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Difference between revisions of "Riesel number"

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A '''Riesel number''' is a value of k such that k &times; 2<sup>N</sup> - 1 is always composite.
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A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s.
  
Using the same method presented in the [[Sierpinski problem]] article, Riesel found in 1956 that 509203 &times; 2<sup>N</sup> - 1 is always composite.
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Using the same method presented in the [[Sierpiński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite.
  
In order to demonstrate whether 509203 is the smallest Riesel number or not (the '''Riesel conjecture'''), a [[:Category:distributed computing project|distributed computing project]] was created. Its name is [[Riesel Sieve]].
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In order to demonstrate whether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]] was created named [[Riesel Sieve]].
  
 
==See also==
 
==See also==
 
*[[Riesel and Proth Prime Database]]
 
*[[Riesel and Proth Prime Database]]
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*[[Riesel problem 1]]
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*[[Riesel prime]]
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*{{Num|15000}} Riesel numbers in the {{OEIS|l|A101036}}
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*[[Riesel 2 Riesel|Riesel numbers]]
  
 
==External links==
 
==External links==
 
*[http://mathworld.wolfram.com/RieselNumber.html MathWorld]
 
*[http://mathworld.wolfram.com/RieselNumber.html MathWorld]
*[http://en.wikipedia.org/wiki/Riesel_number Wikipedia]
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*[[Wikipedia:Riesel number|Riesel number]]
[[Category:Math]]
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{{Navbox NumberClasses}}
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[[Category:Number]]

Latest revision as of 08:21, 25 March 2024

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A Riesel number is a value of k such that k•2n-1 is always composite for all natural numbers.

Using the same method presented in the Sierpiński problem article, Hans Riesel found in 1956 that 509203•2n-1 is always composite.

In order to demonstrate whether 509203 is the smallest Riesel number or not (the Riesel problem 1), a distributed computing project was created named Riesel Sieve.

See also

External links

Number classes
General numbers
Special numbers
Prime numbers