Crooks fluctuation theorem - Revision history

99.189.174.180 at 05:02, 25 October 2014

2014-10-25T05:02:46Z

← Older revision		Revision as of 07:02, 25 October 2014
Line 1:		Line 1:
	~~{{Infobox number~~		The author is called Wilber Pegues. Kentucky is where I've always been living. The favorite hobby for him and his kids is to play lacross and he would never give it up. Invoicing is what I do for a living but I've always wanted my personal business.<br><br>Here is my page: are psychics real ([http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going www.zavodpm.ru])
	~~\| number = 277~~
	~~\| prime = yes~~
	}}
	~~'''277''' (read as '''two hundred and seventy-seven''')~~ is ~~the [[natural number]] following '''276''~~' and ~~preceding '''278'''.~~

	~~==Mathematical properties==~~
	~~277~~ is ~~the 59th [[prime number]],~~ and ~~is a [[regular prime]].<ref>{{SloanesRef\|sequencenumber=A007703\|name=Regular primes}}</ref>~~
	~~It is the smallest prime ''p'' such that the [[Divergence of the sum of the reciprocals of the primes\|sum of the inverses of the primes]]~~ up ~~to ''p'' is greater than two~~.~~<ref>{{SloanesRef\|sequencenumber=A016088\|name=a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n}}</ref>~~
	~~Since 59 is itself prime, 277~~ is a ~~[[super-prime]]~~.<~~ref~~>~~{{SloanesRef\|sequencenumber=A006450\|name=Primes with prime subscripts}}~~<~~/ref~~> 59 is ~~also a super-prime~~ (it is the 17th prime), as is 17 (the 7th prime). However, 7 is the fourth prime number, and 4 is not prime. Thus, 277 is a super-super-super-prime but not a super-super-super-super-prime.<ref>{{citation
	~~\| first1 =Neil \| last1 = Fernandez~~
	~~\| title = An order of primeness, F(p)~~
	~~\| url =~~ http://~~borve.org/primeness/FOP~~.~~html~~
	~~\| year = 1999}}~~.</ref> It is the largest prime factor of the [[Euclid number]] 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.<ref>{{SloanesRef\|sequencenumber=A002585\|name=Largest prime factor of 1 + (product of first n primes)}}</ref>

	As a member of the [[lazy caterer's sequence]], 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.<ref>{{SloanesRef\|sequencenumber=A000124\|name=Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/~~2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts}}<~~/~~ref>~~
	277 is also a [[Perrin number]], and as such counts the number of [[maximal independent set]]s in an [[icosagon]].<ref>{{SloanesRef\|sequencenumber=A001608\|name=Perrin sequence (or Ondrej Such sequence): a(n) = a(n-~~2) + a(n~~-~~3)}}</ref><ref>{{citation~~
	~~\| author = Füredi, Z. \| authorlink = Zoltán Füredi~~
	~~\| title = The number of maximal independent sets in connected graphs~~
	~~\| journal = Journal of Graph Theory~~
	~~\| volume = 11~~
	~~\| issue = 4~~
	~~\| year = 1987~~
	~~\| pages = 463–470~~
	~~\| doi = 10.1002/jgt.3190110403}}.</ref> There are 277 ways to tile a 3 × 8 rectangle with integer~~-~~sided squares,<ref>{{SloanesRef\|sequencenumber=A002478\|name=Bisection of A000930}}</ref> and 277 degree~~-~~7 [[monic polynomial]]s with integer coefficients and all roots in the [[unit disk]]~~.~~<ref>{{SloanesRef\|sequencenumber=A051894\|name=Number of monic polynomials with integer coefficients of degree n with all roots in unit disc}}</ref>~~
	~~On an infinite [[chessboard]], there are 277 squares that a [[Knight (chess)\|knight]] can reach from a given starting position in exactly six moves~~.~~<ref>{{SloanesRef\|sequencenumber=A118312\|name=Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square}}</ref>~~

	277 appears as the numerator of the fifth term of the [[Taylor series]] for the [[secant function]]:<ref>{{SloanesRef\|sequencenumber=A046976\|name=Numerators of Taylor series for sec(x) = 1/cos(x)}}</ref>
	~~:<math>\sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots</math>~~

	~~Since no number added to the sum of its digits generates 277, it is a [[self number~~]]. The next prime self number is not reached until 367.<ref>{{SloanesRef\|sequencenumber=A006378\|name=Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum}}</ref>

	~~==References==~~
	~~{{reflist}}~~

	~~{{Integers\|2}}~~

	~~{{DEFAULTSORT:277 (Number~~)}}
	~~[[Category:Integers]]~~

	~~[[ca:Nombre 270#Nombres del 271 al 279]]~~

128.179.158.164 at 11:20, 4 January 2014

2014-01-04T11:20:13Z

← Older revision		Revision as of 13:20, 4 January 2014
Line 1:		Line 1:
	~~Myrtle Benny~~ is ~~how I~~'~~m called~~ and ~~I really feel comfortable when people use~~ the ~~complete title~~. ~~His family life in South Dakota but his wife wants them~~ to ~~transfer~~. ~~My working day occupation~~ is a ~~meter reader~~. ~~What I adore performing~~ is ~~taking part in baseball~~ but ~~I haven~~'~~t produced~~ a ~~dime~~ with it.<br><br>~~Here~~ is ~~my homepage:~~ [~~http~~://~~dore~~.~~gia~~.~~ncnu~~.~~edu~~.tw/~~88ipart~~/~~node~~/~~1326254 dore~~.~~gia~~.~~ncnu.edu.tw~~]		{{Infobox number
			\| number = 277
			\| prime = yes
			}}
			'''277''' (read as '''two hundred and seventy-seven''') is the [[natural number]] following '''276''' and preceding '''278'''.

			==Mathematical properties==
			277 is the 59th [[prime number]], and is a [[regular prime]].<ref>{{SloanesRef\|sequencenumber=A007703\|name=Regular primes}}</ref>
			It is the smallest prime ''p'' such that the [[Divergence of the sum of the reciprocals of the primes\|sum of the inverses of the primes]] up to ''p'' is greater than two.<ref>{{SloanesRef\|sequencenumber=A016088\|name=a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n}}</ref>
			Since 59 is itself prime, 277 is a [[super-prime]].<ref>{{SloanesRef\|sequencenumber=A006450\|name=Primes with prime subscripts}}</ref> 59 is also a super-prime (it is the 17th prime), as is 17 (the 7th prime). However, 7 is the fourth prime number, and 4 is not prime. Thus, 277 is a super-super-super-prime but not a super-super-super-super-prime.<ref>{{citation
			\| first1 =Neil \| last1 = Fernandez
			\| title = An order of primeness, F(p)
			\| url = http://borve.org/primeness/FOP.html
			\| year = 1999}}.</ref> It is the largest prime factor of the [[Euclid number]] 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.<ref>{{SloanesRef\|sequencenumber=A002585\|name=Largest prime factor of 1 + (product of first n primes)}}</ref>

			As a member of the [[lazy caterer's sequence]], 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.<ref>{{SloanesRef\|sequencenumber=A000124\|name=Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts}}</ref>
			277 is also a [[Perrin number]], and as such counts the number of [[maximal independent set]]s in an [[icosagon]].<ref>{{SloanesRef\|sequencenumber=A001608\|name=Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3)}}</ref><ref>{{citation
			\| author = Füredi, Z. \| authorlink = Zoltán Füredi
			\| title = The number of maximal independent sets in connected graphs
			\| journal = Journal of Graph Theory
			\| volume = 11
			\| issue = 4
			\| year = 1987
			\| pages = 463–470
			\| doi = 10.1002/jgt.3190110403}}.</ref> There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares,<ref>{{SloanesRef\|sequencenumber=A002478\|name=Bisection of A000930}}</ref> and 277 degree-7 [[monic polynomial]]s with integer coefficients and all roots in the [[unit disk]].<ref>{{SloanesRef\|sequencenumber=A051894\|name=Number of monic polynomials with integer coefficients of degree n with all roots in unit disc}}</ref>
			On an infinite [[chessboard]], there are 277 squares that a [[Knight (chess)\|knight]] can reach from a given starting position in exactly six moves.<ref>{{SloanesRef\|sequencenumber=A118312\|name=Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square}}</ref>

			277 appears as the numerator of the fifth term of the [[Taylor series]] for the [[secant function]]:<ref>{{SloanesRef\|sequencenumber=A046976\|name=Numerators of Taylor series for sec(x) = 1/cos(x)}}</ref>
			:<math>\sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots</math>

			Since no number added to the sum of its digits generates 277, it is a [[self number]]. The next prime self number is not reached until 367.<ref>{{SloanesRef\|sequencenumber=A006378\|name=Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum}}</ref>

			==References==
			{{reflist}}

			{{Integers\|2}}

			{{DEFAULTSORT:277 (Number)}}
			[[Category:Integers]]

			[[ca:Nombre 270#Nombres del 271 al 279]]

134.76.249.10: /* External links */ Link was broken

2011-05-16T14:25:50Z

External links: Link was broken

New page

Myrtle Benny is how I'm called and I really feel comfortable when people use the complete title. His family life in South Dakota but his wife wants them to transfer. My working day occupation is a meter reader. What I adore performing is taking part in baseball but I haven't produced a dime with it.<br><br>Here is my homepage: [http://dore.gia.ncnu.edu.tw/88ipart/node/1326254 dore.gia.ncnu.edu.tw]

← Older revision		Revision as of 07:02, 25 October 2014
Line 1:		Line 1:
	~~{{Infobox number~~		The author is called Wilber Pegues. Kentucky is where I've always been living. The favorite hobby for him and his kids is to play lacross and he would never give it up. Invoicing is what I do for a living but I've always wanted my personal business.<br><br>Here is my page: are psychics real ([http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going www.zavodpm.ru])
	~~\| number = 277~~
	~~\| prime = yes~~
	}}
	~~'''277''' (read as '''two hundred and seventy-seven''')~~ is ~~the [[natural number]] following '''276''~~' and ~~preceding '''278'''.~~

	~~==Mathematical properties==~~
	~~277~~ is ~~the 59th [[prime number]],~~ and ~~is a [[regular prime]].<ref>{{SloanesRef\|sequencenumber=A007703\|name=Regular primes}}</ref>~~
	~~It is the smallest prime ''p'' such that the [[Divergence of the sum of the reciprocals of the primes\|sum of the inverses of the primes]]~~ up ~~to ''p'' is greater than two~~.~~<ref>{{SloanesRef\|sequencenumber=A016088\|name=a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n}}</ref>~~
	~~Since 59 is itself prime, 277~~ is a ~~[[super-prime]]~~.<~~ref~~>~~{{SloanesRef\|sequencenumber=A006450\|name=Primes with prime subscripts}}~~<~~/ref~~> 59 is ~~also a super-prime~~ (it is the 17th prime), as is 17 (the 7th prime). However, 7 is the fourth prime number, and 4 is not prime. Thus, 277 is a super-super-super-prime but not a super-super-super-super-prime.<ref>{{citation
	~~\| first1 =Neil \| last1 = Fernandez~~
	~~\| title = An order of primeness, F(p)~~
	~~\| url =~~ http://~~borve.org/primeness/FOP~~.~~html~~
	~~\| year = 1999}}~~.</ref> It is the largest prime factor of the [[Euclid number]] 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.<ref>{{SloanesRef\|sequencenumber=A002585\|name=Largest prime factor of 1 + (product of first n primes)}}</ref>

	As a member of the [[lazy caterer's sequence]], 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.<ref>{{SloanesRef\|sequencenumber=A000124\|name=Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/~~2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts}}<~~/~~ref>~~
	277 is also a [[Perrin number]], and as such counts the number of [[maximal independent set]]s in an [[icosagon]].<ref>{{SloanesRef\|sequencenumber=A001608\|name=Perrin sequence (or Ondrej Such sequence): a(n) = a(n-~~2) + a(n~~-~~3)}}</ref><ref>{{citation~~
	~~\| author = Füredi, Z. \| authorlink = Zoltán Füredi~~
	~~\| title = The number of maximal independent sets in connected graphs~~
	~~\| journal = Journal of Graph Theory~~
	~~\| volume = 11~~
	~~\| issue = 4~~
	~~\| year = 1987~~
	~~\| pages = 463–470~~
	~~\| doi = 10.1002/jgt.3190110403}}.</ref> There are 277 ways to tile a 3 × 8 rectangle with integer~~-~~sided squares,<ref>{{SloanesRef\|sequencenumber=A002478\|name=Bisection of A000930}}</ref> and 277 degree~~-~~7 [[monic polynomial]]s with integer coefficients and all roots in the [[unit disk]]~~.~~<ref>{{SloanesRef\|sequencenumber=A051894\|name=Number of monic polynomials with integer coefficients of degree n with all roots in unit disc}}</ref>~~
	~~On an infinite [[chessboard]], there are 277 squares that a [[Knight (chess)\|knight]] can reach from a given starting position in exactly six moves~~.~~<ref>{{SloanesRef\|sequencenumber=A118312\|name=Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square}}</ref>~~

	277 appears as the numerator of the fifth term of the [[Taylor series]] for the [[secant function]]:<ref>{{SloanesRef\|sequencenumber=A046976\|name=Numerators of Taylor series for sec(x) = 1/cos(x)}}</ref>
	~~:<math>\sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots</math>~~

	~~Since no number added to the sum of its digits generates 277, it is a [[self number~~]]. The next prime self number is not reached until 367.<ref>{{SloanesRef\|sequencenumber=A006378\|name=Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum}}</ref>

	~~==References==~~
	~~{{reflist}}~~

	~~{{Integers\|2}}~~

	~~{{DEFAULTSORT:277 (Number~~)}}
	~~[[Category:Integers]]~~

	~~[[ca:Nombre 270#Nombres del 271 al 279]]~~