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==Purpose==
 
==Purpose==
The [[Sierpiński problem]] is attempting to prove that k = 78557 is the smallest Sierpiński number. However, 78557 itself is not a prime number.
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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 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 {{Kbn|+|k|n}}.  
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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 September 2020, there are 7 k-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 n ≥ 22,597,256. ([https://www.primegrid.com/stats_psp_llr.php Live status])
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*[https://www.primegrid.com/stats_psp_llr.php Live status]
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*Multi Reservation [[Multi Reservation:18|here]]
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As of {{Multi Reservation:18-Date}}, there are 7 {{Vk}}-values being searched by the project: [[Proth prime 2 79309|79309]], [[Proth prime 2 79817|79817]], [[Proth prime 2 152267|152267]], [[Proth prime 2 156511|156511]], [[Proth prime 2 222113|222113]], [[Proth prime 2 225931|225931]], and [[Proth prime 2 237019|237019]]. The search is at {{Vn}} > {{Num|{{Multi Reservation:18-NMax}}}}.
  
There are also no known primes for k = [[Proth prime 22699|22699]] and [[Proth prime 67607|67607]], but these are already part of the standard Sierpiński problem.
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There are also no known primes for {{Vk}} = [[Proth prime 2 22699|22699]] and [[Proth prime 2 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}}]]
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*2017-09-17: [[Proth prime 2 168451|{{Kbn|+|168451|19375200}}]]
*2016-10-31: [[Proth prime 10223|{{Kbn|+|10223|31172165}}]], eliminating k = 10223 from both the Sierpiński and Prime Sierpiński problems.
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*2016-10-31: [[Proth prime 2 10223|{{Kbn|+|10223|31172165}}]], eliminating {{Vk}} = 10223 from both the Sierpiński and Prime Sierpiński problems.
  
 
==See also==
 
==See also==
 
*[[Sierpiński problem]]
 
*[[Sierpiński problem]]
*[[PrimeGrid]]
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*[[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]]
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{{Navbox PrimeGrid}}
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[[Category:PrimeGrid Prime Sierpiński Problem| ]]

Latest revision as of 11:43, 5 September 2021

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

As of 2023-07-03, there are 7 k-values being searched by the project: 79309, 79817, 152267, 156511, 222113, 225931, and 237019. The search is at n > 28,690,000.

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

See also

External links

PrimeGrid