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Difference between revisions of "PrimeGrid Prime Sierpiński Problem"
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==Purpose== | ==Purpose== | ||
| − | The [[Sierpiński problem]] is attempting to prove that | + | The [[Sierpiński problem]] is attempting to prove that {{Vk}} = 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 | + | 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 {{Vk}} = 271129. To prove that 271129 is the smallest prime Sierpiński number, all prime values of {{Vk}} < 271129 must be shown to produce a prime number of the form {{Kbn|+|k|n}}. |
==Status== | ==Status== | ||
| − | As of October 2020, there are 7 | + | *[https://www.primegrid.com/stats_psp_llr.php Live status] |
| + | *Multi Reservation [[Multi Reservation:18|here]] | ||
| + | As of October 2020, there are 7 {{Vk}}-values being searched by the project: [[Proth prime 79309|79309]], [[Proth prime 79817|79817]], [[Proth prime 152267|152267]], [[Proth prime 156511|156511]], [[Proth prime 222113|222113]], [[Proth prime 225931|225931]], and [[Proth prime 237019|237019]]. The search is at {{Vn}} > {{Num|{{Multi Reservation:18-NMax}}}}. | ||
| − | There are also no known primes for | + | There are also no known primes for {{Vk}} = [[Proth prime 22699|22699]] and [[Proth prime 67607|67607]], but these are already part of the standard Sierpiński problem. |
==History of eliminated candidates== | ==History of eliminated candidates== | ||
*2017-09-17: [[Proth prime 168451|{{Kbn|+|168451|19375200}}]] | *2017-09-17: [[Proth prime 168451|{{Kbn|+|168451|19375200}}]] | ||
| − | *2016-10-31: [[Proth prime 10223|{{Kbn|+|10223|31172165}}]], eliminating | + | *2016-10-31: [[Proth prime 10223|{{Kbn|+|10223|31172165}}]], eliminating {{Vk}} = 10223 from both the Sierpiński and Prime Sierpiński problems. |
==See also== | ==See also== | ||
*[[Sierpiński problem]] | *[[Sierpiński problem]] | ||
| − | *[[PrimeGrid]] | + | *[[PrimeGrid Seventeen or Bust]] |
==External links== | ==External links== | ||
* [https://www.primegrid.com/forum_thread.php?id=972 About the Prime Sierpinski Problem - PrimeGrid forums] | * [https://www.primegrid.com/forum_thread.php?id=972 About the Prime Sierpinski Problem - PrimeGrid forums] | ||
[[Category:PrimeGrid Prime Sierpiński Problem| ]] | [[Category:PrimeGrid Prime Sierpiński Problem| ]] | ||
Revision as of 09:29, 4 October 2020
The Prime Sierpiński Problem is a PrimeGrid sub-project, launched in 2008. It is a continuation of the Prime Sierpinski Project that operated on the Mersenne Forums.
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
- Live status
- Multi Reservation here
As of October 2020, there are 7 k-values being searched by the project: 79309, 79817, 152267, 156511, 222113, 225931, and 237019. The search is at n > 33,582,000.
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.
