Difference between revisions of "Riesel number"

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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.

Number classes

General numbers

Special numbers

Prime numbers

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 {{Stub}}
-A '''Riesel number''' is a value of k such that k &times; 2<sup>n</sup> - 1 is always composite.
+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 [[Sierpiński problem]] article, H.Riesel found in 1956 that 509203 &times; 2<sup>n</sup> - 1 is always composite.
+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 problem]]'''), a [[distributed computing project]] was created named [[Riesel Sieve]].
+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==
 *[[Riesel and Proth Prime Database]]
-*[[Riesel problem]]
+*[[Riesel problem 1]]
 *[[Riesel prime]]
+*{{Num|15000}} Riesel numbers in the {{OEIS|l|A101036}}
+*[[Riesel 2 Riesel|Riesel numbers]]
 ==External links==