# 57 (number)

 ← 56 57 58 →
Cardinal fifty-seven
Ordinal 57th
(fifty-seventh)
Factorization 3 × 19
Divisors 1, 3, 19, 57
Roman numeral LVII
Binary 1110012
Ternary 20103
Quaternary 3214
Quinary 2125
Senary 1336
Octal 718
Duodecimal 4912
Vigesimal 2H20
Base 36 1L36

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

## 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 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.

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

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.[2] The Lie algebra E has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.[3]

## In fiction and media

### In films

• In the first storyboard draft for Pixar's film Cars, the main character, a race car named Lightning McQueen was going to have number 57 as his racing number, in reference to director John Lasseter's birthdate, January 12, 1957. But in the final cut, Lightning's racing number changed to 95.
• The climax of the movie Eraser occurs on Pier 57
• C-57D is the designation of the spaceship featured in the movie Forbidden Planet, and is referenced in the movie Serenity as well.
• Passenger 57, a film starring Wesley Snipes

### In literature

• Summer of Fifty Seven, 2005 novel by Stephen C. Joseph, M.D. published by independent publisher Sunstone Press
• Rudyard Kipling in The Man Who Would be King, short story, has his character Peachy state: "This business is our Fifty-Seven" after he and Daniel are discovered to be men, not gods. This alludes to the Indian Rebellion in 1857, or India's First War of Independence, against British Rule

## 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
• "Prop(osition) 57", one of a number of anti-ketchup packet groups on Facebook designed to bring attention to the shortcomings of take-out condiment packaging; its name is a reference to Heinz Co., which debuted a new design in test markets in early 2010[7]
• A fast food dinner in Pereira, Colombia

## In other fields

• The code for international direct dial phone calls to Colombia is 57.

## References

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. ^ Coxeter, H. S. M. (1982), "Ten toroids and fifty-seven hemidodecahedra", Geometriae Dedicata 13 (1): 87–99, doi:10.1007/BF00149428, MR 679218.
3. ^ Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society 54 (9): 1122–1134, MR 2349532.
4. ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993
5. ^ NASA - Catalog of Solar Eclipse Saros 57
6. ^ NASA - Lunar Eclipses of Saros Series 1 to 175
7. ^ "After 40 years, Heinz revamps ketchup packets", AP, February 4, 2010