26 (number)

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

In mathematics

Poster designed to depict the speciality of the number 26

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 base three (222₃) and in base 12 (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)

^ 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.