# 7

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7 (number)
)
 ← 6 7 8 →
Malayalam

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

As an early

Vietnamese culture, the number seven is sometimes considered unlucky.[citation needed
]

## Evolution of the Arabic digit

In the

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

safe prime (the only Mersenne safe prime), a Leyland prime of the second kind and the fourth Heegner number.[14]

• Seven is the
8
and is the base of the 7-aliquot tree.
• 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
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

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

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
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

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
2. ^ Eeva Törmänen (September 8, 2011). "Aamulehti: Opetushallitus harkitsee numero 7 viivan palauttamista". Tekniikka & Talous (in Finnish). Archived from the original on September 17, 2011. Retrieved September 9, 2011.
3. ^ "Mengapa orang Indonesia menambahkan garis kecil pada penulisan angka tujuh (7)?" (in Indonesian). Quora. Retrieved June 12, 2023.
4. ^ "Education writing numerals in grade 1." Archived 2008-10-02 at the Wayback Machine(Russian)
5. ^
6. ^ Elli Harju (August 6, 2015). ""Nenosen seiska" teki paluun: Tiesitkö, mistä poikkiviiva on peräisin?". Iltalehti (in Finnish).
7. ^ "Μαθηματικά Α' Δημοτικού" [Mathematics for the First Grade] (PDF) (in Greek). Ministry of Education, Research, and Religions. p. 33. Retrieved May 7, 2018.
8. ^ Weisstein, Eric W. "Double Mersenne Number". mathworld.wolfram.com. Retrieved 2020-08-06.
9. ^ "Sloane's A088165 : NSW primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
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.
15. . A frieze pattern can be classified into one of the 7 frieze groups...
16. .
17. ^ Sloane, N. J. A. (ed.). "Sequence A004029 (Number of n-dimensional space groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
18. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-01.
19. ^ Weisstein, Eric W. "Heptagon". mathworld.wolfram.com. Retrieved 2020-08-25.
20. ^ Weisstein, Eric W. "7". mathworld.wolfram.com. Retrieved 2020-08-07.
21. ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers (or 7-gonal numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09.
22. ^ Sloane, N. J. A. (ed.). "Sequence A003215". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
23. .
24. ^ Jardine, Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling.
25. .
26. ^ Dallas, Elmslie William (1855). "Part II. (VII): Of the Circle, with its Inscribed and Circumscribed Figures − Equal Division and the Construction of Polygons". The Elements of Plane Practical Geometry. London: John W. Parker & Son, West Strand. p. 134.
"...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.
27. .
28. .
29. .
30. ^ Sloane, N. J. A. (ed.). "Sequence A068600 (Number of n-uniform tilings having n different arrangements of polygons about their vertices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09.
31. .
32. .
33. .
34. .
35. ^ Császár, Ákos (1949). "A polyhedron without diagonals" (PDF). Acta Scientiarum Mathematicarum (Szeged). 13: 140–142. Archived from the original (PDF) on 2017-09-18.
36. ^ Sloane, N. J. A. (ed.). "Sequence A004031 (Number of n-dimensional crystal systems.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
37. S2CID 124399480
.
38. ^ Sloane, N. J. A. (ed.). "Sequence A256413 (Number of n-dimensional Bravais lattices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
39. .
40. Zbl 0532.55011. Archived from the original
(PDF) on 2021-02-26. Retrieved 2023-02-23.
41. .
42. .
43. ^ Sloane, N. J. A. (ed.). "Sequence A001676 (Number of h-cobordism classes of smooth homotopy n-spheres.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-23.
44. .
45. .
46. .
47. . ...every catastrophe can be composed from the set of so called elementary catastrophes, which are of seven fundamental types.
48. ^ Weisstein, Eric W. "Dice". mathworld.wolfram.com. Retrieved 2020-08-25.
49. ^ "Millennium Problems | Clay Mathematics Institute". www.claymath.org. Retrieved 2020-08-25.
50. ^ "Poincaré Conjecture | Clay Mathematics Institute". 2013-12-15. Archived from the original on 2013-12-15. Retrieved 2020-08-25.
51. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 82
52. ^ Gonzalez, Robbie (4 December 2014). "Why Do People Love The Number Seven?". Gizmodo. Retrieved 20 February 2022.
53. ^ Bellos, Alex. "The World's Most Popular Numbers [Excerpt]". Scientific American. Retrieved 20 February 2022.
54. . Retrieved 20 February 2022.
55. ^
56. , retrieved 2020-11-17
57. .
58. .
59. ^ The Origin of the Mystical Number Seven in Mesopotamian Culture: Division by Seven in the Sexagesimal Number System
60. ^ "Encyclopædia Britannica "Number Symbolism"". Britannica.com. Retrieved 2012-09-07.
61. ISSN 0235-716X
.
62. ^ "Chapter I. The Creative Thesis of Perfection by William S. Sadler, Jr. - Urantia Book - Urantia Foundation". urantia.org. 17 August 2011.
63. ^ Yemaya. Santeria Church of the Orishas. Retrieved 25 November 2022
64. ^ Ergil, Leyla Yvonne (2021-06-10). "Turkey's talisman superstitions: Evil eyes, pomegranates and more". Daily Sabah. Retrieved 2023-04-05.