A 'Mersenne Prime' is prime number one less than a power of two. That is, a prime number of the form M = 2n - 1 for some integer n. They're named after Marin Mersenne (1588-1648), a French friar, who studied them in the early 19th century. If n is composite (not prime), then M is also composite. If n is prime, M may or may not be prime.
The largest known prime number, 282,589,933 − 1, is a Mersenne prime.
See "Mersenne Prime" in Wikipedia.
Also see the "Online Encyclopedia of Integer Sequences: Mersenne Primes here.
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