27 (number)

27 (number)
27 (twenty-seven; Roman numeral XXVII) is the natural number following 26 and preceding 28.
In mathematics
Twenty-seven is equal to the cube of three: ; also 23 (see tetration). It is divisible by the number of prime numbers below it (9).
In decimal, 27 is the first composite number not divisible by any of its digits. In base ten, it is also
It is also the first non-trivial decagonal number.
27 has a prime aliquot sum of 13 (the sixth prime number) in the aliquot sequence (27, 13, 1, 0) of only one composite number, rooted in the 13-aliquot tree.
Whereas the composite index of 27 is 17 (the cousin prime to 13), 7 is the prime index of 17; a prime reciprocal magic square based on multiples of has a magic constant of 27.
In the Collatz conjecture (i.e. the problem), a starting value of 27 requires 3 × 37 = 111 steps to reach 1, more than any smaller number.
The next two larger numbers to require more steps are 54 and 55, where the fourteenth prime number (43) requires twenty-seven steps to reach 1.
Including the null-motif, there are 27 distinct hypergraph motifs.
There are exactly twenty-seven straight lines on a smooth cubic surface, which give a basis of the fundamental representation of Lie algebra .
The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions is 27-dimensional; its automorphism group is the 52-dimensional exceptional Lie algebra
There are twenty-seven sporadic groups, if the non-strict group of Lie type (with an irreducible representation that is twice that of in 104 dimensions) is included.
In Robin's theorem for the Riemann hypothesis, twenty-seven integers fail to hold for values where is the Euler–Mascheroni constant; this hypothesis is true if and only if this inequality holds for every larger
Base-specific
In base ten, if one cyclically rotates the digits of a three-digit number that is a multiple of 27, the new number is also a multiple of 27. For example, 378, 783, and 837 are all divisible by 27.
In similar fasion, any multiple of 27 can be mirrored and spaced with a zero each for another multiple of 27 (i.e. 27 and 702, 54 and 405, and 378 and 80703 are all multiples of 27).
Any multiple of 27 with "000" or "999" inserted yields another multiple of 27 (20007, 29997, 50004, and 59994 are all multiples of 27).
In base 6 (senary), one can readily test for divisibility by 43 (decimal 27) by seeing if the last three digits of the number match 000, 043, 130, 213, 300, 343, 430, or 513.
27 is located at the twenty-eighth (and twenty-ninth) digit after the decimal point in :
If one starts counting with zero, 27 is the second self-locating string after 6, of only a few known.
In science
The atomic number of cobalt.
Dark matter is thought to make up 27% of the universe.
27 is the number of bones in the human hand.
Astronomy
The Messier object M27, a magnitude 7.5 planetary nebula in the constellation Vulpecula, also known as the Dumbbell Nebula.
The New General Catalogue object NGC 27, a spiral galaxy in the Andromeda constellation.
The Saros number of the solar eclipse series, which began on March 9, 1993, BCE and ended on April 16, 713 BCE. The duration of Saros series 27 was 1,280.1 years, and it contained 72 solar eclipses. Further, the Saros number of the lunar eclipse series, which began on July 28, 1926, BCE and ended on January 23, 411 BCE. The duration of Saros series 27 was 1532.5 years, and it contained 86 lunar eclipses.
Electronics
The type 27 vacuum tube (valve), a triode introduced in 1927, was the first tube mass-produced for commercial use to incorporate an indirectly heated cathode. This made it the first vacuum tube that could function as a detector in AC-powered radios. Prior to the introduction of the 27, home radios were powered by a set of three or more storage batteries with voltages of 3 volts to 135 volts.
In language and literature
The number of letters in the Spanish alphabet.
The number of books in the New Testament.
The total number of letters in the Hebrew alphabet (22 regular letters and 5 final consonants).
Alternate name for The Hunt, a book by William Diehl.
Abbé Faria's prisoner number in the book The Count of Monte Cristo.
In Stephen King's novel It, It returns every 27 years to Derry.
In astrology
27 Nakṣatra or lunar mansions in Hindu astrology.
In art
Movies
Summer, or 27 Missing Kisses
Chapter 27-I
27 Dresses
Number 27 (written by Michael Palin)
The 27th Day (Science Fiction Film from 1957)
Music
"27", a song by Fall Out Boy on the album Folie à Deux
"27", a song by Passenger on the album Whispers
"27", a song by Title Fight on the album Shed.
"27", a song by Biffy Clyro on the album Blackened Sky
"27", a song on Machine Gun Kelly's album Bloom
"27 Jennifers", a song by Mike Doughty on the album Rockity Roll
27, an album by South Korean singer Kim Sung-kyu
27, an album by Argentine rock band Ciro y los Persas
Twenty-Seven, an album by The Adicts.
French rapper Kaaris' signature number is 27, from his zip code 93270.
"Twenty Seven Strangers" by Villagers.
27, a Boston-based band
27, an opera by composer Ricky Ian Gordon and librettist Royce Vavrek
27 Club, a list of popular musicians, artists, or actors who died at age 27
"Weird Al" Yankovic has a recurring joke involving the number 27, which is used in several songs.
Other
The Minneapolis-based artist Deuce 7 (a.k.a. Deuce Seven, Twenty Seven, 27).
In sports
The value of all the colors in snooker add up to 27.
The number of outs in a regulation baseball game for each team at all adult levels, including professional play, is 27.
The New York Yankees have won 27 World Series championships, the most of any team in the MLB.
In other fields
Twenty-seven is also:
A-27, American attack aircraft.
The code for international direct-dial phone calls to South Africa.
The name of a cigarette, Marlboro Blend No. 27.
The number of the French department Eure.
See also
List of highways numbered 27
List of highways numbered 27A
References
Further reading
Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987), p. 106.
External links
Prime Curios! 27 from the Prime Pages
Mystery of the number 27 - Large collection of 27 related trivia and facts.
The 27 Project - collection of sightings of 27 in movies, TV, culture and art
Integers