PrimeGrid Prime Sierpiński Problem

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•2^19375200+1
• 2016-10-31: 10223•2^31172165+1, eliminating k = 10223 from both the Sierpiński and Prime Sierpiński problems.

See also

• Sierpiński problem
• PrimeGrid

External links

• About the Prime Sierpinski Problem - PrimeGrid forums