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

In mathematics

Fifty-seven is the sixteenth discrete bi-prime 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).

See also 57-cell.

In science



Astronomy







  • The Saros cycle number of the lunar eclipse series which began on -823 April 16 and ended on 475 June 5. The duration of Saros series 57 was 1298.1 years, and it contained 73 lunar eclipses.


In music



In fiction and media



In other fields

Fifty-seven is:

Historical years

57 A.D., 57 B.C., 1957, 2057, etc.

References




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