# 19 number

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

 Template:Numbers 10s Cardinal nineteen Ordinal 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.

## In science

In astronomy,

Messier object M19, a magnitude 8.5 globular cluster in the constellation Ophiuchus
The New General Catalogue object NGC 19, a barred spiral galaxy in the constellation Andromeda
The Saros number of the solar eclipse series which began on -2333 June 15 and ended on -1035 August 1. The duration of Saros series 19 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number of the lunar eclipse series which began on -2031 March 24 and ended on -733 May 11. The duration of Saros series 19 was 1298.1 years, and it contained 73 lunar eclipses.

## In music

"19" is a 1985 hit song by Paul Hardcastle, with a strong anti-war message, based on 19 being the average age of soldiers in the Vietnam war.

Another acclaimed song with an anti-war sentiment is "I Was Only 19 (A Walk in the Light Green)", by the group Redgum. It reached number one on the Australian charts in 1983.

Other songs with the number in their titles include "Nineteen" by the Old 97's and "Hey, Nineteen" by Steely Dan.

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.

"19th Nervous Breakdown" is a song by the Rolling Stones.

Nineteen is

## In fiction

In Stephen King's The Dark Tower series, nineteen is a number of mystical significance, as the characters come to encounter it in some form everywhere they turn. King was nineteen-years-old when he began writing this magnum opus, which he didn't finish until almost thirty years later. In the books, the number 19 comes to denote a sense of unreality and foreboding, making the characters' world seem as unreal to them as to the reader.