Answer:
Every Mersenne number is a prime number is a false statement.
Step-by-step explanation:
Consider the provided information.
Mersenne number are the numbers which is in the form:
[tex]M_n=2^k - 1[/tex]
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.
