23 (number)

← 22 23 24 →
← 20 21 22 23 24 25 26 27 28 29 → List of numbers; Integers; ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twenty-three
Ordinal	rd
Factorization	prime
Divisors	1, 23
Greek numeral	ΚΓ´
Roman numeral	XXIII
Binary	101112
Ternary	2123
Senary	356
Octal	278
Duodecimal	1B12
Hexadecimal	1716

This article is about the number 23. For the year, see 23. For the movies, see 23 (film) and The Number 23. For other uses, see 23 (disambiguation)

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 which is not a twin prime. Twenty-three is also the fifth factorial prime, the second Woodall prime. It is an Eisenstein prime with no imaginary part and real part of the form $3n-1$ .

The fifth Sophie Germain prime and the fourth safe prime, 23 is the next to last member of the first Cunningham chain of the first kind to have five terms (2, 5, 11, 23, 47). Since 14! + 1 is a multiple of 23 but 23 is not one more than a multiple 14, 23 is a Pillai prime. 23 is the smallest odd prime to be a highly cototient number, as the solution to x - φ(x) for the integers 95, 119, 143, 529.

Twenty-three is the aliquot sum of two integers; the discrete semiprimes 57 and 85 and is the base of the 23-aliquot tree.

23 is the first prime $P$ for which unique factorization of cyclotomic integers based on the $P$ 'th root of unity breaks down.

The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.^[1]^[2]

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).

23 also has the distinction of being one of two integers that cannot be expressed as the sum of fewer than 9 cubes of integers (the other is 239). See Waring's problem.

23 is a Wedderburn-Etherington number. The codewords in the perfect (non-extended) binary Golay code are of size 23.

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.

There were 23 problems on David Hilbert's famous list of unsolved mathematical problems, presented to the International Congress of Mathematicians in Paris in 1900.

In base 10, 23 is the second Smarandache-Wellin prime, as it is the concatenation of the base 10 representations of the first two primes (2 and 3) and is itself also prime. It is also a happy number in base 10. 23! is 23 digits long in base 10. There are only three other numbers that have this property: 1, 22, and 24.

The natural logarithms of all positive integers lower than 23 are known to have binary BBP-type formulae.^[3]

In science

The atomic number of vanadium.
The atomic mass number of the stable isotope of sodium.
Normal human sex cells have 23 chromosomes.^[4] Other human cells have 46 chromosomes, arranged in 23 pairs.^[5]

In technology

23 is the TCP/IP port used for telnet and is the default for the telnet command.

In religion

Psalm 23, also known as the Shepherd Psalm, is possibly the most quoted and best known Psalm.^[6] Psalms is also the 23rd book in the Douay-Rheims Bible.
In Islam, the Qur'an was revealed in a total of 23 years to Muhammad.^[7]^[8]
In Abhidharma, the number of anomalous generic types (of a possible 72) - e.g., events are considered sui generis because they are not reducible to either mind or matter — is 23.
Principia Discordia, the sacred text of Discordianism, holds that 23 (along with the discordian prime 5) is one of the sacred numbers of Eris, goddess of discord.

In popular culture

Sports

The number 23 has been retired for quite a few prominent athletes. Michael Jordan wore number 23 (with the exception of a short period of time) when he played professional basketball with the Chicago Bulls and, later, the Washington Wizards. Lebron James, who plays for the Cleveland Cavaliers, also wears the number 23. Australian cricketer Shane Warne wore the number 23 during his career; Don Mattingly of the New York Yankees wore number 23; the New York Yankees retired the number in 1997. Ryne Sandberg, of the Chicago Cubs, wore number 23, which was retired on August 28, 2005. Bob Nystrom of the New York Islanders wore number 23 and has had the number retired in his honour. Bob Gainey, current General Manager and former player for the Montreal Canadiens, had his number 23 retired February 23, 2008. Nathan Scott, a prominent basketball player in the American television serial One Tree Hill, wears the number 23 on his jersey.

As a tribute to Michael Jordan, David Beckham chose 23 as his shirt number at Real Madrid, and subsequently at LA Galaxy.

Manchester City F.C. have not assigned the squad number 23 to any player since 2003. This is because Marc-Vivien Foé, the player who collapsed and died while playing for Cameroon on June 26, 2003, had held this squad number at Manchester City. Club Brugge KV, a Belgian football team, has done the same when their number 23, François Sterchele died on May 8, 2008 in a car accident.

Music

Several songs and albums use the number 23 as their titles, including Tristan Prettyman's debut album, the eleventh song from Tool's fourth full-length studio album 10,000 Days, "Viginti Tres" (Latin for twenty-three).
Blonde Redhead have the album '23' and the song with the same name.
Jimmy Eat World's song "23" appeared 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 Yellowcard both have songs titled "Twenty-Three".
The Posies have a record called Dear 23
The Church's 2009 studio album is called "Untitled #23"

Film and television

23 is a German film about Karl Koch
The Number 23 is a 2007 film starring Jim Carrey.
23 is one of The Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
In The Matrix Reloaded, the Architect tells Neo it is of utmost importance to choose 23 people to repopulate Zion.
In Jeepers Creepers, the Creeper appears every 23 years for 23 days to feast on human flesh.
In the film Vantage Point, all flashbacks take place 23 minutes before the assassination attempt on the president.
As revealed in Japanese film L: Change the World, 23 is the maximum number of days a person may live before he dies by the cause of writing his name in Death Note. Main protagonist L of the film L: Change the World, signs his name in Death Note so to die after 23 days.

Other fields

The 23 Enigma 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.^[9]
Julius Caesar was stabbed 23 times.^[10]

References

^ (sequence A045345 in the OEIS)
^ Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from the The Prime Puzzles & Problems Connection website
^ http://www.math.grinnell.edu/~chamberl/papers/bbp.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."
^ 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
^ Nan Cross: Supported men resisting apartheid conscription Sunday Times (South Africa), 2007-07-22, accessed 2009-01-05. For a short summary on conscientious objection in South Africa, see http://en.wikipedia.org/wiki/Nan_Cross#cite_note-jt-0
^ Woolf Greg (2006), Et Tu Brute? – The Murder of Caesar and Political Assassination, 199 pages – ISBN 1-8619-7741-7

External links

[1] (sequence A045345 in the OEIS)

[2] Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from the The Prime Puzzles & Problems Connection website

[3] ttp://www.math.grinnell.edu/~chamberl/papers/bbp.pdf

[4] 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

[5] 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."

[6] 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."

[7] Living Religions: An Encyclopaedia of the World's Faiths, Mary Pat Fisher, 1997, page 338, I.B. Tauris Publishers,

[8] Qur'an, Chapter 17, Verse 106

[9] Nan Cross: Supported men resisting apartheid conscription Sunday Times (South Africa), 2007-07-22, accessed 2009-01-05. For a short summary on conscientious objection in South Africa, see http://en.wikipedia.org/wiki/Nan_Cross#cite_note-jt-0

[10] Woolf Greg (2006), Et Tu Brute? – The Murder of Caesar and Political Assassination, 199 pages – ISBN 1-8619-7741-7

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