21 (number)

← 20 21 22 →
← 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-one
Ordinal	21st (twenty-first)
Factorization	3 × 7
Divisors	1, 3, 7, 21
Roman numeral	XXI
Binary	101012
Ternary	2103
Quaternary	1114
Quinary	415
Senary	336
Octal	258
Duodecimal	1912
Hexadecimal	1516
Vigesimal	1120
Base 36	L36

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

In mathematics

21 is:

• the fifth discrete semiprime and the second in the (3 × q) family. With 22 it forms the second discrete semiprime pair.
• a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.
• a Fibonacci number.
• a Harshad number.
• a Motzkin number.
• a triangular number.
• an octagonal number.
• 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 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.^[1]

21 has an aliquot sum of 11 though it is the second composite number found in the 11-aliquot tree with the abundant square prime 18 being the first such member. Twenty-one is the first number to be the aliquot sum of three numbers 18, 51, 91.

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

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.
• In Hawaii and New York, 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. 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 some states, 21 is the minimum age, persons may gamble or enter casinos.

In sports

Number 21 on the road bicycle of Ellen van Dijk at the Ronde van Drenthe.

• The jersey number 21 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Cleveland Indians, for Hall of Famer Bob Lemon.
    • The Milwaukee Braves, for Hall of Famer Warren Spahn; the number continues to be honored by the team in its current home of Atlanta.
    • The Pittsburgh Pirates, for Hall of Famer Roberto Clemente, following his death in a plane crash while attempting to deliver humanitarian aid to victims of an earthquake in Nicaragua.
  • In the NBA:
    • The Atlanta Hawks, for Hall of Famer Dominique Wilkins.
    • The Boston Celtics, for Hall of Famer Bill Sharman.
    • The Detroit Pistons, for Hall of Famer Dave Bing.
    • The Sacramento Kings, for Vlade Divac.
    • The Minnesota Timberwolves have not retired the number, but have not issued it since Kevin Garnett was traded from the team in 2007.
  • In the NHL:
    • The Chicago Blackhawks, for Hall of Famer Stan Mikita.
    • The Colorado Avalanche, for Peter Forsberg.
    • The Pittsburgh Penguins, for Michel Brière.
  • No NFL team has retired the number.
• In basketball:
  • 21 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 3x3, a formalized version of three-on-three half-court basketball, the game ends by rule once either team has scored 21 points in regulation.^[2]
• In badminton, and table tennis (before 2001), 21 points are required to win a game.
• In the NASCAR Sprint Cup Series, 21 has long been the number of the car for Wood Brothers Racing.

In other fields

Building called "21" in Zlín, Czech Republic.

Detail of the building entrance

21 is:

• The current century—spanning the years from 2001 to 2100—is referred to as the 21st century. See also: Century 21 (disambiguation).
• The Twenty-first Amendment repealed the Eighteenth Amendment, thereby ending Prohibition.
• Illinois is the 21st state to join the United States.
• 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
• 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.
• 21 is the designation of a US Highway connecting Wytheville, Virginia and Beaufort, South Carolina, a truncation of a route that once connected Cleveland, Ohio and Jacksonville, Florida, among other highways past and present.
• 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.

References

1. C. J. Bouwkamp, and A. J. W. Duijvestijn, "Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25." Eindhoven University of Technology, Nov. 1992.
2. "Article 9 Scoring" (PDF). 3x3 Rules of the Game. FIBA. January 13, 2012. Retrieved November 2, 2012.