57 (number)

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

In mathematics

Fifty-seven is the sixteenth discrete semiprime^[1] (specifically, the sixth semiprime of the form ${\displaystyle 3\cdot q}$, where ${\displaystyle q}$ is a prime strictly larger than 3).^[2] It also forms the fourth discrete semiprime pair with 58.

57 is the third

57 is the fifth Leyland number, as it can be written in the form:^[9]

${\displaystyle 5^{2}+2^{5}=57}$

57 is the number of compositions of 10 into distinct parts.^[10]

57 is the seventh

• 57 non-prismatic
  Kepler-Poinsot star polyhedra that are regular.^[14]
• 57 vertices and hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope.^[15]
• 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

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, the twentieth prime number, is the largest supersingular prime that divides the largest of these groups^[17] while 57, on the other hand, is the fortieth composite number whose sum of divisors σ(57) is 80 and averages 20.^[18][19]

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 II of a biographical article on Grothendieck in Notices of the American Mathematical Society.^[20] However, its veracity is questionable, and it may be a confounded misattribution of the same blunder committed to writing by Hermann Weyl.^[21]

In science

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

Astronomy

• 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.^[22]

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 the movie Eraser (1996), the weapons trade operation took place at the Baltimore Docks, Pier 57.

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 "
  India's First War of Independence
  , against British Rule.
• Battle of Koom Valley on Discworld (a fictional world created by author Terry Pratchett
  )

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

• 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
  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