5

5 (five) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6, and is a prime number. It has attained significance throughout history in part because typical humans have five digits on each hand.

This article is about the number. For the year, see AD 5. For other uses, see 5 (disambiguation), Number Five (disambiguation), and The Five (disambiguation).
← 4 5 6 →
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Cardinalfive
Ordinal5th
(fifth)
Numeral systemquinary
Factorizationprime
Prime3rd
Divisors1, 5
Greek numeralΕ´
Roman numeralV, v
Greek prefixpenta-/pent-
Latin prefixquinque-/quinqu-/quint-
Binary1012
Ternary123
Octal58
Duodecimal512
Hexadecimal516
Greekε (or Ε)
Arabic, Kurdish٥
Persian, Sindhi, Urdu۵
Ge'ez፭
Bengali৫
Kannada೫
Punjabi੫
Chinese numeral五,伍
Devanāgarī५
Hebrewה
Khmer៥
Telugu౫
Malayalam൫
Tamil௫
Thai๕

In mathematics

Five is the third prime number.[1] Because it can be written as 221 + 1, five is classified as a Fermat prime;[1] therefore a regular polygon with 5 sides (a regular pentagon) is constructible with compass and unmarked straightedge. Five is the third Sophie Germain prime,[1] the first safe prime, the third Catalan number,[2] and the third Mersenne prime exponent.[3] Five is the first Wilson prime and the third factorial prime, also an alternating factorial.[4] Five is the first good prime.[5] It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.[1] It is also the only number that is part of more than one pair of twin primes. Five is a congruent number.[6]

Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3.

The number 5 is the fifth Fibonacci number, being 2 plus 3.[1] It is the only Fibonacci number that is equal to its position. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (OEIS: A030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.[7]

5 is the length of the hypotenuse of the smallest integer-sided right triangle.

In bases 10 and 20, 5 is a 1-automorphic number.

Five is the second Sierpinski number of the first kind, and can be written as S2 = (22) + 1.[8]

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group Sn is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K5, the complete graph with 5 vertices.

There are five Platonic solids.[9][1]

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5 because all other numbers written with a 5 in the ones place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five Exceptional Lie groups.

List of basic calculations
Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 × x 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5 ÷ x 5 2.5 1.6 1.25 1 0.83 0.714285 0.625 0.5 0.5 0.45 0.416 0.384615 0.3571428 0.3
x ÷ 5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5x 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125
x5 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293 537824 759375

In the powers of 5, every power ends with the number five and from 53, if the exponent is odd, then the hundreds digit is 1; instead, if it is even, the hundreds digit is 6.

In fifth powers, n5 ends in the same digit as n.

Evolution of the glyph

The evolution of the modern Western glyph for the numeral 5 cannot be traced back to the Indian system as for the numbers 1 to 4. The Kushana and Gupta empires in what is now India had among themselves several different glyphs which bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5.[10] It was from those characters that Europeans finally came up with the modern 5.

While the shape of the 5 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in .

Science

Astronomy

Biology
  • There are generally considered to be five senses.
  • Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.[17]

Computing

Religion and culture

Hinduism
  • The god Shiva has five faces[19] and his Mantra is also called Panchakshari (Five Worded) mantra.
  • The goddess Saraswati, goddess of knowledge and intellectual is associated with Panchami or number 5.
  • There are five elements in this universe: Dharti, Agni, Jal, Vayu evam Akash (Earth, Fire, Water, Air and Space respectively).
  • The most sacred tree in Hinduism has 5 leaves in every leaf stunt.
  • Most of the flowers have 5 petals in them.
  • The epic Mahabharata revolves around the battle between Duryodhana and his 99 other brothers and the 5 pandava princes -Dharma, Arjuna, Bhima, Nakula and Sahadeva.

Christianity

Discordianism
  • In Discordianism, 5 is seen as a very important number. This is demonstrated in the Law of Fives, as well as in the Pentabarf, which contains five rules.
  • Each page of the Principia Discordia—the primary religious document in Discordianism—is labeled with five digits.

Islam

Judaism
  • The Torah contains five books—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch (Greek for "five containers", referring to the scroll cases in which the books were kept), or Humash (חומש, Hebrew for "fifth").[24]
  • The book of Psalms is arranged into five books, paralleling the Five Books of Moses.[25]
  • The Khamsa, an ancient symbol shaped like a hand with four fingers and one thumb, is used as a protective amulet by Jews; that same symbol is also very popular in Arabic culture, known to protect from envy and the evil eye.[26]

Sikhism
  • The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as panj kakars or the "Five Ks" because they start with letter K representing kakka (ਕ) in the Punjabi language's Gurmukhi script. They are: kesh (unshorn hair), kangha (the comb), kara (the steel bracelet), kachhehra (the soldiers shorts), and kirpan (the sword) (in Gurmukhi: ਕੇਸ, ਕੰਘਾ, ਕੜਾ, ਕਛਹਰਾ, ਕਿਰਪਾਨ).[27] Also, there are five deadly evils: kam (lust), krodh (anger), moh (attachment), lobh (greed), and ankhar (ego).

Daoism

Other religions and cultures
  • According to ancient Greek philosophers such as Aristotle, the universe is made up of five classical elements: water, earth, air, fire, and ether. This concept was later adopted by Medieval alchemists and more recently by practitioners of Neo-Pagan religions such as Wicca.
  • The pentagram, or five-pointed star, bears religious significance in various faiths including Baha'i, Christianity, Freemasonry, Satanism, Taoism, Thelema, and Wicca.
  • In Cantonese, "five" sounds like the word "not" (character: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.
  • In East Asian tradition, there are five elements: (water, fire, earth, wood, and metal).[30] The Japanese names for the days of the week, Tuesday through Saturday, come from these elements via the identification of the elements with the five planets visible with the naked eye.[31] Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed calendars combining Western, Chinese-Buddhist, and Japanese names for each weekday.
  • Members of The Nation of Gods and Earths, a primarily African American religious organization, call themselves the "Five-Percenters" because they believe that only 5% of mankind is truly enlightened.[32]

Art, entertainment, and media

Fictional entities
  • James the Red Engine, a fictional character numbered 5.[33]
  • Johnny 5 is the lead character in the film Short Circuit (1986)[34]
  • Number Five is a character in Lorien Legacies[35]
  • Sankara Stones, five magical rocks in Indiana Jones and the Temple of Doom that are sought by the Thuggees for evil purposes[36]
  • The Mach Five (マッハ号 Mahha-gō?), the racing car Speed Racer (Go Mifune in the Japanese version) drives in the anime series of the same name (known as "Mach Go! Go! Go!" in Japan)
  • In the works of J. R. R. Tolkien, five wizards (Saruman, Gandalf, Radagast, Alatar and Pallando) are sent to Middle-earth to aid against the threat of the Dark Lord Sauron[37]
  • In the A Song of Ice and Fire series, the War of the Five Kings is fought between different claimants to the Iron Throne of Westeros, as well to the thrones of the individual regions of Westeros (Joffrey Baratheon, Stannis Baratheon, Renly Baratheon, Robb Stark and Balon Greyjoy)[38]
  • Myst uses the number 5 as a unique base counting system. In The Myst Reader series, it is further explained that the number 5 is considered a holy number in the fictional D'ni society.
  • Number Five is also a character in The Umbrella Academy comic book and TV series adaptation[39]

Films

Music

Groups

Other uses

Television
Stations
  • Channel 5 (UK), a television channel that broadcasts in the United Kingdom[65]
  • 5 (TV channel) (formerly known as ABC 5 and TV5) (DWET-TV channel 5 In Metro Manila) a television network in the Philippines.[66]
Series
  • Babylon 5, a science fiction television series[67]
  • The number 5 features in the television series Battlestar Galactica in regards to the Final Five cylons and the Temple of Five
  • Hi-5 (Australian TV series), a television series from Australia[68]
  • Hi-5 (UK TV series), a television show from the United Kingdom
  • Hi-5 Philippines a television show from the Philippines
  • Odyssey 5, a 2002 science fiction television series[69]
  • Tillbaka till Vintergatan, a Swedish children's television series featuring a character named "Femman" (meaning five), only can utter the word 'five'.
  • The Five (talk show): Fox News Channel roundtable current events television show, premiered 2011. So named for its panel of five commentators.
  • Yes! PreCure 5 is a 2007 anime series which follows the adventures of Nozomi and her friends. It is also followed by the 2008 sequel Yes! Pretty Cure 5 GoGo!
  • Hawaii Five-0, CBS American TV series.[70]

Literature
  • The Famous Five is a series of children's books by British writer Enid Blyton
  • The Power of Five is a series of children's books by British writer and screenwriter Anthony Horowitz
  • The Fall of Five is a book written under the collective pseudonym Pittacus Lore in the series Lorien Legacies
  • The Book of Five Rings is a text on kenjutsu and the martial arts in general, written by the swordsman Miyamoto Musashi circa 1645
  • Slaughterhouse-Five is a book by Kurt Vonnegut about World War II[71]

Sports
  • The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (Europe, Asia, Africa, Australia and Oceania, and the Americas).[72]
  • In AFL Women's, the top level of women's Australian rules football, each team is allowed 5 "interchanges" (substitute players), who can be freely substituted at any time.
  • In baseball scorekeeping, the number 5 represents the third baseman's position.
  • In basketball:
    • The number 5 is used to represent the position of center.
    • Each team has five players on the court at a given time. Thus, the phrase "five on five" is commonly used to describe standard competitive basketball.[73]
    • The "5-second rule" refers to several related rules designed to promote continuous play. In all cases, violation of the rule results in a turnover.
    • Under the FIBA (used for all international play, and most non-US leagues) and NCAA women's rule sets, a team begins shooting bonus free throws once its opponent has committed five personal fouls in a quarter.
    • Under the FIBA rules, A player fouls out and must leave the game after committing five fouls
  • Five-a-side football is a variation of association football in which each team fields five players.[74]
  • In ice hockey:
    • A major penalty lasts five minutes.[75]
    • There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net).[76]
    • The area between the goaltender's legs is known as the five-hole.[77]
  • In most rugby league competitions, the starting left wing wears this number. An exception is the Super League, which uses static squad numbering.
  • In rugby union:
    • A try is worth 5 points.[78]
    • One of the two starting lock forwards wears number 5, and usually jumps at number 4 in the line-out.
    • In the French variation of the bonus points system, a bonus point in the league standings is awarded to a team that loses by 5 or fewer points.

Technology
5 as a resin identification code, used in recycling.
  • 5 is the most common number of gears for automobiles with manual transmission.[79]
  • In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.[80]
  • On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button (on computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not).[81]
  • On most telephones, the 5 key is associated with the letters J, K, and L,[82] but on some of the BlackBerry phones, it is the key for G and H.
  • The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.[83]
  • The resin identification code used in recycling to identify polypropylene.[84]
  • A pentamer is an oligomer composed of five subunits.

Miscellaneous fields
International maritime signal flag for 5
St. Petersburg Metro, Line 5
The fives of all four suits in playing cards

Five can refer to:

gollark: https://media.discordapp.net/attachments/426116061415342080/959130970408247317/IMG_7500.jpg?width=702&height=621
gollark: Their age is then fetched from this later as needed.
gollark: Instances are stored in the superglobal instance array™ the first time they are made.
gollark: Macron can just use error cause inference in case of these errors.
gollark: Just retrieve the phone from the future.

See also

References
  1. Weisstein, Eric W. "5". mathworld.wolfram.com. Retrieved 2020-07-30.
  2. Weisstein, Eric W. "Catalan Number". mathworld.wolfram.com. Retrieved 2020-07-30.
  3. Weisstein, Eric W. "Mersenne Prime". mathworld.wolfram.com. Retrieved 2020-07-30.
  4. Weisstein, Eric W. "Twin Primes". mathworld.wolfram.com. Retrieved 2020-07-30.
  5. Sloane, N. J. A. (ed.). "Sequence A028388 (Good primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  6. Sloane, N. J. A. (ed.). "Sequence A003273 (Congruent numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  7. Weisstein, Eric W. "Perrin Sequence". mathworld.wolfram.com. Retrieved 2020-07-30.
  8. Weisstein, Eric W. "Sierpiński Number of the First Kind". mathworld.wolfram.com. Retrieved 2020-07-30.
  9. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61
  10. Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65
  11. "Atomic Number of Elements in Periodic Table". www.atomicnumber.net. Retrieved 2020-08-02.
  12. Cinalli, G.; Maixner, W. J.; Sainte-Rose, C. (2012-12-06). Pediatric Hydrocephalus. Springer Science & Business Media. p. 19. ISBN 978-88-470-2121-1. The five appendages of the starfish are thought to be homologous to five human buds
  13. Cantelmo, Mr Alessandro; Melina, Mr Giovanni; Papageorgiou, Mr Chris (2019-10-11). Macroeconomic Outcomes in Disaster-Prone Countries. International Monetary Fund. p. 25. ISBN 978-1-5135-1731-5. where Category 5 includes the most powerful hurricane
  14. Lindop, Laurie (2003-01-01). Chasing Tornadoes. Twenty-First Century Books. p. 58. ISBN 978-0-7613-2703-5. The strongest tornado would be an F5
  15. Pugh, Philip (2011-11-02). Observing the Messier Objects with a Small Telescope: In the Footsteps of a Great Observer. Springer Science & Business Media. p. 44. ISBN 978-0-387-85357-4. M5, like the previous objects in the Messier Catalogue is a globular star cluster in Serpen
  16. Ford, Dominic. "The galaxy NGC 5". In-The-Sky.org. Retrieved 2020-08-02.
  17. Kisia, S. M. (2010), Vertebrates: Structures and Functions, Biological Systems in Vertebrates, CRC Press, p. 106, ISBN 978-1-4398-4052-8, The typical limb of tetrapods is the pentadactyl limb (Gr. penta, five) that has five toes. Tetrapods evolved from an ancestor that had limbs with five toes. ... Even though the number of digits in different vertebrates may vary from five, vertebrates develop from an embryonic five-digit stage.
  18. Pozrikidis, Constantine (2012-09-17). XML in Scientific Computing. CRC Press. p. 209. ISBN 978-1-4665-1228-3. 5 5 005 ENQ (enquiry)
  19. Narayan, M. K. V. (2007). Flipside of Hindu Symbolism: Sociological and Scientific Linkages in Hinduism. Fultus Corporation. p. 105. ISBN 978-1-59682-117-0. Shiva has five faces;
  20. "CATHOLIC ENCYCLOPEDIA: The Five Sacred Wounds". www.newadvent.org. Retrieved 2020-08-02.
  21. "PBS - Islam: Empire of Faith - Faith - Five Pillars". www.pbs.org. Retrieved 2020-08-03.
  22. "Why Muslims Pray 5 Times A Day". MuslimInc. 2016-05-20. Retrieved 2020-08-03.
  23. "Panj Tan Paak - The Ahl-e Bayt - The Five Purified Ones of Allah". www.amaana.org. Retrieved 2020-08-03.
  24. Pelaia, Ariela. "Judaism 101: What Are the Five Books of Moses?". Learn Religions. Retrieved 2020-08-03.
  25. Peterson, Eugene H. (2000-01-06). Psalms: Prayers of the Heart. InterVarsity Press. p. 6. ISBN 978-0-8308-3034-3. The Psalms are arranged into five books
  26. Zenner, Walter P. (1988-01-01). Persistence and Flexibility: Anthropological Perspectives on the American Jewish Experience. SUNY Press. p. 284. ISBN 978-0-88706-748-8.
  27. Desai, Anjali H. (2007). India Guide Gujarat. India Guide Publications. p. 36. ISBN 978-0-9789517-0-2. ...he prescribed five sacred symbols to create a unified ident
  28. Chen, Yuan (2014). "Legitimation Discourse and the Theory of the Five Elements in Imperial China". Journal of Song-Yuan Studies. 44 (1): 325–364. doi:10.1353/sys.2014.0000. ISSN 2154-6665.
  29. Katz, Paul R. (1995-01-01). Demon Hordes and Burning Boats: The Cult of Marshal Wen in Late Imperial Chekiang. SUNY Press. p. 55. ISBN 978-1-4384-0848-4. using the title the Five Emperors
  30. Yoon, Hong-key (2006). The Culture of Fengshui in Korea: An Exploration of East Asian Geomancy. Lexington Books. p. 59. ISBN 978-0-7391-1348-6. The first category is the Five Agents [Elements] namely, Water, Fire, Wood, Metal, and Earth.
  31. Walsh, Len (2008-11-15). Read Japanese Today: The Easy Way to Learn 400 Practical Kanji. Tuttle Publishing. ISBN 978-1-4629-1592-7. The Japanese names of the days of the week are taken from the names of the seven basic nature symbols
  32. Smith, David H. (2010-04-06). Religious Giving: For Love of God. Indiana University Press. p. 36. ISBN 978-0-253-00418-5. Nation of Gods and Earths (also known as the Five Percenters),
  33. Allcroft, Britt; Friends, Thomas &; Awdry, W. (2014). James the Splendid Red Engine. Egmont UK Limited. ISBN 978-1-4052-7506-4. Meet Sodor's number 5 engine
  34. O'Sullivan, Emer (2005-03-05). Comparative Children's Literature. Routledge. p. 122. ISBN 978-1-134-40485-8. the super-robot Number 5 in the film Short Circuit,
  35. Lore, Pittacus (2013). The Fall of Five. Michael Joseph. ISBN 978-0-7181-5650-3.
  36. Windham, Ryder (2008). Indiana Jones Collector's Edition. Scholastic. p. 298. ISBN 978-0-545-09183-1. he gave him the five sacred stones with magical properties
  37. Chance, Jane (2016-11-21). Tolkien, Self and Other: "This Queer Creature". Springer. p. 70. ISBN 978-1-137-39896-3. These five included the head wizard,
  38. Jacoby, Henry (2012-02-23). Game of Thrones and Philosophy: Logic Cuts Deeper Than Swords. John Wiley & Sons. p. 34. ISBN 978-1-118-20605-8. ...view the events of A Song of Ice and Fire. As we'll see, the War of the Five Kings
  39. Netflix; Way, Gerard; Ba, Gabriel (2020). The Making of the Umbrella Academy. Dark Horse Comics. p. 21. ISBN 978-1-5067-1357-1.
  40. Palmer, Scott (1988). British Film Actors' Credits, 1895-1987. McFarland. p. 261. ISBN 978-0-89950-316-5.
  41. The Fifth Element (1997), retrieved 2020-08-03
  42. Fast Five (2011), retrieved 2020-08-03
  43. V for Vendetta (2006), retrieved 2020-08-03
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  45. Figes, Orlando (2014-02-11). Natasha's Dance: A Cultural History of Russia. Henry Holt and Company. ISBN 978-1-4668-6289-0. Also sometimes referred to as 'The Mighty Five' or 'Mighty Handful': Balakirev, Rimsky Korsakov, Borodin, Cui and Musorgsky
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