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- Twenty-three is the ninth prime number, the smallest odd prime that 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.
- 23 is the third base-10 repunit prime exponent after 2 and 19.
- 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.
- 23 is the first prime p for which unique factorization of cyclotomic integers based on the p the 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.
- 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 positive 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. 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, 253.
- 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.
- 23 is the smallest prime number p such that the largest consecutive pair of p-smooth numbers is the same as the largest consecutive pair of (p − 1)-smooth numbers, as given in the On-Line Encyclopedia of Integer Sequences sequence A228611. That is, the largest consecutive pair of 23-smooth numbers, (11859210, 11859211), is the same as the largest consecutive pair of 22-smooth numbers, and 23 is the smallest prime for which this is true.
- 23 is the smallest positive solution to Sunzi's original formulation of the Chinese remainder theorem.
In science and technology
- The atomic number of vanadium.
- The atomic mass number of the stable isotope of sodium.
- Normal human sex cells have 23 chromosomes. Other human cells have 46 chromosomes, arranged in 23 pairs.
- Scientific notation for the Avogadro constant is written as 6.02214076×1023.
- 23 is the width of the Arecibo message, sent to space in search for extraterrestrial intelligence.
- 23 is the TCP/IP port used for telnet and is the default for the telnet command.
- The earth's axis is tilted at approximately 23°
- Psalm 23, also known as the Shepherd Psalm, is possibly the most quoted and best known Psalm. 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 Prophet Muhammed.
- 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.
- 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
- Alfred Harth uses 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
- "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 Yellowcard both 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.[which?]
- "23 Minutes in Brussels", a song by Luna on their album Penthouse.
- The composer Alban Berg had a particular interest in the number 23, using it to structure several works. Various suggestions have been made as to the reason for this interest: that he took it from the Biorhythms theory of Wilhelm Fliess, in which a 23-day cycle is considered significant, or because he first suffered an asthma attack on 23rd of the month.[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 Gorillaz, who have even devoted a whole page of their autobiography Rise Of The Ogre to the 23 enigma theory.
Film and television
- 23 is a German film about Karl Koch.
- In Jeepers Creepers, the Creeper appears every 23 years for 23 days to feast on human flesh.
- 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.
- 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.
- In The Matrix Reloaded, the Architect tells Neo it is of utmost importance to choose 23 people to repopulate Zion.
- The Number 23 is a 2007 film starring Jim Carrey about a man who becomes obsessed with the 23 enigma.
- 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 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.
- 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.
- Each national team competing in the FIFA World Cup or FIFA Women's World Cup is allowed a 23-player squad. This squad size has been in place since 2002 for men and 2015 for women.
- Nissan typically uses this number for their Motorsport manufacturer teams, as the numbers 2 and 3 are pronounced "ni" and "san" in Japanese.
- 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.
- Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN 1475717385
- 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 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.
- Weisstein, Eric W. "Cyclotomic Integer". mathworld.wolfram.com. Retrieved 15 January 2019.
- (sequence A045345 in the OEIS)
- Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from The Prime Puzzles & Problems Connection website
- 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 A001190 (Wedderburn-Etherington 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.
- Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 31 May 2016.
- 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."
- "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- RFC 854, Telnet Protocol Specification
- 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
- Jarman, D. (1983). Alban Berg, Wilhelm Fliess and the Secret Programme of the Violin Concerto. The Musical Times Vol. 124, No. 1682 (Apr. 1983), pp. 218-223
- Jarman, D. (1985). The Music of Alban Berg. Berkeley: University of California Press, pp. 228-230
- "Nan Cross: Supported men resisting apartheid conscription", The Sunday Times (South Africa), 2007-07-22, accessed 2009-01-05.
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