Link: https://en.wikipedia.org/wiki/Largest_known_prime_number
The record is currently held by 2^(82,589,933)−1 with 24,862,048 digits, found by GIMPS in December 2018.
October 13, 2024 — Yesterday, a participating GIMPS computer reported a successful Fermat probable prime test to the server! A proof of work was uploaded and certified. This certification proves there were no calculation errors during the probable prime test. Several Lucas-Lehmer tests are underway to definitively proof the number prime. These tests will be run using several different programs and on different hardware. Soon after the result is officially confirmed an announcement will be made with all the details. Assuming the result holds, this new prime will be GIMPS first new prime in nearly six years.