23 (twenty-three) is the natural number following 22 and preceding 24.
Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 11, 13, 17, 19, 23). Twenty-three is also the fifth factorial prime, the second Woodall prime, and a happy number in decimal. It is an Eisenstein prime with no imaginary part and real part of the form It is also the fifth Sophie Germain prime and the fourth safe prime, and the next to last member of the first Cunningham chain of the first kind to have five terms (2, 5, 11, 23, 47). Since 14! + 1 is a multiple of 23, but 23 is not one more than a multiple of 14, 23 is the first Pillai prime. 23 is the smallest odd prime to be a highly cototient number, as the solution to for the integers 95, 119, 143, and 529. The third decimal repunit prime after R2 and R19 is R23, followed by R1031.
The first Mersenne number of the form that does not yield a prime number when inputting a prime exponent is with 
On the other hand, the second composite Mersenne number contains an exponent of twenty-three:
Further in the sequence of Mersenne numbers, the 23rd prime number (83) is an exponent to the 14th composite Mersenne number, which factorizes into two prime numbers, the largest of which is twenty-three digits long when written in base ten:
is also twenty-three digits long in decimal, and there are only three other numbers whose factorials generate numbers that are digits long in base ten: 1, 22, and 24.
The Leech lattice Λ24 is a 24-dimensional lattice through which 23 other positive definite even unimodular Niemeier lattices of rank 24 are built, and vice-versa. Λ24 represents the solution to the kissing number in 24 dimensions as the precise lattice structure for the maximum number of spheres that can fill 24-dimensional space without overlapping, equal to 196,560 spheres. These 23 Niemeier lattices are located at deep holes of radii √ in lattice points around its automorphism group, Conway group . The Leech lattice can be constructed in various ways, which include:
Conway and Sloane provided constructions of the Leech lattice from all other 23 Niemeier lattices.
Twenty-three four-dimensional crystal families exist within the classification of space groups. These are accompanied by six enantiomorphic forms, which maximizes the total count to twenty-nine crystal families. In three dimensions, five cubes can be arranged to form twenty-three free pentacubes, or twenty-nine distinct one-sided pentacubes (counting reflections).
There are 23 three-dimensional uniform polyhedra that are cell facets inside uniform 4-polytopes that are not part of infinite families of antiprismatic prisms and duoprisms: the five Platonic solids, the thirteen Archimedean solids, and five semiregular prisms (the triangular prism, pentagonal prism, hexagonal prism, octagonal prism, and decagonal prism).
23 Coxeter groups of paracompact hyperbolic honeycombs in the third dimension generate 151 unique Wythoffian constructions of paracompact honeycombs. 23 four-dimensional Euclidean honeycombs are generated from the cubic group, and 23 five-dimensional uniform polytopes are generated from the demihypercubic group.
In two-dimensional geometry, the regular 23-sided icositrigon is the first regular polygon that is not constructible with a compass and straight edge or with the aide of an angle trisector (since it is neither a Fermat prime nor a Pierpont prime), nor by neusis or a double-notched straight edge. It is also not constructible with origami, however it is through other traditional methods for all regular polygons.
Main article: 23 § Music
See also: List of highways numbered 23