Home  

Random  

Nearby  



Log in  



Settings  



Donate  



About Wikipedia  

Disclaimers  



Wikipedia





19 (number)





Article  

Talk  



Language  

Watch  

Edit  





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

← 18 19 20 →

10 11 12 13 14 15 16 17 18 19

  • Integers
  • 0 10 20 30 40 50 60 70 80 90

    Cardinalnineteen
    Ordinal19th
    (nineteenth)
    Numeral systemnonadecimal
    Factorizationprime
    Prime8th
    Divisors1, 19
    Greek numeralΙΘ´
    Roman numeralXIX
    Binary100112
    Ternary2013
    Senary316
    Octal238
    Duodecimal1712
    Hexadecimal1316
    Hebrew numeralי"ט
    Babylonian numeral𒌋𒐝

    Mathematics

    edit
     
    19 is a centered triangular number.

    Nineteen is the eighth prime number.

    Number theory

    edit

    19 forms a twin prime with 17,[1]acousin prime with 23,[2] and a sexy prime with 13.[3] 19 is the fifth central trinomial coefficient,[4] and the maximum number of fourth powers needed to sum up to any natural number (see, Waring's problem).[5]

    19 is the eighth strictly non-palindromic number in any base, following 11 and preceding 47.[6] 19 is also the second octahedral number, after 6,[7] and the sixth Heegner number.

    In the Engel expansionofpi,[8] 19 is the seventh term following {1, 1, 1, 8, 8, 17} and preceding {300, 1991, ...}. The sum of the first terms preceding 17 is in equivalence with 19, where its prime index (8) are the two previous members in the sequence.

    Prime properties

    edit

    19 is the seventh Mersenne prime exponent.[9] It is the second Keith number, and more specifically the first Keith prime.[10]Indecimal, 19 is the third full reptend prime,[11] and the first prime number that is not a permutable prime, as its reverse (91) is composite (where 91 is also the fourth centered nonagonal number).[12]

    1729 is also the nineteenth dodecagonal number.[15]

    19, alongside 109, 1009, and 10009, are all prime (with 109 also full reptend), and form part of a sequence of numbers where inserting a digit inside the previous term produces the next smallest prime possible, up to scale, with the composite number 9 as root.[16] 100019 is the next such smallest prime number, by the insertion of a 1.

    Otherwise,   is the second base-10 repunit prime, short for the number  .[18]

    The sum of the squares of the first nineteen primes is divisible by 19.[19]

    Figurate numbers and magic figures

    edit

    19 is the third centered triangular number as well as the third centered hexagonal number.[20][21]

    19 is the first number in an infinite sequence of numbers in decimal 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.[23]
    n = {1, 2, 3, 5, 7, 26, 27, 53, 147, 236, 248, 386, 401}.[24]

    The number of nodesinregular hexagon with all diagonals drawn is nineteen.[25]

      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.[29]

    Collatz problem

    edit

    The Collatz sequence for nine requires nineteen steps to return back to one, more than any other number below it.[33] On the other hand, nineteen requires twenty steps, like eighteen. Less than ten thousand, only thirty-one other numbers require nineteen steps to return back to one:

    {56, 58, 60, 61, 352, 360, 362, 368, 369, 372, 373, 401, 402, 403, 2176, ..., and 2421}.[34]

    In abstract algebra

    edit

    The projective special linear group   represents the abstract structure of the 57-cell: a universal 4-polytope with a total of one hundred and seventy-one (171 = 9 × 19) edges and vertices, and fifty-seven (57 = 3 × 19) hemi-icosahedral cells that are self-dual.[35]

    In total, there are nineteen Coxeter groups of non-prismatic uniform honeycombs in the fourth dimension: five Coxeter honeycomb groups exist in Euclidean space, while the other fourteen Coxeter groups are compact and paracompact hyperbolic honeycomb groups.

    There are infinitely many finite-volume Vinberg polytopes up through dimension nineteen, which generate hyperbolic tilings with degenerate simplex quadrilateral pyramidal domains, as well as prismatic domains and otherwise.[36]

    On the other hand, a cubic surface is the zero set in   of a homogeneous cubic polynomial in four variables   a polynomial with a total of twenty coefficients, which specifies a space for cubic surfaces that is 19-dimensional.[38]

    Finite simple groups

    edit

    19 is the eighth consecutive supersingular prime. It is the middle indexed member in the sequence of fifteen such primes that divide the order of the Friendly Giant  , the largest sporadic group: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}.[39]

      holds (2,3,7)asstandard generators (a,b,ab) that yield a semi-presentation where o(abab2) = 19, while   holds as standard generators (2A, 3A, 19), where o([a, b]) = 9.[41][42]

    In the Happy Family of sporadic groups, nineteen of twenty-six such groups are subquotients of the Friendly Giant, which is also its own subquotient.[47] If the Tits group is indeed included as a group of Lie type,[48] then there are nineteen classes of finite simple groups that are not sporadic groups.

    Worth noting, 26 is the only number to lie between a perfect square (52) and a cube (33); if all primes in the prime factorizationsof25 and 27 are added together, a sum of 19 is obtained.

    Heegner number

    edit

    19 is the sixth Heegner number.[49] 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total.

    The sum of the first six Heegner numbers 1, 2, 3, 7, 11, and 19 sum to the seventh member and fourteenth prime number, 43. All of these numbers are prime, aside from the unit. In particular, 163 is relevant in moonshine theory.

    Science

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

    Religion

    edit

    Islam

    edit

    Baháʼí faith

    edit

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

    Celtic paganism

    edit

    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.[50]

    Music

    edit

    Literature

    edit

    Games

    edit
     
    A 19x19 Go board

    Age 19

    edit

    In sports

    edit

    In other fields

    edit

    References

    edit
    1. ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A088762 (Numbers n such that (2n-1, 2n+3) is a cousin prime pair.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A046117 (Primes p such that p-6 is also prime. (Upper of a pair of sexy primes.))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A002426 (Central trinomial coefficients: largest coefficient of (1 + x + x^2)^n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A002804 ((Presumed) solution to Waring's problem.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers: n is not palindromic in any base b with 2 less than or equal to b less than or equal to n-2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-19.
  • ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-08-17.
  • ^ Sloane, N. J. A. (ed.). "Sequence A006784 (Engel expansion of Pi.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
  • ^ "Sloane's A000043 : Mersenne exponents". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  • ^ Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-05.
  • ^ a b Sloane, N. J. A. (ed.). "Sequence A060544 (Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-30.
  • ^ "19". Prime Curios!. Retrieved 2022-08-05.
  • ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-11.
  • ^ Sloane, N. J. A. (ed.). "Sequence A051624 (12-gonal (or dodecagonal) numbers: a(n) equal to n*(5*n-4).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-21.
  • ^ 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.
  • ^ Sloane, N. J. A. (ed.). "Sequence A088275 (Numbers n such that 10^n + 9 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-28.
  • ^ Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN 1475717385
  • ^ 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.
  • ^ "Sloane's A125602 : Centered triangular numbers that are prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  • ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  • ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-13.
  • ^ 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.
  • ^ 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.
  • ^ Sloane, N. J. A. (ed.). "Sequence A007569 (Number of nodes in regular n-gon with all diagonals drawn.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
  • ^ Trigg, C. W. (February 1964). "A Unique Magic Hexagon". Recreational Mathematics Magazine. Retrieved 2022-07-14.
  • ^ Gardner, Martin (January 2012). "Hexaflexagons". The College Mathematics Journal. 43 (1). Taylor & Francis: 2–5. doi:10.4169/college.math.j.43.1.002. JSTOR 10.4169/college.math.j.43.1.002. S2CID 218544330.
  • ^ Sloane, N. J. A. (ed.). "Sequence A006534 (Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-08.
  • ^ Andrews, William Symes (1917). Magic Squares and Cubes (PDF). Chicago, IL: Open Court Publishing Company. pp. 176, 177. ISBN 9780486206585. MR 0114763. OCLC 1136401. Zbl 1003.05500.
  • ^ Sloane, N. J. A. (ed.). "Sequence A072359 (Primes p such that the p-1 digits of the decimal expansion of k/p (for k equal to 1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-04.
  • ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-06.
  • ^ Sloane, N. J. A. (ed.). "Sequence A006003 (a(n) equal to n*(n^2 + 1)/2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-04.
  • ^ Sloane, N. J. A. "3x+1 problem". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-24.
  • ^ Sloane, N. J. A. (ed.). "Sequence A006577 (Number of halving and tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-24.
    "Table of n, a(n) for n = 1..10000".
  • ^ Coxeter, H. S. M. (1982). "Ten toroids and fifty-seven hemidodecahedra". Geometriae Dedicata. 13 (1): 87–99. doi:10.1007/BF00149428. MR 0679218. S2CID 120672023.
  • ^ 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.
  • ^ Tumarkin, P. (2004). "Hyperbolic Coxeter n-polytopes with n + 2 facets". Mathematical Notes. 75 (5/6). Springer: 848–854. arXiv:math/0301133v2. doi:10.1023/B:MATN.0000030993.74338.dd. MR 2086616. S2CID 15156852. Zbl 1062.52012.
  • ^ Seigal, Anna (2020). "Ranks and symmetric ranks of cubic surfaces". Journal of Symbolic Computation. 101. Amsterdam: Elsevier: 304–306. arXiv:1801.05377. Bibcode:2018arXiv180105377S. doi:10.1016/j.jsc.2019.10.001. S2CID 55542435. Zbl 1444.14091.
  • ^ Sloane, N. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-11.
  • ^ Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics. New York: Oxford University Press. pp. 244–246. doi:10.1007/s00283-008-9007-9. ISBN 978-0-19-280722-9. MR 2215662. OCLC 180766312. Zbl 1113.00002.
  • ^ Wilson, R.A (1998). "Chapter: An Atlas of Sporadic Group Representations" (PDF). The Atlas of Finite Groups - Ten Years On (LMS Lecture Note Series 249). Cambridge, U.K: Cambridge University Press. p. 267. doi:10.1017/CBO9780511565830.024. ISBN 9780511565830. OCLC 726827806. S2CID 59394831. Zbl 0914.20016.
    List of standard generators of all sporadic groups.
  • ^ Nickerson, S.J.; Wilson, R.A. (2011). "Semi-Presentations for the Sporadic Simple Groups". Experimental Mathematics. 14 (3). Oxfordshire: Taylor & Francis: 365. CiteSeerX 10.1.1.218.8035. doi:10.1080/10586458.2005.10128927. MR 2172713. S2CID 13100616. Zbl 1087.20025.
  • ^ Jansen, Christoph (2005). "The Minimal Degrees of Faithful Representations of the Sporadic Simple Groups and their Covering Groups". LMS Journal of Computation and Mathematics. 8. London Mathematical Society: 122−144. doi:10.1112/S1461157000000930. MR 2153793. S2CID 121362819. Zbl 1089.20006.
  • ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-28.
  • ^ Sloane, N. J. A. (ed.). "Sequence A000292". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-28.
  • ^ Sloane, N. J. A. (ed.). "Sequence A051871 (19-gonal (or enneadecagonal) numbers: n(17n-15)/2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-09.
  • ^ John F.R. Duncan; Michael H. Mertens; Ken Ono (2017). "Pariah moonshine". Nature Communications. 8 (1): 2 (Article 670). arXiv:1709.08867. Bibcode:2017NatCo...8..670D. doi:10.1038/s41467-017-00660-y. PMC 5608900. PMID 28935903. ...so [sic] moonshine illuminates a physical origin for the monster, and for the 19 other sporadic groups that are involved in the monster.
  • ^ R. B. Howlett; L. J. Rylands; D. E. Taylor (2001). "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).
  • ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  • ^ Brigid: Triple Goddess of the Flame (Health, Hearth, & Forge)
  • ^ 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.
  • edit

    Retrieved from "https://en.wikipedia.org/w/index.php?title=19_(number)&oldid=1230896757"
     



    Last edited on 25 June 2024, at 09:08  





    Languages

     


    Аԥсшәа
    العربية
    Avañe'
    Azərbaycanca
    تۆرکجه
    Basa Bali
     / Bân-lâm-gú
    Български

    Bosanski
    Català
    Чӑвашла
    Čeština
    ChiShona
    ChiTumbuka
    Cymraeg
    Dansk
    الدارجة
    Deutsch
    Ελληνικά
    Emiliàn e rumagnòl
    Эрзянь
    Español
    Esperanto
    Euskara
    فارسی
    Føroyskt
    Français
    Fulfulde
    Gaeilge
    ГӀалгӀай


    Hausa
    Հայերեն
    Igbo
    Bahasa Indonesia
    Interlingua
    Iñupiatun
    IsiXhosa
    Íslenska
    Italiano
    עברית

     / کٲشُر
    Ikirundi
    Kiswahili
    Kreyòl ayisyen
    Kurdî
    Лакку
    Latviešu
    Lietuvių
    Lingála
    Luganda
    Lombard
    Magyar
    ि
    Македонски

    مازِرونی
    Bahasa Melayu
     
     / Mìng-dĕ̤ng-nḡ
    Nāhuatl
    Na Vosa Vakaviti
    Nederlands

    Napulitano
    Norsk bokmål
    Norsk nynorsk
    Oʻzbekcha / ўзбекча
    پنجابی
    پښتو
    Polski
    Português
    Română
    Runa Simi
    Русский
    Gagana Samoa
    Sesotho sa Leboa
    Sicilianu
    Simple English
    Slovenščina
    Soomaaliga
    کوردی
    Sranantongo
    Српски / srpski
    Suomi
    Svenska
    Tagalog
    Татарча / tatarça


    Türkçe
    Тыва дыл
    Українська
    اردو
    Vahcuengh
    Vepsän kel
    Tiếng Vit
    West-Vlams
    Winaray

    ייִדיש


     

    Wikipedia


    This page was last edited on 25 June 2024, at 09:08 (UTC).

    Content is available under CC BY-SA 4.0 unless otherwise noted.



    Privacy policy

    About Wikipedia

    Disclaimers

    Contact Wikipedia

    Code of Conduct

    Developers

    Statistics

    Cookie statement

    Terms of Use

    Desktop