| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Riesel problem 1"
(new) |
(typo fixed, clarify problem) |
||
| Line 2: | Line 2: | ||
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== | ||
Revision as of 00:45, 4 August 2019
|
This article is only a stub. You can help PrimeWiki by expanding it. |
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.
