Four Antennas ALMA

4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.

In mathematics

Four is the smallest composite number, its proper divisors being and . Four is the sum and product of two with itself: $2$ + $2$ = $4$ = $2$ x $2$, the only number $b$ such that $a$ + $a$ = $b$ = $a$ x $a$, which also makes four the smallest squared prime number $p^$. In Knuth's up-arrow notation, , and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third. On the other hand, the square of four 4², equivalently the fourth power of two 2⁴, is sixteen; the only number that has $a^$ = $b^$ as a form of factorization. Holistically, there are four elementary arithmetic operations in mathematics: addition (+), subtraction (−), multiplication (×), and division (÷); and four basic number systems, the real numbers $\mathbb$, rational numbers $\mathbb$, integers $\mathbb$, and natural numbers $\mathbb$.

Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. $4x$ = $y^$ − $z^$. A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because .

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; for instance cannot be written as the sum of three squares.

There are four all-Harshad numbers: 1, 2, ''4'', and 6. 12, which is divisible by four thrice over, is a Harshad number in all bases except octal.

A four-sided plane figure is a quadrilateral or quadrangle, sometimes also called a ''tetragon''. It can be further classified as a rectangle or ''oblong'', kite, rhombus, and square.

Four is the highest degree general polynomial equation for which there is a solution in radicals.

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.

A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have. The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid. It has four regular triangles as faces that are themselves at dual positions with the vertices of another tetrahedron. Tetrahedra can be inscribed inside all other four Platonic solids, and tessellate space alongside the regular octahedron in the alternated cubic honeycomb.

Four-dimensional space is the highest-dimensional space featuring more than three regular convex figures:
*Two-dimensional: infinitely many regular polygons.
*Three-dimensional: five regular polyhedra; the five Platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
*Four-dimensional: six regular polychora; the 5-cell, 8-cell or tesseract, 16-cell, 24-cell, 120-cell, and 600-cell. The 24-cell, made of regular octahedra, has no analogue in any other dimension; it is self-dual, with its 24-cell honeycomb