4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5.

In mathematics

Four is the smallest composite number, its proper divisors being num: 1 and num: 2. Four is also a highly composite number. The next highly composite number is num: 6.

Four is the second square number, the second centered triangular number.

4 is the smallest squared prime ($p^2$) and the only even number in this form. It has an aliquot sum of 3 which is itself prime. The aliquot sequence of 4 has 4 members (4,3,1,0) and is accordingly the first member of the 3-aliquot tree.

Only one number has an aliquot sum of 4 and that is squared prime 9

The prime factorization of four is two times two.

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). However, it is the largest (and only) composite number $n$ for which $(n\; -\; 1)!\backslash \; \backslash equiv\backslash \; 0\; \backslash \; (\{\backslash rm\; mod\}\backslash \; n)$ is false.

It is also a Motzkin number.

In addition, $2\; +\; 2\; =\; 2\; \backslash times\; 2\; =\; 2^2\; =\; 4$. Continuing the pattern in Knuth's up-arrow notation, $2\; \backslash uparrow\backslash uparrow\; 2\; =\; 2\; \backslash uparrow\backslash uparrow\backslash uparrow\; 2\; =\; 4$, 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. It is the only self-dual regular polyhedron.

Four-dimensional space has the largest number of dimensions used by more than three convex regular figures. There are infinitely many convex regular polygons (two-dimensional); five convex regular polyhedra (three-dimensional, the five Platonic Solids); six convex regular polychora (four-dimensional); and three regular convex polytopes occupying each higher-dimensional space.

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.

Four is the maximum number of dimensions of a real division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius.

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. The largest planar complete graph has four vertices.