23 (number)
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Cardinal | twenty-three | |||
Ordinal | 23rd (twenty-third) | |||
Numeral system | trivigesimal | |||
Factorization | prime | |||
Prime | 9th | |||
Divisors | 1, 23 | |||
Greek numeral | ΚΓ´ | |||
Roman numeral | XXIII | |||
Binary | 101112 | |||
Ternary | 2123 | |||
Senary | 356 | |||
Octal | 278 | |||
Duodecimal | 1B12 | |||
Hexadecimal | 1716 |
23 (twenty-three) is the natural number following 22 and preceding 24.
In mathematics
Twenty-three is the ninth
- 23 is the second
- The sum of the first nine primes up to 23 is a square: and the sum of the first 23 primes is
- In the list of fortunate numbers, 23 occurs twice, since adding 23 to either the fifth or eighth primorial gives a prime number (namely 2333 and 9699713).[14]
- 23 has the distinction of being one of two integers that cannot be expressed as the sum of fewer than 9 cubes of positive integers (the other is 239). See Waring's problem.
- The twenty-third highly composite number 20,160[15] is one less than the last number (the 339th super-prime 20,161) that cannot be expressed as the sum of two abundant numbers.[16]
- Otherwise, is the largest even number that is not the sum of two abundant numbers.
- 23 is the number of binary trees.[18]
- The BBP-type formulae.[19]
- 23 is the first prime p for which unique factorization of cyclotomic integers based on the pth root of unity breaks down.[20]
- 23 is the smallest positive solution to Sunzi's original formulation of the Chinese remainder theorem.
- 23 is the smallest prime such that the largest consecutive pair of smooth numbers(11859210, 11859211) is the same as the largest consecutive pair of smooth numbers.[21]
- According to the birthday paradox, in a group of 23 or more randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday.[22]
- 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 twenty-three odd prime numbers (between 3 and 89 inclusive), are all cluster primes such that every even positive integer can be written as the sum of two prime numbers that do not exceed .[23]
- 23 is the smallest discriminant of imaginary quadratic fields with class number 3 (negated),[24] and it is the smallest discriminant of complex cubic fields (also negated).[25]
- The twenty-third permutable prime in decimal is also the second to be a prime repunit (after ), followed by and .[26][27][28][29]
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
Mersenne numbers
The first
On the other hand, the second composite Mersenne number contains an exponent of twenty-three:
The twenty-third prime number (
Further down in this sequence, the seventeenth and eighteenth composite Mersenne numbers have two prime factors each as well, where the largest of these are respectively twenty-two and twenty-four digits long,
Where prime exponents for and add to 106, which lies in between prime exponents of and , the index of the latter two (17 and 18) in the sequence of Mersenne numbers sum to 35, which is the twenty-third composite number.[33]
is 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
- By means of a matrix of the form where is the identity matrix and is a 24 by 24 mod23 for nonzero n.
- Through the extended binary Golay codeand Witt design , which produce a construction of the 196,560 minimalperfect binary Golay code, which has codewords of size 23. has Mathieu group as itssporadic groups. has a minimum faithful complex representation in 22 dimensions and group-3 actions on 253 objects, with 253 equal to the number of pairs of objects in a set of 23 objects. In turn, is the automorphism group of Mathieu group , which works through to generate 8-element octads whose individual elements occur 253 times through its entire block design.
- Using Niemer lattice D24 of , whereby multiplying D24 by a non-principal ideal of the ring of integers yields the Leech lattice.
Twenty-three four-dimensional
There are 23 three-dimensional
23
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
In science and technology
- The atomic number of vanadium.
- The stable isotope of sodium.
- Normal human
- Scientific notation for the Avogadro constant is written as 6.02214076×1023.[42]
- 23 is the width of the Arecibo message, sent to space in search for extraterrestrial intelligence.
- 23 is the
- The Earth's axis is tilted at approximately 23°.
In religion
- In Biblical numerology, it is associated with Psalm 23, also known as the Shepherd Psalm. It is possibly the most quoted and best known Psalm.[44][45] Psalms is also the 23rd book in the Douay–Rheims Bible.
- In Islam, the
- Muslims believe the first verses of the Qur'an were revealed to the Islamic prophet Muhammad on the 23rd night of the 9th Islamic month, though, its disputed. [48]
- In I Ching divination, Hexagram 23 is 剝 (bō), "peeling" or "splitting apart".
- 5) is one of the sacred numbers of Eris, goddess of discord.
In popular culture
Music
- Alfred Harthuses the number 23 in his artist name Alfred 23 Harth, or A23H, since the year 1+9+8+5 = 23.
- Twentythree is the name of Tristan Prettyman's debut album
- Twentythree an album by Carbon Based Lifeforms
- "Viginti Tres" (Latin for twenty-three) is a song by Tool on their album 10,000 Days
- Blink-182's song "What's My Age Again?" includes the lyrics "nobody likes you when you're 23."
- 23 is an album and title track by Blonde Redhead
- The Incubus song "Pardon Me" includes the lyrics "A decade ago, I never thought I would be, at 23, on the verge of spontaneous combustion, woe is me!" Frontman Brandon Boyd was 23 years old when he wrote the song and described himself as being "kind of obsessive about that number".[49]
- "23" is a song by Jimmy Eat World, on their album Futures. The number also appears in the songs "Christmas Card" and "12."23".95" as well as on some items of clothing produced by the band.
- Four tet and Yellowcardboth have songs titled "Twenty-Three".
- Dear 23, an album by The Posies
- Untitled 23, an album by The Church
- Noah23 has several albums which reference the number 23, such as Neophyte Phenotype, Rock Paper Scissors, and Upside Down Bluejay, all of which have 23 tracks. His stage name also references the number.
- "23 Minutes in Brussels", a song by Luna on their album Penthouse.
- The composer Biorhythms theory of Wilhelm Fliess, in which a 23-day cycle is considered significant,[50] or because he first suffered an asthma attack on 23rd of the month.[51][importance?]
- "23" is a single by Mike Will Made It
- On the cover of The Beatles' 1969 album Yellow Submarine the number 23 is displayed on the chest of one of the Blue Meanies.
- Network 23 refers to members of the Spiral Tribe. Sometimes 23 used to discretely mark the spots of a freetekno rave.
- The number 23 is used a lot throughout the visuals and music by the band Rise Of The Ogre to the 23 enigmatheory.
Film and television
- 23 is a German film about Karl Koch.[52]
- In Jeepers Creepers, the Creeper appears every 23 years for 23 days to feast on human body parts
- In L: Change the World, the protagonist L signs his own name in the Death Note notebook and somehow knows that he has given himself 23 days to live, revealing a 23-day rule for the maximum number of days a person may live after they are added to the Japanese god of death's Death Note.[53]
- The 1980s TV series Max Headroom was set at Network 23.
- In The Big Lebowski, the main characters deliberately use only lane 23 at the bowling alley.[citation needed]
- In The Matrix Reloaded, the Architect tells Neo it is of utmost importance to choose 23 people to repopulate Zion.
- In the TV series Lost, 23 is one of the 6 reoccurring numbers (4, 8, 15, 16, 23, 42) that appear frequently throughout the show.
- The Number 23 is a 2007 film starring Jim Carrey about a man who becomes obsessed with the 23 enigma.[54]
Other fields
- 23 skidoo (phrase) (sometimes 23 skiddoo) is an American slang phrase popularized during the early 20th century. 23 skidoo has been described as "perhaps the first truly national fad expression and one of the most popular fad expressions to appear in the U.S".
- The 23 enigma, proposed by William S. Burroughs plays a prominent role in the plot of the Illuminatus! Trilogy by Robert Shea and Robert Anton Wilson.
- The 23, in South Africa, refers to the 23 conscientious objectors who publicly refused to do military service in the Apartheid army in 1987. The following years the number increased to 143 (in 1988) and 771 (in 1989), with Apartheid being dismantled from 1990 onwards.[55]
- X-23 is a character in the Marvel Universe. She is named for being the 23rd attempt to create a female genetic twin of Wolverine after attempts to create a male clone failed.
- 23 is the number of times Julius Caesar was stabbed in the Theatre of Pompey.
In sports
- Each national team competing in the FIFA Women's World Cup is allowed a 23-player squad. This squad size has been in place since 2015.
References
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- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A088054 (Factorial primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A050918 (Woodall primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ 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."
- ^ Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ 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.
- ^ (sequence A045345 in the OEIS)
- ^ "Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k". www.primepuzzles.net. Retrieved 29 November 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A005235 (Fortunate numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 9 October 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A048242 (Numbers that are not the sum of two abundant numbers (not necessarily distinct).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 9 October 2023.
- ^ "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.
- ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- ^ Chamberland, Marc. "Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes" (PDF).
- ^ Weisstein, Eric W. "Cyclotomic Integer". mathworld.wolfram.com. Retrieved 15 January 2019.
- ^ 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.
- ^ Weisstein, Eric W. "Birthday Problem". mathworld.wolfram.com. Retrieved 19 August 2020.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A006203 (Discriminants of imaginary quadratic fields with class number 3 (negated).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20 March 2024.
- ^ Sloane, N. J. A. (ed.). "Sequence A023679 (Discriminants of complex cubic fields (negated).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20 March 2024.
- ISBN 1475717385
- ^ Sloane, N. J. A. (ed.). "Sequence A003459 (Absolute primes (or permutable primes): every permutation of the digits is a prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 January 2024.
- ^ Sloane, N. J. A. (ed.). "Sequence A004022 (Primes of the form (10^k - 1)/9. Also called repunit primes or repdigit primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 January 2024.
- ^ Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's) equal to (10^n - 1)/9 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 January 2024.
- ^ Sloane, N. J. A. (ed.). "Sequence A000225 (Mersenne numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 February 2023.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 9 January 2024.
- S2CID 202575295.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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
- ^ 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
- ^ 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."
- S2CID 242934226.
- RFC 854, Telnet Protocol Specification
- ^ ""The Lord is My Shepherd, I Shall Not Want" – Meaning of Psalm 23 Explained". Christianity.com. Retrieved 7 June 2021.
- ^ 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."
- ^ Living Religions: An Encyclopaedia of the World's Faiths, Mary Pat Fisher, 1997, page 338, I.B. Tauris Publishers,
- ^ Qur'an, Chapter 17, Verse 106
- ^ Quran, Chapter 97
- ^ Rampton, Mike (19 October 2019). "A Deep Dive Into Incubus' Pardon Me Video". kerrang.com.
- JSTOR 962034.
- ISBN 978-0-520-04954-3.
- ^ 23 (1998) – Hans-Christian Schmid | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
- ^ L: Change the World (2008) – Hideo Nakata | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
- ^ The Number 23 (2007) – Joel Schumacher | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved 12 August 2020
- ^ "Nan Cross: Supported men resisting apartheid conscription". Sunday Times. 22 July 2007. Retrieved 4 March 2023 – via PressReader.