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42 (forty-two) is the natural number following 41 and preceding 43. The number has received considerable attention in popular culture due to its appearance in The Hitchhiker's Guide to the Galaxy, as "the Answer to the Ultimate Question of Life, the Universe, and Everything."

## In mathematics

Forty-two is an abundant number; its 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 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.

42 is the product of the first three terms of Sylvester's sequence; like the first five such numbers it is also a primary pseudoperfect number.

It is the sum of the totient function for the first eleven integers.

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.

It is the reciprocal of a Bernoulli number.

It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function". In particular, Conrey & Ghosh have conjectured

{1 \over T}\int_0^T \left| \zeta\left({1 \over 2} + it\right) \right|^6\,dt \sim {42 \over 9!}\prod_p \left\{1-{1\over p}\right\}^4 \left( 1 + {4 \over p} + {1 \over p^2} \right) \log^9 T,

where the infinite product is over all prime numbers, p.

It is a pronic number, and the third pentadecagonal number. It is a meandric number and an open meandric number.

Since the greatest prime factor of 422 + 1 = 1765 is 353 and thus more than 42 twice, 42 is a Størmer number.

42 is a perfect score on the USA Math Olympiad (USAMO) and International Mathematical Olympiad (IMO).

In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).

The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.

The 3 × 3 × 3 magic cube with rows summing to 42.
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, comprises 3 cubes whose sum of values is 42.

## In science

• The atomic number of molybdenum.
• The angle in degrees for which a rainbow appears.
• 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, evacuate it (remove the air), and then just 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. Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity's force would be lessened, so would the distance traveled at an equal rate. The same idea was proposed by Lewis Carroll in Sylvie and Bruno, volume 2, chapter 7, without calculation.

## In religion

There are 42 principles of Ma'at, the Ancient Egyptian personification of physical and moral law, order, and truth. In the judgement scene described in the Egyptian and the Book of the Coming/Going Forth by Day (the Book of the Dead (which evolved from the Coffin Texts and the Pyramid Texts)), there are 42 Gods and Goddesses of Egypt, personifying the principles of Ma'at, who ask questions of the departed, while Thoth records the answers, and the deceased's heart is weighed against the feather of Truth (Ma'at). These 42 correspond to the 42 Nome (Governmental Units) of Egypt. If the departed successfully answers all 42, s/he becomes an Osiris.

42 is the number with which God creates the Universe in Kabalistic 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 (see further up this page) and the Kabbalah's Forty-Two Lettered Name, they are probably not identical due to the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.

The number 42 appears in various contexts in Christianity. There are 42 generations (names) in the Gospel of Matthew's version of the Genealogy of Jesus; it is prophesied that for 42 months the Beast will hold dominion over the Earth (Revelation 13:5); 42 men of Beth-azmaveth were counted in the census of men of Israel upon return from exile (Ezra 2:24); God sent bears to maul 42 of the youths who mock Elisha for his baldness (2 Kings 2:23), etc.

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.

## In popular culture

### In The Hitchhiker's Guide to the Galaxy

Many occurrences of the number 42 in pop culture can be attributed as an homage to Douglas Adams' book The Hitchhiker's Guide to the Galaxy, in which the number 42 is The Answer to the Ultimate Question of Life, the Universe, and Everything, as calculated by an enormous supercomputer over a period of 7.5 million years. According to the fifth Hitchhiker volume, Mostly Harmless, 42 is the location of Stavromula Beta. Thus, 42 may be the world's longest written riddle, since the riddle of the question to the answer was raised in the first volume, and not answered until the final page of the fifth, and then passes unnoticed by the story's ever-bumbling characters. Adams later (1994) created the 42 Puzzle, a game based on the number 42.

### In music

 Arabic ٤٢ Bulgarian четиридесет и две Catalan quaranta-dos Chinese 四十二 Croatian četrdeset i dva Czech čtyřicet dva Danish toogfyrre Dutch tweeënveertig Spanish Cuarenta y dos Esperanto Kvardek Du Estonian nelikümmend kaks Filipino apatnapu't dalawa French quarante-deux Georgian ორმოცდაორი [ormocdaori] German zweiundvierzig Macedonian четириесет и два Hebrew מב (Mem Bet) Hindi बयालीस, ४२ Hungarian negyvenkettő Indonesian empat puluh dua Italian quarantadue Icelandic fjörutíu og tveir Japanese 四十二 (よんじゅうに) Korean 사십이 (마흔둘) Latvian četrdesmit divi Lietuvių Keturiasdešimt du Lojban vore Maltese tnejn u erbghin Norwegian førtito Persian چهل و دو Polish czterdzieści dwa Portuguese quarenta e dois Romanian patruzeci şi doi Russian сорок два Serbian четрдесет и два (alt. четрдесетдва) Slovene dvainštirideset Slovak štyridsaťdva Spanish cuarenta y dos Swedish fyrtiotvå Tamil நாற்பத்திரண்டு Thai สี่สิบสอง Turkish kırk iki Suomeksi neljäkymmentäkaksi Vietnamese bốn mươi hai Welsh pedwar-deg-dau, dau-ar-ddeugain

### In television and film

• The Kumars at No. 42 television series. In 2003, Sanjeev Bhaskar hosted a BBC show nominating The Hitchhiker's Guide to the Galaxy as Britain's Best Loved Book.
• 42 is one of The Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
• A made for TV movie 42: Forty Two Up - an installment in a series of documentaries wherein the director revisits the same group of British-born individuals every 7 years.
• 42 is an episode of Doctor Who, set in real time lasting approximately 42 minutes.
• 42 is the name of Buzz Lightyear's space ship from Pixar's animated science fiction series Buzz Lightyear of Star Command.
• In an episode of "House M.D" Dr. House claims that his favorite number is 42.
• In Monty Python's film And Now for Something Completely Different, the famous "How Not to be Seen" sketch is presented as "H.M. Government Public Service film No. 42."
• In A Clockwork Orange Alex browses through records in a record store and we see a record of the, at this time fictional, band Level 42.
• It has been noted on the BBC Show, Top Gear, by Presenter Jeremy Clarkson that mysterious racing driver, 'The Stig' can "solve the Da Vinci Code in 42 seconds."
• In an episode of "Stargate Atlantis" it is revealed that Rodney Mckay's password is made up of the birth years of several notable minds throughout history, and ends with the number 42. The character John Sheppard reveals that the number is the ultimate answer to life, the universe and everything, to the confusion of his alien companion.

### In video games

• 42 Entertainment is the company responsible for several alternate reality games, including I Love Bees and Year Zero.
• In the PC game, Spore, reaching the center of the galaxy yields a powerful item known as the "Staff of Life" which has a limited 42 uses. It also grants the player an achievement titled "42".
• In the 2008 game Fable II, the last in a series of ancient artifacts the player can find says "Now just think of the number 42."
• 101010 (42 in Binary) is an open-source Java game.
• In the Champions Online MMORPG it states during a loading screen "your lucky numbers are 2, 5 and 42"
• In Valve Corporation's Left 4 Dead 2, 42 is the number of Moustachios that must be shot in the Dark Carnival campaign's Whack-a-Mole style mini-game in order to unlock the STACH WACKER achievement.

## In technology

42 is a common magic number used by programmers:

• In the TIFF image file format, the second 16-bit word of every file is 42, which is used together with the first word to indicate byte order.

• Advanced Micro Device's One off Overlocking CPU was named Phenom 42, with the number being partially from the book The Hitchhikers Guide to the Galaxy.

## In other fields

• Popular gadget magazine Stuff did not produce an issue numbered 42, in honor of the book, instead, the 41st issue was followed by the 43rd

## Notes

1. J. B. Conrey & A. Ghosh, "A conjecture for the sixth power moment of the Riemann zeta-function" International Mathematics Research Notices (1998)
2. J. B. Conrey & S. M. Gonek, "High moments of the Riemann zeta-function" Duke Math J. 107 3 (2001): 577 – 604
3. Alex Zhai ties for second-highest score in 2007 USA Mathematical Olympiad - By Andrew Lovdahl Gargoyle staff reporter Posted Monday, May 7, 2007, The OG, news & student awards - Online Gargoyle
4. CBC News staff, " Canadian math champ's skills add up to a perfect score" CBC News July 20, 2004. "A 16-year-old Canadian was one of four students who achieved a perfect score at an international mathematics competition. Jacob Tsimerman of Toronto scored 42 out of 42, making him one of 45 individual gold medallists at the 45th International Mathematical Olympiad in Athens."
5. 42: Forty Two Up at IMDB
6. Allpar: Richard Petty and a history of Petty Racing

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