57 (number)
(Redirected from Grothendieck prime)
| ||||
|---|---|---|---|---|
| Cardinal | fifty-seven | |||
| Ordinal | 57th (fifty-seventh) | |||
| Factorization | 3 × 19 | |||
| Divisors | 1, 3, 19, 57 | |||
| Greek numeral | ΝΖ´ | |||
| Roman numeral | LVII | |||
| Binary | 1110012 | |||
| Ternary | 20103 | |||
| Senary | 1336 | |||
| Octal | 718 | |||
| Duodecimal | 4912 | |||
| Hexadecimal | 3916 | |||
57 (fifty-seven) is the natural number following 56 and preceding 58. It is a composite number.
In mathematics
[edit]57 is semiprime[1] a Blum integer,[2] and a Leyland number.[3]
The split Lie algebra E7+1/2 has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.[4]
Although fifty-seven is not prime, it is jokingly known as the Grothendieck prime after a legend according to which the mathematician Alexander Grothendieck supposedly gave it as an example of a particular prime number.[5] The joke is that he is famous for working abstractly, without concrete examples. However, while the veracity of this legend about Grothendieck is unclear, it is known that this very error was committed by another famous mathematician Hermann Weyl in a published article.[6]
In science
[edit]- The atomic number of lanthanum (La), the first of the lanthanides
Astronomy
[edit]- 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.[7]
In fiction and media
[edit]In films
[edit]- 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
[edit]- 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
[edit]- 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
[edit]- The Fabulous 57 were disk jockeys on WMCA 570 Radio, New York City during the 1960s
In television
[edit]- 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
- 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
[edit]- 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
[edit]- "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
[edit]- The number of the French department Moselle
In places
[edit]- Carnegie Hall is on West 57th Street in New York City
In transportation and vessels
[edit]- 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
[edit]- The code for international direct dial phone calls to Colombia is 57.
- The number of the laps of the Bahrain Grand Prix.
See also
[edit]References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society, 54 (9): 1122–1134, MR 2349532
- ^ Jackson, Allyn (2004b). "Comme Appelé du Néant—As if Summoned from the Void: The Life of Alexandre Grothendieck" (PDF). Notices of the American Mathematical Society. 51 (10). Providence, RI: American Mathematical Society: 1196, 1197. MR 2104915. Zbl 1168.01339.
- ^ Weyl, Hermann (1951). "A Half-Century of Mathematics". American Mathematical Monthly. 58 (5). Washington, D.C.: Mathematical Association of America: 532. doi:10.1080/00029890.1951.11999734. JSTOR 2306319. S2CID 126101329.
- ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993