Question

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

Answer 1

there is only one right answer

Answer 2

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

The numbers we are examining are: 83, 113, 31, and 51.

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

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

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

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

Thus, the prime numbers in the form \(2n - 1\) from your list are 83, 113, and 31. All three are correct, but if you are looking for a single number as a response, you can choose any of these three.

If the question asks for only one response, you could just provide **83**, but **113** and **31** are also valid.

Answer 3

Thank you for the clarification! Based on the requirement to select only one correct answer, and considering the focus on primes in the form \(2n - 1\), we should narrow it down.

Looking at the numbers provided (83, 113, 31, and 51):

- 83: \(2n - 1\) form with \(n=42\) and is prime.
- 113: \(2n - 1\) form with \(n=57\) and is prime.
- 31: \(2n - 1\) form with \(n=16\) and is prime.
- 51: is not prime.

In the context of typical mathematics questions about primes often focusing on smaller numbers or selecting the first one mentioned, **31** is the smallest number among the primes given.

If only one answer is needed, that answer is:

**31**

Please note that it depends on the specific context of the question; in other circumstances, any of these valid prime answers could be appropriate. However, since there is a constraint to pick **one**, the choice would be **31**.