57 (number)

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

70811298
Cardinal seventy million eight hundred eleven thousand two hundred ninety-eight
Ordinal 70811298th
(seventy million eight hundred eleven thousand two hundred ninety-eighth)
Factorization 2 × 32× 3933961
Divisors 1, 3, 19, 57
Roman numeral N/A
Binary 1000011100001111110101000102
Ternary 112210201202112003
Quaternary 100320133222024
Quinary 1211114301435
Senary 110054220306
Octal 4160772428
Duodecimal 1B86A91612
Hexadecimal 4387EA216
Vigesimal 122B84I20
Base 36 165QCI36

In mathematics[edit]

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 12 has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.[6]

In science[edit]

Astronomy[edit]

In fiction and media[edit]

In films[edit]

  • 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 games[edit]

In literature[edit]

  • Summer of Fifty Seven, 2005 novel by Stephen C. Joseph, M.D. published by independent publisher Sunstone Press
  • 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 radio[edit]

In television[edit]

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
  • "Prop(osition) 57", one of a number of anti-ketchup packet groups on Facebook designed to bring attention to the shortcomings of take-out condiment packaging; its name is a reference to Heinz Co., which debuted a new design in test markets in early 2010[8]
  • A fast food dinner in Pereira, Colombia

In music[edit]

In organizations[edit]

In places[edit]

In transportation and vessels[edit]

In other fields[edit]

References[edit]

  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, MR 679218, doi:10.1007/BF00149428 .
  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
  8. ^ "After 40 years, Heinz revamps ketchup packets", AP, February 4, 2010