# Mersenne prime (or Marsenne prime)

A Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form 2^n-1 for some integer n.

The first few Mersenne primes are 3, 7, 31, 127 (corresponding to n = 2, 3, 5, 7). There are only a finite number of Mersenne primes, and the largest known one as of 2019 is 2^77232917-1, with 22,338,618 digits.

Mersenne primes are named after the French mathematician Marin Mersenne, who studied them in the early 17th century. Mersenne primes have been studied extensively since then, and there is a particular interest in Mersenne primes of the form 2^p-1, where p is itself a prime, known as a Mersenne prime.

### Is 63 a Mersenne prime?

No, 63 is not a Mersenne prime.

A Mersenne prime is a prime number of the form M_n = 2^n - 1, where n is a positive integer. 63 does not fit this form, as it is not of the form 2^n - 1 for any integer n.

It is worth noting that 3, 7, 31, and 127 are all Mersenne primes, as they are of the form 2^n - 1 for n = 2, 3, 5, and 7, respectively.

#### How do you find the Mersenne prime number?

The Mersenne prime number can be found by using the Mersenne prime formula which is:

M_p = 2^p - 1

where p is a prime number.

For example, if p = 3, then the Mersenne prime number would be:

M_3 = 2^3 - 1 = 7

To find larger Mersenne prime numbers, you can simply use a larger value for p in the formula.

### What are the first 5 Mersenne prime numbers?

The first five Mersenne prime numbers are as follows:

3, 7, 31, 127, 8191. Why is 2 A Mersenne prime? 2 is a Mersenne prime because it is a prime number that is one less than a power of 2. In other words, it is a prime number that can be expressed as 2^n - 1 for some integer n. What is the largest known Mersenne prime? The largest known Mersenne prime is \$2^{74,207,281}-1\$, which was discovered in January 2016 by a team of researchers from the Great Internet Mersenne Prime Search (GIMPS). This number has over 22 million digits, and is more than twice as large as the previous record holder.