7 (number)

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[edit] In mathematics

Seven is the fourth prime number.
Seven is a Mersenne prime, since 2³ - 1 = 7.
Seven is the fourth Mersenne prime exponent.
Seven is the first Newman-Shanks-Williams prime.
Seven is the third Lucas prime.
Seven is the first Woodall prime.
Seven is the second lucky prime.
Seven is the second safe prime.
Seven is the fourth factorial prime
Seven is both a Carol number and a Kynea number.
Seven is the smallest number that can't be represented as a sum of fewer than four nonzero squares.
Seven is a self number.
Seven is the smallest happy number, except for the trivial example of 1.
Although the divisible by seven (7) test is not well known (especially compared to the popular divisible by three (3) test), there is an easy way to test if a natural number is evenly divisible by seven (7). See also Divisibility rule.

Remove the last digit,
Double it, and
Subtract it from the remaining digits.
If the result is negative and there are 2 or more digits, drop the negative sign.
Repeat until you end up with a result that is a multiple of seven (7). (i.e. -7, 0, or +7)

For example, the number 1358 is evenly divisible by seven, since:

135 - (8*2) = 119

11 - (9*2) = -7

Using Number Theory the proof is rather easy, once we rewrite the number n in the form:

n = 10a + b

Where:

a is the remaining digits, and

b is the last digit.

Then:

10a + b = 0 (mod 7)

5 * (10a + b) = 0 (mod 7)

49a + a + 5b = 0 (mod 7)

a + 5b - 7b = 0 (mod 7)

a - 2b = 0 (mod 7)

999,999 divided by 7 is exactly 142,857, so vulgar fractions with 7 in the denominator have six-digit repeating sequences in their decimal expansions. 1/7 = 0.142857142....
A seven-sided polygon is a heptagon. The regular n-gons for n ≤ 6 can be constructed by compass and straightedge alone, but the regular heptagon cannot. Figurate numbers representing heptagons (including seven) are called heptagonal numbers. Seven is also a centered hexagonal number.
There are seven frieze groups, the groups consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers.
A group or a series of seven is a heptad.
7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined.

[edit] In numeral systems

Base	Numeral system
2	binary	111
3	ternary	21
4	quaternary	13
5	quinary	12
6	senary	11
7	septenary	10
over 7 (octal, decimal, etc)		7

In quaternary, 7 is the smallest prime with a composite sum of digits.

[edit] 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
$7 \times x$	7	14	21	28	35	42	49	56	63	70		77	84	91	98	105	112	119	126	133	140		147	154	161	168	175		350	700	7000

Division	1	2	3	4	5	6	7	8	9	10
Division	11	12	13	14	15
$7 \div x$	7	3.5	$2.\overline{3}$	1.75	1.4	$1.1\overline{6}$	1	0.875	$0.\overline{7}$	0.7
$7 \div x$	$0.\overline{6}\overline{3}$	$0.58\overline{3}$	$0.\overline{5}3846\overline{1}$	0.5	$0.4\overline{6}$
$x \div 7$	$0.\overline{1}4285\overline{7}$	$0.\overline{2}8571\overline{4}$	$0.\overline{4}2857\overline{1}$	$0.\overline{5}7142\overline{8}$	$0.\overline{7}1428\overline{5}$	$0.\overline{8}5714\overline{2}$	1	$1.\overline{1}4285\overline{7}$	$1.\overline{2}8571\overline{4}$	$1.\overline{4}2857\overline{1}$
$x \div 7$	$1.\overline{5}7142\overline{8}$	$1.\overline{7}1428\overline{5}$	$1.\overline{8}5714\overline{2}$	2	$2.\overline{1}4285\overline{7}$

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13
$7 ^ x\,$	7	49	343	2401	16807	117649	823543	5764801	40353607	282475249		1977326743	13841287201	96889010407
$x ^ 7\,$	1	128	2187	16384	78125	279936	823543	2097152	4782969	10000000		19487171	35831808	62748517

Radix	1	5	10	15	20	25	30	40	50	60	70	80	90	100
Radix	110	120	130	140	150	200	250	500	1000	10000	100000	1000000
$x_{7} \$	1	5	$13_{7} \$	$21_{7} \$	$26_{7} \$	$31_{8} \$	$36_{8} \$	$50_{8} \$	$62_{8} \$	$74_{8} \$	$106_{8} \$	$120_{8} \$	$132_{8} \$	$144_{8} \$
$x_{7} \$	$156_{8} \$	$170_{8} \$	$202_{8} \$	$214_{8} \$	$226_{8} \$	$310_{8} \$	$372_{8} \$	$764_{8} \$	$1750_{8} \$	$23420_{8} \$	$303240_{8} \$	$3641100_{8} \$

[edit] Evolution of the glyph

In the beginning, various Hindus wrote 7 more or less in one stroke as a curve that looks like an uppercase J upside down. The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the character more rectilinear. The eastern Arabs developed the character from a 6-look-alike into an uppercase V-look-alike. Both modern Arab forms influenced the European form, a two-stroke character consisting of a horizontal upper line joined at its right to a line going down to the bottom left corner, a line that is slightly curved in some font variants. As is the case with the European glyph, the Cham and Khmer glyph for 7 also evolved to look like their glyph for 1, though in a different way, and so they were also concerned with making their 7 more different. For the Khmer this often involved adding a horizontal line above the glyph. This is analogous to the horizontal stroke through the middle that is sometimes used in handwriting in the Western world but which is almost never used in computer fonts. This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph for one in writings that use a long upstroke in the glyph for one.

On the seven-segment displays of pocket calculators and digital watches, 7 is the number with the most common glyph variation (0, 6 and 9 also have variant glyphs). Most calculators use three line segments, but on Sharp, Casio and a few other brands of calculators, 7 is written with four line segments. The reason is that 7 is written as in ① in Japan, Korea and so on.

In fonts with text figures, 7 usually has a descender, for example, .

[edit] In science

The number of spots in a common ladybug.

[edit] Chemistry

The atomic number of nitrogen.
The number of periods, or horizontal rows of elements, on the periodic table.
The number of carbon atoms in heptane, a hydrocarbon.
The neutral pH - the pH level of pure water.

[edit] Astronomy

The number of objects in the solar system visible to the naked eye — the Sun, the Moon and the five classical naked eye planets: Mars, Mercury, Jupiter, Venus, and Saturn.
Messier object M7, a magnitude 3.5 open cluster in the constellation Scorpius.
The New General Catalogue object NGC 7, a 14th magnitude spiral galaxy in the constellation Sculptor
The seven daughters of Atlas in the Pleiades (also called the "seven sisters").
The number of saints appear in a constellation called "Saptharishi Mandalam" in Indian astronomy.
The number of stars in the constellation of Ursa major.
The Saros number of the solar eclipse series which began on -2590 April 8 and ended on -1310 May 16. The duration of Saros series 7 was 1280.1 years, and it contained 72 solar eclipses.
The Saros number of the lunar eclipse series which began on -2595 July 15 and ended on -1008 February 22. The duration of Saros series 7 was 1586.6 years, and it contained 89 lunar eclipses.
The Roman numeral VII stands for white dwarfs in the Yerkes spectral classification scheme.
The Roman numeral VII (usually) stands for the seventh-discovered satellite of a planet or minor planet (e.g. Jupiter VII)

[edit] In technology

The code for international direct dial phone calls to Russia and Kazakhstan
The number of digits in an American telephone number, excluding the area code
The number of individual segments in one digit on a digital clock or calculator seven-segment display screen
In Microsoft's Rich Text Format specification, seven and all numbers congruent to it modulo 256 refer to variants of the German language.
In ASCII character set, the bell character
A global push email provider from Redwood City, California: SEVEN Networks, Inc.
A e-commerce company from Cancun, Mexico: Seven Global.

[edit] In religion

In Judaism:
- A highly symbolic number in the Torah, alluding to the infusion of spirituality and Godliness into the Creation. For example:
1. God rested on and sanctified the 7th day (Shabbat)
2. A seven-day purification period is required for one who has become tamei to become tahor
3. The Shemittah (Sabbatical) year arrives every 7th year
4. The Jubilee (Yovel) year comes after 7 times 7 years
5. The Counting of the Omer leading up to the Giving of the Torah is expressed as "7 times 7 weeks"
- The weekly Torah portion is divided into seven aliyahs, and seven men or boys over the age of 13 are called up for the reading of these aliyahs during Shabbat morning services
- Seven blessings are recited under the chuppah during a Jewish wedding ceremony
- David was the seventh son of Jesse
- A Jewish bride and groom are feted with seven days of festive meals after their wedding, known as Sheva Berachot ("Seven Blessings")
- The number of Ushpizzin (also known as the "Seven Shepherds") who visit the sukkah during the holiday of Sukkot: Abraham, Isaac, Jacob, Joseph, Moses, Aaron, and David
- The number of nations God told the Israelites they would displace when they entered the land of Israel (Deut. 7:1): the Hittite, the Girgashite, the Amorite, the Canaanite, the Perizzite, the Hivite, and the Jebusite
- In Breslov tradition, the seven orifices of the face (2 eyes, 2 nostrils, 2 ears, and the mouth) are called "The Seven Candles"
In Islam:
- The number of ayat in surat al-Fatiha
- The number of heavens in Islamic tradition
- The number of Earths in Islamic tradition
- The numbers 7, 70, 70,000, etc. are used in Islamic traditions to denote an infinite or high number. In Arabic, 70, 70,000, etc. is used to mean infinite. This is because 1 is the smallest number, 2 is just after 1, 5 and 10 are exact, 4 and 6 are just before and after 5, and 9 is just before 10. This leaves 3, 7, and 8. 8 is closer to the end although it is larger. 8 is also an even number, so divisible by 2. Between 3 and 7, 3 is smaller so 7 is chosen to represent infinite.
In Christianity:
- The number of churches of Asia to which the Book of Revelation is addressed
- The number of the Seven Deadly Sins: Lust, Gluttony, Avarice, Envy, Wrath, Sloth, and Pride.
- The number of the Seven Virtues: Chastity, Moderation, Liberality, Charity, Meekness, Zeal and Humility, corresponding to the seven deadly sins.
- The seven terraces of Mount Purgatory (one per deadly sin)
- The number of sacraments in the Roman Catholic faith
- The number of heads of the beast of the Book of Revelation, and of some other monsters, like the hydra and the number of seals.
- In the New Testament, the Gospel of Matthew 18:21, Jesus says to Peter to forgive seventy times seven people. ^[1]
The number of times Cain will be avenged by God if he is murdered. Gen 4:15
In the Bible, the number seven is the perfect number, six is imperfect.
The number of Archangels according to some systems. Seven Archangels
The minor symbol number of yang from the Taoist yin-yang
The number of palms in an Egyptian Sacred Cubit
The number of ranks in Mithraism
The number seven is of particular significance within Cherokee cosmology
In Buddhism, Buddha walked 7 steps at his birth.

[edit] In mythology

In Khasi mythology, the seven divine women who were left behind on earth and became the ancestresses of all humankind
The number of gateways traversed by Inanna during her descent into the underworld
The number of sleeping men in the Christian myth of the "Seven Sleepers"
The number of sages in Hindu mythology. Their wives are the goddesses referred to as the "Seven Mothers"
The number of main islands of mythological Atlantis
In Guaraní mythology, the number of prominant legendary monsters.
Seven Lucky Gods exist in Japanese mythology.

[edit] In psychology

The Magical Number Seven, Plus or Minus Two is a 1956 paper by cognitive psychologist George Miller who found a correlation between various human cognitive capacity limits within the range 7±2.
When asked to choose a number between 1 and 10, the most common number chosen appears to be 7. This choice appears to be driven by peoples idea of the properties a random number should have.

[edit] In music

The number of notes in the traditional Western musical scale
In music, the Roman numeral vii is the subtonic (bVII) or leading tone (VII) scale degree, chord, or diatonic function, when distinguished V = major and v = minor.
The number of completed, numbered symphonies of Jean Sibelius and Sergei Prokofiev
A pop music singer in South Korea : 세븐 ; SE7EN (singer)
A five-piece teenybopper band from the late 1980s.
A current band called Seven Mary Three.
A band from the 90s Seven Red Seven

Seven is part of all of the name of many musical works:

[edit] Albums

A 2004 album by The Tea Party: see Seven circles (Tea Party album.
A 2003 album by Atmosphere: see Seven's Travels.
A 2003 album by Enrique Iglesias: see 7 (Enrique Iglesias album).
A 2002 EP by U2: see 7 (EP).
A 2000 album by S Club 7: see 7 (S Club 7 album).
A 1997 album by Zap Mama: see 7 (Zap Mama album).
A 1996 album by Apoptygma Berzerk: see 7 (Apoptygma Berzerk album).
A 1996 album The Don Killuminati: The 7-Day Theory by Tupac Shakur.
A 1992 album by James: see Seven (James album).
A 1986 album by George Strait: see 7 (George Strait album).
A 1985 album by David Meece: see 7 (David Meece album).
A 1983 album by Duran Duran.
A 1981 album by Madness: see 7 (Madness album).
A 1980 album by Jon Anderson: Song of Seven
A 1974 album by Poco.
A 1974 album by Bob Seger: see Seven (Bob Seger album).
A 1991 album by Mannheim Steamroller: see Fresh Aire 7
The albums Keeper of the Seven Keys: Part One, Keeper of the Seven Keys: Part Two, Keeper of the Seven Keys: The Legacy by Helloween.
The 1988 album Seventh Son of a Seventh Son by Iron Maiden, based on a book with the same name by Orson Scott Card. Also their seventh studio album.
The 2000 album The Seventh Song by Steve Vai, a compilation of the seventh songs of his previous albums.

[edit] Songs

The song "Seven Years" by Saosin
The song "Song of Seven" by Jon Anderson
The song "Seven" by David Bowie
The song "Seven" by Sunny Day Real Estate
The song "Seven" by Gackt
The song "Seven" by Necrophagist
The song "7" by Prince
The song "Seven Nation Army" by The White Stripes
The song "Seven Seas of Rhye" by Queen
The song "Song Seven" by Interpol
The song "Keeper of the Seven Keys" by Helloween
The song "Seven Years Down" Rancid
The song "Seven Years" by Saosin
The song "Magnificent Seven" by The Clash
The short instrumental piece "7" by Moby
The song "seven bridges road" by The Eagles
"Seven", a song by The Long Winters from the 2006 album Putting the Days to Bed
The song "Seven Year Ache" by Rosanne Cash
The song "Seven Seconds" by Youssou N'Dour and Neneh Cherry which topped the charts in 1994 by PSK Teenage God

[edit] In television

The name of one of the monsters in the cartoon television show Seven Little Monsters.
Seven, an episodic character from the sitcom Married... with Children.
In Star Trek: Voyager, Seven of Nine (also called Seven for short) is one of the crewmembers.
In Seinfeld, the name George Costanza desired to give his first-born (with Susan Ross); he later falsely claimed that he had promised this to the widow of baseball great Mickey Mantle, whose number was 7.
The name of a television show 7th Heaven.
Seven Network, a television network in Australia
The number of currently identified biological Cylon models, out of a possible 12, in the television show, Battlestar Galactica.

[edit] In film

The musical film Seven Brides For Seven Brothers
The film Se7en, directed in 1995 by David Fincher
In the Disney film Herbie Goes to Monte Carlo (1977), the car number of Giselle, the Lancia Scorpion with whom Herbie falls in love
James Bond's agent secret number is 007
In the Disney film Snow White and the Seven Dwarfs
In the film "The Benchwarmers", Number 7 is the name of the robotic butler
The film Lucky number s7evin, directed in 2006 by Paul McGuigan
The film The Magnificent Seven starring Yul Brynner.
The Japanese film Seven Samurai directed by Akira Kurosawa.
The Swedish film The Seventh Seal directed by Ingmar Bergman.
In the film 2001: A Space Odyssey (film), Dave Bowman encounters seven octahedron during his journey through the infinite.

[edit] In sports

In Ultimate (sport), the number of players on the field for each team.
In team handball, the number of players on each team including the goalkeeper.
In rugby league, the scrum-half/halfback
In rugby union, the openside flanker
In baseball, seven represents the left fielder's position
Seven Cycles, a bicycle manufacturer
Retired jersey number of former baseball player Mickey Mantle and former hockey player Ted Lindsay.
Retired jersey number of John Elway, Hall of Fame quarterback of the Denver Broncos.
Number associated with former England national team captain David Beckham.
The car number for NASCAR driver Robby Gordon.
Jersey number of Ben Roethlisberger, quarterback of the Pittsburgh Steelers
Jersey number of Michael Vick, quarterback of the Atlanta Falcons
Jersey number of Matt Leinart, quarterback of the Arizona Cardinals
Jersey number of Byron Leftwich, quarterback of the Jacksonville Jaguars
Jersey number of Renato Gaúcho, soccer world champion with Grêmio in 1983

[edit] In other fields

International maritime signal flag for 7

The reason for 7 being a lucky number symbolically (such as in the bible), is because it represents the union of man and woman, since the number for women is 4 and the number for men is 3.
Seven candles are lit in the kinara during the African-American celebration of Kwanzaa, which is a seven-day holiday
It is traditionally thought that there are seven continents on Earth.
Seven is the smallest positive integer requiring more than one syllable in English.
There are seven musicians in a septet and seven babies born in a set of septuplets. The most famous set of septuplets are the McCaughey Septuplets, who were born in 1997.
The British fifty-pence and twenty-pence coins are heptagons, with the sides curved to give them a constant diameter.
Many cities are claimed to be constructed amidst seven hills; see Seven hills of Rome.
Serial sevens are used as a diagnostic test in medicine.
In linguistics, the "7" is sometimes used to represent a glottal stop, as a substitute for ʔ.
The Harry Potter series has several references to the number seven.
Game developer Bungie Studios use the number 7 extensively throughout all their games. For example a character in the Halo games is called 343 Guilty Spark, 343 being 7 to the power of 3.
In Fist of the North Star (Hokuto no Ken), the main character, Kenshiro, is also known as "the man with seven wounds" for the seven scars on his body in the shape of the Big Dipper.
Year 7 is the first year of secondary education in England and Wales, equivalent to the American 6th grade.
Seventh grade is the seventh year of American education since kindergarten.

Seven is also:

The largest number of sticks (or other cylindrical objects) that can be tied into a bundle such that the shape of the bundle remains fixed.
The number of openings into the human head (mouth, two eyes, two ears, two nostrils).
The number of spheres in the Ptolemaic system
The traditional number of Wonders of the Ancient World.
Viewed as a lucky number in both Japanese Culture and many Western cultures.
The number of days in a week.
The number of the ages of man into which William Shakespeare divided a lifetime
The figurative number of seas
The number of colors of the rainbow (the asteroid 7 Iris is named after the rainbow goddess Iris)
The number of chakras.
The number of basic principles of the bushido
The number of points on a sheriff's star
In Galician folklore, a seventh son will be a werewolf. In other folklores, after six daughters, the seventh child is to be a son and a werewolf. In other European folklores, the seventh son of a seventh son will be a vampire.
When rolling two standard six-sided dice, seven is the number most likely to occur. It is the sum of any two opposite sides on a standard six-sided die
The number of dwarves in the movie Snow White
The number of rings given to the Dwarf Lords in J.R.R. Tolkien's The Lord of the Rings
The Heptarchy, from the (Greek for seven realm, is the name applied by historians to the period (500-850 AD) in English history after the Anglo-Saxon conquest of England, derived from the seven kingdoms of Northumbria, Mercia, East Anglia, Essex, Kent, Sussex, and Wessex, which eventually merged to become the Kingdom of England during the early 10th century.
September was the seventh month in the ancient Roman calendar, as its name indicates. After the reform that led to the current order, the seventh month is July.
Septidi was the seventh day of the decade in the French Revolutionary Calendar
The traditional count of Basque provinces as expressed in the slogan Zazpiak Bat
The Seven Sages of Greece: Solon, Chilon, Thales, Bias, Cleobulus, Pittacus and Periander.
Cibola was one of the legendary Seven Cities of Gold the Spanish thought existed.
In tarot, card No. 7 is "the Chariot"
In casinos, the line 7-7-7 (triple seven, not seven hundred seventy seven) is a common winning line on slot machines

[edit] Names and titles

Seven or 7 is all or part of a number of names and titles of people, artworks or organizations, including:

Sevens, a card game
An agency of photojournalists founded by seven photographers
Canadian fashion photographer Sev Seven
Musician/actor Andre Benjamin's and singer Erykah Badu's son, Seven.
The stage name of musician Keith Volpone
SE7EN (singer), a Korean R&B/hip-hop singer
Se7en, a 1995 movie
Part of the names of:
- Aleksis Kivi's "Seven Brothers", the most famous book of Finnish literature
- Seven Pillars of Wisdom, a book written by T. E. Lawrence
- The Secret Seven, name of children adventure book by Enid Blyton
- The book Seven Years in Tibet
- Kurosawa's film Seven Samurai, that inspired the 1960 movie with Steve McQueen The Magnificent Seven and its own sequels
- Several groupings called the Seven Sisters
- The Anime Eureka Seven
- The Seven Virgins:
  - The Seven Virgins mountain range in Sri Lanka, which was the scene of an air disaster on 4 December 1974, involving a DC-8 Series 55F passenger jetliner operated by the charter company Martinair which left 191 dead.
  - the Saptha Kanniyar were seven faithful devotees of Siva, who give birth to seven boys, in Hindu mythology.
  - An anonymous 17th Century carol, The Seven Virgins.
- Seven Sisters, a 1998 song album by pop singer Meja
- Seven of Nine, a crewmember in the Star Trek universe
- Rugby Sevens, a variant of rugby union and rugby league that contains only seven players per side instead of the standard 15 (union) or 13 (league)
- The Rugby World Cup Sevens, the World Cup for the union version of Sevens
- The IRB Sevens World Series, also in the union version of Sevens, which has included the following events at some point:
  - Australia Sevens (new for 2006-07)
  - Dubai Sevens
  - Hong Kong Sevens, the most famous event in the series
  - London Sevens
  - Paris Sevens (future status to be determined)
  - Standard Chartered Sevens Singapore (future status to be determined)
  - South Africa Sevens
  - USA Sevens
  - Wellington Sevens
- The Seven Habits of Highly Effective People, a book by Stephen Covey
- The metal band Avenged Sevenfold, also known as A7X.
- Seven Nation Army, a single by the White Stripes
007, codename for James Bond, a fictional secret spy agent
In the InuYasha series, the Shichinintai are, as their name says, a band of seven mercenaries.
There are seven games in the World Series, the championship of baseball.
In the Fushigi Yuugi series, the four beast gods each have seven warriors. The Genbu Seven, the Byakko Seven, the Seiryuu Seven, and the Suzaku Seven.
In the One Piece series, the Seven Warlords of the Sea (known in Japan as the Shichibukai, or Seven Arm Seas), are seven powerful pirates.
The number of individual personalities serving Harman Smith as part of the group of assassins called the Killer7, hence the title of the game.
In the catalan culture, 7 is present in a lot of popular stories like "Les set cabretes i el llop".
Number 7 is a popular brand of Canadian cigarettes.

Number 7 cigarette package; they have been restyled somewhat since this scan.
7up is a popular soft drink.
7-Eleven is the of a convience store based in the U.S.
Seven Jeans, also known as Seven '7' for all Mankind, a brand of designer jeans.

[edit] Historical years

A.D. 7, 7 B.C., 1907, 2007, etc.

[edit] Notes

^ "21 Then Peter came to Jesus and asked, 'Lord, how many times shall I forgive my brother when he sins against me? Up to seven times?' 22 Jesus answered, 'I tell you, not seven times, but seventy-seven times' ...". [1]

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