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•2^{n}+1.
Status
As of 2024-04-07, there are 7 k-values being searched by the project: 79309, 79817, 152267, 156511, 222113, 225931, and 237019. The search is at n > 30,935,000.
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