26 (number)

26 (twenty-six) is the natural number following 25 and preceding 27.

In mathematics

26 is the seventh discrete semiprime ( $2\times 13$ )^[1] and the fifth with 2 as the lowest non-unitary factor thus of the form (2.q), where q is a higher prime.
26 is the smallest even number n such that both n + 1 and n − 1 are composite.
With an aliquot sum of 16, within an aliquot sequence of five composite numbers (26,16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
26 is the only integer that is one greater than a square (5² + 1) and one less than a cube (3³ − 1).^[2]
26 is a telephone number, specifically, the number of ways of connecting 5 points with pairwise connections.^[3]
There are 26 sporadic groups.^[4]
The 26-dimensional Lorentzian unimodular lattice II_25,1 plays a significant role in sphere packing problems and the classification of finite simple groups. In particular, the Leech lattice is obtained in a simple way as a subquotient.
26 is the smallest number that is both a nontotient and a noncototient number.
26 is the number of permutations of {a, b, c, d, e} with only one ascent.^[5]^[a]
There are 26 faces of a rhombicuboctahedron.^[6]
When a 3 × 3 × 3 cube is made of 27 unit cubes (e.g. Rubik's Cube), 26 of them are viewable as the exterior layer.
A cube has 26 elements: 6 faces, 12 edges, and 8 vertices.
A 26-sided polygon is called an icosihexagon.^[7]
φ(26) = φ(σ(26)).^[8]

Twenty-six is a repdigit in bases three (222₃) and twelve (22₁₂).

In base ten, 26 is the smallest positive integer that is not a palindrome to have a square (26² = 676) that is a palindrome.

26 is the gematric number, being the sum of the Hebrew characters (Hebrew: יהוה) being the name of the god of Israel – YHWH (Yahweh).
26 is also the gematric number for GOD with the corresponding substitutions in English (i.e. A=1, B=2, C=3, and so on)
In the Tenrikyo religion of Japan, 26 is frequently used, since it marks the lunar calendar date of its founder Nakayama Miki's first divine revelation and also her death.

Messier 26 is an open cluster of stars in the southern constellation of Scutum.
NGC 26 is a spiral galaxy in the Pegasus constellation.

^ 26 is the sixteenth composite, an index value equal to the sum of prime factors of 26 (2, and 13), and 1 (i.e., its aliquot part); this is also the total sum of permutations of only one ascent in all of {a, b}, {a, b, c} and {a, b, c, d}, individually numbering 1, 4, and 11, respectively.^[5]

^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ "The number 26, between 25 and 27" (PDF). Retrieved 2012-06-05.
^ "Sloane's A000085 : Involution numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-12-03.
^ Wilson, Robert (2009-12-14). The Finite Simple Groups. Springer Science & Business Media. p. 183. ISBN 978-1-84800-987-5. In this chapter we introduce the 26 sporadic simple groups.
^ ^a ^b Sloane, N. J. A. (ed.). "Sequence A000295 (Eulerian numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-28.
^ Saiber, Arielle. Measured Words: Computation and Writing in Renaissance Italy. University of Toronto Press. p. 51. ISBN 978-0-8020-3950-7. large, transparent rhombicuboctahedron (a polyhedron with twenty-six faces,
^ "polygon". www.2dcurves.com. Retrieved 2021-02-02.
^ Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.