Question

mersenne primes are always of the form 2^n - 1 where n is any positive integer. true or false

Answer 1

True. Mersenne primes are indeed prime numbers that are of the specific form \(2^n - 1\), where \(n\) is a positive integer. However, for \(2^n - 1\) to be a prime number, \(n\) itself must also be prime. Therefore, while all Mersenne primes are of the form \(2^n - 1\) for some positive integer \(n\), not all numbers of that form are prime.