Number 57

57 (fifty-seven) is the natural number following 56 and preceding 58.

In mathematics

Fifty-seven is the sixteenth discrete semiprime, and the fourth discrete bi-prime pair with 58. It is a Blum integer since its two prime factors are both Gaussian primes. It is also an icosagonal (20-gonal) number and a repdigit in base-7 (111).

57 is the fourth Leyland number, as it can be written in the form:
:$5^ + 2^ = 57$

57 is the number of compositions of 10 into distinct parts.

With an aliquot sum of 23, fifty-seven is the first composite member of the 23-aliquot tree.

57 is the seventh fine number, equivalently the number of ordered rooted trees with ''seven'' nodes having root of even degree.

In geometry, there are:
*57 uniform star polyhedra in the third dimension, including four Kepler-Poinsot star polyhedra that are regular.
*57 vertices and hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope.
*57 uniform prismatic 5-polytopes in the fifth dimension based on four different finite prismatic families, and inclusive of one special non-Wythoffian figure: the grand antiprism prism.
*57 uniform prismatic 6-polytopes in the sixth dimension, as prisms of all non-prismatic uniform 5-polytopes.

The split Lie algebra E has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E₈ is also 57-dimensional.

57 lies between prime numbers 53 and 61, which are the only two prime numbers less than 71 that do not divide the order of any sporadic group, inclusive of the six pariahs. 71 is the largest supersingular prime that divides such groups.

Although fifty-seven is not prime, it is jokingly known as the "Grothendieck prime" after a story in which mathematician Alexander Grothendieck supposedly gave it as an example of a particular prime number. This story is repeated in Part 2 of a biographical article on Grothendieck in
''Notices of the American Mathematical Society''.

In science

*The atomic number of lanthanum (La), the first of the lanthanides

Astronomy

* Messier object M57, a magnitude 9.5 planetary nebula in the constellation Lyra, also known as the Ring Nebula
* The New General Catalogue object NGC 57, an elliptical galaxy in the constellation Pisces.The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993
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In fiction and media

In films

* ''Passenger 57'', a film starring Wesley Snipes
* In the movie '' Contagion'', Vaccine #57 successfully protects the lab monkey from infection.
* ''The Terminal'' (2004) starring Tom Hanks. There are 57 members of the jazz band that Viktor Navorski carries a picture of with him.

In games

* In the game ''Hollow Knight'', a character named Zote the Mighty has 57 precepts, all of which offer rather humorous, lackluster, or completely bad advice to the player.

In literature

* In Rudyard Kipling's short story "The Man Who Would Be King", the character Peachy states: "This business is our Fifty-Seven" after he and Daniel are discovered to be men, not gods. This alludes to the Indian Rebellion in 1857, or India's First War of Independence, against British Rule.
* B'hrian Bloodaxe, the first Low King of the dwarfs, killed 57 trolls in the legendary Battle of Koom Valley on ''Discworld'' (a fictional world created by author Terry Pratchett)

In radio

* The Fabulous 57 were disk jockeys on WMCA 570 Radio, New York City during the 1960s

In television

* Agent 57 is the name of the master of disguise in the television series ''Danger Mouse''
* ''Exit 57'', a sketch comedy show that aired on Comedy Central from 1995 to 1996 featured Stephen Colbert, Paul Dinello, Jodi Lennon, Mitch Rouse and Amy Sedaris
* The 57th Overlanders is a fictional brigade mentioned in the television series ''Firefly''.
* ''West 57'' was a weekly news-magazine show on CBS, 1985–89, hosted by Meredith Vieira
* The Cartoon Network program ''Metalocalypse'' has a fictional television station WHYK-57
* The ''Robot Chicken'' sketch "Pluto Nash Day" notes that 57 people at 20th Century Fox Studios died amid rioting and suicide
* A ''Robot Chicken'' parody of the NBC TV series ''Heroes'' uses the episode title "Chapter Fifty-seven: Uncle Glen"
* ''Studio 57'' was a dramatic anthology series in 1954, starring Brian Keith and Carolyn Jones

In food

*Heinz 57, a brand of sauce, and the number of varieties of foods claimed to be produced by the H.J. Heinz Company

In music

* "Incident on 57th Street", a song by Bruce Springsteen and the E Street Band, from their 1973 album, ''The Wild, the Innocent and the E Street Shuffle''
* " 57 Channels (And Nothin' On)", a song by Bruce Springsteen, from his 1992 album ''Human Touch''
* " 57", the name of a song by Biffy Clyro on their 2002 debut album, ''Blackened Sky''
* Shure SM57, considered the workhorse of recording microphones

In organizations

*The number of the French department Moselle

In places

*Carnegie Hall is on West 57th Street in New York City

In transportation and vessels

*The model name of a Maybach car
* USS ''Lake Champlain'' (CG 57), a Ticonderoga class cruiser in the United States Navy and the third ship to be named Lake Champlain

In other fields

*The code for international direct dial phone calls to Colombia is 57.
*The number of the laps of the Bahrain Grand Prix.

See also

* List of highways numbered 57

References

{{DEFAULTSORT:57 (Number)
Integers