|Factorization||3 × 19|
|Divisors||1, 3, 19, 57|
Fifty-seven is the sixteenth discrete semiprime and the sixth in the (3.q) family. With 58 it forms the fourth discrete bi-prime pair. 57 has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree. Although 57 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.
57 is a repdigit in base 7 (111).
There are 57 vertices and 57 hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope. The Lie algebra E7 1/ has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.
- 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.
In fiction and media
- In the first storyboard draft for Pixar's film Cars, the main character, a race car named Lightning McQueen was going to have number 57 as his racing number, in reference to director John Lasseter's birthdate, January 12, 1957. But in the final cut, Lightning's racing number changed to 95.
- The climax of the movie Eraser occurs on Pier 57
- C-57D is the designation of the spaceship featured in the movie Forbidden Planet, and is referenced in the movie Serenity as well.
- Passenger 57, a film starring Wesley Snipes
- The movie Contagion (film) Vaccine #57 successfully protects the lab monkey from infection.
- B'hrian Bloodaxe, the first Low King of the dwarfs, killed fifty-seven trolls in the legendary Battle of Koom Valley on Discworld (a fictional world created by author Terry Pratchett)
- In the game Hollow Knight, a character name Zote the Mighty has fifty-seven precepts, all of which offer rather humorous, lackluster, or completely bad advice to the player
- Rudyard Kipling in The Man Who Would be King, short story, has his character Peachy state: "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.
- 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 1995-96 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
- Heinz 57, a brand of sauce, and the number of varieties of foods claimed to be produced by the H.J. Heinz Company
- "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
- 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.
- Jackson, Allyn (November 2004). "Comme Appelé du Néant—As if Summoned from the Void: The Life of Alexandre Grothendieck" (PDF). Notices of the American Mathematical Society. 51 (10).
- "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A051872 : 20-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Coxeter, H. S. M. (1982), "Ten toroids and fifty-seven hemidodecahedra", Geometriae Dedicata, 13 (1): 87–99, doi:10.1007/BF00149428, MR 0679218
- Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society, 54 (9): 1122–1134, MR 2349532
- The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993