55 (number)

Short description: Natural number

| <- 54  | 55 |  56 ->

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← 50 51 52 53 54 55 56 57 58 59 →

List of numbers — Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal| fifty-five
Ordinal| 55th
(fifty-fifth)
Factorization| 5 × 11
Divisors| 1, 5, 11, 55
Greek numeral| ΝΕ´
Roman numeral| LV
Binary| 1101112
Ternary| 20013
Quaternary| 3134
Quinary| 2105
Senary| 1316
Octal| 678
Duodecimal| 4712
Hexadecimal| 3716
Vigesimal| 2F20
Base 36| 1J36

55 (fifty-five) is the natural number following 54 and preceding 56.

## Contents

* 1 Mathematics
* 1.1 Fermat primes
* 2 Science
* 2.1 Astronomy
* 3 Music
* 4 Transportation
* 5 Film
* 6 Years
* 7 Other uses
* 8 See also
* 9 References

## Mathematics

55 is the fifteenth discrete semiprime,[1] and the second with 5 as the lowest non-unitary factor. Thus, of the form 5 × q with q a higher prime, in this case equal to 11.

It contains an aliquot sum of 17; the seventh prime number, within an aliquot sequence of one composite number (55, 17, 1, 0) that is rooted in the 17-aliquot tree.

55 is the tenth Fibonacci number.[2] It is the largest Fibonacci number to also be a triangular number (the tenth as well);[3] it is furthermore the fourth doubly triangular number.[4]

55 is also an early member inside other families of polygonal numbers; it is strictly (when including 0 as the zeroth indexed member) the fifth:

* heptagonal number,[5] and
* square pyramidal number (the sum of the squares of the integers from 1 to 5).[6]

It is also the fourth centered nonagonal number,[7] and the third centered icosahedral number.[8]

In decimal, 55 is a Kaprekar number,[9] whose digit sum is also 10. It is the first number to be a sum of more than one pair of numbers which mirror each other (23 \+ 32 and 14 \+ 41).

### Fermat primes

The prime indices in the prime factorization of 55=5×11 are the respectively the third and fifth, where the first two Fermat primes of the form 22n+1 are 3 and 5[10] (11 is also the third super-prime).

Where 17 — the aliquot part of 55 — is the third Fermat prime, the fifty-fifth prime number 257[11] is the fourth such prime number.[10] The base-ten digit representation of the latter satisfies a subtractive concatenation of 7−2=5, wherein 77 is the fifty-fifth composite number.[12][lower-alpha 1]

In decimal representation, the fifth and largest known Fermat prime is 65537,[10] which contains a "55" string inside (and where as a number, 637 is the eleventh non-trivial decagonal number).[13]

## Science

* The atomic number of caesium.

### Astronomy

* Messier object M55, a magnitude 7.0 globular cluster in the constellation Sagittarius
* The New General Catalogue object NGC 55, a magnitude 7.9 barred spiral galaxy in the constellation Sculptor

## Music

* The name of a song by Kasabian. The song was released as a B side to Club Foot and was recorded live when the band performed at London's Brixton Academy.
* "55", a song by Mac Miller
* "I Can't Drive 55", a song by Sammy Hagar
* "Ol' '55", a song by Tom Waits
* Ol' 55 (band), an Australian rock band.
* Primer 55 an American band
* Station 55, an album released in 2005 by Cristian Vogel
* 55 Cadillac, an album by Andrew W.K.

## Transportation

* In the United States, the National Maximum Speed Law prohibited speed limits higher than 55 miles per hour (90 km/h) from 1974 to 1987

## Film

* 55 Days at Peking a film starring Charlton Heston and David Niven

## Years

* AD 55
* 55 BC
* 1755
* 1855
* 1955

## Other uses

* Gazeta 55, an Albanian newspaper
* Agitation and Propaganda against the State, also known as Constitution law 55, a law during Communist Albania.
* The code for international direct dial phone calls to Brazil
* A 55-gallon drum for containing oil, etc.
* The Élysée, the official residency of the French Republic president, which address is 55 rue du Faubourg-Saint-Honoré in Paris.

## See also

* 55th Regiment of Foot (disambiguation)
* Channel 55 (disambiguation)
* Type 55 (disambiguation)
* Class 55 (disambiguation)
* List of highways numbered 55

## References

1. ↑ 77 is the twenty-second discrete (square-free) semiprime, and 55 is the fifteenth, where 15 is equivalent to the product of 3 × 5, and as such the fourth discrete semiprime.[1]

1. ↑ 1.0 1.1 Sloane, N. J. A., ed. "Sequence A006881 (Squarefree semiprimes: Numbers that are the product of two distinct primes.)". OEIS Foundation. https://oeis.org/A006881. Retrieved 2023-11-04.
2. ↑ "Sloane's A000045 : Fibonacci numbers". OEIS Foundation. https://oeis.org/A000045.
3. ↑ Sloane, N. J. A., ed. "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n.)". OEIS Foundation. https://oeis.org/A000217. Retrieved 2023-11-06.
4. ↑ "Sloane's A000217 : Triangular numbers". OEIS Foundation. https://oeis.org/A000217.
5. ↑ "Sloane's A000566 : Heptagonal numbers". OEIS Foundation. https://oeis.org/A000566.
6. ↑ "Sloane's A000330 : Square pyramidal numbers". OEIS Foundation. https://oeis.org/A000330.
7. ↑ "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". OEIS Foundation. https://oeis.org/A060544.
8. ↑ Sloane, N. J. A., ed. "Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.)". OEIS Foundation. https://oeis.org/A005902. Retrieved 2023-12-29.
9. ↑ "Sloane's A006886 : Kaprekar numbers". OEIS Foundation. https://oeis.org/A006886.
10. ↑ 10.0 10.1 10.2 Sloane, N. J. A., ed. "Sequence A000215 (Fermat numbers: a(n) equal to 2^(2^n) + 1.)". OEIS Foundation. https://oeis.org/A000215. Retrieved 2023-11-04.
11. ↑ Sloane, N. J. A., ed. "Sequence A000040 (The prime numbers.)". OEIS Foundation. https://oeis.org/A000040. Retrieved 2023-12-09.
12. ↑ Sloane, N. J. A., ed. "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". OEIS Foundation. https://oeis.org/A002808. Retrieved 2023-12-09.
13. ↑ Sloane, N. J. A., ed. "Sequence A001107 (10-gonal (or decagonal) numbers: a(n) equal to n*(4*n-3).)". OEIS Foundation. https://oeis.org/A001107. Retrieved 2023-12-09.

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