The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records.
These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers.
is the third cyclotomic polynomial, defined as
Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes.
F(n) is the nth Fibonacci number.