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. “!” is the factorial, “#” is the primorial, and Φ 3 ( x ) {\displaystyle \Phi _{3}(x)} is the third cyclotomic polynomial, defined as x 2 x 1 {\displaystyle 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. F(n) is the nth Fibonacci number.



See also

  • Largest known prime number

References

External links

  • Chris Caldwell, The Largest Known Primes Database at The PrimePages
  • The 5000 largest known primes at The PrimePages
  • The 10,000 largest known probable primes at primenumbers.net
  • PrimeGrid’s 321 Prime Search, about the discovery of 3×26090515−1

Largest Known Primes Prime, Prime numbers, Large

Largest known prime number discovered Human World EarthSky

What is the largest known prime number?

The Largest Prime Number

The world's largest prime number — visualized Boing Boing