14 (number)

14 (fourteen) is the natural number following 13 and preceding 15.
Fourteen is the seventh composite number.
14 is the third distinct semiprime, being the third of the form 2 × q {\displaystyle 2\times q} (where q {\displaystyle q} is a higher prime). More specifically, it is the first member of the second cluster of two discrete semiprimes (14, 15); the next such cluster is (21, 22), members whose sum is the fourteenth prime number, 43.
14 has an aliquot sum of 8, within an aliquot sequence of two composite numbers (14, 8, 7, 1, 0) in the prime 7-aliquot tree.
14 is the third companion Pell number and the fourth Catalan number. It is the lowest even n {\displaystyle n} for which the Euler totient φ ( x ) = n {\displaystyle \varphi (x)=n} has no solution, making it the first even nontotient.
According to the Shapiro inequality, 14 is the least number n {\displaystyle n} such that there exist x 1 {\displaystyle x_{1}} , x 2 {\displaystyle x_{2}} , x 3 {\displaystyle x_{3}} , where:
with x n + 1 = x 1 {\displaystyle x_{n+1}=x_{1}} and x n + 2 = x 2 . {\displaystyle x_{n+2}=x_{2}.}
A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets. This holds even if the reals are replaced by a more general topological space; see Kuratowski's closure-complement problem.
There are fourteen even numbers that cannot be expressed as the sum of two odd composite numbers:
where 14 is the seventh such number.
14 is the number of equilateral triangles that are formed by the sides and diagonals of a regular six-sided hexagon. In a hexagonal lattice, 14 is also the number of fixed two-dimensional triangular-celled polyiamonds with four cells.
14 is the number of elements in a regular heptagon (where there are seven vertices and edges), and the total number of diagonals between all its vertices.
There are fourteen polygons that can fill a plane-vertex tiling, where five polygons tile the plane uniformly, and nine others only tile the plane alongside irregular polygons.
The Klein quartic is a compact Riemann surface of genus 3 that has the largest possible automorphism group order of its kind (of order 168) whose fundamental domain is a regular hyperbolic 14-sided tetradecagon, with an area of 8 π {\displaystyle 8\pi } by the Gauss-Bonnet theorem.
Several distinguished polyhedra in three dimensions contain fourteen faces or vertices as facets:
A regular tetrahedron cell, the simplest uniform polyhedron and Platonic solid, is made up of a total of 14 elements: 4 edges, 6 vertices, and 4 faces.
14 is also the root (non-unitary) trivial stella octangula number, where two self-dual tetrahedra are represented through figurate numbers, while also being the first non-trivial square pyramidal number (after 5); the simplest of the ninety-two Johnson solids is the square pyramid J 1 . {\displaystyle J_{1}.} There are a total of fourteen semi-regular polyhedra, when the pseudorhombicuboctahedron is included as a non-vertex transitive Archimedean solid (a lower class of polyhedra that follow the five Platonic solids).
Fourteen possible Bravais lattices exist that fill three-dimensional space.
The exceptional Lie algebra G2 is the simplest of five such algebras, with a minimal faithful representation in fourteen dimensions. It is the automorphism group of the octonions O {\displaystyle \mathbb {O} } , and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, S {\displaystyle \mathbb {S} } .
The floor of the imaginary part of the first non-trivial zero in the Riemann zeta function is 14 {\displaystyle 14} , in equivalence with its nearest integer value, from an approximation of 14.1347251417 … {\displaystyle 14.1347251417\ldots }
14 is associated with Jesus Christ. There is a fourteen-point silver star marking the traditional spot of Jesus’ birth in the Basilica of the Nativity in Bethlehem. According to the genealogy of Jesus in the Gospel of Matthew, “…there were fourteen generations in all from Abraham to David, fourteen generations from David to the exile to Babylon, and fourteen from the exile to the Messiah” (Matthew 1:17).
The number 14 was linked to Šumugan and Nergal.
Fourteen is: