25

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25 (twenty-five) is the natural number following 24 and preceding 26.

In mathematics

It is a square number, being 5² = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 25 = 3² + 4². Hence it often appears in demonstrations of the Pythagorean theorem.

25 is a centered octagonal number and an automorphic number.

25 has an aliquot sum of 6 and is the first number to have an aliquot sequence that does not culminate in 0 through a prime. Twenty-five is the aliquot sum of three integers; 95, 119, and 143. Twenty-five is the second composite member of the 6-aliquot tree.

It is the smallest base 10 Friedman number as it can be expressed by its own numbers: 5².

It is also a Cullen number. 25 is the smallest pseudoprime satisfying the congruence 7ⁿ = 7 mod n. It is also a Somer pseudoprime based on 6.

25 is the smallest aspiring number — a composite non-sociable number whose aliquot sequence does not terminate.

According to the Shapiro inequality 25 is the least odd integer n such that there exist such that

where x_{n + 1} = x₁,x_{n + 2} = x₂.

Within base 10 one can readily test for divisibility by 25 by seeing if the last two digits of the number match 25, 50, 75 or 00.

25 and 49 are the only perfect squares in the following list:

13,25,37,49,511,613,715,817,919,1021,1123,1225,1327,1429...etc

The formula in this list can be described as 10ⁿ * Z + (2Z + 1) where n clearly depends on the number of digits in Z and in 2Z+1.

In science

• The atomic number of manganese

In religion

• In Ezekiel's vision of a new temple: The number twenty-five is of cardinal importance in Ezekiel's Temple Vision (in the Bible, Ezekiel chapters 40-48).

In sports

• The size of the full roster on a major league baseball team
• The number of points needed to win a set in volleyball under rally scoring rules (except for the fifth set), so long as the losing team's score is two less than the winning team's score (i.e., if the winning team scores 25 points, the losing team can have no more than 23 points)

In other fields

Twenty five is:

• The number of years of marriage marked in a silver wedding anniversary.
• The minimum age of candidates for election to the United States House of Representatives. "Under 25" provides a common cut-off point for designating youth.
• The number of cents in a quarter.
• The usual TCP port for SMTP.
• The designation of United States Interstate 25, a freeway that runs from New Mexico to Wyoming
• The designation of the M25 London Orbital motorway
• Municipal Okrug 25, a municipal okrug of Kirovsky District of Saint Petersburg, Russia
• The (critical) number of Florida electoral votes for the 2000 U.S. presidential election
• The name of the national card game of Ireland and India (Pachisi — Hindi for 25)
• "25", a song by Veruca Salt from their 1994 album American Thighs
• "25th Floor", a song by Patti Smith Group from their 1978 album Easter
• Twenty Five is the name of a 2006 George Michael compilation celebrating 25 years in the music business (1981-2006)
• "25 boy", in Cantonese Chinese, is a slang term meaning "traitor" as used in the Chinese movie Over the Edge.
• The per-second frame rate of the PAL video standard
• The number of the French department Doubs
• 25 random things about me, an Internet meme utilizing Facebook's Notes feature

Historical years

25 A.D., 25 B.C., 1925, 2025, etc.

Slang names

• Pony (British slang for £25)^[1]

References