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This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, including the UK television channel, see 5 (disambiguation)
5 (five) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.
The SI prefix for 10005 is peta (P), and for its reciprocal femto (f).
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In mathematics
Five is the third smallest prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. It is an Eisenstein prime with no imaginary part and real part of the form . It is also the only number that is part of more than one pair of twin primes.
The number 5 is the 5th Fibonacci number, being 2 plus 3. 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), ... ( 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.
5 and 6 form a Ruth-Aaron pair under either definition.
There are five solutions to Znám's problem of length 6.
Five is the second Sierpinski number of the first kind, and can be written as S2=(2^2)+1
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.
Five is also the number of Platonic solids.
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.
Five is a factor of 10, so vulgar fractions with 5 in the denominator do not yield infinite decimal expansions, unlike most other primes. When written in the decimal system, all multiples of 5 will end in either 5 or 0.
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In numbering systems
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The Roman numeral for five is V, which comes from a representation of an outstretched hand.
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Evolution of the glyph
The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Kushana and Gupta Indians 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 look like a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s. It was from those characters that the Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that our modern 5 came from the Khmer.
In fonts with text figures, 5 usually has a descender, for example, .
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In science
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Astronomy
The Roman numeral V (usually) stands for the fifth-discovered satellite of a planet or minor planet (e.g. Jupiter V)
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In religion and culture
Muslims pray to Allah five times a day (Muhammad was said to have bargained it down with Allah from 50).
King David, author of Psalms, arranged the 150 Psalms into five books, paralleling the Five Books of Moses
The Khamsa, an ancient symbol shaped like a hand with five fingers, is used as a protective amulet by Jews and Muslims
According to some traditions of Maya mythology, we are now living in the Fifth World.
In Cantonese, "five" sounds like the word "not" (symbol: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.
In Greek Orthodox Christian mysticism, the number 5 symbolizes the Holy Spirit as the bearer of all life. In the monastic tradition of Mount Athos there exists a "hymn" to the Holy Spirit composed entirely and solely of repetitions of the word "pente" (Greek for "five")
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In music
The Five is the name of a 19th century Russian Group of nationalistic composers who included César Cui, Aleksandr Borodin, Mily Balakirev, Modest Mussorgsky, and Nikolay Rimsky-Korsakov
A Perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
Modern musical notation uses a musical staff made of five horizontal lines.
Using the Latin root, five musicians are called a quintet. One such group whose name celebrates their fiveness are the Jackson Five. (In an episode of Will & Grace guest-starring Janet Jackson, she declared that 5 is a mystical number and for that reason she must have precisely 5 backup dancers).
The Vogues song "Five-o'clock World" came in reference to the hours 9 to 5 (ending at 5 p.m.), which are the hours of a standard work day. There are also five working days (non-week-ends) in a week.
In harmonics - The fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5/1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves + a pure major third. Thus, the interval of 5/4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a capella vocal ensemble singing), will contain such a pure major third.
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In sports
In professional Wrestling, if a wrestler grabs the ropes when he is in a submission hold, the attacking wrestler has up to a 5 count to break the hold until a disqualification is made. This is also the case for choking, grabing the referee and standing to the top of the turnbuckle. Contrary to belief, it is not a four count as emphasised in WWE.
The number of players of a basketball team on the court at a given time.
Also used in basketball to represent the position of center.
In chess, the fewest number of moves a pawn makes to a queening square.
The number of kyu (pupil) grades in judo
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In technology
In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
On most telephones, the 5 key is associated with the letters J, K, and L, but on the BlackBerry it is the key for G and H.
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).
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In other fields
see also 5 (disambiguation)
Five is:
The number of oceans in the world.
The five senses are sight, smell, hearing, touch and taste.
The five basic tastes are sweet, salty, sour, bitter and umami.
The note in the English monetary system that features Elizabeth Fry. (£5 Note)
The smallest Euro banknote. It shows an antique bridge.
Quintessence, meaning 'fifth element', refers to the elusive fifth element that completes the basic four elements (water, fire, air and earth). There is also a movie called The Fifth Element.
The word "punch" comes from the Hindustani for five. Being true to the designation of punch, the drink Five Alive is named for its five ingredients.
A popular Internet catch phrase commonly used on forums such as Something Awful. Posts are given a rating out of five. Posts which receive an average rating of five are referred to as 'top posts' or 'comedy gold'.
There are 5 digits in a United States zip code
An informal term for the British Security Service, MI5
In tarot, card No. 5 is "the Hierophant".
Television network affiliates broadcast on local channel fives include WTTG-TV in Washington, D.C., WPTV-TV in West Palm Beach, Florida, WFXR-TV in Roanoke-Lynchburg, Virginia, KSDK-TV in St. Louis, Missouri, KALB-TV in Alexandria, Louisiana, KHAS-TV in Hastings, Nebraska, KFYR-TV in Bismarck, North Dakota, WLWT-TV in Cincinnati, Ohio, KOBI-TV in Medford, Oregon, WMC-TV in Memphis, Tennessee, and KXAS-TV in Dallas, Texas.
"Five" is the answer to the question asked at the very end of the mathematics quiz show in the movie Little Man Tate (the young protagonist blurts out the answer, but the host mishears it as being the answer from the contestant to whom the question is posed, and declares him the winner).
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Historical years
'''5 A.D.''', 5 B.C., 1905, 2005, etc.
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