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57 (number)

 ← 56 57 58 →
Cardinalfifty-seven
Ordinal57th
(fifty-seventh)
Factorization3 × 19
Divisors1, 3, 19, 57
Greek numeralΝΖ´
Roman numeralLVII
Binary1110012
Ternary20103
Quaternary3214
Quinary2125
Senary1336
Octal718
Duodecimal4912
Vigesimal2H20
Base 361L36

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

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In mathematics

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.[1]

As a semiprime, 57 is a Blum integer since its two prime factors are both Gaussian primes.[2]

57 is a 20-gonal number.[3] It is a Leyland number since 25 + 52 = 57.[4]

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.[5] The 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.[6]

In fiction and media

In films

• 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.

In literature

• 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.

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

References

1. ^ 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).
2. ^ "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A051872 : 20-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ Coxeter, H. S. M. (1982), "Ten toroids and fifty-seven hemidodecahedra", Geometriae Dedicata, 13 (1): 87–99, doi:10.1007/BF00149428, MR 0679218
6. ^ Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society, 54 (9): 1122–1134, MR 2349532
7. ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993