To determine whether a number in the form \(2n - 1\) is prime, we need to know what values of \(n\) give us prime numbers when substituted into the expression. A prime number is defined as a number greater than 1 that has no divisors other than 1 and itself.
Let’s calculate \(2n - 1\) for various integer values of \(n\):
- For \(n = 1\): \(2(1) - 1 = 1\) (not prime)
- For \(n = 2\): \(2(2) - 1 = 3\) (prime)
- For \(n = 3\): \(2(3) - 1 = 5\) (prime)
- For \(n = 4\): \(2(4) - 1 = 7\) (prime)
- For \(n = 5\): \(2(5) - 1 = 9\) (not prime, divisible by 3)
- For \(n = 6\): \(2(6) - 1 = 11\) (prime)
- For \(n = 7\): \(2(7) - 1 = 13\) (prime)
- For \(n = 8\): \(2(8) - 1 = 15\) (not prime, divisible by 3 and 5)
- For \(n = 9\): \(2(9) - 1 = 17\) (prime)
- For \(n = 10\): \(2(10) - 1 = 19\) (prime)
- For \(n = 11\): \(2(11) - 1 = 21\) (not prime, divisible by 3 and 7)
- For \(n = 12\): \(2(12) - 1 = 23\) (prime)
And continuing this process, we find that the numbers in the form of \(2n - 1\) that are prime include 3, 5, 7, 11, 13, 17, 19, and 23, which correspond to \(n\) values of 2, 3, 4, 6, 7, 9, 10, and 12 respectively.
If you have specific options to evaluate, please provide them, and I will determine which among them is prime.