Fifty-seven is the sixteenth discrete
semiprime[1] (specifically, the sixth distinct semiprime of the form , where is a strictly larger prime).[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 story in which mathematician
Alexander Grothendieck supposedly gave it as an example of a particular prime number. This story is repeated in Part II of a biographical article on Grothendieck in Notices of the American Mathematical Society.[20] However, its veracity is questionable, and it may be a confounded misattribution of the same blunder committed to writing by
Hermann Weyl.[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.