# 23 (number)

 ← 22 23 24 →
Cardinal twenty-three
Ordinal 23rd
(twenty-third)
Factorization Prime
Divisors 1, 23
Roman numeral XXIII
Binary 101112
Ternary 2123
Quaternary 1134
Quinary 435
Senary 356
Octal 278
Duodecimal 1B12
Vigesimal 1320
Base 36 N36

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. 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.

Twenty-three is the sum of three other, consecutive, prime numbers; 5, 7 and 11. It is the first prime number showing this characteristic.

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 Pth 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. 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.[3]

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.

## 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.[7] 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.[8][9]
• 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.[10]
• 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

### Music

• Alfred Harth uses the number 23 in his artist name Alfred 23 Harth, or A23H, since the year 1+9+8+5 = 23.
• 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".
• Phuq often uses 23 in his song titles and choice of samples.
• The Posies have a record called Dear 23
• The Church's 2009 studio album is called "Untitled 23"
• Spiral Tribe From its inception, the group was obsessed by the number 23. Members sometimes recorded under the moniker of SP23, and the record label itself was called Network 23.
• Carbon Based Lifeforms released a 2011 album titled "Twentythree."
• Noah23 has several albums which reference the number 23.
• Luna's song "23 Minutes in Brussels" (featuring Tom Verlaine) appears 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,[11] or because he first suffered an asthma attack on 23rd of the month.[12][importance?]
• 23 is a single by Mike Will Made-It released in 2013 featuring Miley Cyrus the Twerker, Wiz Khalifa Mia Khalifa's Bro, and Juicy Jordan.

## References

1. ^ (sequence A045345 in OEIS)
2. ^ Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from The Prime Puzzles & Problems Connection website
3. ^ http://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. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Direct link to value.
7. ^ 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."
8. ^ Living Religions: An Encyclopaedia of the World's Faiths, Mary Pat Fisher, 1997, page 338, I.B. Tauris Publishers,
9. ^ Qur'an, Chapter 17, Verse 106
10. ^ Quran, Chapter 97
11. ^ 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
12. ^ Jarman, D. (1985). The Music of Alban Berg. Berkeley: University of California Press, pp. 228-230
13. ^ Nan Cross: "Supported men resisting apartheid conscription", The Sunday Times (South Africa), 2007-07-22, accessed 2009-01-05.
14. ^ Woolf Greg (2006), Et Tu Brute? – The Murder of Caesar and Political Assassination, 199 pages – ISBN 1-86197-741-7