Difference between revisions of "Riesel problem"

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The '''Riesel problem''' consists in determining the smallest [[Riesel number]].
 
The '''Riesel problem''' consists in determining the smallest [[Riesel number]].
  
In 1956, [[Hans Riesel]] showed that there are an infinite number of integers ''k'' such that ''k &times; 2<sup>n</sup> − 1'' is not prime for any integer ''n''. He showed that the number ''n = {{Num|509203}}'' has this property.
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In 1956, [[Hans Riesel]] showed that there are an infinite number of integers ''k'' such that ''k &times; 2<sup>n</sup> − 1'' is not prime for any integer ''n''. He showed that the number ''k = {{Num|509203}}'' has this property.
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It is conjectured that 509203 is the smallest such number that has this property. To prove this, it suffices to show that there exists a value ''n'' such that ''k &times; 2<sup>n</sup> - 1'' is prime for each k ≤ 509202. As of Aug. 2019, there are 49 k values smaller than 509203 that have no known primes.
  
 
==See also==
 
==See also==

Latest revision as of 00:45, 4 August 2019

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The Riesel problem consists in determining the smallest Riesel number.

In 1956, Hans Riesel showed that there are an infinite number of integers k such that k × 2n − 1 is not prime for any integer n. He showed that the number k = 509,203 has this property. It is conjectured that 509203 is the smallest such number that has this property. To prove this, it suffices to show that there exists a value n such that k × 2n - 1 is prime for each k ≤ 509202. As of Aug. 2019, there are 49 k values smaller than 509203 that have no known primes.

See also

External links