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.
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.
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.
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 June Fourth Massacre in Tiananmen Square.
Due to the association with gangs, in 2012 a school district in Colorado banned the wearing of jerseys that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31).
In 2017, far-right Slovak politician Marian Kotleba was criminally charged for donating 1,488 euros to a charity. The number is a reference to a white supremacist slogan and the Nazi salute.
In 2019, Matteo Salvini, Deputy Prime Minister of Italy and Italian Minister of the Interior, banned the usage of the number 49 from his Facebook profile to prevent any association with the corruption scandal about party subsidies in his party, Lega Nord, which amounted to 49 million euros.