PrimeGrid Generalized Cullen Prime Search

Purpose

The goal of this project is to find Generalized Cullen primes of the form n•bⁿ+1 for bases b which have no known primes.

Status

• Current status
• Multi Reservation 17: The current test size is 7,118,322 digits as of 2025-03-24.
• Important note: Tests are handed out by size instead of n-value. The above multi-reservation is set to the current n-value of the largest base of the project. A calculation must be made for each base so that its corresponding n-value is shown correctly.

The bases currently being searched by the project:

• Base 13
• Base 29
• Base 47
• Base 49
• Base 55
• Base 101
• Base 109
• Base 121

Found primes

Each of these finds was the first known Generalized Cullen prime in that base, eliminating that base from the search.

• 2025-04-17: 4052186•69^4052186+1
• 2021-08-28: 2525532•73^2525532+1
• 2019-09-02: 2805222•25^2805222+1
• 2018-03-11: 1806676•41^1806676+1
• 2018-01-18: 1323365•116^1323365+1
• 2017-08-21: 1341174•53^1341174+1
• 2016-10-08: 682156•79⁶⁸²¹⁵⁶+1
• 2012-01-29: 427194•113⁴²⁷¹⁹⁴+1
• 2010-05-25: 129897•68¹²⁹⁸⁹⁷+1

See also

• PrimeGrid
• Cullen prime

External links

• Generalized Cullen/Woodall Prime Search introduction - PrimeGrid Forums

PrimeGrid

Miscellaneous

Main

Subprojects

Type Proth : 321 Prime Search Proth Prime Search Proth Prime Search Extended Type Sierpiński : Seventeen or Bust Extended Sierpiński Project Prime Sierpiński Problem New 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 Type Cullen/Woodall : Cullen Prime Search Woodall Prime Search Generalized Cullen Prime Search Type Others : AP27 Search Wieferich and Wall-Sun-Sun Prime Search

Completed

GFN b215+1 Fermat Divisor Search 27121 Prime Search Proth Mega Prime Search Sophie Germain Search

Others