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 7
^{n} = 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
x_1, x_2, \dots, x_n such that
- \sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} \frac{n}{2}
where x_{n+1}=x_1, x_{n+2}=x_2.
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 10^n * Z + (2Z + 1)
where n clearly depends on the number of digits in Z and in
2Z+1.
In science
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:
Historical years
25 A.D.,
25
B.C.,
1925,
2025,
etc.
Slang names
- Pony (British slang for £25)
References
- Evans, I.H., Brewer's Dictionary of Phrase and Fable,
14th ed., Cassell, 1990, ISBN 0304340049