7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined.In particular, the equation 2 n в€’ 7 = x 2 is known as the RamanujanвЂ“Nagell equation. 7 is the only number D for which the equation 2 n в€’ D = x 2 has more than two solutions for n and x natural.Seven is the aliquot sum of one number, the cubic number 8 and is the base of the 7-aliquot tree.(See Lagrange's four-square theorem#Historical development.) Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers.It is also a NewmanвЂ“ShanksвЂ“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, the fourth prime number, is not only a Mersenne prime (since 2 3 в€’ 1 = 7) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime. 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. 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.

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. In some Greek dialects of early 12thВ century the longer line diagonal was drawn in a rather semicircular transverse line. 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. 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. For the Khmer this often involved adding a horizontal line to the top of the digit. 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. 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. The eastern Arabs developed the digit from a form that looked something like our 6 to one that looked like an uppercase V. 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. In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase вџЁJвџ© vertically inverted.

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