23 (twenty-three) is the natural number following 22 and preceding 24.
[2] Twenty-three is also the next to last member of the first Cunningham chain of the first kind (2, 5, 11, 23, 47),[3] and the sum of the prime factors of the second set of consecutive discrete semiprimes, (21, 22).
23 is the smallest odd prime to be a highly cototient number, as the solution to
[4] Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
[30] On the other hand, the second composite Mersenne number contains an exponent
The twenty-third prime number (83) is an exponent to the fourteenth composite Mersenne number, which factorizes into two prime numbers, the largest of which is twenty-three digits long when written in base ten:[31][32]
Further down in this sequence, the seventeenth and eighteenth composite Mersenne numbers have two prime factors each as well, where the largest of these are respectively twenty-two and twenty-four digits long,
add to 106, which lies in between prime exponents of
, the index of the latter two (17 and 18) in the sequence of Mersenne numbers sum to 35, which is the twenty-third composite number.
is twenty-three digits long in decimal, and there are only three other numbers
digits long in base ten: 1, 22, and 24.
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 √2 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.
[34] Twenty-three four-dimensional crystal families exist within the classification of space groups.
These are accompanied by six enantiomorphic forms, maximizing the total count to twenty-nine crystal families.
[35] Five cubes can be arranged to form twenty-three free pentacubes, or twenty-nine distinct one-sided pentacubes (with reflections).
[36][37] 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, pentagonal, hexagonal, octagonal, and decagonal prisms).
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
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.
[38] It is also not constructible with origami, however it is through other traditional methods for all regular polygons.