Which of the following groups of numbers are all prime numbers?
A) 7, 17, 29, 49
B) 3, 11, 23, 31
C) 2, 3, 5, 9
D) 2, 5, 15, 19
Answer (1)
Define prime numbers as numbers greater than 1 that are only divisible by 1 and themselves.
Check each option to see if all numbers are prime.
Option A has 49, which is not prime (7*7).
Option C has 9, which is not prime (3*3).
Option D has 15, which is not prime (3*5).
Option B contains only prime numbers: 3, 11, 23, and 31.
The answer is B .
Explanation
Understanding Prime Numbers We need to identify which group contains only prime numbers. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Let's examine each option.
Checking Option A Option A: 7, 17, 29, 49. We need to check if each number is prime. 7 is prime. 17 is prime. 29 is prime. However, 49 is 7 * 7, so it is not prime. Therefore, option A is not the correct answer.
Checking Option B Option B: 3, 11, 23, 31. We need to check if each number is prime. 3 is prime. 11 is prime. 23 is prime. 31 is prime. Therefore, option B is the correct answer.
Checking Option C Option C: 2, 3, 5, 9. We need to check if each number is prime. 2 is prime. 3 is prime. 5 is prime. However, 9 is 3 * 3, so it is not prime. Therefore, option C is not the correct answer.
Checking Option D Option D: 2, 5, 15, 19. We need to check if each number is prime. 2 is prime. 5 is prime. However, 15 is 3 * 5, so it is not prime. 19 is prime. Therefore, option D is not the correct answer.
Final Answer The only group containing all prime numbers is option B: 3, 11, 23, 31.
Examples
Prime numbers are essential in cryptography, which is used to secure online transactions. For example, the RSA algorithm relies on the fact that it is easy to multiply two large prime numbers together, but very difficult to factor the result back into the original primes. This asymmetry is what makes RSA secure and allows for safe communication over the internet. Understanding prime numbers helps in appreciating the fundamentals of modern encryption techniques.
