← 18 19 20 →
Cardinalnineteen
Ordinal19th
(nineteenth)
Numeral systemnonadecimal
Factorizationprime
Prime8th
Divisors1, 19
Greek numeralΙΘ´
Roman numeralXIX
Binary100112
Ternary2013
Octal238
Duodecimal1712
Hexadecimal1316

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

Mathematics

19 is a centered triangular number

19 is the 8th prime number, the seventh Mersenne prime exponent,[1] a Heegner number,[2] the second Keith number (and also the first Keith prime), and the second base-10 repunit prime exponent (for the number 1111111111111111111).[3]

The 19th triangular number is 190 (equivalently, the sum of the first 19 non-zero integers).[8] 19 is the first number in an infinite sequence of numbers whose digits start with 1 and have trailing 9's, that form triangular numbers containing trailing zeroes in proportion to 9s present in the original number; i.e. 19900 is the 199th triangular number, and 1999000 is the 1999th.[9]
Like 19, 199 and 1999 are also both prime, as are 199999 and 19999999. In fact, a number of the form 19n, where n denotes the number of nines that terminate in the number, is prime for n = 1, 2, 3, 5, 7, 26, 27, 53, 147, 236, 248, 386, 401.[10]

If the Tits group is included as a (nonstrict) group of Lie type,[12] then there are 19 finite simple groups that are not sporadic groups. In the Happy Family, 19 of 26 sporadic groups are subquotients of the Friendly Giant, also known as the Monster group.[13]

Science

The James Webb Space Telescope features a design of 19 hexagons.
The James Webb Space Telescope features a design of 19 hexagons.

Religion

Islam

Baháʼí faith

In the Bábí and Baháʼí Faiths, a group of 19 is called a Váhid, a Unity (Arabic: واحد wāhid, "one"). The numerical value of this word in the Abjad numeral system is 19.

Celtic paganism

19 is a sacred number of the goddess Brigid because it is said to represent the 19-year cycle of the Great Celtic Year and the amount of time it takes the Moon to coincide with the winter solstice.[14]

Music

Literature

Games

A 19x19 Go board
A 19x19 Go board

Age 19

In sports

Other fields

References

  1. ^ "Sloane's A000043 : Mersenne exponents". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  2. ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. ^ Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN 1475717385
  4. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  5. ^ Allcock, Daniel (11 July 2006). "Infinitely many hyperbolic Coxeter groups through dimension 19". Geometry & Topology. 10 (2): 737–758. arXiv:0903.0138. doi:10.2140/gt.2006.10.737. S2CID 14378861.
  6. ^ "Sloane's A125602 : Centered triangular numbers that are prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  7. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-13.
  9. ^ Sloane, N. J. A. "Sequence A186076". The On-line Encyclopedia of Integer Sequences. Retrieved 2022-07-13. Note that terms A186074(4) and A186074(10) have trailing 0's, i.e. 19900 = Sum_{k=0..199} k and 1999000 = Sum_{k=0..1999} k...". "This pattern continues indefinitely: 199990000, 19999900000, etc.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A055558 (Primes of the form 1999...999)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-26.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A068174 (Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. Here the property is be a prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-26.
  12. ^ R. B. Howlett; . J. Rylands; D. E. Taylor. "Matrix generators for exceptional groups of Lie type". Journal of Symbolic Computation. 31 (4): 429. doi:10.1006/jsco.2000.0431. ...for all groups of Lie type, including the twisted groups of Steinberg, Suzuki and Ree (and the Tits group).
  13. ^ John F.R. Duncan; Michael H. Mertens; Ken Ono (2017). "Pariah moonshine". Nature Communications. 8: 2 (Article 670). doi:10.1038/s41467-017-00660-y. ...so [sic] moonshine illuminates a physical origin for the monster, and for the 19 other sporadic groups that are involved in the monster.
  14. ^ Brigid: Triple Goddess of the Flame (Health, Hearth, & Forge)
  15. ^ Roush, Gary (2008-06-02). "Statistics about the Vietnam War". Vietnam Helicopter Flight Crew Network. Archived from the original on 2010-01-06. Retrieved 2009-12-06. Assuming KIAs accurately represented age groups serving in Vietnam, the average age of an infantryman (MOS 11B) serving in Vietnam to be 19 years old is a myth, it is actually 22. None of the enlisted grades have an average age of less than 20.