Mohammed is trying to find an expression that will yield a Mersenne prime. Based on the value of the exponent, which of the following options should he choose?
To find a Mersenne prime, Mohammed should choose the option of the form 2^p - 1, where p is a prime number.
To find a Mersenne prime, Mohammed should choose an option with a prime exponent. Mersenne primes are prime numbers that can be expressed in the form 2^n - 1, where n is a prime number. Therefore, he should identify the options with prime exponents, and choose from those.
To find an expression that will yield a Mersenne prime, Mohammed should select an exponent that is a prime number.
A Mersenne prime is a prime number that can be expressed in the form 2^n - 1, where n is an exponent. The exponent must be a prime number for the resulting expression to be a Mersenne prime.
Here are the options Mohammed should consider:
1. Prime numbers: A prime number is a number greater than 1 that has no divisors other than 1 and itself. Mohammed should pick an exponent that is a prime number. For example, 2, 3, 5, 7, 11, etc.
2. Non-prime numbers: If the exponent is a non-prime number, the resulting expression will not yield a Mersenne prime. Therefore, Mohammed should avoid selecting exponents that are non-prime numbers.
By selecting an exponent that is a prime number, Mohammed will have a higher chance of finding a Mersenne prime.