Fifty-seven is the sixteenth discrete
semiprime[1] (specifically, the sixth semiprime of the form , where is a prime strictly larger than 3).[2] It also forms the fourth discrete semiprime pair with
58.
57 is the third
Blum integer since its two prime factors (
3 and
19) are both
Gaussian primes.[3] 57 has an
aliquot sum of
23, which makes it the tenth number to contain a prime aliquot sum.[4] This also makes 57 the first composite member of the 23-aliquot tree (..., 57, 23,
1,
0). The only other numbers to generate an aliquot sum of 57 are
99,
159,
343, 559, and
703;[5] where 343 is the
cube of
7,[6] and 703 the sum of the first thirty-seven nonzero integers.[7] Fifty-seven is also a
repdigit in base-7 (111).[8]
57 is the fifth
Leyland number, as it can be written in the form:[9]
57 is the number of compositions of
10 into distinct parts.[10]
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.[20]
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.[21]
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
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
In Rudyard Kipling's short story "
The Man Who Would Be King", the character Peachy states: "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.