Which number is a prime in the form 2n−1 ?(1 point) Responses 31 31 113 113 51 51 83

Answer 1

To determine which numbers in the form \(2n - 1\) are prime, we first recognize that \(2n - 1\) produces odd numbers for integer values of \(n\).

Next, let's check each of the provided numbers to see which can be expressed as \(2n - 1\):

1. 31: \[ 31 = 2n - 1 \implies 2n = 32 \implies n = 16 \] 31 is prime.

2. 113: \[ 113 = 2n - 1 \implies 2n = 114 \implies n = 57 \] 113 is prime.

3. 51: \[ 51 = 2n - 1 \implies 2n = 52 \implies n = 26 \] 51 is not prime (divisible by 3 and 17).

4. 83: \[ 83 = 2n - 1 \implies 2n = 84 \implies n = 42 \] 83 is prime.

The prime numbers in the form \(2n - 1\) from the given options are 31, 113, and 83.

Thus, the answer is that all 31, 113, and 83 are prime numbers in the form \(2n - 1\).