57 (fifty-seven) is the natural number following 56 and preceding 58.
In mathematics 57 has prime factorization 3 ⋅ 19 {\displaystyle 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 ⋅ 19 {\displaystyle 57=3\cdot 19} is a Blum integer. It is a Leyland number, because 57 = 2 5 + 5 2 {\displaystyle 57=2^{5}+5^{2}} . The split Lie algebra E7+1/2 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.
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