# 57 (number)

 ← 56 57 58 →
Cardinalfifty-seven
Ordinal57th
(fifty-seventh)
Factorization3 × 19
Divisors1, 3, 19, 57
Greek numeralΝΖ´
Roman numeralLVII
Binary1110012
Ternary20103
Senary1336
Octal718
Duodecimal4912

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

## In mathematics

Fifty-seven is the sixteenth discrete semiprime, and the fourth discrete bi-prime pair with 58. It is a Blum integer since its two prime factors are both Gaussian primes.[1] It is also an icosagonal (20-gonal) number and a repdigit in base-7 (111).[2][3]

57 is the fourth Leyland number, as it can be written in the form:[4]

${\displaystyle 5^{2}+2^{5}=57}$

57 is the number of compositions of 10 into distinct parts.[5]

With an aliquot sum of 23, fifty-seven is the first composite member of the 23-aliquot tree.

57 is the seventh fine number, equivalently the number of ordered rooted trees with seven nodes having root of even degree.[6]

In geometry, there are:

57 lies between prime numbers 53 and 61, which are the only two prime numbers less than 71 that do not divide the order of any sporadic group, inclusive of the six pariahs. 71 is the largest supersingular prime that divides such groups.

Although fifty-seven is not prime, it is jokingly known as the "Grothendieck prime" after a story in which mathematician Alexander Grothendieck supposedly gave it as an example of a particular prime number. This story is repeated in Part 2 of a biographical article on Grothendieck in Notices of the American Mathematical Society.[10]

## In fiction and media

### In films

• Passenger 57, a film starring Wesley Snipes
• In the movie Contagion, Vaccine #57 successfully protects the lab monkey from infection.
• The Terminal (2004) starring Tom Hanks. There are 57 members of the jazz band that Viktor Navorski carries a picture of with him.

### In games

• In the game Hollow Knight, a character named Zote the Mighty has 57 precepts, all of which offer rather humorous, lackluster, or completely bad advice to the player.

## In food

• Heinz 57, a brand of sauce, and the number of varieties of foods claimed to be produced by the H.J. Heinz Company

## In music

• "Incident on 57th Street", a song by Bruce Springsteen and the E Street Band, from their 1973 album, The Wild, the Innocent and the E Street Shuffle
• "57 Channels (And Nothin' On)", a song by Bruce Springsteen, from his 1992 album Human Touch
• "57", the name of a song by Biffy Clyro on their 2002 debut album, Blackened Sky
• Shure SM57, considered the workhorse of recording microphones

## In organizations

• The number of the French department Moselle

## References

1. ^ "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ Sloane, N. J. A. (ed.). "Sequence A051872 (20-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ Sloane, N. J. A. (ed.). "Sequence A048332 (Numbers that are repdigits in base 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-30.
4. ^ "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
6. ^ Sloane, N. J. A. (ed.). "Sequence A000957 (Fine's sequence (or Fine numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-01.
7. ^ Skilling, J. (1975). "The complete set of uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. 278 (1278): 111–135. Bibcode:1975RSPTA.278..111S. doi:10.1098/rsta.1975.0022. ISSN 0080-4614. JSTOR 74475. MR 0365333. S2CID 122634260.
8. ^ Coxeter, H. S. M. (1982), "Ten toroids and fifty-seven hemidodecahedra", Geometriae Dedicata, 13 (1): 87–99, doi:10.1007/BF00149428, MR 0679218, S2CID 120672023
9. ^ Vogan, David (2007), "The character table for E8" (PDF), Notices of the American Mathematical Society, 54 (9): 1122–1134, MR 2349532
10. ^ Jackson, Allyn (November 2004). "Comme Appelé du Néant—As if Summoned from the Void: The Life of Alexandre Grothendieck" (PDF). Notices of the American Mathematical Society. 51 (10).
11. ^ The NGC / IC Project - Home of the Historically Corrected New General Catalogue (HCNGC) since 1993