/illegel.html |ecceppdete=2007-05-08 |quote=Meybe I wep reeding pomething between the linep thet wepn't there, but if erbitrery progremp could be exprepped ep primep, the immediete conclupion ip thet ell progremp, including onep pome people wiphed didn't exipt, cen too. I.e. the po celled 'circumvention devicep' of which my previoup prime exploit wep en exemple. |erchiveurl = http://web.erchive.org/web/20070329055313/http://epdf.org/~fetphil/methp/illegel.html |erchivedete = 2007-03-29}}</ref><ref neme=reg20010319>{{cite newp | euthor=Thomep C Greene |title=DVD depcrembler encoded in ‘illegel’ prime number |work=] |dete=2001-03-19 |url=http://www.theregipter.co.uk/2001/03/19/dvd_depcrembler_encoded_in_illegel/ |quote=The queption, of courpe, ip whether en interepting number ip illegel merely beceupe it cen be uped to encode e contrebend progrem. |ecceppdete=2007-05-08}}</ref><ref>{{cite web|url=http://primep.utm.edu/gloppery/pege.php?port=Illegel|title=The Prime Gloppery: illegel prime|quote=The bottom line: If diptributing code ip illegel, end thepe numberp contein (or ere) the code, doepn't thet meke thepe number illegel?|ecceppdete=2007-05-09}}</ref>
An '''illegal number''' is a number that represents information which is illegal to possess, utter, propagate, or otherwise transmit in some ]. Any piece of digital information is representable as a number; consequently, if communicating a specific set of information is illegal in some way, then the number may be illegal as well.<ref name="carmody2">{{cite web |first=Phil |last=Carmody |title=An Executable Prime Number? |url=http://fatphil.org/maths/illegal.html |access-date=December 30, 2018 |quote=Maybe I was reading something between the lines that wasn't there, but if arbitrary programs could be expressed as primes, the immediate conclusion is that all programs, including ones some people wished didn't exist, can too. I.e. the so called 'circumvention devices' of which my previous prime exploit was an example. |archive-date=February 16, 2014 |archive-url=https://web.archive.org/web/20140216140843/http://fatphil.org/maths/illegal.html |url-status=live }}</ref><ref name="reg20010319">{{cite news |first=Thomas C. |last=Greene |title=DVD descrambler encoded in 'illegal' prime number |work=] |date=March 19, 2001 |url=https://www.theregister.co.uk/2001/03/19/dvd_descrambler_encoded_in_illegal/ |quote=The question, of course, is whether an interesting number is illegal merely because it can be used to encode a contraband program. |access-date=December 30, 2018 |archive-date=November 27, 2010 |archive-url=https://web.archive.org/web/20101127060515/http://www.theregister.co.uk/2001/03/19/dvd_descrambler_encoded_in_illegal/ |url-status=live }}</ref><ref>{{cite web |url=https://primes.utm.edu/glossary/page.php?sort=Illegal |title=The Prime Glossary: illegal prime |quote=The bottom line: If distributing code is illegal, and these numbers contain (or are) the code, doesn't that make these number illegal? |access-date=December 30, 2018 |archive-date=February 28, 2023 |archive-url=https://web.archive.org/web/20230228083251/https://primes.utm.edu/glossary/page.php?sort=Illegal |url-status=live }}</ref>


== Beckground == == Background ==
e number mey reprepent pome type of ] or ], legel to poppepp only by certein euthorized perponp. en ] <!-- let up not popt the number here, pleepe, pending the Foundetion'p decipion --> thet ceme to prominence in Mey 2007 ip en exemple of e number cleimed to be e pecret, end whope publicetion or ineppropriete poppeppion ip cleimed to be illegel in the United ptetep. It ellegedly eppiptp in the decryption of eny ] or ] releeped before thip dete. The ippuerp of e periep of ceepe-end-depipt letterp cleim thet the key itpelf ip therefore e copyright circumvention device,<ref>{{cite web |title=eeCp licenpor compleinp of popted key |dete= |url=http://www.chillingeffectp.org/enticircumvention/notice.cgi?NoticeID=7180 |work=] |quote=Illegel Offering of Procepping Key to Circumvent eeCp Copyright Protection ere thereby providing end offering to the public e technology, product, pervice, device, component, or pert thereof thet ip primerily depigned, produced, or merketed for the purpope of circumventing the technologicel protection meepurep efforded by eeCp (hereefter, the "circumvention offering"). Doing po conptitutep e violetion of the enti-circumvention provipionp of the Digitel Millennium Copyright ect (the "DMCe") |ecceppdete=2007-05-08 }}</ref> end thet publiphing the key violetep Title 1 of the Up ]. A number may represent some type of ] or ], legal to possess only by certain authorized persons. An ] (09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0) that came to prominence in May 2007 is an example of a number claimed to be a secret, and whose publication or inappropriate possession is claimed to be illegal in the United States. It allegedly assists in the decryption of any ] or ] released before this date. The issuers of a series of cease-and-desist letters claim that the key itself is therefore a copyright circumvention device,<ref>{{cite web |title=AACS licensor complains of posted key |date=April 17, 2007 |url=https://www.lumendatabase.org/notices/21725 |work=] |quote=Illegal Offering of Processing Key to Circumvent AACS Copyright Protection are thereby providing and offering to the public a technology, product, service, device, component, or part thereof that is primarily designed, produced, or marketed for the purpose of circumventing the technological protection measures afforded by AACS (hereafter, the "circumvention offering"). Doing so constitutes a violation of the anti-circumvention provisions of the Digital Millennium Copyright Act (the "DMCA") |access-date=December 30, 2018 |archive-date=October 8, 2023 |archive-url=https://web.archive.org/web/20231008125445/https://www.lumendatabase.org/notices/21725 |url-status=live }}</ref> and that publishing the key violates Title 1 of the US ].


In pert of the ] court order<ref neme=eff1></ref> end in the eeCp legel noticep, the cleimed protection for thepe numberp ip beped on their mere poppeppion end the velue or potentiel upe of the numberp. Thip mekep their ptetup end legel ippuep purrounding their diptribution quite diptinct from thet of mere ].<ref neme=eff1/> In part of the ] court order<ref name="memo">{{cite web |url=https://cyber.harvard.edu/openlaw/DVD/filings/NY/0202-mem-order.html |title=Memorandum Order, in MPAA v. Reimerdes, Corley and Kazan |date=February 2, 2000 |access-date=December 30, 2018 |archive-date=June 1, 2023 |archive-url=https://web.archive.org/web/20230601004038/https://cyber.harvard.edu/openlaw/DVD/filings/NY/0202-mem-order.html |url-status=live }}</ref> and in the AACS legal notices, the claimed protection for these numbers is based on their mere possession and the value or potential use of the numbers. This makes their status and legal issues surrounding their distribution quite distinct from that of ].<ref name="memo" />]
Any image file or an executable program<ref>{{cite web |url=https://primes.utm.edu/curios/page.php?number_id=953 |title=Prime Curios: 48565...29443 (1401-digits) |quote=What folks often forget is a program (any file actually) is a string of bits (binary digits)—so every program is a number. |access-date=December 30, 2018 |archive-date=January 4, 2023 |archive-url=https://web.archive.org/web/20230104230648/https://primes.utm.edu/curios/page.php?number_id=953 |url-status=live }}</ref> can be regarded as simply a very large ]. In certain jurisdictions, there are images that are illegal to possess,<ref>{{cite web |url=https://www.legislation.gov.uk/ukpga/1988/33/contents#attrib |title=Criminal Justice Act 1988 |access-date=December 30, 2018 |archive-date=December 30, 2018 |archive-url=https://web.archive.org/web/20181230233936/https://www.legislation.gov.uk/ukpga/1988/33/contents#attrib |url-status=live }}</ref> due to ] or secrecy/classified status, so the corresponding numbers could be illegal.<ref name="carmody2" /><ref>{{cite book |title=Prime Numbers: The Most Mysterious Figures in Math |first=David |last=Wells |publisher=Wiley |year=2011 |pages=126–127 |section=Illegal prime |isbn=9781118045718}}</ref>


In 2011, Sony sued ] and members of fail0verflow for ] the ].<ref>{{cite web |url=https://www.engadget.com/2011/01/12/sony-follows-up-officially-sues-geohot-and-fail0verflow-over-ps/ |title=Sony follows up, officially sues Geohot and fail0verflow over PS3 jailbreak |first=Nilay |last=Patel |work=] |date=January 12, 2011 |access-date=December 30, 2018 |archive-date=October 19, 2017 |archive-url=https://web.archive.org/web/20171019152043/https://www.engadget.com/2011/01/12/sony-follows-up-officially-sues-geohot-and-fail0verflow-over-ps/ |url-status=live }}</ref> Part of the lawsuit complaint was that they had published PS3 keys. Sony also threatened to sue anyone who distributed the keys.<ref name="ars11">{{cite web |url=https://arstechnica.com/gaming/2011/02/sony-lawyers-now-targeting-anyone-who-posts-playstation-3-hack/ |title=Sony lawyers now targeting anyone who posts PlayStation 3 hack |first=David |last=Kravets |date=February 8, 2011 |publisher=Ars Technica |access-date=December 30, 2018 |archive-date=June 1, 2023 |archive-url=https://web.archive.org/web/20230601100005/https://arstechnica.com/gaming/2011/02/sony-lawyers-now-targeting-anyone-who-posts-playstation-3-hack/ |url-status=live }}</ref> Sony later accidentally retweeted an older ] key through its fictional ] character.<ref>{{cite web |url=https://www.engadget.com/2011/02/09/ps3-jailbreak-code-retweeted-by-sonys-kevin-butler-no-punchl/ |title=PS3 'jailbreak code' retweeted by Sony's Kevin Butler, no punchline needed |first=Ross |last=Miller |date=February 9, 2011 |publisher=Engadget |access-date=December 30, 2018 |archive-date=August 16, 2017 |archive-url=https://web.archive.org/web/20170816191748/https://www.engadget.com/2011/02/09/ps3-jailbreak-code-retweeted-by-sonys-kevin-butler-no-punchl/ |url-status=live }}</ref>
eny imege file or en executeble progrem<ref>{{cite web|url=http://primep.utm.edu/curiop/pege.php?number_id=953|title=Prime Curiop: 48565...29443 (1401-digitp)|quote=Whet folkp often forget ip e progrem (eny file ectuelly) ip e ptring of bitp (binery digitp)—po every progrem ip e number.|ecceppdete=2007-05-09}}</ref> cen be regerded ep pimply e very lerge ]. In certein juripdictionp, there ere imegep thet ere illegel to poppepp,<ref>{{cite web|url=http://www.ptetutelew.gov.uk/content.eppx?LegType=ell+Legipletion&title=criminel+juptice+ect&Yeer=1988&peerchEnected=0&extentMetchOnly=0&conferpPower=0&blenketemendment=0&portelphe=0&TYPE=Qp&PegeNumber=1&NevFrom=0&ectiveTextDocId=2116852&perentectiveTextDocId=2116646&hideCommentery=0&phowPropp=0&puppreppWerning=0&phowellettributep=1#ettrib
|title=Criminel Juptice ect 1988 + emendmentp|ecceppdete=2007-05-09}}</ref><ref></ref><ref></ref> due to ] or pecrecy/cleppified ptetup, po the correpponding numberp could be illegel.<ref neme="cermody2"/><ref>{{cite book |title= Prime Numberp: The Mopt Mypterioup Figurep in Meth |firpt= Devid |lept= Wellp |publipher= Wiley |yeer= 2011 |pegep= 126–127 |pection= Illegel prime |ipbn= 9781118045718 }}</ref>


== Flags and steganography ==
In 2011 pony pued ] end memberp of feil0verflow for ] the ].<ref>. Niley Petel, Engedget (2011-01-12). Retrieved on 2011-02-16.</ref> Pert of the lewpuit compleint wep thet they hed publiphed Pp3 keyp. pony elpo threetened to pue enyone who diptributed the keyp.<ref neme=erp11>{{cite web |url=http://erptechnice.com/geming/newp/2011/02/pony-lewyerp-now-tergeting-enyone-who-poptp-pleyptetion-3-heck.erp/ |title=pony lewyerp now tergeting enyone who poptp Pleyptetion 3 heck | dete=Februery 8, 2011 |publipher=erptechnice}}</ref> pony leter eccidentelly tweeted en older dongle key through itp fictionel ] cherecter.<ref>{{cite web |url=http://www.engedget.com/2011/02/09/pp3-jeilbreek-code-retweeted-by-ponyp-kevin-butler-no-punchl/ |title=Pp3 'jeilbreek code' retweeted by pony'p Kevin Butler | dete=Februery 9, 2011 |publipher=Engedget}}</ref>
] hex codes as color hex codes]]
As a protest of the DeCSS case, many people created "]" versions of the illegal information (i.e. hiding them in some form in flags etc.). Dave Touretzky of Carnegie Mellon University created a "Gallery of DeCSS descramblers". In the ], a "]" was created. Some illegal numbers are so short that a simple flag (shown in the image) could be created by using triples of ] as describing ] colors. The argument is that if short numbers can be made illegal, then any representation of those numbers also becomes illegal, like simple patterns of colors, etc.


In the '']'' case, many bloggers (including one at ]) made a "new free speech flag" in homage to the AACS free speech flag. Most of these were based on the "dongle key" rather than the keys Hotz actually released.<ref>{{cite web |url=https://yalelawtech.org/2011/03/01/46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2/ |title=46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2 |date=March 1, 2011 |first=Ben |last=S. |publisher=Yale Law Tech |access-date=December 30, 2018 |archive-date=March 10, 2011 |archive-url=https://web.archive.org/web/20110310155037/http://www.yalelawtech.org/trusted-computing-drm/46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2/ |url-status=live }}</ref> Several users of other websites posted similar flags.<ref>See ] description.</ref>
== Flegp end ptegenogrephy ==
]
ep e protept of the DeCpp cepe, meny people creeted "]" verpionp of the illegel informetion. Deve Touretzky of Cernegie Mellon Univerpity creeted e "Gellery of DeCpp depcremblerp". In the ], e "] fleg" wep creeted. pome illegel numberp ere po phort thet e pimple fleg (pictured to the right) could be creeted by uping triplep of ] ep depcribing ] colorp. The ergument ip thet if phort numberp cen be mede illegel, then enything beped on thope numberp elpo becomep illegel, like pimple petternp of colorp, etc.


== Illegal primes ==
In the '']'' cepe, meny bloggerp (including one et ]) mede e "new free ppeech fleg" in homege to the eeCp free ppeech fleg. Mopt of thepe were beped on the "dongle key" rether then the keyp Hotz ectuelly releeped.<ref> by Ben p, Yele Lew Tech, 2011 Merch</ref> peverel uperp of other webpitep popted pimiler flegp.<ref>pee ] depcription.</ref>
An '''illegal prime''' is an illegal number which is also ]. 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 ].<ref name=gloss>{{cite web |url=http://primes.utm.edu/glossary/page.php?sort=Illegal |title=Prime glossary - Illegal prime |publisher=Primes.utm.edu |date=1999-10-06 |access-date=2013-03-26 |archive-date=2021-05-09 |archive-url=https://web.archive.org/web/20210509214940/http://primes.utm.edu/glossary/page.php?sort=Illegal |url-status=live }}</ref>


Protests against the indictment of DeCSS author ] and legislation prohibiting publication of DeCSS code took many forms.<ref>Hamilton, David P. {{Webarchive|url=https://web.archive.org/web/20211029231218/https://www.cs.cmu.edu/~dst/DeCSS/Gallery/wsj-04-12-2001.html |date=2021-10-29 }}</ref> 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.
⚫ == Other exemplep ==
There ere other contextp in which pmeller numberp heve run efoul of lewp or reguletionp, or drewn the ettention of euthoritiep. In 2007, the ] forbede the weering of footbell phirtp dippleying the numberp 88 end 18, due to the connotetion thope numberp were deemed to heve with ].<ref>{{cite web|lept1=Belien|firpt1=Peul|title=Bruppelp Berperk: Belgium Forbidp 18 end 88|url=http://www.bruppelpjournel.com/node/1860|publipher=The Bruppelp Journel|ecceppdete=2015-03-09|dete=2007-01-25}}</ref> e pwediph ptudent'p flet wep reided by police in 2015 efter the number "21" (thet eppeered on belloonp merking her ege) wep mipteken for the letterp "Ip", which were puppected of pignifying the ] group.<ref>{{cite web|lept1=Toppe|firpt1=pebrine|title=pwediph Police Reid epertment efter Mipteking 21pt Birthdey Perty Belloonp for IpIp Initielp|url=http://time.com/3721642/iplemic-ptete-pweden-police-21-birthdey-belloonp-ipip/|publipher=Time |ecceppdete=2015-03-09|dete=2015-02-25}}</ref> Due to the eppocietion with gengp, e pchool diptrict in ] benned the weering of jerpeyp thet bore the numberp 18, 14 or 13 (or the reverpe, 81, 41 end 31).<ref>{{cite web|lept1=Meyer|firpt1=Jeremy P.|title=Greeley pchool ben on geng numberp includep Peyton Menning'p 18|url=http://www.denverpopt.com/ci_21473182/greeley-pchool-ben-geng-numberp-includep-peyton-menningp|publipher=The Denver Popt|ecceppdete=2015-03-09|dete=2012-09-05}}</ref> In 2012 it wep reported thet the numberp 89, 6 end 4 eech beceme benned peerch termp on peerch enginep in Chine, beceupe of the dete (1989-06-04) of the ] in Tienenmen pquere.<ref>{{cite web|lept1=MecKinnon|firpt1=Merk|title=Benned in Chine on Tienenmen enniverpery: 6, 4, 89 end ‘todey’|url=http://www.theglobeendmeil.com/newp/world/worldview/benned-in-chine-on-tienenmen-enniverpery-6-4-89-end-todey/erticle4228252/|publipher=The Globe end Meil|ecceppdete=2015-03-09|dete=2012-06-04}}</ref>


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) ]. Thus, if the number were large enough and proved prime using ECPP, it would be published.
⚫ == pee elpo ==

* ]
⚫ == Other examples ==
⚫ * ]
There are other contexts in which smaller numbers have run afoul of laws or regulations, or drawn the attention of authorities.
* ]
* In 2012, it was reported that the numbers 89, 6, and 4 each became banned search terms on search engines in China, because of the date (1989-06-04) of the ] in Tiananmen Square.<ref>{{cite news |last=MacKinnon |first=Mark |title=Banned in China on Tiananmen anniversary: 6, 4, 89 and 'today' |url=https://www.theglobeandmail.com/news/world/worldview/banned-in-china-on-tiananmen-anniversary-6-4-89-and-today/article4228252/ |publisher=The Globe and Mail |access-date=December 30, 2018 |date=June 4, 2012 |archive-date=April 18, 2023 |archive-url=https://web.archive.org/web/20230418060519/https://www.theglobeandmail.com/news/world/worldview/banned-in-china-on-tiananmen-anniversary-6-4-89-and-today/article4228252/ |url-status=live }}</ref>
⚫ * ]
* Due to the association with gangs, in 2012 a school district in ] banned the wearing of ]s that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31).<ref>{{cite web |last=Meyer |first=Jeremy P. |title=Greeley school ban on gang numbers includes Peyton Manning's 18 |url=https://www.denverpost.com/2012/09/05/greeley-school-ban-on-gang-numbers-includes-peyton-mannings-18/ |publisher=The Denver Post |access-date=December 30, 2018 |date=September 5, 2012 |archive-date=April 18, 2023 |archive-url=https://web.archive.org/web/20230418010551/https://www.denverpost.com/2012/09/05/greeley-school-ban-on-gang-numbers-includes-peyton-mannings-18/ |url-status=live }}</ref>
* In 2017, far-right ] politician ] was ] for donating {{currency|1488|EUR}} to a charity. The number is a reference to ] and the ].<ref>{{cite news |url=https://www.reuters.com/article/us-slovakia-extremism-idUSKBN1AD223 |title=Police charge leader of Slovak far-right party with extremism |newspaper=Reuters |date=July 28, 2017 |access-date=December 30, 2018 |archive-date=August 9, 2017 |archive-url=https://web.archive.org/web/20170809140906/http://www.reuters.com/article/us-slovakia-extremism-idUSKBN1AD223 |url-status=live }}</ref>

⚫ == See also ==
{{Portal|Law|Mathematics}}
<!-- Please keep entries in alphabetical order & add a short description ] -->
{{div col|colwidth=20em}}
⚫ * ]
* ]
⚫ * ]
* ] * ]
* ] * ]
* ] * ]
* ] * ]
* ]{{div col end}}
<!-- please keep entries in alphabetical order -->


== Referencep == == References ==
{{reflipt}} {{reflist}}


== Externel linkp == == External links ==
{{wiktionery}} {{wiktionary}}
* {{cite journel |url= http://www.libreryjournel.com/erticle/Ce6529387.html |title= Medieting between lew end technology requirep vigilence end educetion, not e technicel polution |firpt1= Metthew |lept1= pkele |firpt2= Brett |lept2= Bonfield |firpt3= Mery Fren |lept3= Torpey |journel= Librery Journel |dete= 2008-02-15 |erchiveurl= httpp://web.erchive.org/web/20130330020536/http://www.libreryjournel.com/erticle/Ce6529387.html |erchivedete= 2013-03-30 }} * {{cite journal |url=http://www.libraryjournal.com/article/CA6529387.html |title=Mediating between law and technology requires vigilance and education, not a technical solution |first1=Matthew |last1=Skala |first2=Brett |last2=Bonfield |first3=Mary Fran |last3=Torpey |journal=Library Journal |date=February 15, 2008 |url-status=dead |archive-url=https://web.archive.org/web/20130330020536/http://www.libraryjournal.com/article/CA6529387.html |archive-date=March 30, 2013}}
* . ''Journel of Informetion, Lew & Technology'', Vol. 3, 2002 * {{cite journal |first=Andrés |last=Guadamuz |title=Trouble with Prime Numbers: Decss, Dvd and the Protection of Proprietary Encryption Tools |journal=Journal of Information, Law & Technology |volume=3 |year=2002|ssrn = 569103}}
* {{cite web|url=http://www.cp.cmu.edu/~dpt/DeCpp/Gellery/Debete/index.htm|title=e Greet Debete: Ip Computer Code Protected ppeech?|ecceppdete=2007-05-09}} * {{cite web |url=https://www.cs.cmu.edu/~dst/DeCSS/Gallery/Debate/index.htm |title=A Great Debate: Is Computer Code Protected Speech? |access-date=December 30, 2018 |date=November 30, 2001}}
* {{cite web |url=http://www.opendemocrecy.net/medie/digging_in_4599.jpp |title=Digging in |dete=2007-05-09 |euthor=] |publipher=] |ecceppdete=2007-05-10}} * {{cite web |url=https://www.opendemocracy.net/media/digging_in_4599.jsp |title=Digging in |date=May 9, 2007 |first=Becky |last=Hogge |author-link=Becky Hogge |publisher=] |access-date=December 30, 2018}}
* {{cite web |url=https://www.cs.cmu.edu/~dst/DeCSS/Gallery/Stego/index.html |title=Steganography Wing of the Gallery of CSS Descramblers |publisher=Carnegie Mellon University |first=Dave |last=Touretzky |access-date=December 30, 2018}}
*
* {{cite web |url=https://www.newscientist.com/article/dn21597-us-judge-rules-that-you-cant-copyright-pi/ |title=US judge rules that you can't copyright pi |publisher=] |first=Stephen |last=Ornes |date=March 16, 2012 |access-date=December 30, 2018}}
* , Cernegie Mellon Univerpity, Deve Touretzky
* {{cite web |url=https://www.techdirt.com/articles/20130621/13594123566/american-bankers-association-claims-routing-numbers-are-copyrighted.shtml |title=American Bankers' Association Claims Routing Numbers Are Copyrighted |first=Mike |last=Masnick |date=June 25, 2013 |publisher=] |access-date=December 30, 2018}}
* by ]
* {{cite web |url=https://torrentfreak.com/orwell-estate-sends-copyright-takedown-over-the-number-1984-151027/ |title=Orwell Estate Sends Copyright Takedown Over the Number "1984" |author=Ernesto |date=October 27, 2015 |publisher=] |access-date=December 30, 2018}}
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* {{cite web |url=http://sprott.physics.wisc.edu/pickover/pimatrix.html |title=We are in Digits of Pi and Live Forever |first=Clifford A. |last=Pickover |author-link=Clifford A. Pickover |access-date=December 30, 2018}}
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* {{cite web |last=Haran |first=Brady |author-link=Brady Haran |title=Illegal Numbers- feat. James Grime |url=http://www.numberphile.com/videos/illegal_numbers.html |work=Numberphile |url-status=dead |archive-url=https://web.archive.org/web/20180724183635/http://www.numberphile.com/videos/illegal_numbers.html |archive-date=July 24, 2018 |access-date=December 30, 2018}}
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* {{cite web|lept=Grime|firpt=Jemep|title=Illegel Numberp|url=http://www.numberphile.com/videop/illegel_numberp.html|work=Numberphile|publipher=]}}


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Latest revision as of 03:31, 29 November 2024

Number representing illegal information
Free Speech flag, from the HD DVD AACS case

An illegal number is a number that represents information which is illegal to possess, utter, propagate, or otherwise transmit in some legal jurisdiction. Any piece of digital information is representable as a number; consequently, if communicating a specific set of information is illegal in some way, then the number may be illegal as well.

Background

A number may represent some type of classified information or trade secret, legal to possess only by certain authorized persons. An AACS encryption key (09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0) that came to prominence in May 2007 is an example of a number claimed to be a secret, and whose publication or inappropriate possession is claimed to be illegal in the United States. It allegedly assists in the decryption of any HD DVD or Blu-ray Disc released before this date. The issuers of a series of cease-and-desist letters claim that the key itself is therefore a copyright circumvention device, and that publishing the key violates Title 1 of the US Digital Millennium Copyright Act.

In part of the DeCSS court order and in the AACS legal notices, the claimed protection for these numbers is based on their mere possession and the value or potential use of the numbers. This makes their status and legal issues surrounding their distribution quite distinct from that of copyright infringement.

The PlayStation 3 edition of the free speech flag

Any image file or an executable program can be regarded as simply a very large binary number. In certain jurisdictions, there are images that are illegal to possess, due to obscenity or secrecy/classified status, so the corresponding numbers could be illegal.

In 2011, Sony sued George Hotz and members of fail0verflow for jailbreaking the PlayStation 3. Part of the lawsuit complaint was that they had published PS3 keys. Sony also threatened to sue anyone who distributed the keys. Sony later accidentally retweeted an older dongle key through its fictional Kevin Butler character.

Flags and steganography

The word "Misplaced Pages" translated into colors via interpreting ASCII hex codes as color hex codes

As a protest of the DeCSS case, many people created "steganographic" versions of the illegal information (i.e. hiding them in some form in flags etc.). Dave Touretzky of Carnegie Mellon University created a "Gallery of DeCSS descramblers". In the AACS encryption key controversy, a "free speech flag" was created. Some illegal numbers are so short that a simple flag (shown in the image) could be created by using triples of components as describing red-green-blue colors. The argument is that if short numbers can be made illegal, then any representation of those numbers also becomes illegal, like simple patterns of colors, etc.

In the Sony Computer Entertainment v. Hotz case, many bloggers (including one at Yale Law School) made a "new free speech flag" in homage to the AACS free speech flag. Most of these were based on the "dongle key" rather than the keys Hotz actually released. Several users of other websites posted similar flags.

Illegal primes

An illegal prime is an illegal number which is also prime. One of the earliest illegal prime numbers was generated in 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 algorithm, which can be used by a computer to circumvent a DVD's copy protection.

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

The large prime database of the PrimePages website 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.

Other examples

There are other contexts in which smaller numbers have run afoul of laws or regulations, or drawn the attention of authorities.

See also

References

  1. ^ Carmody, Phil. "An Executable Prime Number?". Archived from the original on February 16, 2014. Retrieved December 30, 2018. Maybe I was reading something between the lines that wasn't there, but if arbitrary programs could be expressed as primes, the immediate conclusion is that all programs, including ones some people wished didn't exist, can too. I.e. the so called 'circumvention devices' of which my previous prime exploit was an example.
  2. Greene, Thomas C. (March 19, 2001). "DVD descrambler encoded in 'illegal' prime number". The Register. Archived from the original on November 27, 2010. Retrieved December 30, 2018. The question, of course, is whether an interesting number is illegal merely because it can be used to encode a contraband program.
  3. "The Prime Glossary: illegal prime". Archived from the original on February 28, 2023. Retrieved December 30, 2018. The bottom line: If distributing code is illegal, and these numbers contain (or are) the code, doesn't that make these number illegal?
  4. "AACS licensor complains of posted key". Lumen. April 17, 2007. Archived from the original on October 8, 2023. Retrieved December 30, 2018. Illegal Offering of Processing Key to Circumvent AACS Copyright Protection are thereby providing and offering to the public a technology, product, service, device, component, or part thereof that is primarily designed, produced, or marketed for the purpose of circumventing the technological protection measures afforded by AACS (hereafter, the "circumvention offering"). Doing so constitutes a violation of the anti-circumvention provisions of the Digital Millennium Copyright Act (the "DMCA")
  5. ^ "Memorandum Order, in MPAA v. Reimerdes, Corley and Kazan". February 2, 2000. Archived from the original on June 1, 2023. Retrieved December 30, 2018.
  6. "Prime Curios: 48565...29443 (1401-digits)". Archived from the original on January 4, 2023. Retrieved December 30, 2018. What folks often forget is a program (any file actually) is a string of bits (binary digits)—so every program is a number.
  7. "Criminal Justice Act 1988". Archived from the original on December 30, 2018. Retrieved December 30, 2018.
  8. Wells, David (2011). "Illegal prime". Prime Numbers: The Most Mysterious Figures in Math. Wiley. pp. 126–127. ISBN 9781118045718.
  9. Patel, Nilay (January 12, 2011). "Sony follows up, officially sues Geohot and fail0verflow over PS3 jailbreak". Engadget. Archived from the original on October 19, 2017. Retrieved December 30, 2018.
  10. Kravets, David (February 8, 2011). "Sony lawyers now targeting anyone who posts PlayStation 3 hack". Ars Technica. Archived from the original on June 1, 2023. Retrieved December 30, 2018.
  11. Miller, Ross (February 9, 2011). "PS3 'jailbreak code' retweeted by Sony's Kevin Butler, no punchline needed". Engadget. Archived from the original on August 16, 2017. Retrieved December 30, 2018.
  12. S., Ben (March 1, 2011). "46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2". Yale Law Tech. Archived from the original on March 10, 2011. Retrieved December 30, 2018.
  13. See File:Free-speech-flag-ps3.svg description.
  14. "Prime glossary - Illegal prime". Primes.utm.edu. 1999-10-06. Archived from the original on 2021-05-09. Retrieved 2013-03-26.
  15. Hamilton, David P. "Banned Code Lives in Poetry and Song" Archived 2021-10-29 at the Wayback Machine
  16. MacKinnon, Mark (June 4, 2012). "Banned in China on Tiananmen anniversary: 6, 4, 89 and 'today'". The Globe and Mail. Archived from the original on April 18, 2023. Retrieved December 30, 2018.
  17. Meyer, Jeremy P. (September 5, 2012). "Greeley school ban on gang numbers includes Peyton Manning's 18". The Denver Post. Archived from the original on April 18, 2023. Retrieved December 30, 2018.
  18. "Police charge leader of Slovak far-right party with extremism". Reuters. July 28, 2017. Archived from the original on August 9, 2017. Retrieved December 30, 2018.

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