86 is the middle number in the second cluster of three discrete biprimes between 85 and 87 being themselves discrete biprimes.
Since it is possible to find sequences of 86 consecutive integers such that each inner member member shares a factor with either the first or the last member, 86 is an Erdős–Woods number.
86 is a repdigit in base 6 (222).
In American English, the number 86 used as a verb, to "eighty-six," means to "ignore" or "get rid of". The first recorded usage of this term occurs in the mid-1930s. There are many theories of the origin of this usage, most pertain either to death or to prohibition.
One of the explanations pertaining to death is the distance of eighty miles out and six feet under meaning when a person who is to be killed by the mafia is forced to dig his own grave many miles away from civilization; or the possibility of a simple variation of the slang term deep six, which has identical meaning, and is simply meant to describe the approximate depth of water (6 fathoms, 11 meters) needed for a burial at sea. The term came into popular use among soldiers and veterans to describe missing soldiers as 86'd. Rather than describe buddies missing in action, it was slang to describe the MIA as being AWOL, therefore violating UCMJ Sub Chapter X Article 86. The public outdoor observatory of the Empire State Building was on the 86th floor; the site of more than 30 suicides. Another origin related to the Empire State Building is the fact that all the elevators stop at the 86th floor. Hence, everyone had to leave. The building opened in 1931, apparently a few years before the term became popular.
Of the explanations pertaining to prohibition, one is a reference to Article 86 of the New York state liquor code which defines the circumstances in which a bar patron should be refused service or "86ed". Others have suggested that this usage originated from the famous Delmonico's Restaurant in New York City, as item number 86 on their menu, their house steak, often ran out during the 19th century. However, there is no recorded usage of this term in the nineteenth century. Yet another explanation is that Chumley's, which was a famous 1900s New York speakeasy, is located at 86 Bedford Street. During Prohibition, an entrance through an interior adjoining courtyard was used, as it provided privacy and discretion for customers. As was a New York tradition, the cops were on the payroll of the bar and would give a ring to the bar that they were coming for a raid. The bartender would then give the command "86 everybody!", which meant that everyone should hightail it out the 86 Bedford entrance because the cops were coming in through the courtyard door.
Another theory has it that this is rhyming slang for "nix"; however, if so, it would be a wholly American origin, and thus would be unusual for rhyming slang.
For many baseball fans, the most popular if misplaced reference was born of the 1986 playoff debacle for the Boston Red Sox. Game 6 and (eventually) the World Series slipped through the glove of first baseman Bill Buckner in the bottom of the 9th inning. The Sox didn't recover from the letdown in time for Game 7 and the New York Mets took the '86 crown. With Red Sox fans long considering the team to be cursed from trading Babe Ruth for cash and the 1986 World Series representing the closest shot the team had at winning the World Series in decades, the term '86 took on the meaning of "not happening." One unusual theory is that there were 86 goals scored in the highest scoring NHL game. For football fans, "to 86" still means "to get rid of," for example, in the Cincinnati Bengals, Chad Ocho Cinco fittingly wears jersey #85, which, coupled with his desire to leave the team, has led to fans urging the Bengals to '86 85'.
86 was also the number of Orthodox Jews that Adolf Hitler personally denounced.