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7

7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube.

This article is about the number. For the year, see AD 7. For other uses, see 7 (disambiguation) and No. 7 (disambiguation).

← 6 7 8 →

seven

7th
(seventh)

septenary

prime

4th

1, 7

Ζ´

VII, vii

hepta-/hept-

septua-

1112

213

116

78

712

716

Z, ζ

፯

٧

۷

৭

七, 柒

७

౭

௭

ז

៧

๗

೭

൭

Է

𒐛

𓐀

_ _...

As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week.[1] 7 is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky.

Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers. (See .)

Lagrange's four-square theorem#Historical development

Seven is the of one number, the cubic number 8 = 23 making it the base of the 7-aliquot tree; it is also, therefore, the sum-of-divisors of only 4, its prime index. Furthermore, the smallest number with seven divisors is 64 = 82.[15]

aliquot sum

The seventh is the second perfect number 28 = 7 × 4,[16] which precedes 6.[17] In decimal representation, the reciprocal of 7 repeats six digits (as 0.142857),[18][19] whose sum when cycling back to 1 is equal to 28. On the other hand, 7 is the number of partitions of 5,[20] a value n which yields the third perfect number 496 for 2n − 1(2n − 1), by the Euclid-Euler theorem.

triangular number

7 is the only number D for which the equation 2n − D = x2 has more than two solutions for n and x . In particular, the equation 2n − 7 = x2 is known as the Ramanujan–Nagell equation.

natural

There are 7 in two dimensions, consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers.[21] These are related to the 17 wallpaper groups whose transformations and isometries repeat two-dimensional patterns in the plane.[22][23] The seventh indexed prime number is seventeen.[24]

frieze groups

As a consequence of and Euler's criterion, all cubes are congruent to 0, 1, or 6 modulo 7.

Fermat's little theorem

A seven-sided shape is a .[25] The regular n-gons for n ⩽ 6 can be constructed by compass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these simple tools.[26] Figurate numbers representing heptagons are called heptagonal numbers.[27] 7 is also a centered hexagonal number.[28]

heptagon

Seven

colors in a rainbow

Seven

continents

Seven climes

The neutral

pH balance

Number of notes in the of Western music

diatonic scale

Number of spots most commonly found on

ladybugs

Atomic number for

nitrogen

Number of

diatomic molecules

Seven basic

crystal systems

Seven and the derivative Seven Heavens

Classical planets

Seven Wonders of the Ancient World

Seven

metals of antiquity

Seven days in the week

Seven Seas

Seven Sages

Seven champions that fought Thebes

and Seven Kings of Rome

Seven hills of Rome

the daughters of Atlas also known as the Pleiades

Seven Sisters

The Pythagoreans invested particular numbers with unique spiritual properties. The number seven was considered to be particularly interesting because it consisted of the union of the physical (number 4) with the spiritual (number 3).[66] In Pythagorean numerology the number 7 means spirituality.


References from classical antiquity to the number seven include:

Seven days (more precisely ) of Creation, leading to the seventh day or Sabbath (Genesis 1)

yom

Seven-fold vengeance visited on upon for the killing of Abel (Genesis 4:15)

Cain

Seven pairs of every clean animal loaded onto the ark by Noah (Genesis 7:2)

Seven years of plenty and seven years of famine in Pharaoh's dream (Genesis 41)

Seventh son of Jacob, , whose name means good luck (Genesis 46:16)

Gad

Seven times bullock's blood is sprinkled before God (Leviticus 4:6)

Seven nations God told the they would displace when they entered the land of Israel (Deuteronomy 7:1)

Israelites

Seven days (de jure, but de facto eight days) of the feast (Exodus 13:3–10)

Passover

Seven-branched or Menorah (Exodus 25)

candelabrum

Seven played by seven priests for seven days to bring down the walls of Jericho (Joshua 6:8)

trumpets

Seven things that are detestable to God (Proverbs 6:16–19)

Seven Pillars of the (Proverbs 9:1)

House of Wisdom

Seven archangels in the deuterocanonical (12:15)

Book of Tobit

(7 notes)

Diatonic scale

Seven colors in the rainbow

Seven continents

Seven liberal arts

Seven Wonders of the Ancient World

Seven days of the

Week

Septenary (numeral system)

Year Seven (School)

Se7en (disambiguation)

Sevens (disambiguation)

One-seventh area triangle

(Ƶ)

Z with stroke

List of highways numbered 7

Wells, D. London: Penguin Group (1987): 70–71

The Penguin Dictionary of Curious and Interesting Numbers