1. In mathematics

2. In science

3. Age 21

4. In sports

5. In other fields

6. References

21 (twenty-one) is the natural number following 20 and preceding 22.

In mathematics

21 is:

• a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.^[1]
• a Fibonacci number.^[2]
• a Harshad number.^[3]
• a Motzkin number.^[4]
• a triangular number.^[5]
• an octagonal number.^[6]
• a composite number, its proper divisors being 1, 3 and 7.
• the sum of the first six natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21), making it a triangular number.
• the sum of the divisors of the first 5 positive integers.
• the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number.
• a repdigit in base 4 (111₄).
• the smallest natural number that is not close to a power of 2, 2ⁿ, where the range of closeness is ±n.
• the smallest number of differently sized squares needed to square the square.^[7]
• the largest n with this property: for any positive integers a,b such that a + b = n, at least one of and is a terminating decimal. See a brief proof below.

Note that a necessary condition for n is that for any a coprime to n, a and n - a must satisfy the condition above, therefore at least one of a and n - a must only have factor 2 and 5.

Let donate the quantity of the numbers smaller than n that only have factor 2 and 5 and that are coprime to n, we instantly have .

We can easily see that for sufficiently large n, , but , as n goes to infinity, thus fails to hold for sufficiently large n.

In fact, For every n > 2, we have

and

so fails to hold when n > 273 (actually, when n > 33).

Just check a few numbers to see that n = 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21.

21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these).^[8]

In science

• The atomic number of scandium.

Age 21

• In several countries 21 is the age of majority. See also: Coming of age.
• In all US states, 21 is the drinking age.
  • However, in Puerto Rico and U.S. Virgin Islands, the drinking age is 18.
• In California, Hawaii, New York, and New Jersey, 21 is the minimum age that one person may purchase cigarettes and other tobacco products.
• In some countries it is the voting age.
• In the United States, 21 is the age at which one can purchase multiple tickets to an R-rated film without providing identification. It is also the age to accompany one under the age of 17 as their parent or adult guardian for an R-rated movie.
• In most US states, 21 is the minimum age at which a person may gamble or enter casinos.
• In 2011, Adele named her second studio album 21, because of her age at the time.

In sports

• Twenty-one is a variation of street basketball, in which each player, of which there can be any number, plays for himself only (i.e. not part of a team); the name comes from the requisite number of baskets.
• In badminton, and table tennis (before 2001), 21 points are required to win a game.
• In AFL Women's, the top-level league of women's Australian rules football, each team is allowed a squad of 21 players (16 on the field and five interchanges).

In other fields

21 is:

• The Twenty-first Amendment repealed the Eighteenth Amendment, thereby ending Prohibition.
• The number of spots on a standard cubical (six-sided) die (1+2+3+4+5+6)
• The number of firings in a 21-gun salute honoring Royalty or leaders of countries
• 21 Guns, a 2009 song by the punk-rock band Green Day
• There are 21 trump cards of the tarot deck if one does not consider The Fool to be a proper trump card.
• The standard TCP/IP port number for FTP connection
• The Twenty-One Demands were a set of demands which were sent to the Chinese government by the Japanese government of Okuma Shigenobu in 1915
• 21 Demands of MKS led to the foundation of Solidarity in Poland.
• In Israel, the number is associated with the profile 21 (the military profile designation granting an exemption from the military service)
• 21 grams is the weight of the soul, according to research by Duncan MacDougall, generally regarded as meaningless.
• The number of the French department Côte-d'Or
• The key value and highest-winning point total of the popular casino game Blackjack
• The number of shillings in a guinea.
• The number of solar rays in the flag of Kurdistan.

References

• 5.56 mm x 45
• 5.56mm x 45
• 5.56mmx45mm
• 5.56 mm x 45 NATO
• 5.56 NATO
• 5.56 x 45 mm
• 5.56 x 45mm
• 5.56 x 45mm NATO
• 5.56×45mm
• 5.56×45mm NATO
• 557
• 557 BC
• 557th Weather Wing
• 558
• 558 BC
• 559
• 559 BC
• 55 AD
• 55 BC
• 55 BCE
• 55 Broadway
• 55 Cancri
• 55 Cancris
• 55 Cancri Solar System
• 55 Cnc