Forty-two is a pronic number and an abundant number; its prime factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form (2 · 3 · r). As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14-member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30. Further, 42 is the 10th member of the 3-aliquot tree. Additional properties of the number 42 include:
It is a Catalan number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3 × 3 × 3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 numbers whose sum of values is 42.
42 is the only known value that is the number of sets of four distinct positive integers a, b, c, d, each less than the value itself, such that ab − cd, ac − bd, and ad − bc are each multiples of the value. Whether there are other values remains an open question.
42 is the resulting number of the original Smith number (4937775 = 3 × 5 × 5 × 65837): Both the sum of its digits (4 + 9 + 3 + 7 + 7 + 7 + 5) and the sum of the digits in its prime factorization (3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)) result in 42.
The angle rounded to whole degrees for which a rainbow appears (the critical angle).
In 1966, mathematician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, remove the air from the tube and fall through. The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration. The time for such a journey works out to be 42 minutes. Even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity (known as a gravity train) always works out to be 42 minutes, so long as the tube remains friction-free, as while the force of gravity would be lessened, the distance traveled is reduced at an equal rate. (The same idea was proposed, without calculation by Lewis Carroll in 1893 in Sylvie and Bruno Concluded.)
In January 2004, asteroid2001 DA42 was given the permanent name 25924 Douglasadams, for the author Douglas Adams who popularized the number 42 and died in 2001. Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, remarked that, with even his initials in the provisional designation, "This was sort of made for him, wasn't it?".
In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately—shi ni (four two)—sound like the word "death".
There are 42 questions asked of persons making their journey through Death. Ma'at, a female personification, considered to be both maternal and a delivering force, is an Ancient Egyptian personification of physical and moral law, order, and truth. In the judgment scene described in the Egyptian and the Book of Pass (the Book of the Dead (which evolved from the Coffin Texts and the Pyramid Texts)), there are 42 questions personifying the analysis of Ma'at. If the departed reasonably can give answers to the 42 questions, they have the potential to either be reincarnate, or if completely successful, reach the ultimate goal of becoming a Star, whereon, they can continue to give Light, and fuel Universal growth.
42 is the number with which God creates the Universe in Kabbalistic tradition. In Kabbalah, the most significant name is that of the En Sof (also known as "Ein Sof", "Infinite" or "Endless"), who is above the Sefirot (sometimes spelled "Sephirot"). The Forty-Two-Lettered Name contains four combined names which are spelled in Hebrew letters (spelled in letters = 42 letters), which is the name of Azilut (or "Atziluth" "Emanation"). While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud and the Kabbalah's Forty-Two Lettered Name, they are probably not identical because of the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.
In Judaism, the number (in the Babylonian Talmud, compiled 375 AD to 499 AD) of the "Forty-Two Lettered Name" ascribed to God. Rab (or Rabhs), a 3rd-century source in the Talmud stated "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights". [Source: Talmud Kidduschin 71a, Translated by Rabbi Dr. I. Epstein]. Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names [Maimonides "Moreh"]. The apparently unpronouncable Tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Two Lettered Name of the Talmud.
The Gutenberg Bible is also known as the "42-line Bible", as the book contained 42 lines per page.
The 2011 book 42: Douglas Adams' Amazingly Accurate Answer to Life, the Universe and Everything examines Adams' choice of the number 42 and also contains a compendium of some instances of the number in science, popular culture, and humour.
Alice's attempts at multiplication (chapter two of Alice in Wonderland) work if one uses base 18 to write the first answer, and increases the base by threes to 21, 24, etc. (the answers working up to 4 × 12 = "19" in base 39), but "breaks" precisely when one attempts the answer to 4 × 13 in base 42, leading Alice to declare "oh dear! I shall never get to twenty at that rate!"
Rule Forty-two in Alice's Adventures in Wonderland ("All persons more than a mile high to leave the court").
In "fit the first" of The Hunting of the Snark the Baker had "forty-two boxes, all carefully packed, With his name painted clearly on each."
The White Queen announces her age as "one hundred and one, five months and a day", which—if the best[clarification needed] possible date is assumed for the action of Through the Looking-Glass—gives a total of 37,044 days. If the Red Queen, as part of the same chess set, is regarded as the same age, their combined age is 74,088 days, or 42 × 42 × 42.
The jersey number of Jackie Robinson, which is the only number retired by all Major League Baseball teams. Although the number was retired in 1997, Mariano Rivera of the New York Yankees, the last professional baseball player to wear number 42, continued to wear it until he retired at the end of the 2013 season. As of the 2014 season, no player will ever again wear the number 42 in Major League Baseball except on Jackie Robinson Day (April 15), when all uniformed personnel (players, managers, coaches, and umpires) wear the number.
42 is the inspiration for the name of the 42 Center of Excellence for Artificial Intelligence, based in Vienna, Austria
42 is the name of a private college of computer science and programming funded in Paris by the businessman and creator of Free, Xavier Niel.
If one were to fold a piece of paper 42 times, it would reach beyond the orbit of the moon.
42 is the number of seats in Social Democratic Youth of Denmark's major council Hovedbestyrelsen. At the 2016 national convention, lowering the number of seats to 32 were discussed, but eventually the convention decided to stick with 42 members.
^Carroll, Lewis (29 December 1893). "Chapter 7". Sylvie and Bruno Concluded. 2. illustrated by Harry Furniss. United Kingdom: Macmillan and Co. Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs half-way down-hill, and that gives it force enough to run the other half up-hill.