The GIMPS distributed computing project (short for Great Internet Mersenne Prime Search) was launched in 1996 by mathematician George Woltman, who developed Prime95, the software used to test whether a number is prime. Scott Kurowski soon developed the PrimeNet system to distribute the work among the computers participating in the project. It is maintained by Aaron Blosser.
The aim of the GIMPS project is to determine whether Mersenne numbers—that is, numbers of the form Mn = 2n – 1, where n is an integer—are prime or not. Mn can be prime only if n is prime, but this condition is not sufficient. Fifty-two Mersenne primes are currently known, and the largest known prime numbers are of this form. Whether infinitely many exist remains unknown. The latest eighteen were found through GIMPS, some by enthusiasts who had made their computers available to the project.
More than two million computers participate in the project. Of course, they do not all run 24 hours a day! Any personal computer can take part, regardless of its operating system, whether Windows or macOS or an open-source system such as Linux or FreeBSD.
After registering at www.mersenne.org, you simply download and install the program, answer a few questions, and let the software run in the background. Generally, this has virtually no effect on the computer's performance.