World Record Generalized Cullen Prime!
On 16 April 2025, 11:37:45 UTC, PrimeGrid's Generalized Cullen/Woodall PrimeSearch found the largest known Generalized Cullen Prime:
4052186 * 69 4052186 +1
Generalized Cullen numbers are of the form: n*bn+1. Generalized Cullen numbers that are prime are called Generalized Cullen primes. For more information, please see
“Cullen prime” in The Prime Glossary.
The prime is 7,451,366 digits long and enters
“The Largest Known Primes Database” ranked 1st for Generalized Cullen Primes and 16th overall. This is the second largest prime ever found by PrimeGrid.
Base 69 was one of 9 primeless Generalized Cullen bases for b ≤121 that PrimeGrid is searching. The remaining bases are 13, 29, 47, 49, 55, 101, 109 & 121.
The discovery was made by Mark Williams of the United States using 8 cores of an AMD EPYC 9554 64-Core Processor with 196GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 10 hours, 15 minutes to complete the probable prime (PRP) test using PRST. Mark is a member of TeAm AnandTech.
The PRP was confirmed prime on 17 April 2025 by an AMD Ryzen 9 7950X3D @ 4.20GHz with 128GB RAM, running Debian 12.5. This computer, using 8 cores, took 12 hours and 32 minutes to complete the primality test using PRST.
For more details, please see the
official announcement.