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7

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

As an early prime number in the series of positive integers, the number seven has symbolic associations in religion, mythology, superstition and philosophy. The seven classical planets resulted in seven being the number of days in a week. 7 is often considered lucky in Western culture and is often seen as highly symbolic.

For early Brahmi numerals, 7 was written more or less in one stroke as a curve that looks like an uppercase ⟨J⟩ vertically inverted (ᒉ). The western Arab peoples' 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 Arab peoples 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. 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 seven-segment displays, 7 is the digit with the most common graphic variation (1, 6 and 9 also have variant glyphs). Most devices use three line segments, but devices made by some Japanese companies such as Sharp and Casio, as well as in the Koreas and Taiwan, 7 is written with four line segments because in those countries, 7 is written with a "hook" on the left, as ① in the following illustration. Further segments can give further variation. For example, Schindler elevators in the United States and Canada installed or modernized from the late 1990s onwards usually use a sixteen segment display and show the digit 7 in a manner more similar to that of handwriting.

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, Indonesia,[citation needed] and some in Britain, Ireland, Israel, Canada, and Latin America, write 7 with a line through the middle (7), sometimes with the top line crooked. The line through the middle is useful to clearly differentiate that digit from the digit one, as they 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, the Netherlands, Finland, Romania, Germany, Greece, and Hungary.[citation needed]

Seven, the fourth prime number, is not only a Mersenne prime (since ) 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 Harshad number, a lucky prime, a happy number (happy prime), a safe prime (the only Mersenne safe prime), a Leyland number of the second kind and 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.

A seven-sided shape is a heptagon. The regular n-gons for n ⩽ 6 can be constructed by compass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these simple tools.

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