42 (number)

← 41 42 43 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-two
Ordinal	nd
Factorization	2 · 3 · 7
Divisors	1, 2, 3, 6, 7, 14, 21, 42
Greek numeral	ΜΒ´
Roman numeral	XLII
Binary	1010102
Ternary	11203
Senary	1106
Octal	528
Duodecimal	3612
Hexadecimal	2A16

42 (forty-two) is the natural number following 41 and preceding 43. The number has received considerable attention in popular culture because of 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 astronomy

• Messier object M42, a magnitude 5.0 diffuse nebula in the constellation Orion, also known as the Orion Nebula
• The New General Catalogue object NGC 42, a spiral galaxy in the constellation Pegasus
• In January 2004, Asteroid 2001 DA42 was given the name Asteroid Douglasadams, named for the author Douglas Adams who popularized the number 42 and died in 2001. With even his initials in the provisional designation, Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, said, "This was sort of made for him, wasn't it?"

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 Nomes (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 because of 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 mocked 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

The number 42 is in 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. In 1994, Adams created the 42 Puzzle, a game based on the number 42.

In the works of Lewis Carroll

Like Adams, Lewis Carroll made repeated use of this number in his writings. (Likewise, Adams named the episodes of the original radio series of The Hitchhiker's Guide to the Galaxy "fits", the word Carroll used to name the chapters of The Hunting of the Snark).

Examples of Carroll's use of 42:

• Rule Forty-two in Alice's Adventures in Wonderland ("All persons more than a mile high to leave the court".)
• Rule 42 of the Code in the preface to The Hunting of the Snark ("No one shall speak to the Man at the Helm.")
• 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".
• Alice's recital of her "four times table" while falling down the rabbit hole makes sense if the first calculation is made in base 18, the second in base 21, and so on, increasing the base by three each time. Continuing on this pattern "4 × 12" would equal "19" in base 39, but "4 × 13" calculated in base 42, rather than providing the expected "20" would yield "1A". Hence, as Alice cries, "I shall never get to twenty at that rate!"

In music

• Level 42 is an English pop/rock band.
• "42" is one of the tracks on Coldplay's 2008 album Viva la Vida or Death and All His Friends.
• Strigaskór nr. 42 is an Icelandic band.
• "42" is the title of a song by Philadelphia based jam/electronica band The Disco Biscuits.
• "Forty-Two" is the title of a song from The Afters' 2008 album Never Going Back To OK.

In other languages

Arabic	٤٢
Bulgarian	четиридесет и две
Catalan	quaranta-dos
Chinese	四十二
Czech	čtyřicet dva
Danish	toogfyrre
Dutch	tweeënveertig
Esperanto	Kvardek Du
Estonian	nelikümmend kaks
Filipino	apatnapu't dalawa
French	quarante-deux
Georgian	ორმოცდაორი [ormocdaori]
German	zweiundvierzig
Greek	σαρανταδύο
Hebrew	ארבעים ושתיים (Arbayim Ve Shtayim)
Hindi	बयालीस, ४२
Hungarian	negyvenkettő
Icelandic	fjörutíu og tveir
Indonesian	empat puluh dua
Irish	Daichead ceathar
Italian	quarantadue
Japanese	四十二 (よんじゅうに)
Korean	사십이 (마흔둘)
Latvian	četrdesmit divi
Lietuvių	Keturiasdešimt du
Lojban	vore
Macedonian	четириесет и два
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. четрдесет два)
Slovene	dvainštirideset
Slovak	štyridsaťdva
Spanish	cuarenta y dos
Suomeksi	neljäkymmentäkaksi
Swedish	fyrtiotvå
Tamil	நாற்பத்திரண்டு
Thai	สี่สิบสอง
Turkish	kırk iki
Vietnamese	bốn mươi hai
Welsh	pedwar-deg-dau, dau-ar-ddeugain

In television and film

• Fox Mulder, one of the main characters in The X-Files lived in Apartment 42 at 2630 Hegal Place, Alexandria, Virginia.
• 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. It is also the number tied to the character "Kwon".
• 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.
• In the Doctor Who episode Voyage of the Damned, the Tenth Doctor attempts to control a rogue host robot by randomly shouting numbers, including of course, 42.
• 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.
• 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. 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 Destroy All Humans! you go into a parody of Area 51 called Area 42.
• In Lego Batman, Lego Indiana Jones, and the Lego Star Wars games, the maximum amount of studs you can have is 4,200,000,000.
• In The Conduit one of the conspiracy messages reads XLII or 42 in roman numerals
• In Mucky Foot Softwares 'Startopia', the AI Computer advisor is quoted as saying '42. Interesting number don't you think? Although I suppose it's importance is lost on you carbon based lifeforms'

In sports

Jackie Robinson in his now-retired number 42 jersey.

• 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, the last professional baseball player to wear number 42, Mariano Rivera of the New York Yankees, is currently still using it.
• The jersey number of football Hall of Famer, Ronnie Lott, safety for the San Francisco 49ers who retired his jersey number in 2003.
• The jersey number of Pat Tillman, which was retired on November 13, 2004 by Arizona State University.
• The number of laws of cricket.
• The number on Lee Petty's racing car when he raced in NASCAR.
• The number of Juan Pablo Montoya's race car in the NASCAR Sprint Cup Series.

In technology

• Magic numbers 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.
  • In the reiser4 file system, 42 is the inode number of the root directory.

• The GNU C Library, a set of standard routines available for use in computer programming, contains a function—memfrob()—which performs an XOR combination of a given variable and the binary pattern 00101010 (42) as an XOR cipher.

• 42 is the result given by the web search engines Google, Wolfram Alpha and Microsoft's Bing when the query "the answer to life the universe and everything" is entered as a search.

• 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.

• Tiling a plane using regular hexagons, which is honeycomb in appearance, is approximated in a topological sense to an accuracy of better than 1% using a stretcher bond brick pattern with bricks of 42 squares (6 by 7).

In other fields

• Tower 42 is a skyscraper in the City of London, formerly known as the NatWest Tower.
• The name of a Texan trick-taking game played with dominoes (see 42 (dominoes)).
• The number of spots (or pips, circular patches or pits) on a pair of standard six-sided dice.
• In New York City, 42nd Street is a main and very popular two-way thoroughfare. Landmarks on it include the Chrysler Building, Grand Central Station, the main branch of the New York Public Library, and Times Square. The New York City street is also the setting for a movie by the same name (which also gave fame to its eponymous title song), and which later inspired a musical adaptation, 42nd Street.
• 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.

Dates

• 42 B.C., 42 A.D., 1842, 1942, 2042, etc.