57 (fifty-seven) is the natural number following 56 and preceding 58. It is a composite number.
In mathematics
57 has prime factorization <math>3\cdot19</math>, and is therefore a semiprime. Its proper divisors are 1, 3, and 19, whose sum is 23, so 57 is a deficient number. Since both prime factors are congruent to 3 modulo 4, <math>57=3\cdot19</math> is a Blum integer. It is a Leyland number, because <math>57 = 2^5 + 5^2</math>.
The split Lie algebra E<sub></sub> has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E<sub>8</sub> is also 57-dimensional.
Although fifty-seven is not prime, it is jokingly known as the Grothendieck prime after a legend in which the mathematician Alexander Grothendieck gave it as an example of a prime number, not realizing it was divisible by three and nineteen. The same error was made by another famous mathematician, Hermann Weyl, in a published article.