| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "PrimeGrid Prime Sierpiński Problem"
(Description page for PrimeGrid's Prime Sierpinski Problem) |
(→History of eliminated candidates: +2) |
||
| Line 12: | Line 12: | ||
==History of eliminated candidates== | ==History of eliminated candidates== | ||
| + | *2017-09-17: [[Proth prime 168451|{{Kbn|+|168451|19375200}}]] | ||
| + | *2016-10-31: [[Proth prime 10223|{{Kbn|+|10223|31172165}}]], eliminating k = 10223 from both the Sierpiński and Prime Sierpiński problems. | ||
==See also== | ==See also== | ||
Revision as of 03:31, 27 September 2020
The Prime Sierpiński Problem is a PrimeGrid sub-project, launched in 2008.
Purpose
The Sierpiński problem is attempting to prove that k = 78557 is the smallest Sierpiński number. However, 78557 itself is not a prime number.
The Prime Sierpiński Problem wants to find the smallest Sierpiński number that is also a prime number. The smallest known number that meets these conditions is k = 271129. To prove that 271129 is the smallest prime Sierpiński number, all prime values of k < 271129 must be shown to produce a prime number of the form k•2n+1.
Status
As of September 2020, there are 7 k-values being searched by the project: 79309, 79817, 152267, 156511, 222113, 225931, and 237019. The search is at n ≥ 22,597,256. (Live status)
There are also no known primes for k = 22699 and 67607, but these are already part of the standard Sierpiński problem.
History of eliminated candidates
- 2017-09-17: 168451•219375200+1
- 2016-10-31: 10223•231172165+1, eliminating k = 10223 from both the Sierpiński and Prime Sierpiński problems.
