Crooks fluctuation theorem: Difference between revisions
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{{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]] | |||
Revision as of 12:20, 4 January 2014
Template:Infobox number 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.[1] It is the smallest prime p such that the sum of the inverses of the primes up to p is greater than two.[2] Since 59 is itself prime, 277 is a super-prime.[3] 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.[4] It is the largest prime factor of the Euclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.[5]
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.[6] 277 is also a Perrin number, and as such counts the number of maximal independent sets in an icosagon.[7][8] There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares,[9] and 277 degree-7 monic polynomials with integer coefficients and all roots in the unit disk.[10] On an infinite chessboard, there are 277 squares that a knight can reach from a given starting position in exactly six moves.[11]
277 appears as the numerator of the fifth term of the Taylor series for the secant function:[12]
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.[13]
References
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ca:Nombre 270#Nombres del 271 al 279
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef
- ↑ Template:SloanesRef