57 (number)

Last updated
56 57 58
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.

Contents

In mathematics

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 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

Astronomy

In fiction and media

In food

In music

In places

In transportation and vessels

See also

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 NéantAs 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