Question

Every Mersenne number is a prime number.
True
False

Answer 1

Every Mersenne number is a prime number is a false statement.

Explanation:

Consider the provided information.

Mersenne number are the numbers which is in the form:

`M_n=2^k - 1`

Where k is an integer.

The first Mersenne number are:

1, 3, 7, 15, 31, 63, 127, 255, ...

The prime number are the natural number greater than 1 and they cannot be formed by product of two smaller natural numbers.

First few prime number are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29,..

Now observe that 15 is a mersenne number but it is not a prime number as 15 can be formed by product of 3 and 5.

Thus, Every Mersenne number is a prime number is a false statement.