List of largest known primes and probable primes

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. Numbers with more than 2,000,000 digits are shown.

Largest known primes
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. $$\Phi_3(x)$$ is the third cyclotomic polynomial, defined as $$x^2 + x + 1$$.

Largest known probable primes (PRPs)
These are probable primes. Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes.