← 22 23 24 →
Cardinaltwenty-three
Ordinal23rd
(twenty-third)
Numeral systemtrivigesimal
Factorizationprime
Prime9th
Divisors1, 23
Greek numeralΚΓ´
Roman numeralXXIII
Binary101112
Ternary2123
Senary356
Octal278
Duodecimal1B12
Hexadecimal1716

23 (twenty-three) is the natural number following 22 and preceding 24.

In mathematics

Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime.[1] It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 11, 13, 17, 19, 23).[2] Twenty-three is also the fifth factorial prime,[3] the second Woodall prime,[4] and a happy number in decimal.[5] It is an Eisenstein prime with no imaginary part and real part of the form It is also the fifth Sophie Germain prime[6] and the fourth safe prime,[7] and the next to last member of the first Cunningham chain of the first kind to have five terms (2, 5, 11, 23, 47).[8] Since 14! + 1 is a multiple of 23, but 23 is not one more than a multiple of 14, 23 is the first Pillai prime.[9] 23 is the smallest odd prime to be a highly cototient number, as the solution to for the integers 95, 119, 143, and 529.[10] The third decimal repunit prime after R2 and R19 is R23, followed by R1031.[11]

A related coincidence is that 365 times the natural logarithm of 2, approximately 252.999, is very close to the number of pairs of 23 items and 22nd triangular number, 253.

The first Mersenne number of the form that does not yield a prime number when inputting a prime exponent is with [23]

On the other hand, the second composite Mersenne number contains an exponent of twenty-three:

Further in the sequence of Mersenne numbers, the 23rd prime number (83) is an exponent to the 14th composite Mersenne number, which factorizes into two prime numbers, the largest of which is twenty-three digits long when written in base ten:[24][25]

is also twenty-three digits long in decimal, and there are only three other numbers whose factorials generate numbers that are digits long in base ten: 1, 22, and 24.

In geometry

The Leech lattice Λ24 is a 24-dimensional lattice through which 23 other positive definite even unimodular Niemeier lattices of rank 24 are built, and vice-versa. Λ24 represents the solution to the kissing number in 24 dimensions as the precise lattice structure for the maximum number of spheres that can fill 24-dimensional space without overlapping, equal to 196,560 spheres. These 23 Niemeier lattices are located at deep holes of radii 2 in lattice points around its automorphism group, Conway group . The Leech lattice can be constructed in various ways, which include:

Conway and Sloane provided constructions of the Leech lattice from all other 23 Niemeier lattices.[26]

Twenty-three four-dimensional crystal families exist within the classification of space groups. These are accompanied by six enantiomorphic forms, which maximizes the total count to twenty-nine crystal families.[27] In three dimensions, five cubes can be arranged to form twenty-three free pentacubes, or twenty-nine distinct one-sided pentacubes (counting reflections).[28][29]

There are 23 three-dimensional uniform polyhedra that are cell facets inside uniform 4-polytopes that are not part of infinite families of antiprismatic prisms and duoprisms: the five Platonic solids, the thirteen Archimedean solids, and five semiregular prisms (the triangular prism, pentagonal prism, hexagonal prism, octagonal prism, and decagonal prism).

23 Coxeter groups of paracompact hyperbolic honeycombs in the third dimension generate 151 unique Wythoffian constructions of paracompact honeycombs. 23 four-dimensional Euclidean honeycombs are generated from the cubic group, and 23 five-dimensional uniform polytopes are generated from the demihypercubic group.

In two-dimensional geometry, the regular 23-sided icositrigon is the first regular polygon that is not constructible with a compass and straight edge or with the aide of an angle trisector (since it is neither a Fermat prime nor a Pierpont prime), nor by neusis or a double-notched straight edge.[30] It is also not constructible with origami, however it is through other traditional methods for all regular polygons.[31]

In science and technology

In religion

In popular culture

Music

Main article: 23 § Music

Film and television

Other fields

See also: List of highways numbered 23

In sports

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 5 December 2022.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A001223 (Prime gaps: differences between consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 11 June 2023.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A088054 (Factorial primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A050918 (Woodall primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A192580 (Monotonic ordering of set S generated by these rules: if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2 is in S.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 11 June 2023.
    "2, 5, 11, 23, 47 is the complete Cunningham chain that begins with 2. Each term except the last is a Sophie Germain prime A005384."
  9. ^ Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  11. ^ Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN 1475717385
  12. ^ Sloane, N. J. A. (ed.). "Sequence A069151 (Concatenations of consecutive primes, starting with 2, that are also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  13. ^ Weisstein, Eric W. "Cyclotomic Integer". mathworld.wolfram.com. Retrieved 15 January 2019.
  14. ^ (sequence A045345 in the OEIS)
  15. ^ "Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k". www.primepuzzles.net. Retrieved 29 November 2022.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A005235 (Fortunate numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  17. ^ "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 29 November 2010. Retrieved 19 December 2021.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  19. ^ Chamberland, Marc. "Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes" (PDF).
  20. ^ Sloane, N. J. A. (ed.). "Sequence A228611 (Primes p such that the largest consecutive pair of -smooth integers is the same as the largest consecutive pair of -smooth integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
  21. ^ Weisstein, Eric W. "Birthday Problem". mathworld.wolfram.com. Retrieved 19 August 2020.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A038133 (From a subtractive Goldbach conjecture: odd primes that are not cluster primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 26 December 2022.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A000225 (Mersenne numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 February 2023.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A136030 (Smallest prime factor of composite Mersenne numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2023.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A136031 (Largest prime factor of composite Mersenne numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2023.
  26. ^ Conway, John Horton; Sloane, N. J. A. (1982). "Twenty-three constructions for the Leech lattice". Proceedings of the Royal Society A. 381 (1781): 275–283. Bibcode:1982RSPSA.381..275C. doi:10.1098/rspa.1982.0071. ISSN 0080-4630. MR 0661720. S2CID 202575295.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A004032 (Number of n-dimensional crystal families.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 November 2022.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of three dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 6 January 2023.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A038119 (Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ^ Arthur Baragar (2002) Constructions Using a Compass and Twice-Notched Straightedge, The American Mathematical Monthly, 109:2, 151-164, doi:10.1080/00029890.2002.11919848
  31. ^ P. Milici, R. Dawson The equiangular compass December 1st, 2012, The Mathematical Intelligencer, Vol. 34, Issue 4 https://www.researchgate.net/profile/Pietro_Milici2/publication/257393577_The_Equiangular_Compass/links/5d4c687da6fdcc370a8725e0/The-Equiangular-Compass.pdf
  32. ^ H. Wramsby, K. Fredga, P. Liedholm, "Chromosome analysis of human oocytes recovered from preovulatory follicles in stimulated cycles" New England Journal of Medicine 316 3 (1987): 121 – 124
  33. ^ Barbara J. Trask, "Human genetics and disease: Human cytogenetics: 46 chromosomes, 46 years and counting" Nature Reviews Genetics 3 (2002): 769. "Human cytogenetics was born in 1956 with the fundamental, but empowering, discovery that normal human cells contain 46 chromosomes."
  34. ^ Newell, David B.; Tiesinga, Eite (2019). The International System of Units (SI). NIST Special Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. S2CID 242934226.
  35. ^ RFC 854, Telnet Protocol Specification
  36. ^ ""The Lord is My Shepherd, I Shall Not Want" – Meaning of Psalm 23 Explained". Christianity.com. Retrieved 7 June 2021.
  37. ^ Miriam Dunson, A Very Present Help: Psalm Studies for Older Adults. New York: Geneva Press (1999): 91. "Psalm 23 is perhaps the most familiar, the most loved, the most memorized, and the most quoted of all the psalms."
  38. ^ Living Religions: An Encyclopaedia of the World's Faiths, Mary Pat Fisher, 1997, page 338, I.B. Tauris Publishers,
  39. ^ Qur'an, Chapter 17, Verse 106
  40. ^ Quran, Chapter 97
  41. ^ Rampton, Mike (19 October 2019). "A Deep Dive Into Incubus' Pardon Me Video". kerrang.com.
  42. ^ Jarman, Douglas (1983). "Alban Berg, Wilhelm Fliess and the Secret Programme of the Violin Concerto". The Musical Times. 124 (1682): 218–223. doi:10.2307/962034. JSTOR 962034.
  43. ^ Jarman, Douglas (1985). The Music of Alban Berg. University of California Press. ISBN 978-0-520-04954-3.
  44. ^ 23 (1998) – Hans-Christian Schmid | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
  45. ^ L: Change the World (2008) – Hideo Nakata | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
  46. ^ The Number 23 (2007) – Joel Schumacher | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
  47. ^ "Nan Cross: Supported men resisting apartheid conscription". Sunday Times. 22 July 2007. Retrieved 4 March 2023 – via PressReader.