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57 (number)

From Wikipedia, the free encyclopedia
(Redirected from Grothendieck prime)
← 56 57 58 →
Cardinalfifty-seven
Ordinal57th
(fifty-seventh)
Factorization3 × 19
Divisors1, 3, 19, 57
Greek numeralΝΖ´
Roman numeralLVII
Binary1110012
Ternary20103
Senary1336
Octal718
Duodecimal4912
Hexadecimal3916

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

In mathematics

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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

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Astronomy

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In fiction and media

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In films

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  • 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

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  • 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

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In radio

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In television

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In food

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  • 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

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  • "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

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  • The number of the French department Moselle

In places

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In transportation and vessels

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In other fields

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See also

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References

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  1. ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society, 54 (9): 1122–1134, MR 2349532
  5. ^ 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.
  6. ^ 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.
  7. ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993