55 (number)

← 54 55 56 →
← 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
Senary	1316
Octal	678
Duodecimal	4712
Hexadecimal	3716

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

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 $55=5\times 11$ are the respectively the third and fifth, where the first two Fermat primes of the form $2^{2^{n}}+1$ 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]^[a] 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

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.

References

^ 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]