Question

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

31
31

51
51

113
113

83

Answer 1

To determine which numbers are prime in the form \( 2n - 1 \), we need to check if each provided number can be expressed in that form where \( n \) is an integer.

1. **For \( 31 \)**:
\[
31 = 2n - 1 \implies 32 = 2n \implies n = 16
\]
Since \( 31 \) is prime.

2. **For \( 51 \)**:
\[
51 = 2n - 1 \implies 52 = 2n \implies n = 26
\]
Since \( 51 \) is not prime (it equals \( 3 \times 17 \)).

3. **For \( 113 \)**:
\[
113 = 2n - 1 \implies 114 = 2n \implies n = 57
\]
Since \( 113 \) is prime.

4. **For \( 83 \)**:
\[
83 = 2n - 1 \implies 84 = 2n \implies n = 42
\]
Since \( 83 \) is prime.

From the evaluation:
- \( 31 \) is prime
- \( 113 \) is prime
- \( 83 \) is prime
- \( 51 \) is not prime

The numbers that are prime in the form \( 2n - 1 \) among the options are **31, 113, and 83**. If asked for just one prime number, it can be any of these: **31**.