Q: What is the definition of Mersenne numbers?

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The first four Mersenne prime numbers are 2, 3, 5, and 7.

Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime. When a new Mersenne prime is discovered, so is a new perfect number.

There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.

A Mersenne number is a number that can be written as 2n - 1. A Mersenne prime is a Mersenne number that is a prime number. Here are some Mersenne primes: 22 - 1 = 3 23 - 1 = 7 25 - 1 = 31 27 - 1 = 127

It is, as of now, an open question whether there are a finite or an infinite number of Mersenne primes. At the beginning of the 21st century there were 47 known Mersenne primes, the highest being 43,112,609.

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Mersenne numbers are named after the French monk Marin Mersenne who studied them in the early 17th century.

The first four Mersenne prime numbers are 2, 3, 5, and 7.

Let p = any prime number. (2p -1) is called a Mersenne number. Any such number that is prime is called a Mersenne Prime. Father Mersenne wrote a list of numbers of this type which he thought were prime, but a few were not. In fact, most of the large Mersenne numbers are not prime, but all the really large numbers that have been proved to be prime are Mersenne Primes.

Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime. When a new Mersenne prime is discovered, so is a new perfect number.

There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.

A Mersenne number is a number that can be written as 2n - 1. A Mersenne prime is a Mersenne number that is a prime number. Here are some Mersenne primes: 22 - 1 = 3 23 - 1 = 7 25 - 1 = 31 27 - 1 = 127

It is, as of now, an open question whether there are a finite or an infinite number of Mersenne primes. At the beginning of the 21st century there were 47 known Mersenne primes, the highest being 43,112,609.

Did you mean what Mersenne numbers are prime? If a number is a prime, how is it not a prime at the same time? Anyways, M11, or (2^11) - 1, I think is the lowest Mersenne Number Mp that isn't prime, when p is prime. Any Mersenne Number where p is not prime cannot be prime.

Mersenne primes are mostly of interest as mathematical curios. A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.

A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.

3, 7, 31, 127, 8191.

A Mersenne number is one less than a positive power of two. Since the positive power of two is always even, one less than that is always odd.