57 (number) – Wikipedia

Natural number

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

In mathematics[edit]

Fifty-seven is the sixteenth discrete semiprime, and the fourth discrete bi-prime pair with 58. It is a Blum integer since its two prime factors are both Gaussian primes,^[1] and a repdigit in base-7 (111).^[2]

57 is the fifth Leyland number, as it can be written in the form:^[3]

${displaystyle 5^{2}+2^{5}=57}$

57 is the number of compositions of 10 into distinct parts.^[4]

With an aliquot sum of 23, fifty-seven is the first composite member of the 23-aliquot tree.

57 is the seventh fine number, equivalently the number of ordered rooted trees with seven nodes having root of even degree.^[5]

57 is also the number of nodes in a regular octagon when all of its diagonals are drawn,^[6] and the first non-trivial icosagonal (20-gonal) number.^[7]

In geometry, there are:

The split Lie algebra E_7+1/2 has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E₈ is also 57-dimensional.^[10]

57 lies between prime numbers 53 and 61, which are the only two prime numbers less than 71 that do not divide the order of any sporadic group, inclusive of the six pariahs. 71, the twentieth prime number, is the largest supersingular prime that divides the largest of these groups^[11] while 57, on the other hand, is the fortieth composite number whose sum of divisors σ(57) is 80 and averages 20.^[12][13]

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 2 of a biographical article on Grothendieck in
Notices of the American Mathematical Society.^[14]

In science[edit]

Astronomy[edit]

In fiction and media[edit]

In films[edit]

• Passenger 57, a film starring Wesley Snipes
• 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[edit]

• 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[edit]

In radio[edit]

In television[edit]

In food[edit]

• Heinz 57, a brand of sauce, and the number of varieties of foods claimed to be produced by the H.J. Heinz Company

In music[edit]

• “Incident on 57th Street”, a song by Bruce Springsteen and the E Street Band, from their 1973 album, The Wild, the Innocent and the E Street Shuffle
• “57 Channels (And Nothin’ On)”, a song by Bruce Springsteen, from his 1992 album Human Touch
• “57”, the name of a song by Biffy Clyro on their 2002 debut album, Blackened Sky
• Shure SM57, considered the workhorse of recording microphones

In organizations[edit]

• The number of the French department Moselle

In places[edit]

In transportation and vessels[edit]

In other fields[edit]

See also[edit]

References[edit]