55 (number)

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:

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It is also the fourth centered nonagonal number,^[5] and the third centered icosahedral number.^[6]

In decimal, 55 is a Kaprekar number,^[7] 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 [math]\displaystyle{ 55 = 5 \times 11 }[/math] are the respectively the third and fifth, where the first two Fermat primes of the form [math]\displaystyle{ 2^{2^n} + 1 }[/math] are [math]\displaystyle{ 3 }[/math] and [math]\displaystyle{ 5 }[/math]^[8] (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^[9] is the fourth such prime number.^[8] The base-ten digit representation of the latter satisfies a subtractive concatenation of [math]\displaystyle{ 7 - 2 = 5 }[/math], wherein 77 is the fifty-fifth composite number.^{[10][lower-alpha 1]}

In decimal representation, the fifth and largest known Fermat prime is 65537,^[8] which contains a "55" string inside (and where as a number, 637 is the eleventh non-trivial decagonal number).^[11]

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

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