Question:
Let \( p_1 \) and \( p_2 \) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \( p_1 \) and \( p_2 \)?
Let \( p_1 \) and \( p_2 \) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \( p_1 \) and \( p_2 \)?
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Remember, the product of two distinct prime numbers is always composite. Understanding prime number properties is crucial for number theory problems.
Updated On: Jan 30, 2026
- \( p_1 + p_2 \) is not a prime number.
- \( p_1 p_2 \) is not a prime number.
- \( p_1 + p_2 + 1 \) is a prime number.
- \( p_1 p_2 + 1 \) is a prime number.
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The Correct Option is B
Solution and Explanation
A prime number is defined as a number that has exactly two distinct positive divisors: 1 and itself.
For any two arbitrary prime numbers \( p_1 \) and \( p_2 \), their product \( p_1 p_2 \) will always have more than two divisors (i.e., 1, \( p_1 \), \( p_2 \), and \( p_1 p_2 \)), which means it cannot be a prime number.
Thus, the correct answer is (B).Was this answer helpful?
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