19 (number)

Mathematics

19 is the eighth prime number. 19 forms a twin prime with 17, a cousin prime with 23, and a sexy prime with 13. 19 is a strictly non-palindromic number in any base, and a Heegner number. 19 is the maximum number of fourth powers needed to sum up to any natural number (see, Waring's problem). It is the number of compositions of 8 into distinct parts.

The number of nodes in regular hexagon with all diagonals drawn is nineteen.

• The only nontrivial normal magic hexagon is composed of nineteen cells, where every diagonal of consecutive hexagons has sums equal to 38, or twice 19.
• A hexaflexagon is a strip of nineteen alternating triangular faces that can flex into a regular hexagon, such that any two of six colorings on triangles can be oriented to align on opposite sides of the folded figure. \tfrac {1} {19} can be used to generate the first full, non-normal prime reciprocal magic square in decimal whose rows, columns and diagonals — in a 18 x 18 array — all generate a magic constant of 81 = 92.

Finite simple groups

19 is a supersingular prime, a member in the sequence of fifteen such primes that divide the order of the Friendly Giant \mathrm {F_{1}}. Additionally, 19 also divides the orders of the Janko groups \mathrm {J_{1}} and \mathrm {J_{3}}.

Science

• The James Webb Space Telescope's optical elements are in an array of 19 hexagons, wherein 18 segmented primary mirrors focus light into a centered secondary mirror situated above the collecting mirrors, that in-turn reflects back onto the telescope's central imagers. It is a shape akin to the order-3 magic hexagon.
• The Metonic cycle is almost exactly 19 years long.

Religion

Islam

• The number of angels guarding Hell ("Hellfire") ("Saqar") according to the Qur'an: "Over it are nineteen" (74:30),after which the Qur'an describes this number as being "a trial for those who disbelieve" (74:31), a sign for people of the scripture to be "convinced" (74:31) and that believers "will increase in faith" (74:31) due to it.
• The Number of Verse and Sura together in the Qur'an which announces Jesus son of Maryam's (Mary's) birth (Qur'an 19:19).

Baháʼí Faith

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

• The Baháʼí calendar is structured such that a year contains 19 months of 19 days each (along with the intercalary period of Ayyám-i-Há), as well as a 19-year cycle and a 361-year (19x19) supercycle.
• The Báb and his disciples formed a group of 19.
• There were 19 Apostles of Bahá'u'lláh.

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.

Music

• 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. See 19 equal temperament.
• Some organs use the 19th harmonic to approximate a minor third.

Literature

• Stephen King's eight-book epic The Dark Tower saga employs the number 19 in books The Dark Tower: The Gunslinger, The Dark Tower V: Wolves of the Calla, The Dark Tower VI: Song of Susannah, The Dark Tower VII: The Dark Tower, and The Wind Through the Keyhole as a mysterious and important number. They refer to the "ka-tet of 19", "Directive Nineteen," many names add up to 19, 19 seems to permeate every aspect of Roland and his traveler's lives. In addition, the number ends up being a powerful key.

Games

• Though the maximum score for a cribbage hand is 29, there is no combination of cards that adds up to 19 points. Many cribbage players, therefore, jokingly refer to a zero-point hand as "a 19 hand".

Age 19

• In four countries (Algeria, South Korea, United States (Alabama and Nebraska), and Canada), 19 is the age of majority.
• In two countries (South Korea and Canada), 19 is the minimum legal drinking age.
• In three countries (Algeria, South Korea, and Canada), 19 is the minimum legal smoking age.
• The minimum age for the NBA draft is 19 years old.

In sports

• In golf, the '19th hole' is the clubhouse bar and in match play, if there is a tie after 18 holes, an extra hole(s) is played. In miniature golf, it is an extra hole on which the winner earns an instant prize.

References

References

1. {{Cite OEIS. A006512. Greater of twin primes.
2. {{Cite OEIS. A088762. Numbers n such that (2n-1, 2n+3) is a cousin prime pair.
3. {{Cite OEIS. A046117. Primes p such that p-6 is also prime. (Upper of a pair of sexy primes.)
4. {{Cite OEIS. A003173. heegner numbers
5. {{Cite OEIS. A002804. (Presumed) solution to Waring's problem.
6. {{Cite OEIS. A032020. Number of compositions of n such that no two adjacent parts are equal (Carlitz compositions).
7. {{Cite OEIS. A007569. Number of nodes in regular n-gon with all diagonals drawn.
8. Trigg, C. W.. (February 1964). "A Unique Magic Hexagon".
9. (January 2012). "Hexaflexagons". [[Taylor & Francis]].
10. Andrews, William Symes. (1917). "Magic Squares and Cubes". [[Open Court Publishing Company]].
11. {{Cite OEIS. A002267. The 15 supersingular primes.
12. (2006). "Symmetry and the Monster: One of the Greatest Quests of Mathematics". [[Oxford University Press]].
13. (2021). "Misteri Alam Malaikat". Pustaka al-Kautsar.
14. "Surah Al-Muddaththir - 30-31".
15. Blog, Quran Talk. (2020-09-17). "19 Angels or 19 Miracle". Quran Talk Blog.
16. "Surah Maryam - 19".
17. Sabah, Nassir. (2024-05-27). "Mary, Jesus, and the Number 19 in the Quran". Medium.
18. [https://www.mimosaspirit.com/blogs/news/brigit-triple-goddess-of-the-flame-health-hearth-the-forge Brigid: Triple Goddess of the Flame (Health, Hearth, & Forge)]