Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
 Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

# PrimeGrid Prime Sierpiński Problem

Jump to: navigation, search

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 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.