57 (number)


57 is the natural number following 56 and preceding 58.

In mathematics

Fifty-seven is the sixteenth discrete semiprime and the sixth in the 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.
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.
There are 57 vertices and 57 hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope. 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.

In science

In films

.* Passenger 57, a film starring Wesley Snipes