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 42
^{2} + 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
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
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 sports
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
Historical years
Notes
- J. B. Conrey & A. Ghosh, "A conjecture for the sixth power
moment of the Riemann zeta-function" International Mathematics
Research Notices (1998)
- J. B. Conrey & S. M. Gonek, "High moments of the Riemann
zeta-function" Duke Math J. 107 3 (2001):
577 – 604
- 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
- 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."
- 42: Forty Two Up at IMDB
- Allpar: Richard Petty and a history of Petty
Racing