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In page Mersenne prime:

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Since Mersenne numbers grow very rapidly, the search for Mersenne primes is a difficult task, even though there is a simple efficient test to determine whether a given Mersenne number is prime: the Lucas–Lehmer primality test (LLT), which makes it much easier to test the primality of Mersenne numbers than that of most other numbers of the same size. The search for the largest known prime has somewhat of a cult following.[citation needed] Consequently, a large amount of computer power has been expended searching for new Mersenne primes, much of which is now done using distributed computing.