57 (number)

57
Cardinal fifty-seven
Ordinal 57th
(fifty-seventh)
Factorization 3 \cdot 19
Divisors 1, 3, 19, 57
Roman numeral LVII
Binary 1110012
Octal 718
Duodecimal 4912
Hexadecimal 3916

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

Contents

In mathematics

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 Grothendieck supposedly gave it as an example of a particular prime number.[1]

As a semiprime, 57 is a Blum integer since its two prime factors are both Gaussian primes.

57 is a 20-gonal number. It is a Leyland number since 25 + 52 = 57.

57 is a repdigit in base 7 (111).

See also 57-cell.

In science

Astronomy

In music

In fiction and media

In other fields

Fifty-seven is:

Historical years

AD 57, 57 BC, 1957, 2057, etc.

References

  1. ^ This story is repeated in Part 2 of the AMS Notices biographical article on Grothendieck (Notices, Vol. 51, No. 10, November 2004; the article is available here).
  2. ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993
  3. ^ NASA - Catalog of Solar Eclipse Saros 57
  4. ^ NASA - Lunar Eclipses of Saros Series 1 to 175
  5. ^ "After 40 years, Heinz revamps ketchup packets", AP, Feb. 4, 2010