When written in base 16 (hexidecimal), this 1401 digit prime number found by Phil Carmody forms a gzip file of the C-source code that decrypts the DVD Movie encryption scheme (DeCSS).

4856507896573978293098418946942861377074420873513579240196520736
6869851340104723744696879743992611751097377770102744752804905883
1384037549709987909653955227011712157025974666993240226834596619
6060348517424977358468518855674570257125474999648219418465571008
4119086259716947970799152004866709975923596061320725973797993618
8606316914473588300245336972781813914797955513399949394882899846
9178361001825978901031601961835034344895687053845208538045842415
6548248893338047475871128339598968522325446084089711197712769412
0795862440547161321005006459820176961771809478113622002723448272
2493232595472346880029277764979061481298404283457201463489685471
6908235473783566197218622496943162271666393905543024156473292485
5248991225739466548627140482117138124388217717602984125524464744
5055834628144883356319027253195904392838737640739168912579240550
1562088978716337599910788708490815909754801928576845198859630532
3823490558092032999603234471140776019847163531161713078576084862
2363702835701049612595681846785965333100770179916146744725492728
3348691600064758591746278121269007351830924153010630289329566584
3662000800476778967984382090797619859493646309380586336721469695
9750279687712057249966669805614533820741203159337703099491527469
1835659376210222006812679827344576093802030447912277498091795593
8387121000588766689258448700470772552497060444652127130404321182
610103591186476662963858495087448497373476861420880529443

In 2001, while researching a topic for a talk by Professor Chris Caldwell, Phil Carmody made a discovery; a 1811 digit executable prime, which is also allegedly illegal (the DeCSS algorithm).

The purpose of the research was to discover if an executable prime was feasible to generate, and whether an arbitrary executable could be turned into a prime.

Carmody's research led him to use the DeCSS code as his test executable, and here is the result; an ELF executable of the DeCSS code; and the world's first non-trivial executable titanic prime:

493108359702850190027577767239076495728490777215020863208075
018409792627885097658864557802013660073286795447341128317353
678312015575359819785450548115719393458773300380099326195058
764525023820408110189885042615176579941704250889037029119015
870030479432826073821469541570330227987557681895601624030064
111516900872879838194258271674564774816684347928464580929131
531860070010043353189363193439129486044503709919800477094629
215581807111691530318762884778783541575932891093295447350881
882465495060005019006274705305381164278294267474853496525745
368151170655028190555265622135314631042100866286797114446706
366921982586158111251555650481342076867323407655054859108269
562666930662367997021048123965625180068183236539593483956753
575575324619023481064700987753027956186892925380693305204238
149969945456945774138335689906005870832181270486113368202651
590516635187402901819769393767785292872210955041292579257381
866058450150552502749947718831293104576980909153046133594190
302588132059322774443852550466779024518697062627788891979580
423065750615669834695617797879659201644051939960716981112615
195610276283233982579142332172696144374438105648552934887634
921030988702878745323313253212267863328370279250997499694887
759369159176445880327183847402359330203748885067557065879194
611341932307814854436454375113207098606390746417564121635042
388002967808558670370387509410769821183765499205204368255854
642288502429963322685369124648550007559166402472924071645072
531967449995294484347419021077296068205581309236268379879519
661997982855258871610961365617807456615924886608898164568541
721362920846656279131478466791550965154310113538586208196875
836883595577893914545393568199609880854047659073589728989834
250471289184162658789682185380879562790399786294493976054675
348212567501215170827371076462707124675321024836781594000875
05452543537

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Source:
http://asdf.org/~fatphil/maths/illegal.html