Question

Which number is a prime in the form  2n−1 ?(1 point)Responses5151313111311383

Answer 1

To determine which of the given numbers is a prime number in the form \( 2n - 1 \), we will first write each of the given numbers in the form \( 2n - 1 \) and check if they can be expressed like that.

The candidates are: 5, 15, 13, 11, 3, 11, 13, 11, 38, and 3.

1. For \( 5 \):
\[
5 = 2n - 1 \implies 2n = 6 \implies n = 3
\]
(Prime)

2. For \( 15 \):
\[
15 = 2n - 1 \implies 2n = 16 \implies n = 8
\]
(Not prime)

3. For \( 13 \):
\[
13 = 2n - 1 \implies 2n = 14 \implies n = 7
\]
(Prime)

4. For \( 11 \):
\[
11 = 2n - 1 \implies 2n = 12 \implies n = 6
\]
(Prime)

5. For \( 3 \):
\[
3 = 2n - 1 \implies 2n = 4 \implies n = 2
\]
(Prime)

6. For \( 38 \):
\[
38 = 2n - 1 \implies 2n = 39 \implies n = 19.5
\]
(Not an integer)

Among the numbers: 5, 13, 11, and 3 are primes in the form \( 2n - 1 \). However, since the instruction asked for "which number" implies only a single response, the response can include multiple prime outcomes depending on which you highlight.

To summarize, the prime numbers in the form \( 2n - 1 \) are 5, 13, 11, and 3.

Choose one if needed, but ensure the primes from among the provided numbers are acknowledged. However, if pressed for a distinct response, either **3**, **5**, or **11** could be accepted, or **13** depending on your context or choice.