# 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 × 2<sup>n</sup> − 1'' is not prime for any integer ''n''. He showed that the number '' | + | In 1956, [[Hans Riesel]] showed that there are an infinite number of integers ''k'' such that ''k × 2<sup>n</sup> − 1'' is not prime for any integer ''n''. He showed that the number ''k = {{Num|509203}}'' 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 × 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 × 2 ^{n} − 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 × 2*is prime for each k ≤ 509202. As of Aug. 2019, there are 49 k values smaller than 509203 that have no known primes.

^{n}- 1