5

This article is about the number. For the years, see 5 BC and AD 5. For other uses, see 5 (disambiguation), Number Five (disambiguation), and The Five (disambiguation).

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Cardinal	five
Ordinal	5th (fifth)
Numeral system	quinary
Factorization	prime
Prime	3rd
Divisors	1, 45
Greek numeral	Ε´
Roman numeral	V, v
Greek prefix	penta-/pent-
Latin prefix	quinque-/quinqu-/quint-
Binary	1012
Ternary	123
Senary	56
Octal	58
Duodecimal	512
Hexadecimal	516
Greek	ε (or Ε)
Arabic, Kurdish	٥
Persian, Sindhi, Urdu	۵
Ge'ez	፭
Bengali	৫
Kannada	೫
Punjabi	੫
Chinese numeral	五
Armenian	Ե
Devanāgarī	५
Hebrew	ה
Khmer	៥
Telugu	౫
Malayalam	൫
Tamil	௫
Thai	๕
Babylonian numeral	𒐙
Egyptian hieroglyph, Chinese counting rod	|||||
Maya numerals	𝋥
Morse code	.....

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

The first Pythagorean triple

Historically, 5 has garnered attention throughout history in part because human limbs have five digits.

In mathematics

• Five is the third-smallest prime number, equal to the sum of the only consecutive positive integers to also be prime numbers (2 + 3).
• 5 is the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5).
• In geometry, the regular five-sided pentagon is the first regular polygon that does not tile the plane with copies of itself.
• A conic is uniquely determined using five points.
• There are 5 exceptional Lie groups as well as 5 of Mathieu groups that are sporadic groups.
• 5 is the only number that is part of more than one pair of twin primes, (3, 5) and (5, 7); this makes it the first balanced prime with equal-sized prime gaps above and below it (of 2).
• 5 is the first safe prime, where $(p-1)/2$ for a prime $p$ is also prime (2)
• 5 is the first good prime.
• 11, the fifth prime number, is the next good prime. It also forms the first pair of sexy primes with 5.
• 5 is also the first of the three known Wilson primes (5, 13, 563), where the square of a prime $p^{2}$ divides $(p-1)!+1.$ In the case of $p=5$,$(5-1)!+1=4!+1=24+1=25=5^{2}.$
• 5 is the total number of known unitary perfect numbers, which are numbers that are the sums of their positive proper unitary divisors.
• 5 is conjectured to be the only odd, untouchable number; if this is the case, then five will be the only odd prime number that is not the base of an aliquot tree.
• Every odd number greater than 5 is conjectured to be expressible as the sum of three prime numbers, this is also known as the odd Goldbach conjecture. A proof exists for this conjecture, but it is not fully published.
• Every odd number greater than one is the sum of at most five prime numbers (as a lower limit).
• There are five Platonic solids.
• There are five countably infinite Ramsey classes of permutations.
• A pentagram is a five-pointed polygram.
• 5 is the lower bound of the Hadwiger–Nelson problem.
• There are five complex exceptional Lie algebras: ${\mathfrak {g}}_{2}$, ${\mathfrak {f}}_{4}$, ${\mathfrak {e}}_{6}$, ${\mathfrak {e}}_{7}$, and ${\mathfrak {e}}_{8}$.

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		1.2	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		7776	16807	32768	59049	100000	161051	248832	371293	537824	759375

Evolution of the Arabic digit

The evolution of the modern Western digit for the numeral for five is traced back to the Indian system of numerals, where on some earlier versions, the numeral bore resemblance to variations of the number four, rather than "5" (as it is represented today). The Kushana and Gupta empires in what is now India had among themselves several forms that bear no resemblance to the modern digit. Later on, Arabic traditions transformed the digit in several ways, producing forms that were still similar to the numeral for four, with similarities to the numeral for three; yet, still unlike the modern five. It was from those digits that Europeans finally came up with the modern 5 (represented in writings by Dürer, for example).

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

On the seven-segment display of a calculator and digital clock, it is represented by five segments at four successive turns from top to bottom, rotating counterclockwise first, then clockwise, and vice-versa. It is one of three numbers, along with 4 and 6, where the number of segments matches the number.

Other fields

Astronomy

There are five Lagrangian points in a two-body system.

Biology

There are usually considered to be five senses (in general terms); the five basic tastes are sweet, salty, sour, bitter, and umami. Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity. Five is the number of appendages on most starfish, which exhibit pentamerism.

Computing

5 is the ASCII code of the Enquiry character, which is abbreviated to ENQ.

Literature

Poetry

A pentameter is verse with five repeating feet per line; the iambic pentameter was the most prominent form used by William Shakespeare.

Music

Modern musical notation uses a musical staff made of five horizontal lines. A scale with five notes per octave is called a pentatonic scale. A perfect fifth is the most consonant harmony, and is the basis for most western tuning systems. 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 plus 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.

Five is the lowest possible number that can be the top number of a time signature with an asymmetric meter.

Religion

Judaism

The Book of Numbers is one of five books in the Torah; the others being the books of Genesis, Exodus, Leviticus, and Deuteronomy. They 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"). 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.

Christianity

There are traditionally five wounds of Jesus Christ in Christianity: the nail wounds in Christ's two hands, the nail wounds in Christ's two feet, and the Spear Wound of Christ (respectively at the four extremities of the body, and the head).

Islam

The Five Pillars of Islam.

Mysticism

Gnosticism

The number five was an important symbolic number in Manichaeism, with heavenly beings, concepts, and others often grouped in sets of five.

Alchemy

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. There are five elements in the universe according to Hindu cosmology: dharti, agni, jal, vayu evam akash (earth, fire, water, air and space, respectively). 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. There are also five elements in the traditional Chinese Wuxing.

Quintessence, meaning "fifth element", refers to the elusive fifth element that completes the basic four elements (water, fire, air, and earth), as a union of these. The pentagram, or five-pointed star, bears mystic significance in various belief systems including Baháʼí, Christianity, Freemasonry, Satanism, Taoism, Thelema, and Wicca.

Miscellaneous fields

The fives of all four suits in playing cards

• "Give me five" is a common phrase used preceding a high five.
• 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).
• The number of dots in a quincunx.

See also

5 (disambiguation)

References

Further reading

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

External links

• Prime curiosities: 5
• Media related to 5 (number) at Wikimedia Commons