26 (number)

Template:Redirect2 Template:Infobox 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 ($2\times 13$) 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 (5Template:Sup + 1) and one less than a cube (3Template:Sup − 1).
• 26 is a telephone number, specifically, the number of ways of connecting 5 points with pairwise connections.
• There are 26 sporadic groups.
• 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.Template:Efn
• There are 26 faces of a rhombicuboctahedron.
• 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.
• φ(26) = φ(σ(26)).

Properties of its positional representation in certain radixes

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.

In religion

• 26 is the gematric number, being the sum of the Hebrew characters (Template:Langx) 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.

External links

• Prime Curios! 26 from the Prime Pages