Number 7

Mathematics[edit]

• Seven, the fourth prime number, is not only a Mersenne prime (since 2³ − 1 = 7) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime. It is also a Newman–Shanks–Williams prime, a Woodall prime, a factorial prime, a lucky prime, a happy number(happy prime), a safe prime (the only Mersenne safe prime) and the fourth Heegner number.
• 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 aliquot sum of one number, the cubic number 8 and is the base of the 7-aliquot tree.
• n = 7 is the first natural number for which the next statement does not hold: "Two nilpotent endomorphisms from Cⁿ with the same minimal polynomial and the same rank are similar."
• 7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined.
• 7 is the lowest dimension of a known exotic sphere, although there may exist as yet unknown exotic smooth structures on the 4-dimensional sphere.
• 999,999 divided by 7 is exactly 142,857. Therefore, when a vulgar fraction with 7 in the denominator is converted to a decimal expansion, the result has the same six-digit repeating sequence after the decimal point, but the sequence can start with any of those six digits.^[1] For example, 1/7 = 0.142 857 142.... and 2/7 = 0.285 714 285...

In fact, if one sorts the digits in the number 142857 in ascending order, 124578, it is possible to know from which of the digits the decimal part of the number is going to begin with. The remainder of dividing any number by 7 will give the position in the sequence 124578 that the decimal part of the resulting number will start. For example, 628/7= 89 + 5/7; here 5 is the remainder, and would correspond to number 7 in the ranking of the ascending sequence. So in this case, 628/7 = 89.714285. Another example, 5238/7 = 748 + 2/7, hence the remainder is 2, and this corresponds to number 2 in the sequence. In this case, 5238/7 = 748.285714.

• A seven-sided shape 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.
• Seven is the first integer reciprocal (multiplicative inverse) with infinitely repeating sexagesimal representation.
• There are seven frieze groups, the groups consisting of symmetries of the plane whose group of translations is isomorphic to the group ofintegers.
• There are seven fundamental types of catastrophes.

Graph of the probability distribution of the sum of 2 six-sided dice

• When rolling two standard six-sided dice, seven has a 6 in 36 (or 1/6) probability of being rolled (1–6, 6–1, 2–5, 5–2, 3–4, or 4–3), the greatest of any number.
• The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved.

Numeral systems[edit]

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.

Old Testament[edit]

Seven Days of Creation - 1765 book

The number seven in the seven days of Creation is typological and the number seven appears commonly elsewhere in the Bible. These include:

• Seven days of Creation (Genesis 1) e.g., God rested on and sanctified the seventh day (Sabbath)
• Anyone who dares to kill Cain 'will suffer vengeance seven times over' (Genesis 4:15)
• Lamech in his "Song of the Sword" claims that 'if Cain shall be avenged sevenfold', he himself shall be 'seventy-sevenfold' (Genesis 4:24)
• Noah is commanded to bring seven pairs of every clean animal onto the ark (Genesis 7:2)
• Seven years of plenty and seven years of famine in Pharaoh's dream (Genesis 41)
• In regards to the sin sacrifice, the anointed priest was to sprinkle the bullock's blood seven times before the lord (Leviticus 4:6)
• Seven days of the feast of Passover (Exodus 13:3–10)
• Seven day week and the pattern concerning distribution and use of manna (Exodus 16)
• The Menorah (Hebrew: מנורה), is a seven-branched candelabrum lit by olive oil in the Tabernacle and the Temple in Jerusalem (Exodus 25)
• Seven year cycle around the years of Jubilee (Leviticus 25)
• Jericho's walls fall on the seventh day after seven priests with seven trumpets march around the city seven times (Joshua 6:8)
• King David had seven older brothers (1 Samuel 16)
• Seven things that are detestable to the LORD (Proverbs 6:16–19)
• Seven Pillars of the House of Wisdom (Proverbs 9:1)
• The woman with seven sons in 2 Maccabees.

New Testament[edit]

• Seven loaves multiplied into seven basketfuls of surplus (Matthew 15:32–37)
• Peter asked Jesus if he should forgive those who sinned against him up to 7 times; Jesus responded by saying to forgive them 'seventy times seven times', remembering so the curse of Cain and the song of Lamech in Genesis 4.^[6]
• Seven demons were driven out of Mary Magdelene. (Luke 8:2).
• The seven last sayings of Jesus on the cross.
• Seven men of honest report, full of the Holy Ghost and wisdom (Acts 6:3)
• In the Book of Revelation, seven is a central figure of quantities: Seven Spirits of God, Seven Churches (to which the book is addressed);
• Seven of the following appear in Revelation: golden lampstands(1:12), stars(1:16), torches of fire(4:5) seals(5:1), angels and their trumpets(8:2), last plagues(15:1), golden bowls(15:7), thunders(10:3), horns and eyes(5:6), diadems(12:3) and kings(17:10). SeeCategory:Seven in the Book of Revelation.

Other sevens in Christian knowledge and practice include:

• The Seven Corporal Acts of Mercy and Seven Spiritual Acts of Mercy of Roman Catholic, Anglican, and other traditions
• The Seven deadly sins: lust, gluttony, greed, sloth, wrath, envy, and pride
• Seven Gifts of the Holy Spirit
• The Seven Joys of the Virgin Mary, of Roman Catholic, Anglican, and other traditions
• The Seven Sacraments in the Catholic faith (though some traditions assign a different number)
• The Seven Sorrows of the Virgin Mary, of Roman Catholic, Anglican, and other traditions
• There are seven suicides mentioned in the Bible (OT and NT).^[7]
• The seven terraces of Mount Purgatory (one per deadly sin)
• The Seven Virtues: chastity, temperance, charity, diligence, kindness, patience, and humility
• In the genealogy in the Gospel of Luke, Jesus is 77th in a direct line
• The number of heads of the three beasts (7 × 10 × 7 + 7 × 10 × 10 + 7 × 10 = 1260) of the Book of Revelation, and the seven seals

Hinduism[edit]

• The Sanskrit word sapta refers to number seven.
• Indian Music has "Saptak Swaras," seven octats (sa re ga ma pa dha ni) which are basics of music, using which hundreds of Ragas are composed.
• Celestial group of seven stars are named as "Sapta Rishi" based on the seven great saints.
• Seven Promises, Seven Rounds in Hindu Wedding and Seven Reincarnation
• According to Hinduism, there are seven worlds in the universe, seven seas in the world and seven Rishies (seven gurus) called sapta rishis.
• Seven hills at tirumala also known as ezhu malaiyan means Sevenhills god
• There are 7 Chakras in the basic model used in various eastern traditions and philosophies.

Islam[edit]

• The number of ayat in surat al-Fatiha
• The number of layers of the Earth in Islamic religion is seven
• The number of skies in Islamic religion is seven
• The number of circumambulations (Tawaf) that are made around the Kaaba
• The number of walks between Al-Safa and Al-Marwah mountains—that is travelling back and forth—seven times during the ritual pilgrimages of Hajj and Umrah
• The number of heavens in Islamic religion, i.e. levels in heaven.
• The number of hells in hell is also seven i.e. levels in hell.
• The number of doors to hell is seven (for heaven the number of doors is eight).
• In Verse 12:46 (see Islamic view of Joseph) of the Quran, Joseph (Yusef) is asked to interpret the King's dream where seven fat cows were dreamt to have been devoured by seven skinny cows and seven green spikes, and others shrivelled.
• The number of the big sins or vices is seven which are from a Hadith of the prophet Mohamed : "Avoid the seven sins polytheism, witchcraft, the killing of the soul which Allah has forbidden except by right, consuming riba, consuming the wealth of the orphan, to escape from the battles and slandering chaste women"

Judaism[edit]

• Shiv`a (another pronunciation of the Hebrew word for 7—(Hebrew: שבעה ; "seven")), is the number of days of mourning. Hence, one sits Shiva. As in Shiva (Judaism)
• The weekly Torah portion is divided into seven aliyahs, and seven Jewish men (or boys over the age of 13 who are considered men; Bar Mitzvah) 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.
• 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, theGirgashite, 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."
• The 7 Sephirot of primary conscious emotion that are attributes of the creator.

Astrology[edit]

• The number of daughters of Atlas in the Pleiades (also called the "Seven Sisters")
• The number of saints appearing in a constellation called "Saptharishi Mandalam" in Indian astronomy.

Others[edit]

Deity, being, or character

The Seven Lucky Gods in Japanese mythology

• The Seven Lucky Gods refer to the seven gods of good fortune inJapanese mythology.
• The number of archangels according to some systems.
• In Buddhism, Buddha walked 7 steps at his birth.
• In Khasi mythology, the seven divine women who were left behind on earth and became the ancestresses of all humankind.
• 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."
• In Iran,^[8] German, Spanish, and other cultures that speak Romance Languages, cats are said to have 7 lives as opposed to English, where cats are said to have 9 lives.
• In Irish mythology, the epic hero Cúchulainn is associated with the number 7. He has 7 fingers on each hand, 7 toes on each foot, and 7 pupils in each eye. In the Irish epic Táin Bó Cúailnge, Cúchulainn is 7 years old when he receives his first weapons and defeats the armies of the Ulaidh and his son Connla is 7 years old when he is slain by Cúchulainn in "The Death of Aife's Only Son."
• 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 child with special powers of healing and clairvoyant seeing, and in other cultures that seventh son of a seventh son would be a vampire.
• In Guaraní mythology, the number of prominent legendary monsters.
• In the eponymous British folk tale, Thomas the Rhymer went to live in the faerie kingdom for 7 years.
• Mahatma Gandhi's list of the destructive Seven Blunders of the World that cause violence: Wealth without work, pleasure without conscience, knowledge without character, commerce without morality, science without humanity, religion without sacrifice and politics without principle.
• The cosmogony of Urantia ^[9] gives an explanation to the sacredness of the number 7 in some religions, including those based on a triple deity: 7 indeed is the number of all the possible combinations of three elements taken one by one, two by two, or by three. It therefore expresses all the associative possibilities of the three fundamental aspects of the absolute (Christian Trinity, for example, or Trimurti in Hinduism) which organizes the Creation. The seventh of these combinations being the one that combines the three aspects, 7 therefore also expresses spiritual achievement.

Place

• The number of main islands of mythological Atlantis.
• The number of gateways traversed by Inanna during her descent into the underworld.
• Cibola was one of the legendary Seven Cities of Gold the Spanish thought existed.
• In the Bahá'í faith, the text The Seven Valleys, by the Prophet-Founder Bahá'u'lláh, relates the journey of the soul through the seven "valleys" of Search, Love, Knowledge, Unity, Contentment, Wonderment, and finally True Poverty and Absolute Nothingness.

Scripture

• Circle Seven Koran, the holy scripture of the Moorish Science Temple of America

Thing, concept, or symbol

• The Seven-Branched Sword in Japanese mythology.
• The Theosophical teachings of Alice A. Bailey divide the human race into seven psychological types called the Seven Rays, which she calls "the basis of New Age psychology".
• 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.

Time

• In British folklore, every 7 years the Queen of the Fairies pays a tithe to Hell (or possibly Hel) in the tale of Tam Lin.

Science[edit]

Astronomy[edit]

• The number of celestial objects in the solar system visible to the naked eye from Earth – 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 number of main stars in the constellations of the Big Dipper and Orion.
• 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 1,586.6 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).

Biology[edit]

• Almost all mammals have 7 cervical vertebrae
• The number of spots on a seven-spot ladybird
• There are 7 types of virus according to the Baltimore classification

Chemistry[edit]

Heptane is an alkane with 7carbon atoms per molecule

• A neutral pH value between acidity and alkalinity
• The atomic number of nitrogen
• Heptane is an alkane with 7 carbon atoms in each molecule

• The number of periods, or horizontal rows of elements, in the periodic table
• The number of principal energy levels for electrons around the nucleus

Physics[edit]

Isaac Newton's 7 colors of the rainbow

• There are 7 SI base units.^[10] These are a coherent set of units defined to measure 7 basic physical properties: metre, kilogram, second, ampere, kelvin, mole, candela. The 7 SI base units are used to define all other SI units, which are known as SI derived units.^[11]
• Isaac Newton identified 7 colors of the rainbow – red, orange, yellow, green, blue, indigo, and violet

Psychology[edit]

• The Magical Number Seven, Plus or Minus Two