Which of the following numbers is a prime in the form 2n−1 ?(1 point)

Question

Responses

127
127

33
33

15
15

63

Answer 1

To determine which of the given numbers is a prime in the form \(2n - 1\), we first need to check if each number can be expressed as \(2n - 1\) for some integer \(n\) and then check if that number is prime.

1. 127:
   Set \(2n - 1 = 127\). \[ 2n = 128 \implies n = 64 \] Check if 127 is prime: The only divisors of 127 are 1 and 127, so it is prime.

2. 33:
   Set \(2n - 1 = 33\). \[ 2n = 34 \implies n = 17 \] Check if 33 is prime: \(33 = 3 \times 11\), so it is not prime.

3. 15:
   Set \(2n - 1 = 15\). \[ 2n = 16 \implies n = 8 \] Check if 15 is prime: \(15 = 3 \times 5\), so it is not prime.

4. 63:
   Set \(2n - 1 = 63\). \[ 2n = 64 \implies n = 32 \] Check if 63 is prime: \(63 = 3 \times 21\), so it is not prime.

The only number among the options provided that is both in the form \(2n - 1\) and prime is 127.