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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
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What are the first 4 mersenne prime numbers?
The first four Mersenne prime numbers are 2, 3, 5, and 7.
What is the relationship between Mersenne prime and perfect numbers?
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.
Are there more mersenne primes known as there are perfect numbers?
There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.
What is the definition of Mersenne numbers?
A Mersenne number is a number of the form 2n-1. When this number is prime, it is known as a Mersenne prime.A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Examples are the Mersenne prime 7 (23 - 1 = 7) and the Mersenne prime 127 (27 - 1 = 127)
How many Mersenne prime numbers are there?
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.
