section_path: Computational methods/Special-purpose algorithms and the largest known prime
section_name: Special-purpose algorithms and the largest known prime
paragraph_text: Special-purpose algorithms and the largest known prime
  
  In addition to the aforementioned tests that apply to any natural number, some numbers of a special form can be tested for primality more quickly.For example, the Lucas–Lehmer primality test can determine whether a Mersenne number (one less than a power of two) is prime, deterministically,in the same time as a single iteration of the Miller–Rabin test. This is why since 1992 (as of December 2018) the largest known prime has always been a Mersenne prime. It is conjectured that there are infinitely many Mersenne primes.
  
  The following table gives the largest known primes of various types. Some of these primes have been found using distributed computing. In 2009, the Great Internet Mersenne Prime Search project was awarded a US$100,000 prize for first discovering a prime with at least 10 million digits. The Electronic Frontier Foundation also offers $150,000 and $250,000 for primes with at least 100 million digits and 1 billion digits, respectively.