# 42 (number)

 ← 41 42 43 →
Cardinal forty-two
Ordinal 42nd
(forty-second)
Factorization 2 × 3 × 7
Divisors 1, 2, 3, 6, 7, 14, 21, 42
Roman numeral XLII
Unicode symbol(s)
Greek prefix μβ
Binary 1010102
Ternary 11203
Quaternary 2224
Quinary 1325
Senary 1106
Octal 528
Duodecimal 3612
Vigesimal 2220
Base 36 1636

42 (forty-two) is the natural number that succeeds 41 and precedes 43.

## Mathematics

Forty-two is a pronic number[1] 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 the third primary pseudoperfect number.[2]
• It is a Catalan number.[3] 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 an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices.
• It is the number of partitions of 10—the number of ways of expressing 10 as a sum of positive integers (note a different sense of partition from that above).
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, is composed of 3 numbers whose sum of values is 42.
• It is the third pentadecagonal number.[4] It is a meandric number and an open meandric 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 that
${\displaystyle {1 \over T}\int _{0}^{T}\left|\zeta \left({1 \over 2}+it\right)\right|^{6}\,dt\sim {42 \over 9!}\prod _{p}\left\{1-{1 \over p}\right\}^{4}\left(1+{4 \over p}+{1 \over p^{2}}\right)\log ^{9}T,}$
.
where the infinite product is over all prime numbers, p.[5][6]
• 42 is a Størmer number.[7]
• 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 abcd, acbd, and adbc are each multiples of the value. Whether there are other values remains an open question.[8]
• 42 is a (2,6)-perfect number (super-multiperfect), as σ2(n) = σ(σ(n)) = 6n.[9]
• 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 dimension of the Borel subalgebra in the exceptional Lie algebra e6 is 42.
• 42 is the largest number n such that there exist positive integers p, q, r with 1 = 1/n + 1/p + 1/q + 1/r
• 42 is the smallest number k such that for every Riemann surface C, #Aut(C) ≤ k deg(KC) = k(2g − 2) (Hurwitz's automorphisms theorem)
• In base 10, this number is a Harshad number[10] and a self number,[11] while it is a repdigit in base 4 (as 222).
• 42 is a perfect score on the USA Math Olympiad (USAMO)[12] and International Mathematical Olympiad (IMO).[13]
• 42 is the maximum of core points awarded in International Baccalaureate Diploma Programme.

## Science

• 42 is the atomic number of molybdenum.
• 42 is the atomic mass of one of the naturally occurring stable isotopes of calcium.
• 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.[14] 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.[15][16] (The same idea was proposed, without calculation by Lewis Carroll in 1893 in Sylvie and Bruno Concluded.[17])

## Religion

• In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately—shi ni (four two)—sound like the word "death".[20]
• 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").[21] 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.
• 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 teenage boys 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.[citation needed]
• The Gutenberg Bible is also known as the "42-line Bible", as the book contained 42 lines per page.
• The Forty-Two Articles (1552), largely the work of Thomas Cranmer, were intended to summarise Anglican doctrine, as it now existed under the reign of Edward VI.
• The Sutra of 42 Sections is a Buddhist scripture.

## Popular culture

### The Hitchhiker's Guide to the Galaxy

The Answer to the Ultimate Question of Life, The Universe, and Everything.

The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything", calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is. Thus, to calculate the Ultimate Question, a special computer the size of a small planet was built from organic components and named "Earth". The Ultimate Question "What do you get when you multiply six by nine?" was found by Arthur Dent and Ford Prefect in the second book of the series, "The restaurant at the end of the Universe". This appeared first in the radio play and later in the novelization of The Hitchhiker's Guide to the Galaxy. The fact that Adams named the episodes of the radio play "fits", the same archaic title for a chapter or section used by Lewis Carroll in "The Hunting of the Snark", suggests that Adams was influenced by Carroll's fascination with and frequent use of the number[original research?]. The fourth book in the series, the novel So Long, and Thanks for All the Fish, contains 42 chapters. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta. In 1994 Adams created the 42 Puzzle, a game based on the number 42.

The 2011 book 42: Douglas Adams' Amazingly Accurate Answer to Life, the Universe and Everything[22] examines Adams' choice of the number 42 and also contains a compendium of some instances of the number in science, popular culture, and humour.

### Works of Lewis Carroll

Lewis Carroll, who was a mathematician,[23] made repeated use of this number in his writings.[24]

Examples of Carroll's use of 42:

• Alice's Adventures in Wonderland has 42 illustrations.
• Alice's attempts at multiplication (chapter two of Adventures 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").
• Rule 42 of the Code in the preface[25] 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."[25]
• 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.[26]

### Sports

Jackie Robinson in his now-retired number 42 jersey.

## References

1. ^ "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A051867 : 15-gonal (or pentadecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ J. B. Conrey & A. Ghosh, "A conjecture for the sixth power moment of the Riemann zeta-function" International Mathematics Research Notices (1998)
6. ^ J. B. Conrey & S. M. Gonek, "High moments of the Riemann zeta-function" Duke Math J. 107 3 (2001): 577–604
7. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
8. ^ Differently Perfect – mathpages.com
9. ^
10. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
11. ^ "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
12. ^ 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
13. ^ 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."
14. ^ Cooper, Paul W. (1966). "Through the Earth in Forty Minutes". American Journal of Physics. 34 (1): 68–69. doi:10.1119/1.1972773.
15. ^ "To Everywhere in 42 Minutes". Time. February 11, 1966. Archived from the original on 12 May 2008. Retrieved 2008-05-18.
16. ^ "Jumping into a 7,965 mile deep hole". Archived from the original on June 2, 2008. Retrieved 2008-05-18.
17. ^ 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.
18. ^ Lee Middleton; Jayanthi Sivaswamy (2002). "Framework for practical hexagonal-image processing". Journal of Electronic Imaging. 11 (104). doi:10.1117/1.1426078. Retrieved January 17, 2010.
19. ^ "Maximum password age". Microsoft TechNet. Retrieved 15 January 2014.
20. ^ Niiya, Brian. Japanese American history: an A-to-Z reference from 1868 to the present. Facts on File, Inc., 1993, p. 352
21. ^ Joel Primack; Nancy E. Abrams. "In A Beginning...Quantum Cosmology and Kabbalah" (PDF). Retrieved 2008-03-14.
22. ^ Gill, Peter (February 3, 2011). "42: Douglas Adams' Amazingly Accurate Answer to Life the Universe and Everything". London: Guardian. Retrieved 3 April 2011.
23. ^ Lewis Carroll and Douglas Adams
24. ^ The Mystery of Lewis Carroll, Jenny Woolf
25. ^ a b
26. ^ What Lewis Carroll Taught Us: Alice's creator knew all about role-playing. by Seth Lerer, March 4, 2010
27. ^ "Watson Jeopardy! computer: Ken Jennings describes what it's like to play against a machine.". Slate. Retrieved 2 October 2015.
28. ^ Parker, Lara (August 17, 2015). "I Went To Sydney To Find P. Sherman 42 Wallaby Way". BuzzFeed. Retrieved June 6, 2016.
29. ^ "42: Neues KI-Start-up von Jajah-Gründer Daniel Mattes". Futurezone. Retrieved 2015-11-22.
30. ^ http://scienceblogs.com/startswithabang/2009/08/31/paper-folding-to-the-moon/