Fifty-seven is the sixteenth discrete semiprime and the sixth in the (3.q) 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 Grothendieck advances it as an example of a particular prime number.
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 (111).
Ah yes, that old Grothendiek prime joke makes me laugh every time!