* Seven is the fourth prime number. It is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since it is itself the exponent for another Mersenne prime (127). It is also a NewmanShanksWilliams prime, a Woodall prime, a factorial prime, a lucky prime, a happy number, a safe prime and the fourth Heegner number.
* Seven is the only number less than 15 which cannot be represented as the sum of the squares of three integers.
* Seven is the aliquot sum of one number, the cubic number 8 and is the base of the 7aliquot tree.
It is also said to be a lucky number
* n = 7 is the first natural number for which the next statement does not hold: "Two nilpotent endomorphisms from Cn with the same minimal polynomial and the same rank are similar."
* 7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined[citation needed].
* 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 sixdigit repeating sequence after the decimal point, but the sequence can start with any of those six digits.[1] For example, 1/7 = 0.142 857 142.... and 2/7 = 0.285 714 285...
* A sevensided shape is a heptagon. The regular ngons 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.
* Seven is the sum of any two opposite sides on a standard sixsided die. When rolling two standard sixsided dice, seven has a 6 in 36 (or 1/6th) probability of being rolled (1–6, 6–1, 2–5, 5–2, 3–4, or 4–3), the greatest of any number.
* 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.
WTF
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