21 ( twenty-one ) is the natural number following 20 and preceding 22 .
24-776: (Redirected from Twenty One ) [REDACTED] Look up twenty-one in Wiktionary, the free dictionary. Twenty-one , XXI or 21 may refer to: 21 (number) , the natural number following 20 and preceding 22 One of the years 21 BC , AD 21 , 1921 , 2021 Films [ edit ] 21 (2008 film) , starring Kevin Spacey, Laurence Fishburne, Jim Sturgess, and Kate Bosworth Twenty-One (1991 film) , starring Patsy Kensit Twenty-One (1923 film) , starring Richard Barthelmess Twenty-One (1918 film) , starring Bryant Washburn Science [ edit ] Scandium ,
48-2382: A {\displaystyle a} and n − a {\displaystyle n-a} only has factors 2 {\displaystyle 2} and 5 {\displaystyle 5} (for a representation in base ten ). Let A ( n ) {\displaystyle A(n)} denote the quantity of the numbers smaller than n {\displaystyle n} that only have factor 2 {\displaystyle 2} and 5 {\displaystyle 5} and that are coprime to n {\displaystyle n} , we instantly have φ ( n ) 2 < A ( n ) {\displaystyle {\frac {\varphi (n)}{2}}<A(n)} . We can easily see that for sufficiently large n {\displaystyle n} , A ( n ) ∼ log 2 ( n ) log 5 ( n ) 2 = ln 2 ( n ) 2 ln ( 2 ) ln ( 5 ) . {\displaystyle A(n)\sim {\frac {\log _{2}(n)\log _{5}(n)}{2}}={\frac {\ln ^{2}(n)}{2\ln(2)\ln(5)}}.} However, φ ( n ) ∼ n e γ ln ln n {\displaystyle \varphi (n)\sim {\frac {n}{e^{\gamma }\;\ln \ln n}}} where A ( n ) = o ( φ ( n ) ) {\displaystyle A(n)=o(\varphi (n))} as n {\displaystyle n} approaches infinity ; thus φ ( n ) 2 < A ( n ) {\displaystyle {\frac {\varphi (n)}{2}}<A(n)} fails to hold for sufficiently large n {\displaystyle n} . In fact, for every n > 2 {\displaystyle n>2} , we have So φ ( n ) 2 < A ( n ) {\displaystyle {\frac {\varphi (n)}{2}}<A(n)} fails to hold when n > 273 {\displaystyle n>273} (actually, when n > 33 {\displaystyle n>33} ). Just check
72-405: A b {\displaystyle {\tfrac {a}{b}}} and b a {\displaystyle {\tfrac {b}{a}}} is a terminating decimal; see proof below: For any a {\displaystyle a} coprime to n {\displaystyle n} and n − a {\displaystyle n-a} , the condition above holds when one of
96-541: A transition metal in the periodic table 21 Lutetia , an asteroid in the asteroid belt Music [ edit ] XXI (band) , a band formerly known as A Feast for Kings Twenty One Pilots , American musical duo 21 Savage , an Atlanta-based rapper Albums [ edit ] 21 (EP) , a 2015 EP by Hunter Hayes 21 (Omarion album) , 2006 21 (Adele album) , 2011 21 (Rage album) , 2012 Twenty One (Geri Allen album) , 1994 Twenty One (Mystery Jets album) , 2008 Twenty 1 ,
120-452: A 1991 album by Chicago XXI , a 2015 box set by Rammstein Songs [ edit ] "21" (The Paddingtons song) , 2004 "21" (Hunter Hayes song) , 2015 "21" (Polo G song) , 2020 "21", a song by Corey Hart on Young Man Running "21", a song by Craig Davis from 22 (2022) "21", a song by DaBaby from Blank Blank "21", a song by Dean from 130 mood: TRBL "21",
144-441: A body of generally accepted but not entirely uniform rules that players understand to apply to all drinking activity and include rules for example, that drinkers must keep their little finger up whilst drinking, only drink with their left hand and, in some circles, that using the word "drink" be prohibited and replaced with words such as "consume" or "imbibe". Andy, Bill, Cath, Dan, Ed and Fran are sitting with Andy at 12 o'clock, and
168-406: A circle, facing inwards. The game begins with one player calling the direction of play by saying, "I propose a game of XXXX! To my left..." or "To my right..." followed by a sequential series of numbers beginning with one. Variations exist for the proposal of the game depending on personal rules; this is due to some variants calling for any person who says the number "21" to drink. For example: As
192-444: A few numbers to see that the complete sequence of numbers having this property is { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 11 , 12 , 15 , 21 } . {\displaystyle \{2,3,4,5,6,7,8,9,11,12,15,21\}.} 21 is the smallest natural number that is not close to a power of two ( 2 n ) {\displaystyle (2^{n})} , where
216-420: A heavy drinking penalty (e.g. finishing their drink), creates a new rule , then restarts the game from 1. Variations on the standard rules include: Examples of new rules that could be instated by a player forced to call 21: It is also commonplace to declare (either at the start of the game or as an additional rule) that the game be played according to the so-called " International Drinking Rules ". These are
240-449: A prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11 , 1 , 0 ); it is the second composite number with an aliquot sum of 11 , following 18 . 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
264-414: A song by Gracie Abrams on Minor (EP) "21", a 2015 song by Cory Marks from This Man "21", a 2010 song by Flo Rida from Only One Flo (Part 1) "21", a 2018 song by Mitch James 21?! , a 2008 song and EP by Marya Roxx "Twenty One", a song by The Shirelles "Twenty One", a song by Khalid from Free Spirit "Twenty-One", a song by The Eagles from Desperado "Twenty One",
SECTION 10
#1732772758157288-682: A song by The Cranberries from No Need to Argue "Twenty One", a song by Corey Smith Games and sports [ edit ] Twenty-One (card game) , forerunner of Blackjack and Pontoon 21 (drinking game) , a counting game 21, also "Counting to 21 game" or "21 game", a Nim-style counting game Twenty-one (basketball) , a basketball variation Twenty-One (game show) , an American game show from 1956 to 1958 and in 2000 Catch 21 , an American game show based on Blackjack Other uses [ edit ] 21 (novel) or The Final Unfinished Voyage of Jack Aubrey , by Patrick O'Brian, 2004 "21" ( Boardwalk Empire ) , an episode of
312-432: A sum of 427 when excluding a square of side length 7 {\displaystyle 7} ; this sum represents the largest square-free integer over a quadratic field of class number two, where 163 is the largest such ( Heegner ) number of class one. 427 number is also the first number to hold a sum-of-divisors in equivalence with the third perfect number and thirty-first triangular number ( 496 ), where it
336-640: Is a drinking game . The game progresses by counting up from 1 to 21, with the player who calls "21" suffering a drinking penalty before the next round starts. The loser may add 1 new rule to the game, and starts the new round. This was created in the Swan and 3 Cygnets pub in Durham City by Alan Smith, Ian Crosby, Stephen Rickaby, Andrew Barras, Paul Nicholson, Kieran Walker, Gavin Southwell, Mark Thompson, Brian Griffen, and Paul Jones. Players are arranged in
360-773: Is also the fiftieth number to return 0 {\displaystyle 0} in the Mertens function . While 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 , 31 , 37 , 41 , 43 , 47 , 67 , 73 } , {\displaystyle \Phi _{s}(P)=\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,67,{\mathbf {73}}\},}
384-428: Is also the first non-trivial octagonal number . It is the fifth Motzkin number , and the seventeenth Padovan number (preceded by the terms 9 , 12 , and 16 , where it is the sum of the first two of these). In decimal , the number of two-digit prime numbers is twenty-one (a base in which 21 is the fourteenth Harshad number ). It is the smallest non-trivial example in base ten of a Fibonacci number (where 21
408-457: Is the 21st century AD, under the Gregorian calendar . 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 (111 4 ). As a biprime with proper divisors 1 , 3 and 7 , twenty-one has
432-471: Is the 8th member, as the sum of the preceding terms in the sequence 8 and 13 ) whose digits ( 2 , 1 ) are Fibonacci numbers and whose digit sum is also a Fibonacci number ( 3 ). It is also the largest positive integer n {\displaystyle n} in decimal such that for any positive integers a , b {\displaystyle a,b} where a + b = n {\displaystyle a+b=n} , at least one of
456-617: 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 ) + ( 1 + 2 + 4 ) + ( 1 + 5 ) = 21 {\displaystyle {\begin{aligned}1&+2+3+4+5+6=21\\1&+(1+2)+(1+3)+(1+2+4)+(1+5)=21\\\end{aligned}}} 21
480-650: The Boardwalk Empire television series 21 Club , a former restaurant and nightclub in New York City Twentyone Lake , a lake in Minnesota Caterham 21 , a roadster See also [ edit ] 021 (disambiguation) Twenty to One , a 1935 British musical comedy List of highways numbered 21 [REDACTED] Topics referred to by the same term This disambiguation page lists articles associated with
504-411: The game progresses, each player in turn must recite one to four numbers, counting in sequence from where the previous player left off: If a player makes a mistake, then they suffer a small to moderate drinking penalty (e.g. 2 fingers of drink) and then restart the game from 1. Mistakes include: Assuming there are no mistakes, the game will continue in sequence up to 21. The player who calls 21 suffers
SECTION 20
#1732772758157528-591: The range of nearness is ± n . {\displaystyle \pm {n}.} Twenty-one is the smallest number of differently sized squares needed to square the square . The lengths of sides of these squares are { 2 , 4 , 6 , 7 , 8 , 9 , 11 , 15 , 16 , 17 , 18 , 19 , 24 , 25 , 27 , 29 , 33 , 35 , 37 , 42 , 50 } {\displaystyle \{2,4,6,7,8,9,11,15,16,17,18,19,24,25,27,29,33,35,37,42,50\}} which generate
552-461: The same number. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=21&oldid=1259546612 " Category : Lists of ambiguous numbers Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages twenty-one The current century
576-509: The twenty-first composite number 33 is the largest member of a like definite quadratic 7–integer matrix Φ s ( 2 Z ≥ 0 + 1 ) = { 1 , 3 , 5 , 7 , 11 , 15 , 33 } {\displaystyle \Phi _{s}(2\mathbb {Z} _{\geq 0}+1)=\{1,3,5,7,11,15,{\mathbf {33}}\}} representative of all odd numbers. 21 is: 21 (drinking game) 21 , Bagram , or Twenty Plus One
#156843