7

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

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Cardinal	seven
Ordinal	7th (seventh)
Numeral system	septenary
Factorization	prime
Prime	4th
Divisors	1, 7
Roman numeral	VII, vii
Greek prefix	hepta-/hept-
Latin prefix	septua-
Binary	1112
Ternary	213
Quaternary	134
Quinary	125
Senary	116
Octal	78
Duodecimal	712
Hexadecimal	716
Vigesimal	720
Base 36	736
Greek numeral	Z, ζ
Amharic	፯
Arabic, Kurdish, Persian	٧
Sindhi, Urdu	۷
Bengali	৭
Chinese numeral	七, 柒
Devanāgarī	७
Telugu	౭
Tamil	௭
Hebrew	ז
Khmer	៧
Thai	๗
Kannada	೭
Malayalam	൭

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

The seven Classical planets resulted in seven being the number of days in a week. 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.

It is the first natural number whose pronunciation contains more than one syllable.

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. 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 our 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. 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, and some in Britain and Ireland 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, France, Italy, Belgium, Finland, Romania, Germany, Greece, and Hungary.

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. 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), a Leyland prime of the second kind 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.
• 7 is the only number D for which the equation 2ⁿ − D = 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.
• 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. 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.

• 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.
• There are seven frieze groups, the groups consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers.
• 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 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. The opposite sides of a standard six-sided dice always add to 7.
• 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.

Basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10	15	25	50	100	1000
7 × x	7	14	21	28	35	42	49	56	63	70	105	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	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
7x	7	49	343	2401	16807	117649	823543	5764801	40353607	282475249
x7	1	128	2187	16384	78125	279936	823543	2097152	4782969	10000000

Radix	1	5	10	15	20	25	30	40	50	60	70	80	90	100
	110	120	130	140	150	200	250	500	1000	10000	100000	1000000
x7	1	5	137	217	267	347	427	557	1017	1147	1307	1437	1567	2027
	2157	2317	2447	2607	3037	4047	5057	13137	26267	411047	5643557	113333117

In science

• Seven colors in a rainbow: ROYGBIV
• Seven Continents
• Seven Seas
• Seven climes
• The neutral pH balance
• Number of music notes in a scale
• Number of spots most commonly found on ladybugs
• Atomic number for Nitrogen

In Psychology

• Seven, plus or minus two as a model of working memory.
• Seven psychological types called the Seven Rays in the teachings of Alice A. Bailey
• In Western Culture, Seven is consistently listed as people's favorite number.
• When guessing numbers 1-10 the number 7 is most likely to be picked.
• Seven-year itch: happiness in marriage said to decline after 7 years

In culture

In literature

• Seven Dwarfs

In sports

• Sports with seven players per side
  • Kabaddi
  • Rugby sevens
  • Water Polo
  • Netball
  • Handball
  • Flag Football
  • Ultimate Frisbee
• 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.

See also

• Diatonic scale
• Lucky number
• Symbolism of the number 7
• 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
• Z with stroke (Ƶ)
• List of highways numbered 7

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group (1987): 70–71