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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).

## 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.

Fifty-seven is:

## Historical years

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

## References

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