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Message: <blockquote data-quote="imhotep" data-source="post: 30262890" data-attributes="member: 562115">Mersenne primes are of the form 2^n - 1  where n is a prime. They are interesting to Mathematicians as they are in direct correspondence to Perfect numbers.The Euclid–Euler theorem relates Perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form 2^n−1(2^n − 1), where 2^n − 1 is a prime number. The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "if" and "only if" aspects of the theorem.Generally Primes are useful in cryptography.  For eg RSA is based on two primes - but note that these are not very large Mersenne primes.Generalized Mersenne Prime Numbers are used in Elliptical Curve Cryptography and Random Number Generation. I don't know of any use in finding large Mersenne Primes other than for interest and Mathematical research.PS: Perfect NumbersA perfect number is defined as a positive integer which is equal to the sum of its positive divisors, excluding the number itself. The smallest perfect number is 6, which is the sum of 1, 2, and 3.he first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.</blockquote>

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