On 28 August 2021, 09:10:17 UTC, PrimeGrid’s Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:

2525532*73^2525532+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 4,705,888 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1^st for Generalized Cullen primes and 24^th overall.

Base 73 was one of 10 primeless Generalized Cullen bases for b ≤121 that PrimeGrid is searching. The remaining bases are 13, 29, 47, 49, 55, 69, 101, 109 & 121.

The discovery was made by Tom Greer (tng) of the United States using an Intel(R) Core(TM) i9-10920X CPU @ 3.50GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 10 hours, 40 minutes to complete the primality test using LLR2. Tom is a member of the Antarctic Crunchers team.

The prime was verified on 28 August 2021, 18:01 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 3 hours and 39 minutes to complete the primality test using LLR2.

For more details, please see the official announcement.