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

• Live status
• Multi Reservation here

As of 2024-11-12, there are 7 k-values being searched by the project: 79309, 79817, 152267, 156511, 222113, 225931, and 237019. The search is at n > 33,582,000.

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

• 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 Seventeen or Bust

External links

• About the Prime Sierpinski Problem - PrimeGrid forums

PrimeGrid

Miscellaneous

Main

Subprojects

Type Proth : 321 Prime Search 27121 Prime Search Proth Prime Search Proth Prime Search Extended Proth Mega Prime Search Type Sierpiński : Seventeen or Bust Extended Sierpiński Project Prime Sierpiński Problem Sierpiński base 5 Type Riesel : The Riesel Problem Riesel base 5 Type Fermat : Generalized Fermat Prime Search b216+1 b217+1 b218+1 b219+1 b220+1 b221+1 b222+1 Fermat Divisor Search Type Cullen/Woodall : Cullen Prime Search Woodall Prime Search Generalized Cullen Prime Search Type Others : AP27 Search Sophie Germain Search Wieferich and Wall-Sun-Sun Prime Search

Completed

GFN b215+1

Others