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19 (number)

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19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

Cardinal 19
nineteen
Ordinal 19th
nineteenth
Factorization prime
Divisors 1, 19
Roman numeral XIX
Binary 10011
Hexadecimal 13

In mathematics

Nineteen is the 8th smallest prime number. The sequence continues 23, 29, 31, 37... 19 is the seventh Mersenne prime exponent.

It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 1, 9, 10, 19...

With respect to divisibility, nineteen has a very simple test: 19 divides 100a + b if and only if it divides a + 4b.

Nineteen is a centered triangular number, centered hexagonal number, and an octahedral number.

Every positive integer is the sum of at most nineteen fourth powers (see Waring's problem).

The decimal expansion of 1/19 has a period of maximum length: 18 digits.

Nineteen is a Heegner number and a strictly non-palindromic number.

19 is the fourth alternating factorial.

In science

Astronomy

In religion

In music

"19" is a 1985 hit song by Paul Hardcastle, with a strong anti-war message, based on 19 reportedly being the average age of United States soldiers killed in the Vietnam War (this is widely disputed). The song was parodied by British satirist Rory Bremner as N-n-nineteen, Not Out, the title referring to the English cricket team's risible performance against the West Indies in the previous year.

I Was Only 19 (A Walk in the Light Green), by the Australian group Redgum reached number one on the Australian charts in 1983, and a hip-hop version of the song produced by The Herd was voted in the top ten songs of 2005 by listeners of radio station Triple J.

Other songs with the number 19 in their titles:

"Nineteen" by the Old 97's
"Hey, Nineteen" by Steely Dan
"19th Nervous Breakdown" by the Rolling Stones
"Nineteen Forever" by Joe Jackson
Nineteen has been used as an alternative to twelve for a division of the octave into equal parts. This idea goes back to Salinas in the sixteenth century, and is interesting in part because it gives a system of meantone tuning, being close to 1/3 comma meantone.

In other fields

Nineteen is

Historical years

A.D. 19, 19 B.C., 1919, 2019, etc.

External links

 


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