A generalised Fermat Prime is a prime number of the form for a >0. It is called ‘generalised’ as a Fermat Prime is a number of this form with a = 0.
The discovery was made by Sylvanus A. Zimmerman of the United States.
“Until now only 392 generalised Fermat primes had been found: this new discovery makes 393. At 6,253,210 digits long, it’s now the 12th largest of all known primes, and the second-largest known non-Mersenne prime.”