26 (number)

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

In mathematics

Inherent mathematical properties

Twenty-six is a composite number, its proper divisors being 1, 2, and 13. 26 is the only number between a square number and a cube number, the numbers being 25 (5 squared) and 27 (3 cubed). This was first proved by Pierre de Fermat.

It is the 7th distinct biprime (2.13) and the 5th with 2 as its lowest non-unitary prime factor. The aliquot sum of 26 is 16 with an aliquot sequence of 8 members ; (26,16,15,9,4,3,1,0), leading to 0 through the prime 3 the 6th composite number so to do and so the sixth member of the 3-aliquot tree.

There is no solution to the equation φ(x) = 26, making 26 a nontotient. Nor is there a solution to x - φ(x) = 26, making 26 a noncototient.

In the classification of finite simple groups there are 26 sporadic groups.

Properties of its positional representation in certain radixes

Twenty six is a repdigit in base three (222) and in base twelve (22).

In base ten, 26 is the smallest number which is not a palindrome, but has a square which is (26^2=676).

Twenty-six is the number of five-digit prime quadruplets, the first of which is {13001, 13003, 13007, 13009}^[1].

In science

• The atomic number of iron
• The number of spacetime dimensions in bosonic string theory.

Astronomy

• Messier object M26, a magnitude 9.5 open cluster in the constellation Scutum

• The New General Catalogue object NGC 26, a spiral galaxy in the constellation Pegasus

• The Saros number of the solar eclipse series which began on -2022 March 29 and ended on -724 May 17. The duration of Saros series 26 was 1298.1 years, and it contained 73 solar eclipses.

• The Saros number of the lunar eclipse series which began on -1937 August 28 and ended on -386 March 17. The duration of Saros series 26 was 1550.5 years, and it contained 87 lunar eclipses.

In religion

• 26 is the gematria of the four-letter name of God
• According to Jewish chronology, God gave the Torah in the 26th generation since Creation

In other fields

Twenty-six is:

• The number of letters in the English and Interlingua alphabets, if capital letters are not distinguished from lowercase letters.
• The number of miles in a marathon rounded down (26 miles and 385 yards).
• Michigan is the 26th state to be admitted to the United States.
• Often the number of episodes in a television program each year; this allows one new show per week for half the year, and one rerun per week for the rest of the year.
• The alias of punk rock singer Doc Corbin Dart
• The age at which males can no longer be drafted in the United States
• A Rubik's Cube can always be solved in 26 moves or less^[2].
  • The "joke throw" in the game of darts, where a player throws 20, 5 and 1 when aiming for 20 (or treble 20). In professional darts, throwing 26 usually results in sneers or laughter from the audience.
  • A dice game popular in the midwest United States from the 1930s to 1950s; players had to roll a chosen number 26 times or more, exactly 13 or fewer than 10^[3].

    Calendar years

    In the Julian and Gregorian calendars:

    • 26 A.D.
    • 26 B.C.
    • 1926
    • 2026

    References

    • Prime Curios! 26 from the Prime Pages
    1. ^ Number of n-digit prime quadruplets
    2. ^ D. Kunkle and G. Cooperman, "Twenty-Six Moves Suffice for Rubik's Cube", Proc. of International Symposium on Symbolic and Algebraic Computation (ISSAC '07), ACM Press, 2007, 235--242.
    3. ^ "Twenty-six." Encyclopædia Britannica. Encyclopædia Britannica 2007 Ultimate Reference Suite. Chicago: Encyclopædia Britannica, 2007.

    
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