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Difference between revisions of "PrimeGrid Prime Sierpiński Problem"
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| − | The '''Prime Sierpiński Problem''' is a [[PrimeGrid]] sub-project, launched in 2008. | + | The '''Prime Sierpiński Problem''' is a [[PrimeGrid]] sub-project, launched in 2008. It is a continuation of the [https://www.mersenneforum.org/showthread.php?t=2665 Prime Sierpinski Project] that operated on the Mersenne Forums. |
==Purpose== | ==Purpose== | ||
Revision as of 03:34, 27 September 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
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.
