# 7

(Redirected from 7 (number))

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

 ← 6 7 8 →
Cardinalseven
Ordinal7th
(seventh)
Numeral systemseptenary
Factorizationprime
Prime4th
Divisors1, 7
Greek numeralΖ´
Roman numeralVII, vii
Greek prefixhepta-/hept-
Latin prefixseptua-
Binary1112
Ternary213
Senary116
Octal78
Duodecimal712
Greek numeralZ, ζ
Amharic
Arabic, Kurdish, Persian٧
Sindhi, Urdu۷
Bengali
Chinese numeral七, 柒
Devanāgarī
Telugu
Tamil
Hebrewז
Khmer
Thai
Malayalam

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.[citation needed] It 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.[citation needed]

## Evolution of the Arabic digit

In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase ⟨J⟩ vertically inverted (ᒉ). The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs developed the digit from a form that looked something like 6 to one that looked like an uppercase V. Both modern Arab forms influenced the European form, a two-stroke form consisting of a horizontal upper stroke joined at its right to a stroke going down to the bottom left corner, a line that is slightly curved in some font variants. As is the case with the European digit, the Cham and Khmer digit for 7 also evolved to look like their digit 1, though in a different way, so they were also concerned with making their 7 more different. For the Khmer this often involved adding a horizontal line to the top of the digit.[1] 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 writing that uses a long upstroke in the glyph for 1. In some Greek dialects of the early 12th century the longer line diagonal was drawn in a rather semicircular transverse line.

On the seven-segment displays of pocket calculators and digital watches, 7 is the digit with the most common graphic variation (1, 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 because in Japan, Korea and Taiwan 7 is written with a "hook" on the left, as ① in the following illustration.

While the shape of the character for the digit 7 has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender (⁊), as, for example, in  .

Most people in Continental Europe,[2] Indonesia,[3] and some in Britain, Ireland, and Canada, as well as Latin America, write 7 with a line in the middle ("7"), sometimes with the top line crooked. The line through the middle is useful to clearly differentiate the digit from the digit one, as the two can appear similar when written in certain styles of handwriting. This form is used in official handwriting rules for primary school in Russia, Ukraine, Bulgaria, Poland, other Slavic countries,[4] France,[5] Italy, Belgium, the Netherlands, Finland,[6] Romania, Germany, Greece,[7] and Hungary.[citation needed]

## Mathematics

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.[8] It is also a Newman–Shanks–Williams prime,[9] a Woodall prime,[10] a factorial prime,[11] a Harshad number, a lucky prime,[12] a happy number (happy prime),[13] a safe prime (the only Mersenne safe prime), a Leyland prime of the second kind and the fourth Heegner number.[14]

• 7 is the only number D for which the equation 2nD = x2 has more than two solutions for n and x natural. In particular, the equation 2n − 7 = x2 is known as the Ramanujan–Nagell equation.
A heptagon in Euclidean space is unable to generate uniform tilings alongside other polygons, like the regular pentagon. However, it is one of fourteen polygons that can fill a plane-vertex tiling, in its case only alongside a regular triangle and a 42-sided polygon (3.7.42).[23][24] This is also one of twenty-one such configurations from seventeen combinations of polygons, that features the largest and smallest polygons possible.[25][26]
Seven of eight semiregular tilings are Wythoffian, the only exception is the elongated triangular tiling.[28] Seven of nine uniform colorings of the square tiling are also Wythoffian, and between the triangular tiling and square tiling, there are seven non-Wythoffian uniform colorings of a total twenty-one that belong to regular tilings (all hexagonal tiling uniform colorings are Wythoffian).[29]
In two dimensions, there are precisely seven 7-uniform Krotenheerdt tilings, with no other such k-uniform tilings for k > 7, and it is also the only k for which the count of Krotenheerdt tilings agrees with k.[30][31]
Also, the lowest known dimension for an exotic sphere is the seventh dimension, with a total of 28 differentiable structures; there may exist exotic smooth structures on the four-dimensional sphere.[42][43]
In hyperbolic space, 7 is the highest dimension for non-simplex hypercompact Vinberg polytopes of rank n + 4 mirrors, where there is one unique figure with eleven facets.[44] On the other hand, such figures with rank n + 3 mirrors exist in dimensions 4, 5, 6 and 8; not in 7.[45] Hypercompact polytopes with lowest possible rank of n + 2 mirrors exist up through the 17th dimension, where there is a single solution as well.[46]
• When rolling two standard six-sided dice, seven has a 6 in 62 (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.[48] The opposite sides of a standard six-sided dice always add to 7.

### 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 × 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 11 12 13 14 15
7 ÷ x 7 3.5 2.3 1.75 1.4 1.16 1 0.875 0.7 0.7 0.63 0.583 0.538461 0.5 0.46
x ÷ 7 0.142857 0.285714 0.428571 0.571428 0.714285 0.857142 1.142857 1.285714 1.428571 1.571428 1.714285 1.857142 2 2.142857
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
7x 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407
x7 1 128 2187 16384 78125 279936 823543 2097152 4782969 10000000 19487171 35831808 62748517
Radix 1 5 10 15 20 25 50 75 100 125 150 200 250 500 1000 10000 100000 1000000
x7 1 5 137 217 267 347 1017 1357 2027 2367 3037 4047 5057 13137 26267 411047 5643557 113333117

#### In decimal

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.[51] For example, 1/7 = 0.142857 142857... and 2/7 = 0.285714 285714....

In fact, if one sorts the digits in the number 142,857 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.

## Classical antiquity

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).[55] In Pythagorean numerology the number 7 means spirituality.

References from classical antiquity to the number seven include:

## Religion and mythology

### Judaism

The number seven forms a widespread typological pattern within Hebrew scripture, including:

• Seven days (more precisely yom) of Creation, leading to the seventh day or Sabbath (Genesis 1)
• Seven-fold vengeance visited on upon Cain for the killing of Abel (Genesis 4:15)
• 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, Gad, whose name means good luck (Genesis 46:16)
• Seven times bullock's blood is sprinkled before God (Leviticus 4:6)
• Seven nations God told the Israelites they would displace when they entered the land of Israel (Deuteronomy 7:1)
• Seven days (de jure, but de facto eight days) of the Passover feast (Exodus 13:3–10)
• Seven-branched candelabrum or Menorah (Exodus 25)
• Seven trumpets played by seven priests for seven days to bring down the walls of Jericho (Joshua 6:8)
• Seven things that are detestable to God (Proverbs 6:16–19)
• Seven Pillars of the House of Wisdom (Proverbs 9:1)
• Seven archangels in the deuterocanonical Book of Tobit (12:15)

References to the number seven in Jewish knowledge and practice include:

• Seven divisions of the weekly readings or aliyah of the Torah
• Seven Jewish men (over the age of 13) called to read aliyahs in Shabbat morning services
• Seven blessings recited under the chuppah during a Jewish wedding ceremony
• Seven days of festive meals for a Jewish bride and groom after their wedding, known as Sheva Berachot or Seven Blessings
• Seven Ushpizzin prayers to the Jewish patriarchs during the holiday of Sukkot

### Christianity

Following the tradition of the Hebrew Bible, the New Testament likewise uses the number seven as part of a typological pattern:

References to the number seven in Christian knowledge and practice include:

### Islam

References to the number seven in Islamic knowledge and practice include:

### Hinduism

References to the number seven in Hindu knowledge and practice include:

Other references to the number seven in Eastern traditions include:

### Other references

Other references to the number seven in traditions from around the world include:

## In culture

### In sports

• Sports with seven players per side
• Seven is the least number of players a soccer team must have on the field in order for a match to start and continue.
• A touchdown plus an extra point is worth seven points.

## Notes

1. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.67
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3. ^ "Mengapa orang Indonesia menambahkan garis kecil pada penulisan angka tujuh (7)?" (in Indonesian). Quora. Retrieved June 12, 2023.
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5. ^
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10. ^ "Sloane's A050918 : Woodall primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
11. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
12. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
13. ^ "Sloane's A035497 : Happy primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
14. ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
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"...It will thus be found that, including the employment of the same figures, there are seventeen different combinations of regular polygons by which this may be effected; namely, —
When three polygons are employed , there are ten ways; viz., 6,6,63.7.423,8,243,9,183,10,153,12,124,5,204,6,124,8,85,5,10.
With four polygons there are four ways, viz., 4,4,4,43,3,4,123,3,6,63,4,4,6.
With five polygons there are two ways, viz., 3,3,3,4,43,3,3,3,6.
With six polygons one way — all equilateral triangles [ 3.3.3.3.3.3 ]."
Note: the only four other configurations from the same combinations of polygons are: 3.4.3.12, (3.6)2, 3.4.6.4, and 3.3.4.3.4.
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