Which of the following numbers is a prime in the form 2n−1
To determine whether a number in the form 2n-1 is prime, we need to check if it is divisible by any number from 2 to its square root.
For the given options:
a) 14 = 2 * 7. Therefore, it is not prime.
b) 15 = 3 * 5. Therefore, it is not prime.
c) 16 = 2 * 2 * 2 * 2. Therefore, it is not prime.
d) 17. Since 17 is a prime number, it cannot be factored into smaller integers. Therefore, it is prime.
Therefore, the number 17 is a prime number in the form 2n-1.
To determine which of the following numbers is a prime in the form 2n - 1, we need to check each number individually.
Let's go through each option and check if it meets the criteria:
1. 5: If we put n = 3 into the formula 2n - 1, we get 2(3) - 1 = 6 - 1 = 5. This fulfills the condition.
2. 9: If we put n = 5 into the formula 2n - 1, we get 2(5) - 1 = 10 - 1 = 9. This also fulfills the condition.
3. 13: If we put n = 7 into the formula 2n - 1, we get 2(7) - 1 = 14 - 1 = 13. This number fulfills the condition as well.
4. 16: If we put n = 9 into the formula 2n - 1, we get 2(9) - 1 = 18 - 1 = 17. This number does not fulfill the condition.
Therefore, the prime number in the form 2n - 1 is 17.
To find out which number among the given numbers is a prime in the form 2n−1, we need to substitute each number into the equation and check if the resulting value is a prime number.
Let's go through the given numbers one by one and substitute them into the equation:
1. 2(1)−1 = 1
2. 2(2)−1 = 3
3. 2(3)−1 = 5
4. 2(4)−1 = 7
From the given options, only the number 7 is a prime number in the form 2n−1. The numbers 1, 3, and 5 are not prime.
Therefore, the number 7 is the answer.
Note: To determine if a resulting value is a prime number, you can use various methods such as checking for divisibility by smaller primes or using methods like the Sieve of Eratosthenes.