26 (twenty-six) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 25 and preceding 27.

In mathematics

*26 is the seventh discrete

semiprime In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime n ...

(

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 Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic material ...

. *With an

aliquot sum In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociabl ...

of 16, within an

aliquot sequence In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Def ...

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 An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

that is one greater than a square (5 + 1) and one less than a cube (3 − 1). *26 is a

telephone number A telephone number is the address of a Telecommunications, telecommunication endpoint, such as a telephone, in a telephone network, such as the public switched telephone network (PSTN). A telephone number typically consists of a Number, sequ ...

, specifically, the number of ways of connecting 5 points with pairwise connections. *There are 26

sporadic group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

s. *The 26-dimensional Lorentzian

unimodular lattice In geometry and mathematical group theory, a unimodular lattice is an integral Lattice (group), lattice of Lattice (group)#Dividing space according to a lattice, determinant 1 or −1. For a lattice in ''n''-dimensional Euclidea ...

II_25,1 plays a significant role in

sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...

problems and the

classification of finite simple groups In mathematics, the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every List of finite simple groups, finite simple group is either cyclic group, cyclic, or alternating gro ...

. In particular, the

Leech lattice In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by Er ...

is obtained in a simple way as a subquotient. *26 is the smallest number that is both a

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...

and a

noncototient In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function In number theory ...

number. *26 is the number of permutations of with only one

ascent Ascent or The Ascent may refer to: Publications * ''Ascent'' (magazine), an independent, not-for-profit magazine * ''Ascent'' (journal), a literary journal based at Concordia College * ''Ascent'' (novel), by Jed Mercurio * '' Times Ascent'', a ...

. *There are 26 faces of a

rhombicuboctahedron In geometry, the rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for ''truncated cuboctahedral rhombus'', w ...

. *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 The face is the front of the head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect the ...

, 12 edges, and 8 vertices. * A 26-sided

polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...

is called an icosihexagon. *φ(26) = φ(σ(26)).

Properties of its positional representation in certain radixes

Twenty-six is a

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

in bases

three 3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies ...

(222₃) and twelve (22₁₂). In

base ten The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of t ...

, 26 is the smallest positive integer that is not a

palindrome A palindrome (Help:IPA/English, /ˈpæl.ɪn.droʊm/) is a word, palindromic number, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as ''madam'' or ''racecar'', the date "Twosday, 02/02/2020" and th ...

to have a

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

(26² =

676 __NOTOC__ Year 676 ( DCLXXVI) was a leap year starting on Tuesday of the Julian calendar. The denomination 676 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe ...

) that is a palindrome.

In religion

* 26 is the gematric number, being the sum of the Hebrew characters () being the name of the god of Israel –

YHWH The TetragrammatonPronounced ; ; also known as the Tetragram. is the four-letter Hebrew-language theonym (transliterated as YHWH or YHVH), the name of God in the Hebrew Bible. The four Hebrew letters, written and read from right to left, a ...

(''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 is a Japanese new religion which is neither strictly monotheistic nor pantheistic, originating from the teachings of a 19th-century woman named Nakayama Miki, known to her followers as "Oyasama". Followers of Tenrikyo believe that God of Orig ...

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.

In science

* Messier 26 is an

open cluster An open cluster is a type of star cluster made of tens to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way galaxy, and ...

stars A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of ...

in the southern constellation of Scutum. *

NGC 26 NGC 26 is a spiral galaxy in the Pegasus constellation. It was discovered on 14 September 1865 by Heinrich Louis d'Arrest. NGC 23 group NGC 26 is part of the NGC 23 group A group is a number of persons or things that are located, gathered, ...

is a

spiral galaxy Spiral galaxies form a galaxy morphological classification, class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''

in the

Pegasus Pegasus (; ) is a winged horse in Greek mythology, usually depicted as a white stallion. He was sired by Poseidon, in his role as horse-god, and foaled by the Gorgon Medusa. Pegasus was the brother of Chrysaor, both born from Medusa's blood w ...

constellation.

References

External links

Prime Curios! 26
from the

Prime Pages The PrimePages is a website about prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is ...

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