57 (number)

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

In mathematics

57 has prime factorization $3\cdot 19$, 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, $57=3\cdot 19$ is a Blum integer. It is a Leyland number, because $57=2^5+5^2$.

The split Lie algebra [[E7½|E_{Template:Sfrac}]] has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E₈ 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.