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
- The movie Contagion (film) 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.
- 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
- The number of the French department Moselle
- 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