57 (number)

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

← 56 57 58 →
Cardinalfifty-seven
Ordinal57th
(fifty-seventh)
Factorization3 × 19
Divisors1, 3, 19, 57
Greek numeralΝΖ´
Roman numeralLVII
Binary1110012
Ternary20103
Octal718
Duodecimal4912
Hexadecimal3916

In mathematicsEdit

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 scienceEdit

AstronomyEdit

In fiction and mediaEdit

In filmsEdit

  • 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 gamesEdit

In literatureEdit

In radioEdit

In televisionEdit

In foodEdit

  • Heinz 57, a brand of sauce, and the number of varieties of foods claimed to be produced by the H.J. Heinz Company

In musicEdit

  • "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 organizationsEdit

  • The number of the French department Moselle

In placesEdit

In transportation and vesselsEdit

In other fieldsEdit

See alsoEdit

ReferencesEdit

  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, S2CID 120672023
  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