Editing Lucas–Lehmer primality test (section)

== Applications ==

The Lucas–Lehmer test was the main primality test used by the [[Great Internet Mersenne Prime Search]] (GIMPS) to locate large primes until 2021. This search has been successful in locating many of the largest primes known to date.<ref>[http://primes.utm.edu/largest.html#biggest The "Top Ten" Record Primes], [[The Prime Pages]]</ref> In 2021, GIMPS switched to an even faster variant of [[Fermat's primality test]] for locating probable Mersenne primes, and only uses Lucas–Lehmer to verify these probable primes as actual primes.

The test is considered valuable because it can provably test a large set of very large numbers for primality within an affordable amount of time. In contrast, the equivalently fast [[Pépin's test]] for any [[Fermat number]] can only be used on a much smaller set of very large numbers before reaching computational limits.