25 (number)

← 24 25 26 →
← 20 21 22 23 24 25 26 27 28 29 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twenty-five
Ordinal	25th (twenty-fifth)
Factorization	5^2
Divisors	1, 5, 25
Roman numeral	XXV
Binary	110012
Ternary	2213
Quaternary	1214
Quinary	1005
Senary	416
Octal	318
Duodecimal	2112
Hexadecimal	1916
Vigesimal	1520
Base 36	P36

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

In mathematics

25 is a square

It is a square number, being 5² = 5 × 5. It is one of two two-digit numbers whose square and higher powers of the number also ends in the same last two digits, e.g. 25² = 625, the other is 76. It is the smallest square that is also a sum of two (non-zero) squares: 25 = 3² + 4². Hence it often appears in illustrations of the Pythagorean theorem.

25 is a centered octagonal number,^[1] a centered square number,^[2] and an automorphic number.^[3]

25 percent (%) is equal to 1/4.

25 has an aliquot sum of 6 and number 6 is the first (or smallest) 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 digits: 5².^[4]

It is also a Cullen number.^[5] 25 is the smallest pseudoprime satisfying the congruence 7ⁿ = 7 mod n.

25 is the smallest aspiring number — a composite non-sociable number whose aliquot sequence does not terminate.^[6]

According to the Shapiro inequality, 25 is the least odd integer n such that there exist x₁, x₂, …, x_n such that

$\sum _{{i=1}}^{{n}}{\frac {x_{i}}{x_{{i+1}}+x_{{i+2}}}}<{\frac {n}{2}}$

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 00, 25, 50 or 75.

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 10ⁿZ + (2Z + 1) where n depends on the number of digits in Z and in 2Z + 1.

In base 30, 25 is a 1-automorphic number (displayed as the numeral 'P' or 'R' dependent on the chosen digit set), and in base 10 a 2-automorphic number.

In science

• The atomic number of manganese.
• The percent DNA overlap of a half-sibling, grandparent, grandchild, aunt, uncle, niece, nephew, identical twin cousin (offspring of identical twins), double cousin.^[7]

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 The Book of Revelation's New International Version (1984): "Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads."^[8]
• In Islam, there are twenty-five prophets mentioned in the Quran.

In sports

• The size of the full roster on a Major League Baseball team for most of the season, except for regular-season games on or after September 1, when teams expand their roster to 40 players.
• In baseball, the number 25 is typically reserved for the best slugger on the team. Examples include Mark McGwire, Barry Bonds, and Mark Teixeira.
• 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 U.S. college football, schools that are members of NCAA Division I FBS are allowed to provide athletic scholarships to a maximum of 25 new football players (i.e., players who were not previously receiving scholarships) each season.

In other fields

Twenty five is:

• The part of the name of LSD-25 molecule.
• 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.
• The (critical) number of Florida electoral votes for the 2000 U.S. presidential election.
• The name of the national board game of India (Pachisi — Hindi for 25).
• The name of an Irish card game, see Spoil Five.
• The per-second frame rate of the PAL video standard.
• 25, the name of Adele's 2015 album, named for her age in that year.
• The number of the French department Doubs.
• The temperature, in Celsius, at which some characteristics of semiconductors are specifically given in a datasheet.

Slang names

• Pony (British slang for £25)^[9]

References

1. "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. "Sloane's A003226 : Automorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. "Sloane's A036057 : Friedman numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. "Sloane's A002064 : Cullen numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. "Sloane's A063769 : Aspiring numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
7. http://genetics.thetech.org/ask/ask450
8. "Revelation 4:4 Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads". Bible.cc. Retrieved 2013-05-03.
9. Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9