Definitions

# 5 (number)

This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation).
5
Cardinal 5
five
Ordinal 5th
fifth
Numeral system quinary
Factorization prime
Divisors 1, 5
Roman numeral V
Roman numeral (Unicode) Ⅴ, ⅴ
Arabic ٥
Arabic (Urdu) ۵
Ge'ez
Bengali
Chinese numeral 五，伍
Devanāgarī
Hebrew ה (He)
Khmer
Thai
prefixes penta-/pent- (from Greek) quinque-/quinqu-/quint- (from Latin)
Binary 101
Octal 5
Duodecimal 5
Vigesimal 5

5 (five) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.

## Mathematics

Five is between 4 and 6 and is the third 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 $3n - 1$. It is also the only number that is part of more than one pair of twin primes.

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.

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.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, as is the case with most primes, 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 21 22 23 24 25 50 100 1000
$5 times x$ 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 250 500 5000

Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
$5 div x$ 5 2.5 $1.overline\left\{6\right\}$ 1.25 1 $0.8overline\left\{3\right\}$ $0.overline\left\{7\right\}1428overline\left\{5\right\}$ 0.625 $0.overline\left\{5\right\}$ 0.5 $0.overline\left\{4\right\}overline\left\{5\right\}$ $0.41overline\left\{6\right\}$ $0.overline\left\{3\right\}8461overline\left\{5\right\}$ $0.3overline\left\{5\right\}7142overline\left\{8\right\}$ $0.overline\left\{3\right\}$
$x div 5$ 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
$5 ^ x,$ 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125
$x ^ 5,$ 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293

## 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. The Khmer glyph develops from the Kushana/Ândhra/Gupta numeral, its shape looking like a modern day version with an extended swirled 'tail' [G Ifrah, The Universal History of Numbers ]

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 .

## Religion and culture

Judeo-Christian

• 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").
• The book of Psalms is arranged 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.
• 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").Islamic
• Muslims pray to Allah five times a day
• In Islam, particularly Shia Islam, the Panjetan or the Five Holy Purified Ones are the members of Muhammad's family including: Muhammad, Ali, Fatima, Hasan, Husayn and is often symbolically represented by an image of the Khamsa.
• There are five basic "pillars" of Islam.Sikh
• 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 in the Punjabi language. They are: Kesh (unshorn hair), Kangha (the comb), Kara (the steel bracelet), Kachh (the soldiers shorts), and Kirpan (the sword).Other
• According to some traditions of Maya mythology, we are now living in the Fifth World.
• According to various mythologies, namely that of Wicca, the universe is comprised of five classical elements: water, earth, air, fire and ether.
• 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 Discordianism, 5 is seen as a very important number as demonstrated in the Law of Fives and The Pentabarf, which contains five rules. Each page of the Principia Discordia, the primary religious document in Discordianism, is also labeled with 5 digits.
• In East Asian tradition, there are five elements: (water, fire, earth, wood and metal). 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. 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.
• In some cultures there are five cardinal directions, including the center.

## Music

1. 5, the pseudonym of American musician Craig Jones, when performing with Slipknot
• 5 is a song from après les dancings album by Travis Bürki.
• 5 is an album by Lenny Kravitz.
• A Perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
• Bands with "five" in their name include We Five, Five for Fighting, Click Five, MC5 (short for "Motor City Five"), Ben Folds Five and the Five Man Electrical Band.
• Five Minutes Alone is a song by Heavy metal group Pantera
• Five Minutes Of Funk is a song by New York rapper Whodini
• 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 cappella vocal ensemble singing), will contain such a pure major third.
• Jurassic 5 is a hip hop crew whose second full length album was titled "Power In Numbers."
• Maroon 5 is a pop/rock band from Los Angeles, California, that has become popular thanks to songs such as "Harder To Breathe" and "This Love." The band won the Grammy Award for Best New Artist in 2005.
• Modern musical notation uses a musical staff made of five horizontal lines.
• Take Five is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.
• 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.
• The name of the band The Fifth Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.*There was a British boy band called 5ive.
• The number of completed, numbered piano concertos of Ludwig van Beethoven and Camille Saint-Saëns.
• 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.
• Using the Latin root, five musicians are called a quintet, e.g. the Jackson Five. (In season 7 episode 2 of Will & Grace "Back Up, Dancer" guest-starring Janet Jackson, she declared that 5 is a mystical number and for that reason she must have precisely 5 backup dancers).

## Technology

• 5 is the most common number of gears for automobiles with manual transmission.
• In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
• 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).
• 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.
• The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
• The resin identification code used in recycling to identify polypropylene.

Five is:

## References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 58 - 67