21 (twenty-one) is the natural number following 20 and preceding 22.
The current century is the 21st century AD, under the Gregorian calendar.
Contents
Mathematics
Twenty-one is the fifth distinct semiprime, and the second of the form
3
×
q
{\displaystyle 3\times q}
where
q
{\displaystyle q}
is a higher prime. It is a repdigit in quaternary (1114).
Properties
As a semiprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0). 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35). There are 21 prime numbers with 2 digits. There are a total of 21 prime numbers between 100 and 200.
21 is the first Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.
While 21 is the sixth triangular number, it is also the sum of the divisors of the first five positive integers:
1
+
2
+
3
+
4
+
5
+
6
=
21
1
+
(
1
+
2
)
+
(
1
+
3
)
Quadratic matrices in Z
The twenty-first prime number 73 is the largest member of Bhargava's definite quadratic 17–integer matrix
Φ
s
(
P
)
{\displaystyle \Phi _{s}(P)}
representative of all prime numbers:
Φ
s
(
P
)
=
{
2
,
3
,
5
,
7
,
11
,
13
,
17
,
19
,
23
,
29
,
Age 21
In thirteen countries, 21 is the age of majority. See also: Coming of age.
In eight countries, 21 is the minimum age to purchase tobacco products.
In seventeen countries, 21 is the drinking age.
In nine countries, it is the voting age.
In the United States:
21 is the minimum age at which a person may gamble or enter casinos in most states (since alcohol is usually provided).
21 is the minimum age to purchase a handgun or handgun ammunition under federal law.
In some states, 21 is the minimum age to accompany a learner driver, provided that the person supervising the learner has held a full driver license for a specified amount of time. See also: List of minimum driving ages.
In sports
In NASCAR, 21 has been used by Wood Brothers Racing and Ford for decades. The team has won 99 NASCAR Cup Series races, a majority with 21, and 5 Daytona 500s.
In other fields
There are 21 shillings in a guinea.
There are 21 firings in a 21-gun salute honoring royalty or leaders of countries.
21 is associated with the profile 21 (in Israel, the military profile designation granting an exemption from the military service).
21 is a crucial number in a family of card games like twenty-one or blackjack.
