Question

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

Answer 1

To determine which number is prime in the form \(2n - 1\), we need to consider values of \(n\) that make \(2n - 1\) yield a prime number.

For \(n = 1\):
\[
2(1) - 1 = 1 \quad (\text{not prime})
\]

For \(n = 2\):
\[
2(2) - 1 = 3 \quad (\text{prime})
\]

For \(n = 3\):
\[
2(3) - 1 = 5 \quad (\text{prime})
\]

For \(n = 4\):
\[
2(4) - 1 = 7 \quad (\text{prime})
\]

For \(n = 5\):
\[
2(5) - 1 = 9 \quad (\text{not prime, since } 9 = 3 \times 3)
\]

For \(n = 6\):
\[
2(6) - 1 = 11 \quad (\text{prime})
\]

For \(n = 7\):
\[
2(7) - 1 = 13 \quad (\text{prime})
\]

For \(n = 8\):
\[
2(8) - 1 = 15 \quad (\text{not prime, since } 15 = 3 \times 5)
\]

For \(n = 9\):
\[
2(9) - 1 = 17 \quad (\text{prime})
\]

For \(n = 10\):
\[
2(10) - 1 = 19 \quad (\text{prime})
\]

As we see, there are multiple values of \(n\) for which \(2n - 1\) results in a prime number, such as \(n = 2, 3, 4, 6, 7, 9,\) and \(10\).

So, the answer is that various numbers in the form \(2n - 1\) can be prime, including 3, 5, 7, 11, 13, 17, and 19, among others.