57 (number)

← 56 57 58 →
← 50 51 52 53 54 55 56 57 58 59 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifty-seven
Ordinal	57th (fifty-seventh)
Factorization	3 × 19
Divisors	1, 3, 19, 57
Greek numeral	ΝΖ´
Roman numeral	LVII, 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

57 is semiprime, ^[1] a Blum integer, ^[2] and a Leyland number. ^[3]

The split Lie algebra E_⁠7+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 in which the mathematician Alexander Grothendieck gave it as an example of a prime number, not realizing it was divisible by three. ^[5] The same error was made by another famous mathematician, Hermann Weyl, in a published article. ^[6]

In science

• The atomic number of lanthanum (La), the first of the lanthanides

Astronomy

• 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

• Passenger 57 , a film starring Wesley Snipes
• Agent 57 is the name of the master of disguise in the television series Danger Mouse
• West 57 was a weekly news-magazine show on CBS, 1985–89, hosted by Meredith Vieira
• Studio 57 was a dramatic anthology series in 1954, starring Brian Keith and Carolyn Jones

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

See also

• List of highways numbered 57

References

1. Sloane, N. J. A. (ed.). "SequenceA001358(Semiprimes (or biprimes): products of two primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA016105(Blum integers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA076980(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. An old conjecture of Goldbach's maintains that there even come along again and again pairs of primes of the smallest possible difference 2, like 57 and 59.
7. The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993