Four
Four is the smallest composite number, its proper divisors being 1 and 2. Four is also a highly composite number. The next highly composite number is 6. Four is the second square number, the second centered triangular number.
 Four is the only number in the English language for which the number of letters in its name is equal to the number itself.
Four is the smallest composite number that is equal to the sum of its prime factors. As a consequence of this, it is the smallest Smith number.
It is also a Motzkin number.
In addition, . Continuing the pattern in Knuth's up-arrow notation, , and so on, for any number of up arrows.
A four-sided plane figure is a quadrilateral (quadrangle) or square, sometimes also called a tetragon. A circle divided by 4 makes right angles. Because of it, four (4) is the base number of plane (mathematics). Four cardinal directions, four seasons, duodecimal system, and vigesimal system are based on four.
A solid figure with four faces is a tetrahedron. The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices.
The smallest non-cyclic group has four elements; it is the Klein four-group. Four is also the order of the smallest non-trivial groups that are not simple.
The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this.
Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.
Four is the number of n-Queens Problem solutions for n = 6.
There are four basic arithmetic operations: addition, subtraction, multiplication and division.
The Cartesian coordinate system for a plane has four quadrants.
Four is the first positive non-Fibonacci number.
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y2 - z2.
Four is an all-Harshad number and a semi-meandric number. | 
