Forty-two

The forty-two (42) is the natural number that follows forty-one and precedes forty-three.

Mathematical properties

• It's a semi-perfect number.

• It is an abundant number (the sum of its own dividers gives a greater result than the number).
• A number from Catalan.
• It's a Harshad number and a Moran number.
• A pie number.
• Sphenic number.
• It's a self-number.

Sum decomposition of three integer cubes

The decomposition of a number in the sum of three integer cubes, takes the form:

${displaystyle N=X^{3}+Y^{3}+Z^{3}}$

being ${displaystyle N}$ a positive integer, and ${displaystyle (X,Y,Z)}$ three integers (positive or negative). It is a diophantic equation (a type of problems with integers that were already studied in classical Greece).

This simple condition (from an arithmetic point of view) is extraordinarily difficult to solve from a numerical point of view, since there is no choice but to check huge combinations of numbers (with the help of auxiliary algorithms, which allow rule out certain triplet numbers a priori). In fact, the challenge was raised in 1954, and since then all cases between 0 and 100 have been solved, except for case number 33 (solved by Andrew Bookerm in April 2019) and case number 42 (solved by Bookern himself and by Andrew Sutherland in September 2019). The problem has eluded mathematicians for 65 years.

The decomposition found of the number 42 is the following:

${displaystyle 42=(-80538738812075974)^{3}+8043575817515^{3} +12602123297335631^{3}}}$

To obtain the gigantic computing power necessary to address the problem, a collaborative network system was used over the internet, called Charity Engine, which uses the surplus computing power of 500,000 home computers, selflessly donated by their owners to through an online application.

Chemistry

• It's the atomic number of molybdenum.

In computing

• Magical number used by programmers
  • The character represented by the number 42 in the ASCII system is the *, the asterisk, also known as a wild character.
  • In all images in TIFF format, the second word of 16 bits is 42, which is used together with the first word to indicate the order of the bytes
  • In the reiser4 file system, 42 is the root directory inode number.
• The GNU C library, routine sets used in programming, contains a function—memfrob()—which runs XOR operations on a certain variable using the binary number 00101010 (42) as XOR encryption.
• 42 is the result obtained from Google search engines, DuckDuckGo, Wolfram Alpha and Bing when the query "the answer to life the universe and everything" is entered.
• The Microsoft Windows 3.x logo consists of 42 squares that form the left tail.
• Facebook chat had a special emoticon, when a person wrote ":42:" in the chat, the number appeared blank on a red box.

Pop Culture

• It is the answer of the meaning of life, the universe and everything else, according to the book Guide to the galactic autostopian, by Douglas Adams.
• 42 is the sixth and last number of the series Lost.
• In the series The X-Files the protagonist, Fox Mulder, lives in department 42.
• It's atomic number for cobalt.
• It is the height in inches to which the fences are located.
• 42 is the title of an episode Doctor Who.
• It was the number used by Jackie Robinson when he played with the Brooklyn Dodgers, which is retired on all the teams of the Great Leagues.
• «42» is the title of a song by the British band Coldplay.
• «42» is the title of a song from the album "Mixtape" of the 3Racha South Korean trio (inforMARE)

Binary symbology in popular culture

Adding online, this 3x3x3 bucket always gives 42.

Given its binary representation, 101010, it is of great significance, for example, for Geek and geek culture, as can be seen in the aforementioned science fiction theme (The X-Files, The Hitchhiker's Guide to the Galaxy, Lost…). The geek group Geeks Without Bounds, used the date of the binary representation (October 10, 2010) to launch their campaign (101010 +) GWOBorg Hackathon) for access to information in disadvantaged countries.

In this sense, even Canonical decided to release Ubuntu 10.10 (Maverick Meerkat) with slogans such as round, perfect.... although in reality the release date may seem obvious.

For other groups such as environmentalists it has also been significant. Greenpeace, for example, took advantage of the date to launch its campaign Greenpeace 10/10/10 Day of Climate Action (Climate Solutions Day) leading a global action also undertaken in the same sense by the NGO 350.org.

Meanwhile, Twitter and Facebook also established such a date as El día del porno (hashtag #diaporno) due to its representation in Roman numerals (XXX).