CHSH inequality - Revision history

69.199.251.170 at 21:40, 28 October 2014

2014-10-28T21:40:18Z

← Older revision		Revision as of 23:40, 28 October 2014
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	In [[number theory]], a '''Sierpinski''' or '''Sierpiński number''' is an odd [[natural number]] ''k'' such that ''k''2<sup>''n''</sup> + 1 is [[composite number\|composite]], for all natural numbers ''n''; in 1960, [[Wacław Sierpiński]] proved that there are [[Infinity\|infinitely]] many odd [[integer]]s ''k'' which have this property.

	~~In other words, when ''k'' is a Sierpiński number, all members of the following [[Set (mathematics)\|set]] are composite:~~

	~~:<math>\left\{\,k 2^n + 1 : n \in\mathbb{N}\,\right\}.</math>~~		Introduction. The [http://www.bing.com/search?q=author%27s&form=MSNNWS&mkt=en-us&pq=author%27s author's] name is Dalton but it's not the maximum masucline name out that there. The favorite hobby for him and his kids is to drive and he's been really doing it for quite some time. He operates as a cashier. His wife and him chose to live on in South Carolina additionally his family loves them. Go to his website to find out more: http://prometeu.net<br><br>Also visit my blog post :: [http://prometeu.net clash of clans triche]

	~~Numbers in such a set with odd ''k'' and ''k'' < 2<sup>''n''</sup> are [[Proth number]]s.~~

	~~==Known Sierpiński numbers==~~
	~~The sequence of currently ''known'' Sierpiński numbers begins with:~~
	~~: 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, 965431, … {{OEIS\|A076336}}~~.

	The number 78557 was proved to be a Sierpiński number by [[John Selfridge]] in 1962, who showed that all numbers of the form 78557·2<sup>''n''</sup>+1 have a [[factorization\|factor]] in the [[covering set]] {3, 5, 7, 13, 19, 37, 73}. For another known Sierpiński number, 271129, the covering set is {3, 5, 7, 13, 17, 241}. All currently known Sierpiński numbers possess similar covering sets.<ref name="PG">[http://~~primes~~.~~utm~~.~~edu~~/~~glossary/page.php~~?~~sort~~=~~SierpinskiNumber Sierpinski number at The Prime Glossary]</ref>~~

	==~~The Sierpiński problem=~~=

	~~{{Further\|Seventeen or Bust}}~~

	~~{{unsolved\|mathematics\|Is 78,557 the smallest Sierpiński number?}}~~

	~~The~~ ''~~'Sierpiński problem''' is: "What is~~ the ~~smallest Sierpiński number?"~~

	~~In 1967, Sierpiński~~ and ~~Selfridge [[conjecture]]d that 78,557~~ is ~~the smallest Sierpiński number,~~ and ~~thus the answer to the Sierpiński problem.~~

	~~To show that 78,557~~ really ~~is the smallest Sierpiński number, one must show that all the odd numbers smaller than 78,557 are ''not'' Sierpiński numbers~~. ~~That is, for every odd ''k'' below 78,557 there exists~~ a ~~positive integer ''n'' such that ''k''2<sup>''n''</sup>+1 is prime~~.~~<ref name="PG" /> {{As of\|2013\|12}}, there are only six candidates:~~
	~~: ''k'' = 10223, 21181, 22699, 24737, 55459,~~ and ~~67607~~
	~~which have not been eliminated as possible Sierpiński numbers~~.~~<ref>[~~http://~~seventeenorbust~~.com/stats/rangeStatsEx.mhtml Seventeen or Bust: Project Stats]</ref> [[Seventeen or Bust]] (with [[PrimeGrid]]), a [[distributed computing]] project, is testing these remaining numbers. If the project finds a prime of the form ''k''2<~~sup~~>~~''n''~~<~~/sup~~>~~+1 for every remaining ''k'', the Sierpiński problem will be solved.~~

	~~==See also==~~
	~~{{Portal\|Mathematics}}~~
	* [[Riesel number]]

	~~==References==~~
	~~{{Reflist}}~~

	~~==Further reading==~~
	*{{citation \|first=Richard K. \|last=Guy \|authorlink=Richard K. Guy \|title=Unsolved Problems in Number Theory \|publisher=[[Springer-Verlag]] \|location=New York \|year=2004 \|page=120 \|isbn=0-387-20860-7 }}

	~~==External links==~~
	*[http:~~//www.prothsearch.net/sierp.html The Sierpinski problem~~: ~~definition and status]~~
	*{{MathWorld\| urlname=SierpinskisCompositeNumberTheorem \|title=Sierpinski's composite number theorem}}
	*[http://~~www~~.~~mersenneforum.org/showthread.php?t=2665 The Prime Sierpinski Problem], a related question.~~

	~~{{Classes~~ of ~~natural numbers}}~~
	~~{{DEFAULTSORT:Sierpinski Number}}~~
	~~[[Category:Prime numbers]]~~
	~~[[Category:Number theory]]~~
	~~[[Category:Conjectures\|Sierpinski-Selfridge conjecture]]~~
	~~[[Category:Unsolved problems in mathematics\|Sierpinski problem]]~~
	~~[[Category:Science and technology in Poland]~~]

en>Zimboras: /* Statement of the inequality */

2014-01-02T22:14:33Z

Statement of the inequality

← Older revision		Revision as of 00:14, 3 January 2014
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	~~There~~ are many ~~proven methods to treat hemorrhoids~~ which ~~are effective for extended term hemorrhoid relief~~. ~~Because~~, ~~whilst hemorrhoids, like other diseases have a hereditary component -~~ when a ~~mom or daddy had them you're more likely to receive them - they also are influenced by lifestyle. Some~~ of the ~~elements which lead to the occurrence of hemorrhoids~~ are ~~chronic irregularity~~, ~~sitting for long periods of time~~, ~~plus~~ a ~~sofa potato lifestyle~~. So, ~~hemorrhoids could~~ be ~~healed or at least place into substantial remission~~ by ~~utilizing some common sense life-style techniques. I will focus found on~~ the ~~easiest of these techniques to implement.~~<br><br>~~Hemorrhoid is~~ a ~~swollen vein inside~~ the ~~rectal region~~. ~~Normally individuals that suffer from hemorrhoid normally feel irritated plus disturbed The common symptoms of hemorrhoid~~ is ~~itching~~, ~~swelling~~, ~~inflammation~~, ~~severe pain and there are times that bleeding occurs~~. ~~As a individual feel all of theses symptoms, then it happens to be significant which you need to do anything regarding it~~. ~~You have to ensure which you see the most perfect~~ [http://~~hemorrhoidtreatmentfix~~.~~com~~/~~external-hemorrhoid-treatment external hemorrhoids treatment~~] ~~which can suit you right.~~<br>~~<br>Another treatment for hemorrhoids~~ is ~~to utilize witch hazel. It's been shown to succeed at helping decrease swelling~~ and ~~helps with healing hemorrhoids~~ that ~~are bleeding. If your piles are extremely swollen~~, ~~this can undoubtedly enable we now.<br><br>Step 6 - Try A Suppository. The cheapest thing inside this category~~ is ~~petroleum jelly. Many of~~ the ~~suppositories to be had over~~ the ~~counter are created of the same type of elements. This means you are able~~ to ~~benefit from an inexpensive generic brand plus receive~~ the ~~same therapeutic relief~~.~~<br><br>Many of~~ the ~~time you'll like to remain at home inside purchase to do anything with~~ the ~~pain you are experiencing. Nowadays hemorrhoids~~ are not ~~really a big deal due to the accessibility of those hemorrhoid treatments~~. ~~The best treatment~~ for ~~this really is to understand the cause of hemorrhoid and recognize the procedures~~ that ~~will assist you receive out of which painful condition.~~<br><br>So, ~~because it turns out~~ there are ~~a great deal of options. I can~~'~~t remember all fancy names~~, ~~however I remember rubber bands~~, ~~lasers~~, ~~plus operation~~ with ~~REAL scalpels being revealed~~. ~~Yes,~~ the ~~whole range from medieval torture instruments to Star Wars weapons. And they sought to utilize THOSE aspects - in THAT region!~~<br><br>~~It has been proven to~~ be ~~efficient by tons of people through success stories inside an underground manner of alternative medication~~. The ~~program contains component resources, charts, audio classes~~ and ~~commonly all which we need to eliminate a hemorrhoids once and for all~~. ~~I actually think which the H Miracle System is~~ a ~~good recommendation~~. ~~There are numerous testimonials from people whom have even gotten rid~~ of ~~extremely severe hemorrhoid conditions.~~		In [[number theory]], a '''Sierpinski''' or '''Sierpiński number''' is an odd [[natural number]] ''k'' such that ''k''2<sup>''n''</sup> + 1 is [[composite number\|composite]], for all natural numbers ''n''; in 1960, [[Wacław Sierpiński]] proved that there are [[Infinity\|infinitely]] many odd [[integer]]s ''k'' which have this property.

			In other words, when ''k'' is a Sierpiński number, all members of the following [[Set (mathematics)\|set]] are composite:

			:<math>\left\{\,k 2^n + 1 : n \in\mathbb{N}\,\right\}.</math>

			Numbers in such a set with odd ''k'' and ''k'' < 2<sup>''n''</sup> are [[Proth number]]s.

			==Known Sierpiński numbers==
			The sequence of currently ''known'' Sierpiński numbers begins with:
			: 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, 965431, … {{OEIS\|A076336}}.

			The number 78557 was proved to be a Sierpiński number by [[John Selfridge]] in 1962, who showed that all numbers of the form 78557·2<sup>''n''</sup>+1 have a [[factorization\|factor]] in the [[covering set]] {3, 5, 7, 13, 19, 37, 73}. For another known Sierpiński number, 271129, the covering set is {3, 5, 7, 13, 17, 241}. All currently known Sierpiński numbers possess similar covering sets.<ref name="PG">[http://primes.utm.edu/glossary/page.php?sort=SierpinskiNumber Sierpinski number at The Prime Glossary]</ref>

			==The Sierpiński problem==

			{{Further\|Seventeen or Bust}}

			{{unsolved\|mathematics\|Is 78,557 the smallest Sierpiński number?}}

			The '''Sierpiński problem''' is: "What is the smallest Sierpiński number?"

			In 1967, Sierpiński and Selfridge [[conjecture]]d that 78,557 is the smallest Sierpiński number, and thus the answer to the Sierpiński problem.

			To show that 78,557 really is the smallest Sierpiński number, one must show that all the odd numbers smaller than 78,557 are ''not'' Sierpiński numbers. That is, for every odd ''k'' below 78,557 there exists a positive integer ''n'' such that ''k''2<sup>''n''</sup>+1 is prime.<ref name="PG" /> {{As of\|2013\|12}}, there are only six candidates:
			: ''k'' = 10223, 21181, 22699, 24737, 55459, and 67607
			which have not been eliminated as possible Sierpiński numbers.<ref>[http://seventeenorbust.com/stats/rangeStatsEx.mhtml Seventeen or Bust: Project Stats]</ref> [[Seventeen or Bust]] (with [[PrimeGrid]]), a [[distributed computing]] project, is testing these remaining numbers. If the project finds a prime of the form ''k''2<sup>''n''</sup>+1 for every remaining ''k'', the Sierpiński problem will be solved.

			==See also==
			{{Portal\|Mathematics}}
			* [[Riesel number]]

			==References==
			{{Reflist}}

			==Further reading==
			*{{citation \|first=Richard K. \|last=Guy \|authorlink=Richard K. Guy \|title=Unsolved Problems in Number Theory \|publisher=[[Springer-Verlag]] \|location=New York \|year=2004 \|page=120 \|isbn=0-387-20860-7 }}

			==External links==
			*[http://www.prothsearch.net/sierp.html The Sierpinski problem: definition and status]
			*{{MathWorld\| urlname=SierpinskisCompositeNumberTheorem \|title=Sierpinski's composite number theorem}}
			*[http://www.mersenneforum.org/showthread.php?t=2665 The Prime Sierpinski Problem], a related question.

			{{Classes of natural numbers}}
			{{DEFAULTSORT:Sierpinski Number}}
			[[Category:Prime numbers]]
			[[Category:Number theory]]
			[[Category:Conjectures\|Sierpinski-Selfridge conjecture]]
			[[Category:Unsolved problems in mathematics\|Sierpinski problem]]
			[[Category:Science and technology in Poland]]

128.151.242.123: /* Experiments using the CHSH test */

2012-08-09T16:45:30Z

Experiments using the CHSH test

New page

There are many proven methods to treat hemorrhoids which are effective for extended term hemorrhoid relief. Because, whilst hemorrhoids, like other diseases have a hereditary component - when a mom or daddy had them you're more likely to receive them - they also are influenced by lifestyle. Some of the elements which lead to the occurrence of hemorrhoids are chronic irregularity, sitting for long periods of time, plus a sofa potato lifestyle. So, hemorrhoids could be healed or at least place into substantial remission by utilizing some common sense life-style techniques. I will focus found on the easiest of these techniques to implement. Hemorrhoid is a swollen vein inside the rectal region. Normally individuals that suffer from hemorrhoid normally feel irritated plus disturbed The common symptoms of hemorrhoid is itching, swelling, inflammation, severe pain and there are times that bleeding occurs. As a individual feel all of theses symptoms, then it happens to be significant which you need to do anything regarding it. You have to ensure which you see the most perfect [http://hemorrhoidtreatmentfix.com/external-hemorrhoid-treatment external hemorrhoids treatment] which can suit you right. Another treatment for hemorrhoids is to utilize witch hazel. It's been shown to succeed at helping decrease swelling and helps with healing hemorrhoids that are bleeding. If your piles are extremely swollen, this can undoubtedly enable we now. Step 6 - Try A Suppository. The cheapest thing inside this category is petroleum jelly. Many of the suppositories to be had over the counter are created of the same type of elements. This means you are able to benefit from an inexpensive generic brand plus receive the same therapeutic relief. Many of the time you'll like to remain at home inside purchase to do anything with the pain you are experiencing. Nowadays hemorrhoids are not really a big deal due to the accessibility of those hemorrhoid treatments. The best treatment for this really is to understand the cause of hemorrhoid and recognize the procedures that will assist you receive out of which painful condition. So, because it turns out there are a great deal of options. I can't remember all fancy names, however I remember rubber bands, lasers, plus operation with REAL scalpels being revealed. Yes, the whole range from medieval torture instruments to Star Wars weapons. And they sought to utilize THOSE aspects - in THAT region! It has been proven to be efficient by tons of people through success stories inside an underground manner of alternative medication. The program contains component resources, charts, audio classes and commonly all which we need to eliminate a hemorrhoids once and for all. I actually think which the H Miracle System is a good recommendation. There are numerous testimonials from people whom have even gotten rid of extremely severe hemorrhoid conditions.